Real-time Imaging For Cardiac Flow Measurements€¦ · 3.3 Results 46 3.3.1 Image Quality 46 3.3.2...
Transcript of Real-time Imaging For Cardiac Flow Measurements€¦ · 3.3 Results 46 3.3.1 Image Quality 46 3.3.2...
Real-time Imaging For Cardiac
Flow Measurements
MPhil to PhD Transfer Report
Jennifer Steeden
28th September 2009
Primary Supervisor David Atkinson
Secondary Supervisor Vivek Muthurangu
Publications
ISMRM ʼ09 Poster Edgar J Muthurangu V Taylor A Atkinson D Undersampled Spirals for Real-time Flow Measurements Proc Intl Soc Mag Reson Med 17 (2009) 20091855 ISMRM Flow workshop Sept rsquo09
Steeden J Atkinson D Taylor A Muthurangu V Real-time Flow Measurements for
the Assessment of Hemodynamic Response to Exercise
Under Review with JRMI
Steeden J Atkinson D Taylor A Muthurangu V Assessing Vascular Response To Exercise using a combination of Real-time Spiral Phase Contrast MR and Non-invasive Blood Pressure Measurements
i
CONTENTS
1 INTRODUCTION 1 11 Achieving Real‐time Imaging 2 111 Alternative trajectories 3 112 Parallel Imaging 5
12 Measuring Flow with MRI 7 121 Implementation of Phase Contrast Imaging 8 122 Accuracy of PC‐MRI 9 123 Concomitant Gradients in Flow Imaging 11 124 Additional Phase Offsets 13
13 Exercise Testing 14
2 LITERATURE REVIEW 16 21 Real‐time Flow Measurements 16 211 Efficient trajectories 16 212 Parallel Imaging 19
22 Performing MRI during exercise 22 221 Imaging During Suspension of Exercise 22 222 Imaging During Continuation of Exercise 23 223 Upright exercise 26 224 Measurement of Ventricle Volume During Exercise 27
23 Assessment of hemodynamic response using MRI 27
3 REALshyTIME FLOW MEASUREMENTS FOR THE ASSESSMENT OF HEMODYNAMIC
RESPONSE TO EXERCISE 32 31 Development of Real‐Time Flow Sequence 32 311 Maxwell Correction 35 312 Residual Phase Offsets 37
32 Methods 40 321 Study Population 40 322 Exercise Protocol 40 323 MR Protocol 41 3231 Standard flow assessment 42 3232 Real‐time flow assessment 42 3233 Real‐time volume assessment 43
324 Validation Experiments 43 3241 Flow Pump Validation 44 3242 In‐vivo Validation 44
ii
325 Analysis 44 3251 Image Analysis 44 3252 Statistical Analysis 45
33 Results 46 331 Image Quality 46 332 Phantom Validation 47 333 In‐vivo Validation 48 334 Vascular Hemodynamics During Exercise 50
34 Discussion 52 341 Limitations 53 342 RF Shielding 54 343 Conclusion 56
35 Hemodynamic Response To Mental Stress 56
4 FUTURE WORK 58 41 Discussion of Potential Projects 59 411 Improvement of Image Quality 59 4111 Discussion 62
412 Variable Density Spirals and kt‐SENSE 62 4121 Discussion 66
413 Fourier Velocity Encoding 66 4131 Discussion 67
414 Diffusion Weighted Imaging 67 4141 Discussion 68
415 Clinical validation 68 4151 Discussion 68
416 ldquoPre‐referencerdquo flow 69 4161 Discussion 73 4162 Initial results 73
417 Speeding up Reconstruction 77 4171 Discussion 79 4172 Further Use of GPUs 80
42 Time Scale 81
REFERENCES 83
1
1 INTRODUCTION
Real-time imaging is essential in areas of magnetic resonance imaging (MRI) where
conventional MRI techniques are too slow Real-time imaging is especially important
in applications where there is motion present for example in cardiac imaging
Conventional cardiac MRI techniques use cardiac gating to reduce artifacts from
motion of the heart however this greatly increases scan time and has limitations in
its use
Conventional cardiac MRI uses electrocardiogram (ECG) gating to synchronize the
acquisition of data with cardiac motion This limits image artifacts and allows different
phases of the cardiac cycle to be accurately captured Images from cardiac gated
sequences are formed over many cardiac cycles and reconstructed as an lsquoaveragersquo
cardiac cycle ECG gated images are therefore susceptible to artifacts from
additional motion eg respiratory motion There are some simple techniques to
reduce respiratory motion including breath-hold imaging However many patients
with cardiac disease have difficulty in holding their breath therefore multiple signal
averages may be performed or respiratory gating may be used ndash these techniques
greatly increase scan time Other forms of motion are more difficult to control
Successful cardiac gating requires a good quality periodic ECG waveform for
accurate detection of the R-wave Therefore conventional MRI techniques are
unsuccessful in subjects with arrhythmias or where there is an unreliable ECG
signal In these applications real-time imaging is highly desirable as it does not
require ECG gating Real-time MRI acquires data very rapidly (ie each frame takes
less than 100ms) making it less susceptible to motion This allows a great reduction
2
in scan time and may also allow observation of beat-to-beat variations (which are not
seen in conventional imaging) Real-time imaging does however come at the cost of
lower spatial resolution and also lower effective-temporal resolution
Real-time imaging is also essential in imaging subjects during exercise because
bull ECG gating is unreliable
bull Breath-holding is not feasible
bull High heart rates are observed
bull Excessive motion from breathing and exercise
MRI is a well validated method of measuring flow at rest however in this study we
would like to be able to measure flow during exercise with the use of real-time
imaging This will allow quantification of hemodynamic response to exercise and
assessment of vascular disease
11 Achieving Real-time Imaging
Real-time imaging requires data to be acquired very rapidly Common ways to
reduce acquisition times include
bull Reducing the matrix size
bull Rectangular field-of-view (where less lines are acquired at the top and
bottom of k-space)
bull Partial Fourier encoding (where less lines are acquired at the bottom of k-
space and the missing lines are calculated from the Hermitian symmetry of
k-space)
bull Sliding window reconstruction (where data is shared between frames)
In this study we are interested in reducing scan times further than these common
methods can achieve This study focuses on the use of alternative trajectories and
parallel imaging to achieve very high temporal resolution imaging
3
111 Alternative trajectories
Conventionally in MRI data is acquired one k-space line at a time This is a very
popular method of imaging as the gradient design is simple and the data lies on a
Cartesian grid Acquiring data in this way is very slow as only a small portion of k-
space is covered after each excitation and there are a large number of excitations
Methods of speeding up acquisition while maintaining data on a Cartesian grid
include the use of echo planar imaging (EPI) Single shot EPI is possible where the
entire of k-space is filled after one excitation or segmented EPI can be used where a
part of k-space is filled after each excitation
To convert k-space data into the image domain a Fourier transform must be applied
The fastest and most efficient method of performing a Fourier transform is with the
Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform
Cartesian grid This means that k-space data acquired using non-uniform Cartesian
trajectories or non-Cartesian trajectories require the data to be resampled onto a
uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)
Gridding of data in MRI requires convolution of the k-space data with a convolution
kernel Ideally a SINC kernel would be used however as this is an infinite function
the computation would be impractical The choice of kernel is a trade-off between
processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly
used in MRI (3) as it has minimal residual aliasing and allows a relatively short
computation time It also has an analytic expression for its properties in the Fourier
domain
Non-Cartesian trajectories may offer more efficient methods of covering k-space or
non-uniform coverage of k-space The most common non-Cartesian trajectories used
in MRI include radials and spirals (see Figure 1) This study focuses on the use of
Spiral trajectories (4) as they provide a highly efficient method of traversing k-space
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
i
CONTENTS
1 INTRODUCTION 1 11 Achieving Real‐time Imaging 2 111 Alternative trajectories 3 112 Parallel Imaging 5
12 Measuring Flow with MRI 7 121 Implementation of Phase Contrast Imaging 8 122 Accuracy of PC‐MRI 9 123 Concomitant Gradients in Flow Imaging 11 124 Additional Phase Offsets 13
13 Exercise Testing 14
2 LITERATURE REVIEW 16 21 Real‐time Flow Measurements 16 211 Efficient trajectories 16 212 Parallel Imaging 19
22 Performing MRI during exercise 22 221 Imaging During Suspension of Exercise 22 222 Imaging During Continuation of Exercise 23 223 Upright exercise 26 224 Measurement of Ventricle Volume During Exercise 27
23 Assessment of hemodynamic response using MRI 27
3 REALshyTIME FLOW MEASUREMENTS FOR THE ASSESSMENT OF HEMODYNAMIC
RESPONSE TO EXERCISE 32 31 Development of Real‐Time Flow Sequence 32 311 Maxwell Correction 35 312 Residual Phase Offsets 37
32 Methods 40 321 Study Population 40 322 Exercise Protocol 40 323 MR Protocol 41 3231 Standard flow assessment 42 3232 Real‐time flow assessment 42 3233 Real‐time volume assessment 43
324 Validation Experiments 43 3241 Flow Pump Validation 44 3242 In‐vivo Validation 44
ii
325 Analysis 44 3251 Image Analysis 44 3252 Statistical Analysis 45
33 Results 46 331 Image Quality 46 332 Phantom Validation 47 333 In‐vivo Validation 48 334 Vascular Hemodynamics During Exercise 50
34 Discussion 52 341 Limitations 53 342 RF Shielding 54 343 Conclusion 56
35 Hemodynamic Response To Mental Stress 56
4 FUTURE WORK 58 41 Discussion of Potential Projects 59 411 Improvement of Image Quality 59 4111 Discussion 62
412 Variable Density Spirals and kt‐SENSE 62 4121 Discussion 66
413 Fourier Velocity Encoding 66 4131 Discussion 67
414 Diffusion Weighted Imaging 67 4141 Discussion 68
415 Clinical validation 68 4151 Discussion 68
416 ldquoPre‐referencerdquo flow 69 4161 Discussion 73 4162 Initial results 73
417 Speeding up Reconstruction 77 4171 Discussion 79 4172 Further Use of GPUs 80
42 Time Scale 81
REFERENCES 83
1
1 INTRODUCTION
Real-time imaging is essential in areas of magnetic resonance imaging (MRI) where
conventional MRI techniques are too slow Real-time imaging is especially important
in applications where there is motion present for example in cardiac imaging
Conventional cardiac MRI techniques use cardiac gating to reduce artifacts from
motion of the heart however this greatly increases scan time and has limitations in
its use
Conventional cardiac MRI uses electrocardiogram (ECG) gating to synchronize the
acquisition of data with cardiac motion This limits image artifacts and allows different
phases of the cardiac cycle to be accurately captured Images from cardiac gated
sequences are formed over many cardiac cycles and reconstructed as an lsquoaveragersquo
cardiac cycle ECG gated images are therefore susceptible to artifacts from
additional motion eg respiratory motion There are some simple techniques to
reduce respiratory motion including breath-hold imaging However many patients
with cardiac disease have difficulty in holding their breath therefore multiple signal
averages may be performed or respiratory gating may be used ndash these techniques
greatly increase scan time Other forms of motion are more difficult to control
Successful cardiac gating requires a good quality periodic ECG waveform for
accurate detection of the R-wave Therefore conventional MRI techniques are
unsuccessful in subjects with arrhythmias or where there is an unreliable ECG
signal In these applications real-time imaging is highly desirable as it does not
require ECG gating Real-time MRI acquires data very rapidly (ie each frame takes
less than 100ms) making it less susceptible to motion This allows a great reduction
2
in scan time and may also allow observation of beat-to-beat variations (which are not
seen in conventional imaging) Real-time imaging does however come at the cost of
lower spatial resolution and also lower effective-temporal resolution
Real-time imaging is also essential in imaging subjects during exercise because
bull ECG gating is unreliable
bull Breath-holding is not feasible
bull High heart rates are observed
bull Excessive motion from breathing and exercise
MRI is a well validated method of measuring flow at rest however in this study we
would like to be able to measure flow during exercise with the use of real-time
imaging This will allow quantification of hemodynamic response to exercise and
assessment of vascular disease
11 Achieving Real-time Imaging
Real-time imaging requires data to be acquired very rapidly Common ways to
reduce acquisition times include
bull Reducing the matrix size
bull Rectangular field-of-view (where less lines are acquired at the top and
bottom of k-space)
bull Partial Fourier encoding (where less lines are acquired at the bottom of k-
space and the missing lines are calculated from the Hermitian symmetry of
k-space)
bull Sliding window reconstruction (where data is shared between frames)
In this study we are interested in reducing scan times further than these common
methods can achieve This study focuses on the use of alternative trajectories and
parallel imaging to achieve very high temporal resolution imaging
3
111 Alternative trajectories
Conventionally in MRI data is acquired one k-space line at a time This is a very
popular method of imaging as the gradient design is simple and the data lies on a
Cartesian grid Acquiring data in this way is very slow as only a small portion of k-
space is covered after each excitation and there are a large number of excitations
Methods of speeding up acquisition while maintaining data on a Cartesian grid
include the use of echo planar imaging (EPI) Single shot EPI is possible where the
entire of k-space is filled after one excitation or segmented EPI can be used where a
part of k-space is filled after each excitation
To convert k-space data into the image domain a Fourier transform must be applied
The fastest and most efficient method of performing a Fourier transform is with the
Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform
Cartesian grid This means that k-space data acquired using non-uniform Cartesian
trajectories or non-Cartesian trajectories require the data to be resampled onto a
uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)
Gridding of data in MRI requires convolution of the k-space data with a convolution
kernel Ideally a SINC kernel would be used however as this is an infinite function
the computation would be impractical The choice of kernel is a trade-off between
processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly
used in MRI (3) as it has minimal residual aliasing and allows a relatively short
computation time It also has an analytic expression for its properties in the Fourier
domain
Non-Cartesian trajectories may offer more efficient methods of covering k-space or
non-uniform coverage of k-space The most common non-Cartesian trajectories used
in MRI include radials and spirals (see Figure 1) This study focuses on the use of
Spiral trajectories (4) as they provide a highly efficient method of traversing k-space
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
ii
325 Analysis 44 3251 Image Analysis 44 3252 Statistical Analysis 45
33 Results 46 331 Image Quality 46 332 Phantom Validation 47 333 In‐vivo Validation 48 334 Vascular Hemodynamics During Exercise 50
34 Discussion 52 341 Limitations 53 342 RF Shielding 54 343 Conclusion 56
35 Hemodynamic Response To Mental Stress 56
4 FUTURE WORK 58 41 Discussion of Potential Projects 59 411 Improvement of Image Quality 59 4111 Discussion 62
412 Variable Density Spirals and kt‐SENSE 62 4121 Discussion 66
413 Fourier Velocity Encoding 66 4131 Discussion 67
414 Diffusion Weighted Imaging 67 4141 Discussion 68
415 Clinical validation 68 4151 Discussion 68
416 ldquoPre‐referencerdquo flow 69 4161 Discussion 73 4162 Initial results 73
417 Speeding up Reconstruction 77 4171 Discussion 79 4172 Further Use of GPUs 80
42 Time Scale 81
REFERENCES 83
1
1 INTRODUCTION
Real-time imaging is essential in areas of magnetic resonance imaging (MRI) where
conventional MRI techniques are too slow Real-time imaging is especially important
in applications where there is motion present for example in cardiac imaging
Conventional cardiac MRI techniques use cardiac gating to reduce artifacts from
motion of the heart however this greatly increases scan time and has limitations in
its use
Conventional cardiac MRI uses electrocardiogram (ECG) gating to synchronize the
acquisition of data with cardiac motion This limits image artifacts and allows different
phases of the cardiac cycle to be accurately captured Images from cardiac gated
sequences are formed over many cardiac cycles and reconstructed as an lsquoaveragersquo
cardiac cycle ECG gated images are therefore susceptible to artifacts from
additional motion eg respiratory motion There are some simple techniques to
reduce respiratory motion including breath-hold imaging However many patients
with cardiac disease have difficulty in holding their breath therefore multiple signal
averages may be performed or respiratory gating may be used ndash these techniques
greatly increase scan time Other forms of motion are more difficult to control
Successful cardiac gating requires a good quality periodic ECG waveform for
accurate detection of the R-wave Therefore conventional MRI techniques are
unsuccessful in subjects with arrhythmias or where there is an unreliable ECG
signal In these applications real-time imaging is highly desirable as it does not
require ECG gating Real-time MRI acquires data very rapidly (ie each frame takes
less than 100ms) making it less susceptible to motion This allows a great reduction
2
in scan time and may also allow observation of beat-to-beat variations (which are not
seen in conventional imaging) Real-time imaging does however come at the cost of
lower spatial resolution and also lower effective-temporal resolution
Real-time imaging is also essential in imaging subjects during exercise because
bull ECG gating is unreliable
bull Breath-holding is not feasible
bull High heart rates are observed
bull Excessive motion from breathing and exercise
MRI is a well validated method of measuring flow at rest however in this study we
would like to be able to measure flow during exercise with the use of real-time
imaging This will allow quantification of hemodynamic response to exercise and
assessment of vascular disease
11 Achieving Real-time Imaging
Real-time imaging requires data to be acquired very rapidly Common ways to
reduce acquisition times include
bull Reducing the matrix size
bull Rectangular field-of-view (where less lines are acquired at the top and
bottom of k-space)
bull Partial Fourier encoding (where less lines are acquired at the bottom of k-
space and the missing lines are calculated from the Hermitian symmetry of
k-space)
bull Sliding window reconstruction (where data is shared between frames)
In this study we are interested in reducing scan times further than these common
methods can achieve This study focuses on the use of alternative trajectories and
parallel imaging to achieve very high temporal resolution imaging
3
111 Alternative trajectories
Conventionally in MRI data is acquired one k-space line at a time This is a very
popular method of imaging as the gradient design is simple and the data lies on a
Cartesian grid Acquiring data in this way is very slow as only a small portion of k-
space is covered after each excitation and there are a large number of excitations
Methods of speeding up acquisition while maintaining data on a Cartesian grid
include the use of echo planar imaging (EPI) Single shot EPI is possible where the
entire of k-space is filled after one excitation or segmented EPI can be used where a
part of k-space is filled after each excitation
To convert k-space data into the image domain a Fourier transform must be applied
The fastest and most efficient method of performing a Fourier transform is with the
Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform
Cartesian grid This means that k-space data acquired using non-uniform Cartesian
trajectories or non-Cartesian trajectories require the data to be resampled onto a
uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)
Gridding of data in MRI requires convolution of the k-space data with a convolution
kernel Ideally a SINC kernel would be used however as this is an infinite function
the computation would be impractical The choice of kernel is a trade-off between
processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly
used in MRI (3) as it has minimal residual aliasing and allows a relatively short
computation time It also has an analytic expression for its properties in the Fourier
domain
Non-Cartesian trajectories may offer more efficient methods of covering k-space or
non-uniform coverage of k-space The most common non-Cartesian trajectories used
in MRI include radials and spirals (see Figure 1) This study focuses on the use of
Spiral trajectories (4) as they provide a highly efficient method of traversing k-space
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
1
1 INTRODUCTION
Real-time imaging is essential in areas of magnetic resonance imaging (MRI) where
conventional MRI techniques are too slow Real-time imaging is especially important
in applications where there is motion present for example in cardiac imaging
Conventional cardiac MRI techniques use cardiac gating to reduce artifacts from
motion of the heart however this greatly increases scan time and has limitations in
its use
Conventional cardiac MRI uses electrocardiogram (ECG) gating to synchronize the
acquisition of data with cardiac motion This limits image artifacts and allows different
phases of the cardiac cycle to be accurately captured Images from cardiac gated
sequences are formed over many cardiac cycles and reconstructed as an lsquoaveragersquo
cardiac cycle ECG gated images are therefore susceptible to artifacts from
additional motion eg respiratory motion There are some simple techniques to
reduce respiratory motion including breath-hold imaging However many patients
with cardiac disease have difficulty in holding their breath therefore multiple signal
averages may be performed or respiratory gating may be used ndash these techniques
greatly increase scan time Other forms of motion are more difficult to control
Successful cardiac gating requires a good quality periodic ECG waveform for
accurate detection of the R-wave Therefore conventional MRI techniques are
unsuccessful in subjects with arrhythmias or where there is an unreliable ECG
signal In these applications real-time imaging is highly desirable as it does not
require ECG gating Real-time MRI acquires data very rapidly (ie each frame takes
less than 100ms) making it less susceptible to motion This allows a great reduction
2
in scan time and may also allow observation of beat-to-beat variations (which are not
seen in conventional imaging) Real-time imaging does however come at the cost of
lower spatial resolution and also lower effective-temporal resolution
Real-time imaging is also essential in imaging subjects during exercise because
bull ECG gating is unreliable
bull Breath-holding is not feasible
bull High heart rates are observed
bull Excessive motion from breathing and exercise
MRI is a well validated method of measuring flow at rest however in this study we
would like to be able to measure flow during exercise with the use of real-time
imaging This will allow quantification of hemodynamic response to exercise and
assessment of vascular disease
11 Achieving Real-time Imaging
Real-time imaging requires data to be acquired very rapidly Common ways to
reduce acquisition times include
bull Reducing the matrix size
bull Rectangular field-of-view (where less lines are acquired at the top and
bottom of k-space)
bull Partial Fourier encoding (where less lines are acquired at the bottom of k-
space and the missing lines are calculated from the Hermitian symmetry of
k-space)
bull Sliding window reconstruction (where data is shared between frames)
In this study we are interested in reducing scan times further than these common
methods can achieve This study focuses on the use of alternative trajectories and
parallel imaging to achieve very high temporal resolution imaging
3
111 Alternative trajectories
Conventionally in MRI data is acquired one k-space line at a time This is a very
popular method of imaging as the gradient design is simple and the data lies on a
Cartesian grid Acquiring data in this way is very slow as only a small portion of k-
space is covered after each excitation and there are a large number of excitations
Methods of speeding up acquisition while maintaining data on a Cartesian grid
include the use of echo planar imaging (EPI) Single shot EPI is possible where the
entire of k-space is filled after one excitation or segmented EPI can be used where a
part of k-space is filled after each excitation
To convert k-space data into the image domain a Fourier transform must be applied
The fastest and most efficient method of performing a Fourier transform is with the
Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform
Cartesian grid This means that k-space data acquired using non-uniform Cartesian
trajectories or non-Cartesian trajectories require the data to be resampled onto a
uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)
Gridding of data in MRI requires convolution of the k-space data with a convolution
kernel Ideally a SINC kernel would be used however as this is an infinite function
the computation would be impractical The choice of kernel is a trade-off between
processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly
used in MRI (3) as it has minimal residual aliasing and allows a relatively short
computation time It also has an analytic expression for its properties in the Fourier
domain
Non-Cartesian trajectories may offer more efficient methods of covering k-space or
non-uniform coverage of k-space The most common non-Cartesian trajectories used
in MRI include radials and spirals (see Figure 1) This study focuses on the use of
Spiral trajectories (4) as they provide a highly efficient method of traversing k-space
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
2
in scan time and may also allow observation of beat-to-beat variations (which are not
seen in conventional imaging) Real-time imaging does however come at the cost of
lower spatial resolution and also lower effective-temporal resolution
Real-time imaging is also essential in imaging subjects during exercise because
bull ECG gating is unreliable
bull Breath-holding is not feasible
bull High heart rates are observed
bull Excessive motion from breathing and exercise
MRI is a well validated method of measuring flow at rest however in this study we
would like to be able to measure flow during exercise with the use of real-time
imaging This will allow quantification of hemodynamic response to exercise and
assessment of vascular disease
11 Achieving Real-time Imaging
Real-time imaging requires data to be acquired very rapidly Common ways to
reduce acquisition times include
bull Reducing the matrix size
bull Rectangular field-of-view (where less lines are acquired at the top and
bottom of k-space)
bull Partial Fourier encoding (where less lines are acquired at the bottom of k-
space and the missing lines are calculated from the Hermitian symmetry of
k-space)
bull Sliding window reconstruction (where data is shared between frames)
In this study we are interested in reducing scan times further than these common
methods can achieve This study focuses on the use of alternative trajectories and
parallel imaging to achieve very high temporal resolution imaging
3
111 Alternative trajectories
Conventionally in MRI data is acquired one k-space line at a time This is a very
popular method of imaging as the gradient design is simple and the data lies on a
Cartesian grid Acquiring data in this way is very slow as only a small portion of k-
space is covered after each excitation and there are a large number of excitations
Methods of speeding up acquisition while maintaining data on a Cartesian grid
include the use of echo planar imaging (EPI) Single shot EPI is possible where the
entire of k-space is filled after one excitation or segmented EPI can be used where a
part of k-space is filled after each excitation
To convert k-space data into the image domain a Fourier transform must be applied
The fastest and most efficient method of performing a Fourier transform is with the
Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform
Cartesian grid This means that k-space data acquired using non-uniform Cartesian
trajectories or non-Cartesian trajectories require the data to be resampled onto a
uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)
Gridding of data in MRI requires convolution of the k-space data with a convolution
kernel Ideally a SINC kernel would be used however as this is an infinite function
the computation would be impractical The choice of kernel is a trade-off between
processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly
used in MRI (3) as it has minimal residual aliasing and allows a relatively short
computation time It also has an analytic expression for its properties in the Fourier
domain
Non-Cartesian trajectories may offer more efficient methods of covering k-space or
non-uniform coverage of k-space The most common non-Cartesian trajectories used
in MRI include radials and spirals (see Figure 1) This study focuses on the use of
Spiral trajectories (4) as they provide a highly efficient method of traversing k-space
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
3
111 Alternative trajectories
Conventionally in MRI data is acquired one k-space line at a time This is a very
popular method of imaging as the gradient design is simple and the data lies on a
Cartesian grid Acquiring data in this way is very slow as only a small portion of k-
space is covered after each excitation and there are a large number of excitations
Methods of speeding up acquisition while maintaining data on a Cartesian grid
include the use of echo planar imaging (EPI) Single shot EPI is possible where the
entire of k-space is filled after one excitation or segmented EPI can be used where a
part of k-space is filled after each excitation
To convert k-space data into the image domain a Fourier transform must be applied
The fastest and most efficient method of performing a Fourier transform is with the
Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform
Cartesian grid This means that k-space data acquired using non-uniform Cartesian
trajectories or non-Cartesian trajectories require the data to be resampled onto a
uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)
Gridding of data in MRI requires convolution of the k-space data with a convolution
kernel Ideally a SINC kernel would be used however as this is an infinite function
the computation would be impractical The choice of kernel is a trade-off between
processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly
used in MRI (3) as it has minimal residual aliasing and allows a relatively short
computation time It also has an analytic expression for its properties in the Fourier
domain
Non-Cartesian trajectories may offer more efficient methods of covering k-space or
non-uniform coverage of k-space The most common non-Cartesian trajectories used
in MRI include radials and spirals (see Figure 1) This study focuses on the use of
Spiral trajectories (4) as they provide a highly efficient method of traversing k-space
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
4
Spiral trajectories acquire a large proportion of the data to be acquired after each
excitation and they do not acquire the corners of k-space which are not necessary
for reconstruction As spiral trajectories start in the centre of k-space they have a
very short TE which means there is very little time for spins to dephase due to
motion This makes spiral trajectories optimal for measuring flow (5)
Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral
In order to acquire data on a spiral trajectory the gradient waveforms required are
sinusoidal in shape and are both frequency and amplitude modulated At the start of
the readout the gradients are limited by the slew rate however once the maximum
gradient amplitude has been reached this then limits the gradient waveforms Spiral
trajectories are designed using the following formulae (6)
euro
k( t) = λθ ( t)eiθ (t ) Equation 1
euro
λ =N int
D Equation 2
where
euro
k t( ) is the k-space position at time t
euro
θ t( ) is the azimuth angle (rad)
euro
N int is the
number of spiral interleaves required and
euro
D is the field of view (m) A spiral trajectory
that has multiple interleaves uses the same trajectory for each interleave however
each interleave is rotated by a multiple of
euro
2π N int radians
a) b) c)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
5
112 Parallel Imaging
It is possible to further speed up image acquisition by missing out some of the data in
k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal
resolution by missing out entire lines of k-space (eg only acquiring every other line
gives a two-fold acceleration) In Spiral imaging the same principle can be used by
missing out entire spiral interleaves
Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral
When reconstructing an accelerated Cartesian acquisition aliasing occurs where
replicas of the subject appear in the image along the phase-encode direction (see
Figure 3) spaced at FOVacceleration factor This is because an increase in the
spacing between lines in k-space causes an effective decrease in the FOV resulting
in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls
across the entire reconstructed image (see Figure 3) that are not related to the
anatomical region that generated the aliasing
Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory
a) b) c) d)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
6
In order to reconstruct accelerated MRI data parallel-imaging is used where multiple
coils acquire data in parallel Although not the first parallel-imaging implementation
one simple method of parallel-imaging is SENSE (sensitivity encoding) which was
described by Pruessmann in 1999 (7) Other methods of parallel imaging not
investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)
kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)
In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply
information about the origin of the signal in the image domain and remove aliasing
artifacts There are two methods of measuring the coil sensitivities (7) one method
requires a separate scan to be performed prior to the SENSE scan and the other
method uses the data from the scan to calculate the coil sensitivities The first
method requires a low resolution full FOV images to be acquired for each of the coils
along with a full FOV image from the body coil (which is assumed to be
homogeneous) The second method calculates an average full FOV image for each
coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo
magnitude image is formed from the sum-of-squares of all coils The coil sensitivities
are calculated by the division of each of the coil images by the body coil image
SENSE reconstruction of an accelerated Cartesian data set can be efficiently
performed by direct unfolding of the aliased images in the image domain (7)
However for undersampled spiral data the relationship between the pixels in the
aliased images and their contribution to the pixels in the full FOV image is not clear
(as seen in Figure 3) Pruessmann described a method of reconstructing
undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses
an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A
generalized diagram of the CG algorithm is shown in Figure 4
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
7
Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)
12 Measuring Flow with MRI
MRI is a proven method of measuring flow at rest (1314) Measurements of flow are
very important in assessing cardiac performance and MRI allows visualization and
quantification of flow Clinical assessment of flow leads to detection management
and monitoring of heart disease
MRI is inherently motion sensitive as the applied magnetic gradients alter the
resonant frequency of spins according to the Larmor equation
euro
ω(x) = γ(B0 + x sdotGx ) Equation 3
where
euro
ω is the precessional frequency (rads)
euro
γ is the gyromagentic ratio (radsT)
Bo is the main magnetic field (T) and
euro
G is the strength of the gradient (T) at position
euro
x (m) This means that spins accumulate a phase over time depending on their
location according to the equation
euro
φ t( ) = γ G(u)x(u)du0
t
int
Equation 4
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
8
where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u
(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is
linearly proportional to the velocity of that spin
euro
φ(t) = γ M0x0 + M1v0 + + 1nMn
dnxdt 2
t= 0
+
Equation 5
where Mn is the nth gradient moment and
euro
x0 and
euro
v0 are the initial displacement and
velocity of the spins along the direction of the gradient The sensitivity to velocity can
be seen in Equation 5 to be related to the first order gradient moment (M1)
The encoding of velocity in the phase of an MR signal is known as phase contrast
(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be
calculated The flow velocity is determined by the pixel intensity values in the phase
images and the flow volume is the flow velocity in a pixel multiplied by the pixel
volume Therefore the flow volume in a vessel can be calculated by summing the
flow volumes for all pixels within the vessel
121 Implementation of Phase Contrast Imaging
The motion sensitizing gradients
required to encode flow in MRI are
applied after the RF excitation and
before the readout gradient Flow
can be measured in any direction by
placing the motion sensitizing
gradients on the appropriate axis
however in this study we are only
interested in through-plane flow
where the gradients are played out
Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
9
on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two
lobes of equal area but opposite polarity (see Figure 5) Because the net area of
these two gradients is zero (ie M0 is zero) stationary spins accumulate no net
phase Assuming there is no accelerative or higher order motion of spins Equation 5
can be seen to simplify to
euro
φ = γv sdot M1 Equation 6
The velocity encoding (VENC) determines the maximum velocity that can correctly
be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value
(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions
are made one which is velocity compensated (ie has a VENC of zero) and one
which is velocity encoded The phases of the resultant images are subtracted in
order to remove phase offsets from additional sources eg B0 inhomogeneities or
eddy currents Therefore the phase difference is more commonly expressed as a
difference in the first order moments of the two images
euro
ΔM1
euro
Δφ = γv sdot ΔM1 Equation 7
Where the VENC can be calculated as
euro
VENC =π
γΔM1 Equation 8
122 Accuracy of PC-MRI
The accuracy of PC-MRI is very important Many studies have looked at the errors in
flow measurements Lotz et al (14) found a 3 difference between flow in the
ascending aorta and the pulmonary artery using a retrospective gated and breath-
hold sequence with an intra-observer variability of 2 and inter-observer variability
of 3 They also found a ~10 difference between cardiac output measured by
phase-contrast and by a modified thermodilution technique (14)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
10
The accuracy of PC-MRI depends on
bull Adequate temporal resolution to accurately detect the peak flow velocities
bull Adequate spatial resolution to prevent partial-volume effects
bull A suitable match between the velocities in the vessel of interest and the
chosen VENC
o If the VENC is too small then wrap occurs where the phase shift is
greater than plusmnπc
o If the VENC is too large then noise may mask the true velocities ndash this
is known as the velocity-to-noise ratio (VNR)
bull The angle of the imaging plane to the main direction of flow ndash most precise
measurements are obtained if the plane is orthogonal to the flow for through-
plane flow
bull The presence of background phase offsets which may arise from concomitant
gradients or eddy currents (described in sections 123 and 124 respectively)
bull The accuracy of vessel segmentation
Tang et al (16) described the main factors that affect the accuracy of PC flow
measurements as being partial-volume effects and intravoxel phase dispersion
Partial-volume effects are observed when there is a mixture of stationary and flowing
spins within a voxel ndash this is important in voxels that are on vessel boundaries In
these edge pixels the volume flow rate is normally overestimated because the area of
the pixel is overestimated while the velocity is accurately measured The smaller the
vessel (or the larger the pixels) the larger the relative number of pixels influenced by
partial-volume effects compared to the number of pixels fully in the vessel thus the
greater partial-volume effects influence the flow measurement Intravoxel dephasing
occurs when there are spins with different velocities within a voxel which destroy
phase coherence ndash this may be caused by accelerative spins turbulent spins or
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
11
magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing
are reduced by increasing spatial resolution
Greil et al (17) performed a study on a
pulsatile flow phantom where the number
of pixels in the cross-section of the
phantom was varied (by changing the
matrix size and the FOV) from 145 to 16
They found that the percent error grew
linearly with increasing FOV (as seen in
Figure 6) for each 20-mm increment the
percent error increased by a mean of
07 When only 16 pixels were used in the cross section of the vessel the flow rate
was overestimated by a mean of 90 No statistical significance was found in
percentage error for varying slice thickness (from 4-8mm) slice inclination (up to
40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the
addition of background phase correction Greil concludes that providing the spatial
resolution is great enough PC-MRI is an accurate and robust method of measuring
flow (17)
123 Concomitant Gradients in Flow Imaging
Concomitant gradients (also known as Maxwell gradients) are unintentional gradients
with nonlinear spatial dependence which occur in addition to desired linear magnetic
field gradients These additional gradients are a consequence of Maxwellrsquos equations
for the divergence and curl of the magnetic field
Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
12
Concomitant gradients cause undesired phase offsets in images and therefore
incorrect velocity measurements in PC-MRI The concomitant gradient field can be
calculated (18) from the equation
euro
Bc xyzt( ) =12B0
Gx2z2 +Gy
2z2 +Gz2 x 2 + y 2
4minusGxGzxz minusGyGzyz
Equation 9
Therefore the phase accumulated from concomitant gradients is
euro
Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10
From these equations the residual phase in PC-MRI caused by concomitant
gradients (after the phase difference calculation) can be found (18)
euro
Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz
Equation 11
where
euro
A =γ2B0
Gx2(t) +Gy
2(t)( ) fe1 minus Gx2(t) +Gy
2(t)( ) fe2 dtint
B =γ8B0
Gz2(t) fe1 minusGz
2(t) fe2 dtint
C = minusγ2B0
Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint
D = minusγ2B0
Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint
Equation 12
The first flow image here is denoted fe1 and the second flow image is denoted fe2
The integrals are evaluated over a time period from the end of the RF excitation
pulse to the beginning of the ADC readout
Maxwell gradients also affect all imaging gradients and may play an important roll in
spiral imaging (19) In spiral imaging the effect of concomitant gradients is much
harder to correct as each point in the readout has to be corrected by a different
phase offset from the concomitancy of the gradients
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
13
124 Additional Phase Offsets
Additional phase offsets in PC imaging have been widely observed (2021) These
phase offsets may arise from inhomogeneities in the magnetic field and eddy current
effects They are affected by many parameters including the imaging position VENC
maximum gradient amplitude and maximum gradient slew rate Like concomitant
gradients these offsets cause incorrect velocity measurements in PC-MRI
Commonly manual post processing techniques are used to remove additional phase
offsets One such method involves estimation of the phase offset from a region of
stationary tissue near to the vessel of interest (141720) ndash this method does not work
well in the great vessels as there is very little surrounding stationary tissue
Alternatively a separate scan may be performed on a stationary phantom with
identical imaging parameters to calculate the phase offsets in the same region as
the vessel (22) This is time consuming and inconvenient in clinical practice as it
must be carried out for every individual PC image acquired
One semi-automated method was first described by Walker et al in 1993 (23) This
method assumes the phase offsets vary linearly in space This surface is estimated
by fitting a plane through stationary pixels in the phase image and subtracting this
plane from the velocity images This technique is widely used (1720212425) as it
can be completely automated and therefore does not require any additional
processing by the user However this technique will not work for very noisy data or
data where there is very little stationary tissue
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
14
13 Exercise Testing
Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a
common medical exam carried out to assess for cardiac disease In common stress
testing the patient is placed on a treadmill and the level of exercise is progressively
increased Normally only the ECG heart rate and blood pressure of the subject are
recorded - these are not sensitive markers of early vascular disease Therefore the
sensitivity of exercise testing could be improved through additional measurements of
cardiac output systemic vascular resistance (SVR) and vascular compliance (C)
SVR is the amount of resistance to flow that must be overcome to push blood
through the peripheral circulatory system SVR is calculated as the mean arterial
blood pressure divided by the cardiac output
Compliance is a measure of the ability of the wall of a blood vessel to distend and
increase volume with increasing transmural pressure A simple approximation of
compliance is the ratio of stroke volume to pulse pressure However this is thought to
overestimate true arterial compliance (26) The pulse pressure method is thought to
give a more accurate estimation of true compliance by parameter optimization of the
two-element Windkessel model (27) as discussed further in section 23
The calculation of both SVR and C require measurements of flow as well as blood
pressure measurements Normally in SVR and C measurements catheters are used
to measure pressure and the Fick principle is used to quantify flow Previous studies
measuring SVR and C using MRI are discussed in section 23
Instead of using exercise to increase the load on the heart a pharmacological stress
test can be used ndash one such pharmacological agent is called dobutamine
Pharmacological stress tests are important in subjects with physical limitations eg
severe arthritis prior injury reduced exercise tolerance however exercise testing is
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
15
advantageous over pharmacological stress tests due to the physiologic effects that
exercise also has on blood pressure and heart rate During exercise adverse
symptoms may also be observed by the physician (including exercise-induced
irregular heart beats) and the subjects tolerance to exercise can also be assessed
There are also no potential side-effects to the agents used
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
16
2 Literature Review
In this section literature on the following areas will be discussed
bull Real-time flow measurements
bull Performing MRI during exercise
bull Assessment of hemodynamic response using MRI
21 Real-time Flow Measurements
Real-time flow measurements have been achieved through the use of efficient
trajectories (eg EPI and spirals) and more recently through the use of parallel
imaging
211 Efficient trajectories
The use of spiral trajectories to measure flow volumes in real-time was first
investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32
cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per
encoding) Sixteen PC frames were acquired over two cardiac cycles in the first
cycle 16 phase-compensated data sets were acquired and in the second cycle 16
phase encoded data sets were acquired This allowed an effective temporal
resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady
flow phantom to measure through-plane and in-plane flow The results from the
spiral sequence were compared to those obtained using a conventional sequence
and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen
between the techniques used (see Figure 7)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
17
Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow
Gatehouse also performed an in-vivo
experiment measuring the flow in
the descending aorta in normal
volunteers where the spiral
sequence was found to detect a
lower velocity than the conventional
sequence (see Figure 8) This is
thought to be due to the lower spatial resolution of the spiral scan causing greater
partial volume effects (see section 122)
In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved
spiral trajectories with a water-selective spectral-spatial excitation pulse (duration
7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC
readouts to maintain temporal coherence so that each interleave was acquired once
with flow compensated gradients and once with flow encoding gradients before the
next interleave was acquired This meant that ECG-gating was not required In this
study 3 spiral interleaves (each with 16ms duration) were used with the following
parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak
further increased the effective temporal resolution of his sequence by the use of a
a) b)
Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
18
sliding window reconstruction This allowed an effective temporal resolution of ~6
imagessec with a spatial resolution of 24x24 mm
Nayak showed a good correlation (within 5)
between a reference PC sequence and the
spiral flow sequence in a constant flow
phantom with through-plane and in-plane
measurements (see Figure 9) Experiments
in a pulsatile flow pump showed that the
spiral sequence was able to accurately
capture the shape and peak of the velocity
waveform compared to results obtained from
continuous-wave Doppler ultrasound Nayak
also showed the use of this sequence in-vivo (with no validation) to observe aortic
and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow
through the iliac aorta bifurcation through-plane flow in the popliteal artery during
systole and through-plane flow in the coronaries during diastole Nayak discusses the
need for greater temporal resolution and better visualization of fast flow which could
be improved through shorter excitations and shorter readout gradients
Other non-spiral trajectories have been used for real-time flow imaging Klein et al
(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83
framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein
compared vessel diameter and velocity measurements between the fast EPI-PC
sequence and a standard PC sequence in large and medium sized vessels (with
diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1
Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
19
Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels
A good agreement was found in the measured size of the vessel diameter from the
fast EPI-PC sequence and the standard PC sequence for both large and medium
size vessels However a good agreement the peak velocity and flow volumes
measured from the two techniques was only found in the large vessels (see Table 1)
This demonstrates well the need for acceptable spatial resolution to prevent partial
volume effects (see section 122)
212 Parallel Imaging
Further increases in temporal resolution have been achieved through the use of
parallel-imaging including SENSE (see section112) One such study (which does
not acquire data in real-time however uses retrospective gating to achieve higher
temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum
studied rapid left-to-right shunt quantification in 25 children by combining a standard
gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3
were investigated allowing scan-time to be reduced to 28 and 19 of the standard
PC-MRI protocol respectively These reductions are not as expected as the standard
PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE
PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The
spatial resolution achieved in this study was111309423x31mm2 with an effective temporal
resolution of ~20-25 framescycle
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
20
Beerbaum demonstrated a good correlation in a pulsatile flow pump between the
ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=
0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC
sequence and the undersampled sequences for the QpQs ratio in the pulmonary
artery This can be seen in Figure 10 where the results are shown from SENSEx2
Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)
Beerbaum extended this study in 2005 to measure flow in 13 healthy adult
volunteers using this technique (31) Beerbaum discusses the drawbacks of this
technique which include the need for a 1-minute scan at the beginning of the
examination to calculate the coil sensitivities (see section 112) Also a large FOV
was necessary to enable the SENSE reconstruction to perform correctly which
meant a reduction in the spatial resolution
In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE
method which removed the need for an additional scan to calculate coil sensitivities
Nezafat used an undersampled spiral sequence where adaptive coil sensitivities
(which can track changes from respiratory motion) were calculated from a full
unaliased images (see section 112) Nezafat used this method to measure flow in
the ascending aorta of healthy volunteers using the following parameters
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
21
TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz
interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of
27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved
The paper does not show any validation of the sequence in-vivo but states that ldquoThe
blood velocity measured with the real-time was compared with the [standard] gated
sequence and showed excellent agreement [with the spiral-SENSE sequence] with a
slight underestimation of the peak blood flow due to averaging of blood flow through
the cardiac phaserdquo (32)
Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with
SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix
size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of
27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a
reduced the number of k-space lines per TR to 19 This allowed a temporal resolution
of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a
separate 1min scan was performed to calculate the coil sensitivities Koperich
validated the real-time EPI-PC sequence using a pulsatile flow phantom by
comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good
correlation was found (r=0999) with a moderate overestimation (y=126x+003) and
relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in
14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by
conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI
was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with
limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of
agreement from 087-119) in the aorta
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
22
22 Performing MRI during exercise
Most studies investing the response to exercise with MRI use supine ergometers as
it is not possible for subjects to be upright within normal scanners The first studies to
measure response to exercise using MRI required ECG gating in order to achieve
suitable temporal resolution In these studies the subjects were often required to
suspend exercise in order to perform MRI measurements This is non-physiological
as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also
makes ramped exercise protocols difficult to perform
221 Imaging During Suspension of Exercise
The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)
This study uses the single-shot spiral PC-technique developed by Gatehouse (5)
described in section 211 with the addition of a section-selective excitation Imaging
was performed at rest and immediately after exercise in 10 healthy volunteers in the
descending thoracic aorta at the mid-ventricular level Low spatial resolution was
achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an
effective temporal resolution of ~50ms was achieved (by acquiring the flow
compensated and flow encoded data in separate heart cycles) Mohiaddin observed
the expected hemodynamic changes an increase in the mean and peak aortic flow
and a decrease in the time to peak aortic flow as seen in Table 2
Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
23
In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-
gated PC-imaging in a single breath-hold immediately after stopping exercise Nine
healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W
and 131W) where imaging lasted 12 cardiac cycles Even after suspension of
exercise at 131W two measurements failed and two other measurements skipped 1-
2 heart beats due to triggering problems They claim that the heart rate in the
subjects decreased less than 4 during the first six heart beats and less than 13
after the first 12 heart beats making scanning directly post-exercise representative of
controlled exercise levels They observed that retrograde flow patterns in the
abdominal aorta are reduced with increasing levels of exercise as seen in Table 3
Table 3 Hemodynamic response to exercise as observed by Pederson (36)
Pederson et al (37) have also used this technique to measure the flow in the
Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients
with total cavopulmonary connection (TCPC)
222 Imaging During Continuation of Exercise
More accurate hemodynamic responses are obtained when MRI imaging can be
performed during the continuation of exercise ndash this also allows ramped protocols As
previously discussed ECG gating is generally unreliable during exercise due to
excessive motion however some studies have used ECG gated sequences to
measure flow during the continuation of exercise
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
24
In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy
volunteers using retrospective gating from a peripheral pulse unit attached to one of
the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta
were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the
peripheral gating device used in the present study heart rate measurements were
adequate in all subjects Tests performed in a small number of volunteers using
standard ECG gating during exercise yielded an ECG signal too distorted to
guarantee reliable flow measurementsrdquo Gating data during continuation of exercise
would be expected to give many image artifacts due to excessive motion however
Niezen states that ldquoalthough motion artifacts increased with higher workloads image
quality was sufficient to obtain reliable flow measurements during exerciserdquo
In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow
in the caval veins and in the aorta at rest and during the continuation of exercise (at
workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)
segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a
temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At
each exercise level 120 consecutive PC images were acquired in the Aorta IVC and
SVC and the blood flow and stroke volume were measured over two respiratory
cycles as seen in Table 4
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
25
This study confirmed that resting Inferior Vena Cava (IVC) flow has marked
respiratory variability in the TCPC circulation It also indicates that the venous return
in the TCPC circulation is influenced by the cardiac output respiration and a
peripheral pump (that acts through muscles surrounding venous capacitance vessels
in the body) The relative contribution of these three mechanisms is thought to
change from rest to exercise states
Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
26
223 Upright exercise
Some studies have been
carried out by Cheng et al
(40-42) measuring flow using a
low-field (05T) open-bore MRI
system which allowed upright
exercise
This system was developed in
2003 (40) when it was tested
on one volunteer using an
ECG-gated sequence with
respiratory compensation
during the continuation of
exercise
A study in 10 healthy children was carried out in 2004 using the same ECG-gated
sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min
during exercise Exercise intensity corresponding to a 50 increase in heart rate
caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and
91 respectively with a mean blood flow increase in the SVC of only 36 and in
the IVC of 238
In 2005 an upright exercise study on 17 healthy children and adults (42) was
compared with supine results from Niezen et al (38) (described in section 222)
Cheng observes that with comparable exercise workloads and increases in heart
rate an upright posture produces greater ranges in mean blood flow rate and stroke
volume than a supine posture In the study by Cheng (42) 8 of 51 flow
Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
27
measurements could not be used due to excessive body and respiratory motion
which caused inadequate image quality
224 Measurement of Ventricle Volume During Exercise
Previous studies by Roest et al (4344) have measured left ventricular volumes after
suspension of exercise using a prospectively gated breath-hold EPI sequence
A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured
left ventricular volume in 12 healthy volunteers during continuation of exercise using
a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)
using kt-SENSE In each frame 16 radial projections were acquired The sampling
pattern was rotated in subsequent frames so that 8 consecutive frames comprised a
fully sampled k-space This allowed temporal resolution of 35ms to be achieved with
a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired
consecutively in the short axis to cover the entire ventricle This sequence has
previously been validated at rest (46)
In this study Lurz observed that stroke volume increased with exercise due to a
significant decrease in biventricular end systolic volume (ESV) and no change in end
diastolic volumes (EDV) in the left or right ventricles
23 Assessment of hemodynamic response using MRI
In the pulmonary vasculature MR flow measurements have been combined with
invasive pressure measurements to calculate vascular resistance (47) and
compliance (48)
Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24
subjects by combining MRI flow measurements with simultaneous invasive pressure
measurements The PVR measurements derived from MR were compared to those
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
28
derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100
oxygen + 20ppm NO A summary of their results is shown in Table 5
Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)
Muthurangu et al showed reasonable agreement between Fick and MRIndashderived
PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there
was less agreement between the methods and with 100 oxygen there was a large
bias It was believed that these errors were from inaccuracies in the Fick method
rather than the MR as Fick is known to be inaccurate in the presence of high blood
flow and high concentrations of oxygen (47)
Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)
Bland Altman Analysis () PVR Fick (WUm2)
PVR PC-MRI (WUm2)
Correlation coefficient Bias Lower
limit Upper limit
Baseline 47plusmn46 46plusmn35 091 (Plt005)
23 455 502
30 oxygen + 20ppm NO
33plusmn32 37plusmn21 078 (Plt005)
280 953 1513
100 oxygen + 20ppm NO
24plusmn23 30plusmn19 059 (P=002)
542 660 1744
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
29
Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with
pulmonary hypertension using the same technique as Muthurangu These studies
also show good correlation between PC flow volumes and alternative volume
measurements for the measurement of PVR however in these studies they are
unable to perform simultaneous invasive blood pressure measurements (instead the
blood pressure was measured directly before the subject was moved into the MR)
Muthurangu et al (48) have measured vascular compliance in 17 subjects using the
two-element Windkessel model (discussed in section13) by combining PC-MRI
measurements with simultaneous invasive blood pressure data The equation
defining the windkessel model is
euro
˙ Q (t) =P(t)
R+ C dP(t)
dt Equation 13
where P is pressure R is vascular resistance C is compliance and Q is measured
flow curve over time (t) In this study a series of modeled pressure curves (P) were
generated using values of C between 0001 and 70 mlmmHg Compliance was
taken to be the value that produced the best match with the actual pulse pressure
See (48) for further details
Compliance measured with the pulse pressure method (Cppm) was correlated with
that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO
A summary of the results can be seen in Table 6 and Figure 13
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
30
Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)
In all cases there was a significant difference between mean Cppm and Csv (P lt
005)
Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)
Lankhaar et al (51) has extended the technique used by Muthuragu et al by using
the three-element windkessel model to measure resistance compliance and
characteristic impedance by combining invasive blood pressure measurements with
MRI flow measurements
Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient
Bias Lower limit
Upper limit
30 O2
187 (128)
099 (068)
Csv = 186Cppm+ 002
099 (Plt0001)
61 38 84
30 O2 + 20ppm NO
201 (099)
106 (058)
Csv = 183Cppm+ 007
097 (Plt0001)
61 37 85
Overall - - Csv = 185Cppm+ 004
098 (Plt0001)
61 38 84
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
31
From the literature review it can be seen that
bull Spiral trajectories have previously been combined with phase contrast
techniques used to successfully measure flow in MRI
bull Data undersampling and SENSE reconstructions have been successfully used
to measure flow in real-time
bull A few previous studies have been able to measure flow-volume response
during exercise using MRI however many of these studies do not acquire data
in real-time
bull A few previous studies have combined MRI flow measurements with invasive
blood pressure measurement in order to quantify pulmonary vascular
resistance and compliance
In this study a real-time flow sequence will be developed using an undersampled
spiral trajectory which is reconstructed using a SENSE algorithm This will be used
to measure flow-volume response to exercise and these results combined with non-
invasive blood pressure measurements to quantify pulmonary vascular resistance
and compliance in the Aorta
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
32
3 REAL-TIME FLOW MEASUREMENTS FOR THE
ASSESSMENT OF HEMODYNAMIC RESPONSE TO
EXERCISE
The aims of this study were to
bull Develop an in-house real-time flow sequence and online reconstruction
bull Validate this sequence in a flow phantom
bull Validate this sequence in-vivo at rest and during exercise
bull Demonstrate the feasibility of using this sequence to measure the
hemodynamic response to exercise
31 Development of Real-Time Flow Sequence
As described in section 11 real-time imaging in this study was achieved by the use
of efficient spiral trajectories and undersampling of data The spiral trajectories were
designed using adapted code developed by Brain Hargreaves (52) This takes into
account the FOV number of interleaves maximum slew rate maximum gradient
amplitude sampling period and k-space radius required
The sequence developed uses a standard PC technique (12) to measure through-
plane flow The PC readouts were interleaved to maintain temporal coherence so
that each spiral interleave was acquired once with flow compensated gradients and
once with flow encoding gradients before the next spiral interleave was acquired
The resulting flow data was formed by subtraction of the phase information from the
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
33
two images A sequence diagram can be seen in Figure 14 for one pair of spiral
readouts
Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed
In spiral imaging it is necessary to keep the readout times relatively short to ensure
signal throughout the entire readout and to reduce cumulative trajectory errors
(which may lead to image rotation or blurring) The length of the readout train
regardless of matrix size can be altered by the number of spiral interleaves used
However the overall scan time is increased when using multiple interleaves as
multiple excitations (and flow gradients) are also required Therefore there is a trade
off between the overall scan time and the resultant image quality
In parallel imaging there is also a trade-off between the undersampling factor used
and the resultant image quality The greater the undersampling the lower the
resultant SNR
Flow compensated gradients
Flow encoded gradients
Flow compensated readout
Flow encoded readout
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
34
euro
SNRSENSE =SNRNORMAL
g R Equation 14
where g is the lsquogeometry factorrsquo which determines how independent the coils used
are and R is the acceleration factor When undersampling a spiral data set the un-
accelerated number of interleaves must be exactly divisible by the acceleration factor
used In this study a trade-off was reached to achieve the desired temporal resolution
while maintaining acceptable image quality A good compromise was achieved with
the use of eight spiral interleaves undersampled by a factor of four ndash this means that
only two spiral interleaves were acquired per frame The sampling pattern was
rotated for each frame so that four consecutive PC frames comprised a fully sampled
k-space with eight interleaves as seen in Figure 15
Frame 1
Interleave 1 Interleave 5
Frame 2
Interleave 2 Interleave 6
Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
35
This undersampled data was reconstructed online using an iterative SENSE
algorithm (see section 112) All coil sensitivity and regularization information
required for the reconstruction process was calculated from the sum-of-squares of all
coil data over all time frames (as described in section112)
311 Maxwell Correction
The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a
gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus
largely neglected in most imaging situations (18) However in this study we are using
a low-field system (15T) with a high amplitude gradient system (40mTm) and for this
application are generally interested in performing imaging off-centre Therefore
concomitant magnetic fields were observed to be important in the resultant phase
contrast images from the developed sequence (see Table 7) Maxwell correction was
performed to remove the effects of concomitant gradients originating from the flow
encoding gradients (18) (see section 123) as seen in Table 7
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
36
Without Maxwell Correction
Maxwell Correction With Maxwell Correction
Scale
Transverse (isocentre)
Sagital (isocentre)
Coronal (isocentre)
Double oblique
Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC
No additional Maxwell correction was carried out for the spiral readout gradients (19)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
37
312 Residual Phase Offsets
When investigating the effects of concomitant gradient correction on double oblique
orientations it was seen that Maxwell correction did not entirely remove the
background phase offsets (see Table 7) However it was observed that if the TE time
(ie the time between the end of the flow encoding gradients and the beginning of the
readout) was increased (see Table 8a) or the slew rate of the flow encoding
gradients was decreased (and the TE was minimized see Table 8b) the phase
offsets were reduced These observations imply that the phase offsets are a result of
residual eddy currents from the flow compensationflow encoding gradients This has
been commonly noted previously (see section 124)
To reduce these background offsets a similar principle to Walker (23) was used (see
section 124) where stationary tissue was identified by the intensity of the pixels in
an average magnitude image (over all time frames) and also by the standard
deviation of the pixels in the phase image The residual phase was observed to be
predominantly linear (with some higher order terms ndash see Figure 16) and did not
change significantly over an in-vivo time series A quadratic surface
(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a
time averaged phase image) using a Cholesky decomposition algorithm This
surface was then subtracted from each of the phase images to correct for residual
background phase errors (see Table 9)
Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
38
Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)
39
Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)