3D Steady-State Diffusion-Weighted Imaging with

Trajectory Using Radially Batched Internal Navigator Echoes

(TURBINE)

Jennifer A. McNab, Daniel Gallichan, Karla L. Miller

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain, University of Oxford, Oxford, UK

Corresponding Author: Jennifer A. McNabOxford Centre for Functional Magnetic Resonance Imaging of the BrainJohn Radcliffe HospitalHeadington, OxfordOX3 9DU, United KingdomE-mail: jmcnab@fmrib.ox.ac.uk

Word Count: 2798

Running Head: Steady-State Diffusion-Weighted Imaging with TURBINE

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Abstract

While most DWI is acquired using single-shot diffusion-weighted spin-echo (DW-SE) EPI, steady-

state DWI is an alternative method with the potential to achieve higher-resolution images with

less distortion. Steady-state DWI is, however, best suited to a segmented 3D acquisition and thus

requires 3D navigation to fully correct for motion artifacts. In this paper, a method for 3D motion-

corrected steady-state DWI is presented. The method uses a unique acquisition and reconstruc-

tion scheme named Trajectory Using Radially Batched Internal Navigator Echoes (TURBINE).

Steady-state DWI with TURBINE uses slab-selection and a short EPI read-out each TR. Succes-

sive EPI read-outs are rotated about the phase-encode axis. For image reconstruction, batches

of cardiac-synchronized read-outs are used to form 3D navigators from a fully-sampled central k-

space cylinder. In vivo steady-state DWI with TURBINE is demonstrated in human brain. Motion

artifacts are corrected using refocusing reconstruction and TURBINE images prove less distorted

compared to 2D single-shot DW-SE-EPI.

Keywords: diffusion, steady-state, motion-correction;

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Introduction

Diffusion-weighted imaging (DWI) is sensitive to the self-diffusion of water molecules. In brain

tissue, biological membranes and barriers hinder the diffusion of water along certain orientations,

thereby rendering DWI an effective method to non-invasively interrogate tissue microstructures.

DWI is used routinely in the clinical diagnosis of acute stroke [1] and to differentiate between cysts

and other neurological lesions [2]. More recently the neuroscience community has capitalized on

multi-orientation DWI measurements to study the orientation and structural properties of white

matter pathways [3]. There remain, however, several technical challenges that limit the utility of

DWI including the need for increased resolution and reduced distortions. At the current standard

resolution of around 8 mm3 small stroke lesions may not be detectable. For diffusion tensor imag-

ing and tractography a combination of white matter (WM) and grey matter (GM) within each

voxel give rise to an ambiguous mixture of putatively anisotropic diffusion in WM and isotropic

diffusion in GM. Decreased voxel sizes should also limit the incidence of intra-voxel crossing or

“kissing” fibres, situations which can also give rise to ambiguity. Severe distortions are also a

serious problem for conventional 2D single-shot diffusion-weighted spin echo (DW-SE) EPI. The

long EPI read-out is prone to distortions caused by susceptibility differences at air-tissue interfaces

and with the increasing trend towards higher static magnetic field strengths, these susceptibility

artifacts are exacerbated. Parallel imaging can be used to reduce the time to acquirea single-shot

image [4] thereby providing the potential to improve resolution and/or reduce distortions at the

cost of some loss in SNR. However, current techniques are in practice limited to accelerations of

2-3.

Recently, steady-state DWI with a heavily segmented 3D acquisition has been shown to be an

efficient method for achieving high resolution (0.8 mm isotropic), low distortion DWI in fixed

human brains [5,6]. Steady-state DWI accumulates signal from multiple echoes that are generated

across several TRs and thereby builds a strong sensitivity to diffusion with relatively small gradient

areas and short imaging times [7–9]. These benefits would be useful for in vivo applications as well.

However, applying the same 3D segmented steady-state DWI pulse sequence in vivo leads to severe

artifacts due to the inherent sensitivity to motion (both bulk and physiological) which corrupts

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phase encoding when combining separately-acquired k-space segments. It is for this reason that

standard DWI methods (i.e. 2D DW-SE-EPI) acquire all data required to form an image in a

single-shot.

A compelling method for correcting motion-induced phase errors in 2D is to acquire a low resolution,

full field-of-view (FOV) image, called a navigator image, along with each k-space segment. The

low frequency phase information from the navigator image can be used to correct for phase offsets

between separately acquired k-space segments [10, 11]. These data can accurately measure 2D

rigid body movement, provided the centre of k-space does not shift outside the covered region.

However, cardiac pulsation causes brain tissue to deform in a largely non-linear way and thus more

recent work has extended this concept to include correction of non-linear motion. Non-linear phase

offsets can be measured with 2D navigators, provided the phase offsets vary sufficiently slowly

to be well-described by the low-resolution navigator. The simplest reconstruction operates in

image space and removes the phase measured by the navigator from the (potentially aliased) high-

resolution image data [12,13]. Self-navigating trajectories such as Periodically Rotated Overlapping

ParallEL Lines with Enhanced Reconsturction (PROPELLER) [12], Self-Navigated Interleaved

Spiral (SNAILS) [14] and EPI with Keyhole (EPIK) [15, 16] are highly efficient methods of 2D

navigation because they acquire the 2D navigator and the outer k-space segment in a single read-

out. However, the aforementioned techniques are for 2D imaging, whereas steady-state DWI is best

suited to a 3D acquisition such that the steady-state does not need to be re-established with each

slice.

The challenge in developing a 3D navigated pulse sequence is that it would take a prohibitively

long time to acquire all the data needed for a 3D navigator along with each k-space segment. A

disproportionate amount of time spent acquiring the navigator compared to the associated k-space

segment renders the pulse sequence highly inefficient. As a solution to this problem we propose the

use of a “multi-shot navigator”. Using multiple read-outs to form a navigator is perhaps counter-

intuitive, but if the majority of motion effects are due to cardiac pulsation then these effects should

be highly reproducible and able to be captured using multiple acquisitions. We thus propose that

using the very rapid steady-state DWI pulse sequence, it may be sufficient to form a 3D navigator

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from multiple read-outs acquired during a similar portion of the cardiac cycle. Along these lines

we present an implementation of steady-state-DWI that uses slab-selection and a novel k-space

trajectory named Trajectory Using Radially Batched Internal Navigator Echoes (TURBINE).

This pulse sequence is tested in healthy volunteers and compared with standard 2D DW-SE-EPI

to highlight the reduced levels of distortion.

Methods

Pulse Sequence

The steady-state DWI TURBINE pulse sequence (Fig. 1a) selectively excites a slab and acquires

an EPI read-out each TR with phase-encoding along the same orientation as the slab-selection.

The EPI read-out fully samples the phase-encoding orientation (Fig. 1b) and for successive TRs

the EPI read-outs are rotated about the phase-encoding/slab-select axis (Fig. 1cd) such that they

sample a k-space volume the shape of a Swedish snuff box. By acquiring multiple averages and

monitoring a pulse oximeter and scanner triggers, batches of EPI “blades” acquired during a similar

portion of diastole and with equal angular spacing are formed. The angular spacing for each batch

of cardiac-synchronized blades was chosen such that the central cylinder corresponds to a full-FOV

navigator with 10 mm × 10 mm resolution in the radially sampled plane.

Acquisition

All data were acquired on a Siemens 3T MRI (TIM Trio) using a transmit-receive head coil, in

accordance with the ethics review board at our institution. 3D steady-state DWI TURBINE data

were acquired on 11 healthy volunteers. Three different experiments are presented in this paper.

The first experiment aimed to demonstrate the signal that could be restored using the TURBINE

image reconstruction. 3D steady-state DWI TURBINE data were acquired in a healthy 28 year

old male using three different parameter sets. slab-selection, TE/TR = 28/46 ms, flip angle = 37◦,

FOVread × FOVphase = 210 mm × 31.5 mm, slab thickness = 29 mm, EPI matrix = 140 × 21, 224

k-space radial-encoding positions, resolution = 1.5 mm isotropic, diffusion gradient = 5.3 ms × 38

mT/m (providing equivalent attenuation to a diffusion-weighted spin echo with b = 556 s/mm2),

46 averages, time per volume = 10.3 s.

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The goal of the second experiment was two-fold: 1) to test steady-state DWI with TURBINE with a

larger diffusion-encoding gradient area and 2) to test the reproducibility of repeated measurements.

For this experiment data were acquired in a healthy 33 year old female using TE/TR = 27/41 ms,

flip angle = 37◦, FOVread × FOVphase = 210 mm × 26 mm, slab thickness = 25.8 m, EPI matrix =

120 × 16, 192 k-space radial-encoding positions, resolution = 1.75 mm isotropic, diffusion gradient

= 7.5 ms × 38 mT/m (providing equivalent attenuation to diffusion-weighted spin echo with b =

935 s/mm2), 6 sets of 15 averages, time per volume = 7.9 s.

The third experiment aimed to compare 2D single-shot DW-SE-EPI and 3D steady-state DWI

TURBINE. Data were acquired in a healthy 31 year old female. Cardiac-gated 2D DW-SE-EPI

data were acquired with TE/TR = 97/4200 ms, partial Fourier = 6/8, BW = 1654 Hz/pixel, b

= 1000 s/mm2, 10 averages. 3D steady-state DWI TURBINE data was acquired using TE/TR

= 25/41 ms, flip angle = 37◦, slab thickness = 39 mm, diffusion gradient = 5.3 ms × 38 mT/m,

10 averages, BW = 992 Hz/pixel. Both pulse sequences used FOVread × FOVphase = 212 mm

× 212 mm, voxel size = 2 mm × 2 mm × 2 mm and acquired 21 coronally oriented slices with

diffusion-encoding along anterior-posterior orientation in 1 minute, 15 seconds.

Note that for all steady-state DWI data, the TE is defined as the time between the RF pulse and the

read-out. Pulse oximeter and scanner triggers were recorded for all steady-state DWI experiments

in order to synchronize cardiac pulses with the data acquisition.

Image Reconstruction

All TURBINE images were reconstructed offline. Image analysis was performed using custom

software written in MATLAB v7.4 (MathWorks Inc.). The common even-odd EPI artifact [17]

was correct for using three non-phase-encoded reference lines that were acquired between the RF

pulse and the diffusion-encoding gradient each TR. Retrospective cardiac gating was performed by

eliminating EPI blades acquired less than 150 ms following or 50 ms prior to a cardiac trigger. A

zero-order phase correction was also performed on each EPI blade (i.e. the phase at the centre of k-

space was removed from each data point in the EPI acquisition). This zero-order phase-correction

was intended to remove the effects of bulk, rigid-body shifts, so that once the EPI blades were

combined to form navigators, only cardiac-induced phase-offsets would remain. One would expect

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rigid body rotations to induce a linear phase-ramp across the image-space data, however, no such

effects were detected and thus no rotational corrections were applied.

Batched sets of 16 EPI blades with equal angular spacing and acquired during a similar portion

of diastole were combined (Fig. 2). Cardiac timing for each EPI blade was measured as the delay

between the most recent pulse oximeter trigger and the start of data acquisition. For each set of

16 equally spaced angular positions, the number of cardiac synchronized batches was equal to the

number of averages acquired. Using this scheme, some EPI blades were used in more than one

batch and some were not used at all.

For each 3D interleave the 16 EPI blades were gridded onto a 2× Cartesian grid using sampling

density compensation and a sinc convolution of window width 5. After gridding, two copies of

each k-space interleave were retained. One copy was 3D inverse Fourier transformed to generate

an aliased 3D image volume which includes both high and low frequency information. The second

copy was k-space filtered using a Hanning window with full-width-at-half-maximum = 0.15 to retain

only the low frequency information. The filtered data were then 3D inverse Fourier transformed to

form the 3D navigator with in-plane resolution of 10 mm × 10 mm and through-plane resolution

equal to the full resolution of the acquisition (i.e. 1.5 mm or 2 mm for the data sets presented

here). The 3D navigators and image interleaves were used to perform refocusing reconstruction in

image space [13], which consists of multiplying the 3D image interleaves by the complex conjugate

of their 3D navigators and then summing the “corrected” image interleaves to produce the final

image. A diagram of an essentially identical image reconstruction pipeline can be found in Figure 6

of Pipe et. al. 2002 [12]. There are two main differences between TURBINE image reconstruction

and PROPELLER image reconstruction. Firstly, instead of the “k-space strip” that is used in each

stage of the PROPELLER reconstruction, TURBINE uses a batch of cardiac-synchornized EPI

blades as shown in Fig. 1d. Secondly, for TURBINE all the FFTs and filters are in 3D whereas for

PROPELLER they are in 2D.

Results

Figure 3 shows images acquired with 3D steady-state DWI with TURBINE that have been re-

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constructed in three different ways. In left column of Fig. 3 TURBINE data has been gridded and

inverse Fourier transformed but the retrospective cardiac gating and refocusing reconstruction has

not been applied. In the middle column of Fig. 3 TURBINE data has been reconstructed by first

removing any EPI blades that were acquired during systole and then inverse Fourier transform-

ing the data but still not applying the refocusing reconstruction. Finally in the right column of

Fig. 3 TURBINE data has been retrospectively cardiac-gated by removing EPI blades acquired

during systole and then performing the full refocusing reconstruction pipeline as described in the

image reconstruction section. When no cardiac-gating or motion-correction is applied, images with

diffusion-encoding along left-right and anterior-posterior orientation don’t show any apparent mo-

tion artifacts. The majority of the artifacts arise when diffusion-encoding is applied along the

superior-inferior orientation and this is consistent with previous 2D imaging results [13]. After

removal of data acquired during systole, the images do not improve (Fig. 3 (middle column)), in

fact a reduction in SNR is the only noticeable effect. After the refocusing reconstruction is applied

there is a significant amount of signal restored in the superior-inferior diffusion-encoded image.

However, a comparison of signal values in four gray matter regions where we would expect largely

isotropic diffusion, reveals that, on average, signal values in the S-I diffusion-encoded image are

still 32% lower than in the L-R and A-P diffusion-encoded images.

Figure 4 displays steady-state DWI TURBINE images acquired with a larger diffusion-encoding

gradient area (attenuation equivalent to DW-SE with b = 935 s/mm2) and reconstructed using

the refocusing reconstruction. Sequentially acquired images show excellent reproducibility. The

coefficient of variation maps (Fig. 4 right column) show increased variation in areas of low signal (e.g.

CSF which is highly attenuated) and reduced variation in regions of high signal (e.g. white matter

tracts running orthogonal to the diffusion-encoding gradient) but do not indicate any unexpected

instabilities.

Matched 2D single-shot DW-SE-EPI and 3D steady-state DWI with TURBINE data (Fig. 5)

highlight the reduction in distortions that can be achieved using steady-state DWI with TURBINE.

For 2D single-shot DW-SE-EPI distortions are particularly apparent around the temporal lobe and

are so so severe it would be difficult to match tissue in these regions with the same tissue in a

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conventional structural image.

Discussion

The efficiency of steady-state imaging methods is best capitalized using 3D imaging such that

the steady-state does not need to be re-established for each slice. However, 3D segmented DWI

is a challenging problem due to the inherent sensitivity of DWI to bulk and physiological motion

and the amount of data required to fully correct motion effects in three dimensions. Here we have

presented a novel solution to this problem using a new pulse sequence called steady-state DWI

with TURBINE. We have presented the first steady-state diffusion-weighted images with 3D navi-

gation. To achieve this, the peculiar concept of a “multi-shot navigator” has been introduced and

its feasbility demonstrated.

Cardiac pulsation creates the most tissue deformation along the superior-inferior orientation [18,19]

and our data shows that diffusion-encoding along the superior-inferior axis is indeed the most prob-

lematic (Fig. 3). However, for diffusion-encoding along left-right and anterior-posterior orientations

the TURBINE images don’t show any apparent motion artifacts.

If physiological brain motion is primarily along the S-I orientation it may not seem obvious why a

3D navigator is required. A 3D navigator is required if we expect brain motion to create a gradient

of phase along all three orientations. Phase variation in image space along a particular orientation

will cause a shift in the centre of k-space along that same orientation and if we do not have a

navigator that encompasses the orientation along which we have phase variation then the centre of

k-space can shift outside of the navigator resulting in uncorrectable motion artefacts.

While previous studies [18,19] have found that brain motion consists primarily of displacement along

the S-I axis, these studies also indicate that the motion primarily affects the mid-brain. It is the

variation in the amount of displacement experienced by the mid-brain relative to the surrounding

tissue that causes phase variations along all three axes and therefore necessitates a 3D navigator.

In addition to physiological motion, we speculate that the severe drop-out observed in the frontal

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brain regions in uncorrected S-I diffusion-encoded images (Fig. ??) is due to rigid body motion.

For a person lying in the scanner we would epxect there to be rotation about the L-R axis but

with adequate padding minimal rotation about the S-I or A-P orientations. Rotation of the head

about the L-R axis would cause both the frontal brain regions and inferior-posterior brain regions

(i.e. the cerebellum which is not encompassed y the slab we acquired) to be displaced significantly

along the S-I orientation and therefore result in significant drop-out in these regions when we are

diffusion-encoding along S-I.

The reconstruction scheme presented here combines EPI blades that were acquired during a similar

portion of diastole in different heart beats to form 3D navigators. An alternative method in

which EPI blades acquired during the diastolic portion of the same cardiac cycle were combined

to form 3D navigators was also tested. Acquiring one navigator per heart-beat is feasible from an

acquisition stand-point (i.e. the data required for one 3D navigator takes ∼700 ms and thus can be

acquired within the quiet portion of a single cardiac cycle). However, in our experience refocusing

reconstruction did not improve image quality when combining data from the same cardiac cycle.

This could be due to residual motion during diastole, which although not as severe as systole, still

causes significant phase offsets.

There are of course many additional ways in which the EPI blades could be combined. For example,

a higher priority could be given to cardiac synchronization by allowing the angular spacing to vary

a small amount and/or leaving out EPI blades where an appropriately synchronized read-out is

not available. Once an optimal method for combining batches of EPI blades is determined, it will

likely be beneficial to implement prospective cardiac gating since the retrospective gating becomes

less effective if fewer averages are acquired. Prospective gating will, however, necessitate dummy

scans between cardiac triggers in order to maintain the steady-state throughout [13]. A different

number of EPI blades could also be used to form the 3D navigators. In this study, 16 EPI blades

was chosen in order to achieve an in-plane navigator resolution similar to that which had been used

successfully in 2D imaging [13]. A different image reconstruction approach that may also be worth

exploring is an appropriate version of magntiude-only filtered back projection [20].

With the severity of susceptibility artifacts proportional to main magnetic field strength, diffusion-

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weighted image quality has suffered as methods have been ported largely unchanged from 1.5T to

3T. Field inhomogeneities cause errors in spatial encoding in the vicinity of susceptibility differences.

Long k-space read-outs such as single-shot EPI are particularly vulnerable to susceptibility artifacts

because they allow spins to accrue more artifactual phase resulting in a greater spatial encoding

error. As expected the shorter read-outs used by TURBINE result in reduced distortions (Fig. 5),

a highly desirable characteristic when attempting to study detailed anatomical connections and/or

match DWI to T1 or T2-weighted images. One major difference between the 2D single-shot DW-

SE-EPI data and the 3D steady-state DWI TURBINE data presented in Figure 5 is how we would

expect distortions to propagate. Distortions are primarily expected along the phase-encode axis

which for DW-SE is along an in-plane axis whereas for TURBINE phase-encoding is along the

through-plane axis (i.e. anterior-posterior for the images in Fig. 5). Regardless of this difference,

it is clear that the distortions are reduced when using TURBINE.

In addition to reduced distortions, a 3D segmented pulse sequence also has the potential to achieve

very small isotropic voxels. Unlike 2D imaging which is usually limited to a through-plane resolution

of around 2 mm due to technological constraints associated with thin slice selection, a 3D segmented

pulse sequence is limited only by SNR/time contraints. In order to reduce total raw data size, the

data presented here was acquired with a single channel coil and thus further SNR gains are expected

when a multi-channel coil is used.

While the refocusing reconstruction significantly improves the quality of the S-I diffusion-encode

images, we expect the lower signal values measured in the S-I diffusion-encoded images compared

to diffusion-encoding along L-R or A-P to be problematic for DTI and tractography since there

would be a consistent bias towards the S-I orientation when estimating the orientation of maximum

diffusivity. Therefore, in its current implementation steady-state DWI with TURBINE is limited

to the detection of changes to isotropic diffusion and future work will be aimed at resolving these

signal discrepancies such that DTI and tractography may be feasible.

One way in which TURBINE image quality may be further improved is through the use of a full

least squares reconstruction. Refocusing reconstruction ignores the final step of the least-squares

reconstruction which is the application of the “unmixing operator” to the refocused image [13]. The

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unmixing operator removes motion-induced aliasing by a linear combination that removes coupling

between voxels. If our images contain significant aliased energy, a full least squares reconstruction

could provide considerable further improvement to image quality. The challenge is to find a way to

invert the large mixing matrix, which has a minimum size of N2 × N2 where N2 corresponds to the

number of points in your image. In our case, even if we were to calculate one phase-encoded slice at

a time, the size of our mixing matrix would be 19600 × 19600 which requires a minimum of 1.4 GB

of memory to store. The problem, however, is mathematically similar to a non-Cartesian SENSE

reconstruction [21, 22] and thus an iterative scheme such as the conjugant-gradient reconstruction

which has been proposed for multicoil reconstructions may offer a solution.

TURBINE is currently limited to a slab thickness of only a few centimeters, but there are several

ways in which brain coverage could be extended. Parallel imaging could be used and/or a variable

density k-space trajectory such as EPIK [15,16] would permit a larger slab at the same resolution

whilst still enabling formation of the 3D navigator using the more densely sampled k-space centre.

Alternatively, multiple slabs could be “stitched” together to cover the full brain volume.

From an implementation perspective, for steady-state imaging, gradients are generally played out as

quickly as possible in order to keep the TR short. Steady-state DWI wth TURBINE currently uses

the maximum possible gradient amplitude (38 mT/m) to achieve a diffusion-encoding gradient in

only 5.3 ms. Such rapid ramping of the gradients makes the pulse sequence close to peripheral nerve

stimulation (PNS) limits. The Siemens scanner issues a stimulation warning prior to commencing

the scan and 3 of the 10 volunteers felt they may have experienced some PNS. Thus, the design of

highly efficient DWI methods needs to consider such physiological restrictions.

A concern often raised about steady-state DWI is that its signal properties are unconventional.

The steady-state DWI signal is generated from multiple echoes across several TRs. This type of

signal formation results in a weighted combination of b-values (i.e. a different b-value for each

contributing echo) and a complicated, non-linear dependency on not only the diffusion-encoding

gradient area but also flip angle, TR, T1 and T2 [23]. It has been shown previously, however, that

the signal model for steady-state DWI is robust and permits quantitative measures of diffusion if T1

and T2 measurements are made [6,24]. Additionally, it has been shown that the principal diffusion

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orientation can be determined even without T1 and T2 measures, thereby permitting tractography

applications without any additional data acquisition [6].

Conclusion

In conclusion, this study presents a unique and promising approach towards 3D segmented DWI.

Steady-state DWI has long been recognized as an efficient diffusion imaging method, but the seg-

mented nature of the pulse sequence combined with a strong sensitivity to motion has thus far

prevented its adoption to mainstream applications. It is our hope that, with further refinements,

the TURBINE acquisition and reconstruction scheme may provide a viable option for harnessing

the benefits of steady-state DWI and thus provide an alternative DWI method that will push the

boundaries of what can currently be achieved.

Acknowledgments

Funding for this work was provided by the UK Multiple Sclerosis Society, Royal Academy of

Engineering and the Engineering and Physical Sciences Research Council. The authors would like

to acknowledge helpful discussions with Dr. Matthew Robson.

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Figure Captions

Figure 1: a) Pulse sequence diagram for steady-state DWI using TURBINE. The bottom line

(GSS/PE) represents the axis along which slab-selection and phase-encoding are applied. Gθ rep-

resents the read-out axis which is rotated about the slab-select/phase-encode axis for successive

TRs. b-d) The TURBINE k-space trajectory. An EPI read-out as shown in b) is acquired each TR.

Successive EPI read-outs, as shown in c) and d), are rotated about the slab-select/phase-encoding

axis which in this case is kz.

Figure 2: Diagrams showing how EPI read-outs were combined to form 3D navigators. Each

navigator consisted of 16 EPI read-outs with equal angular spacing. The image in a) describes

the data available to form 3D navigators at a particular set of angular positions. For each angular

k-space position, multiple averages were acquired. The colour scale represents when each EPI-

read-out was acquired with respect to the cardiac cycle, as determined by the delay in time from

the most recent measured cardiac trigger. Black pixels indicate data acquired during systole that

has been discarded. The particular average that is used for the EPI read-out with the lowest

angular position (i.e. starting at the positive kx-axis) determines the cardiac synchronization for a

particular batch of EPI-read-outs that will form a 3D navigator. The reconstruction software then

searches for EPI-readouts at the appropriate positions that were acquired during the same portion

of the cardiac cycle. The ∗ symbols in a) indicate EPI-read-outs that were combined to form one

navigator for this set of positions. In b) the angular positions of these EPI-read-outs are plotted

using the same colour code as in a). c-d) and e-f) show two further examples of data combined to

form navigators for different angular positions and different cardiac timings.

Figure 3: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row),

anterior-posterior (middle row) and superior-inferior (bottom row). Columns left to right show the

effects of cardiac gating and refocusing reconstruction.

Figure 4: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row),

anterior-posterior (middle row) and superior-inferior (bottom row). In the first column, 6 sequen-

tially acquired images are shown. The middle column shows the average of the 6 images shown in

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the left column. The right column shows the coefficient of variation map for the 6 images in the

left column.

Figure 5: A comparison of coronal images at 2 mm isotropic resolution acquired with 2D single-

shot DW-SE-EPI (left column) and 3D steady-state DWI with TURBINE (right column) in the

same healthy volunteer. (a-d) depict the same coronal slice acquired without diffusion-weighting (a-

b) and with diffusion-weighting (c-d). (e-h) depict a different coronal slice again without diffusion

weighting (e-f) and with diffusion weighting (g-h).

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TR!

RF!

!!

Gx-y!

GDiff!

Gz!

"!

G!!!!!"!

#!

SS/PE

$!

%! &! '!

Figure 1: a) Pulse sequence diagram for steady-state DWI using TURBINE. The bottom line(GSS/PE) represents the axis along which slab-selection and phase-encoding are applied. Gθ rep-resents the read-out axis which is rotated about the slab-select/phase-encode axis for successiveTRs. b-d) The TURBINE k-space trajectory. An EPI read-out as shown in b) is acquired each TR.Successive EPI read-outs, as shown in c) and d), are rotated about the slab-select/phase-encodingaxis which in this case is kz.

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Figure 2: Too long to fit on this page, see Figure Captions section.

19

R-L

A-P

S-I

No gatingNo correction

Cardiac GatedNo correction

Cardiac GatedRefocusing Recon

Figure 3: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row),anterior-posterior (middle row) and superior-inferior (bottom row). Columns left to right show theeffects of cardiac gating and refocusing reconstruction.

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S-I

Average

A-P

R-L

0

1

0

1

0

1Coe�cient of VariationRepetitions 1 -6

Figure 4: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row),anterior-posterior (middle row) and superior-inferior (bottom row). In the first column, 6 sequen-tially acquired images are shown. The middle column shows the average of the 6 images shown inthe left column. The right column shows the coefficient of variation map for the 6 images in theleft column.

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Figure 5: A comparison of coronal images at 2 mm isotropic resolution acquired with 2D single-shotDW-SE-EPI (left column) and 3D steady-state DWI with TURBINE (right column) in the samehealthy volunteer. (a-d) depict the same coronal slice acquired without diffusion-weighting (a-b)and with diffusion-weighting (c-d). (e-h) depict a different coronal slice again without diffusionweighting (e-f) and with diffusion weighting (g-h).

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