Post on 16-Jan-2016
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fMRI Methods
Lecture2 – MRI Physics
magnetized materials and moving electric charges.
Magnetic fields
Similarly a moving magnetic field can be used to create electric current (moving charge).
Electric induction
Or you could use an electric current to move a magnet…
Electric induction
Force and field directions
Right hand rule
Protons are positively charged atomic particles that spin about themselves because of thermal energy.
Nuclear spins
μ (magnetic moment) = the torque (turning force) felt by a moving electrical charge as it is put in a magnet field.
Magnetic moment
The size of a magnetic moment depends on how much electrical charge is moving and the strength of the magnetic field it is in.
A Hydrogen proton has a constant electrical charge.
Earth’s magnetic field is relatively small (0.00005 Tesla), so the spins happen in different directions and cancel out.
Spin alignment
But when in a strong external magnetic field (e.g. 1.5 Tesla).
Spin alignment
Sum of magnetic moments in a sample with a particular volume at a given time.
Net magnetization (M)
Hydrogen protons not only spin. They also precess around the axis of the magnetic field.
PrecessionM
agne
tic f
ield
dire
ctio
n
True for all atoms with an odd number of protons
Two factors govern the speed of precession (Larmor frequency): magnetic field strength & gyromagnetic ratio
Larmor frequency = Bo * /2π
Precession speed
Gyromagnetic ratio ( )
Magnetic moment / Angular momentum
Combination of electromagnetic and mechanical forces.
Angular momentum is dependant on the mass of the atom.
Gyromagnetic ratio
Different atoms have different gyromagnetic ratios:
Gyromagnetic ratio
Nucleus Gyromagnetic ratio (γ)1H 267.5137Li 103.96213C 67.26219F 251.662
23Na 70.76131P 108.291
Different atoms placed in the same magnetic field have different Larmor frequencies:
“Tune in” to the Hydrogen frequency.
Larmor frequency
Nucleus Larmor Frequency at 1 Tesla1H 42.576 MGHz7Li 16.546 MGHz13C 10.705 MGHz19F 40.053 MGHz
23Na 11.262 MGHz31P 17.235 MGHz
The hydrogen atoms are precessing around z (direction of B0)
Longitudinal & transverse directions
Net magnetization is all pointing in the z direction
Steady state
Applying a perpendicular magnetic field “flips” the protons
Excitation pulses
Excite the sample in a perpendicular direction and let it relax.
Net magnetization of the sample changes as it relaxes, inducing current to move in a near by coil.
Excitation & Relaxation
Larmor frequency
Defined by the strength of B1 pulse and how long it lasts (T)
θ = *B1*T
This is one of the parameters we set during a scan
It defines how far we “flip” the protons…
Flip angle
xy
z
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z
900 pulse
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z
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z
1800 pulse
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z
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<900 pulse
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>900 pulse
T1: relaxation in the longitudinal directionT2*: relaxation in the transverse plane
T1 and T2/T2*
Changes in the direction of the sample’s net magnetization
Realignment of net magnetization with main magnetic field direction
T1
Before excitation At excitation Relaxation
Net magnetization along the longitudinal direction
T1
T1 = 63% recovery of original magnetization value M0
What influences T1?
Has something to do with the surroundings of the excited atom. The excited hydrogen needs to “pass on” its energy to its surroundings (the lattice) in order to relax.
Different tissues offer different surroundings and have different T1 relaxation times…
We can also introduce external molecules to a particular tissue and change its relaxation time. These are called “contrast agents”…
Loss of net magnetization phase in the transverse plain
T2*/T2
Before excitation At excitation Relaxation
Net magnetization in the transverse plain
T2/T2*
T2 = 63% decay of magnetization in transverse plain
Two main factors effect transverse relaxation:
1. Intrinsic (T2): spin-spin interactions. Mechanical and electromagnetic interactions.
2. Extrinsic (T2’): Magnetic field inhomogeneity. Local fluctuations in the strength of the magnetic field
experienced by different spins.
T2* = T2 - T2’
T2’Magnetic field inhomogeneities
Examples of causes:Transition to air filled cavities (sinusoids)Paramagnetic materials like cavity fillingsMost importantly – Deoxygenated hemoglobin
What influences T2?
Again, has to do with the molecular neighborhood affecting the amount and quality of spin-spin interactions.
Different tissues will have different T2 relaxation times.
The stronger the static magnetic field, the more interactions there are, quicker T2 decay.
MR signalWe only have one measurement:
Measurement of the net magnetization in the transverse plain as the sample relaxes.
Once T2* relaxation is completeProtons precess out of phase in the transverse plain
Net magnetization in transverse plain = 0
Two important scanning parameters:
TR – repetition time between excitation pulses.
TE – time between excitation pulse and data acquisition (“read out”).
Creating scanning protocols with different TR and TE lengths will allow us to derive T1 and T2/T2* relaxation times.
TR and TE
Short TR = weaker MR signal on consecutive pulses.
TR length & MR signal strength
With short TRs relaxation in the longitudinal direction will not be complete. So there will be fewer relaxed protons to excite.
TE: when to measure MR signalWe can measure the amplitude of net magnetization
immediately after excitation or we can wait a bit.
Longer TEs will allow more transverse relaxation to happen and the MR signal will be weaker.
We can scan the brain using different pulse sequences by choosing particular TR and TE values to create images
with different contrasts.
Different image contrasts
TR length will determine how much time the sample has had to relax in the longitudinal direction.
TE will determine how much time the sample has had to relax (loose phase) in the transverse plain.
Measuring the amount of hydrogen in the voxels regardless of their T1 or T2 relaxation constants.
Proton density contrast
This is done using a very long TR and very short TE
Higher intensity in voxels containing more hydrogen protons
Proton density
Measuring how T1 relaxation differs between voxels.This is done using a medium TR and very short TE
T1 contrast
You need to know when largest difference between the tissues will take place…
Images have high intensity in voxels with shorter T1 constants (faster relaxation/recovery = release of more energy)
T1 contrast
CSF: 1800 msGray matter: 650 ms White matter: 500 ms Muscle: 400 msFat: 200 ms
Measuring how T2 relaxation differs between voxels.This is done using a long TR and medium TE
T2/T2* contrast
We can combine a T2 acquisition with proton density…
Images have high intensity in voxels with longer T2 constants (slower relaxation = more detectable energy)
T2 contrast
CSF: 200 msGray Matter: 80 ms White Matter: 60 ms Muscle: 50 msFat: 50 ms
Same as T2 only smaller numbers (faster relaxation)
T2* contrast
CSF: 100 msGray Matter: 40 ms White Matter: 30 ms Fat: 25 ms
T2* = T2 +T2’
T2: Spin-spin interactionsT2’: field inhomogeneities
Exposed iron (heme) molecules create local magnetic inhomogeneities
T2* and BOLD fMRI
BOLD – blood oxygen level dependant
Assuming everything else stays constant during a scan one can measure BOLD changes across time…
More deoxygenated blood = more inhomogeneity
more inhomogeneity = faster relaxation (shorter T2*)
Shorter T2* = weaker energy/signal (image intensity)
So what would increased neural activity cause?
T2* and BOLD
So what happened in particular time points of this scan?
T2* and BOLD
Bloch equation
So far we’ve talked about a bunch of forces and energies changing in a sample across time…
How can we differentiate locations in space and create an image?
MR images
Paul Lauterbur Peter Mansfield
2004 Nobel prize in Medicine
Create magnetic fields in each direction (x,y,z) that move from stronger to weaker (hence gradient).
Spatial gradients
Different magnetic fields at different points in space.
Hydrogen will precess at a different speed in each spatial location.
By “tunning in” on the specific precession speed we can separate different spatial locations.
Similarly to how we “tunned in” on hydrogen atoms…
Spatial gradients
Spatial gradients
64 MHz
65 MHz
66 MHz
63 MHz
62 MHz
G
(-)
(+)
Lot’s of Fourier transforms.
Work in k-space (a vectorial space that keeps track of the spin phase & frequency variation across magnet space).
It’s possible to turn gradients on and off very quickly (ms).
Image reconstruction
Pulse sequences
Spatial gradients
The magnet
Main static field
Extremely large electric charge spinning on a helium cooled (-271o c) super conducting coil.
Earth’s magnetic field 30-60 microtesla.
MRI magnets suitable for scanning humans 1.5-7 T.
Main coils
The bulk of the structure contains the coils generating the static magnetic field and the gradient magnetic fields.
RF coil
Transmit and receive RF coils located close to the sample do the actual excitation and “read out”.
Read Chapters 3-5 of Huettel et. al.
Explain how a spin-echo pulse does the magic of separating T2 relaxation from T2* relaxation. You can include figures/drawings if you like.
Homework!