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Class 2: Basics of fMRI
2012 spring fMRI: theory & practice1
fMRI Setup
2012 spring fMRI: theory & practice 2
The Briefest Possible Explanation of MR Physics I Could Manage
(while still covering important ideas and jargon)
2012 spring fMRI: theory & practice 3
Necessary Equipment
Magnet Gradient Coil RF Coil
Source for Photos: Joe Gati
RF Coil
4T magnet
gradient coil(inside)
2012 spring fMRI: theory & practice 42012 spring fMRI: theory & practice
Step 1: Put Subject in Big Magnet
Protons (hydrogen atoms) have “spins” (like tops). They have
an orientation and a frequency.
When you put a material (like your subject) in an MRI
scanner, some of the protons become oriented with the
magnetic field.2012 spring fMRI: theory & practice 5
2012 spring fMRI: theory & practice
Step 2: Apply Radio Waves
When you apply radio waves (RF pulse) at the appropriate frequency, you can change the orientation of the spins as the protons absorb energy.
After you turn off the radio waves, as the protons return to their original orientations, they emit energy in the form of radio waves.
2012 spring fMRI: theory & practice 62012 spring fMRI: theory & practice
Step 3: Measure Radio Waves
T1 measures how quickly the protons realign with the main magnetic field
T2 measures how quickly the protons give off energy as they recover to equilibrium
fat has high signal bright
CSF has low signal dark
T1-WEIGHTED ANATOMICAL IMAGE T2-WEIGHTED ANATOMICAL IMAGE
fat has low signal dark
CSF has high signal bright
2012 spring fMRI: theory & practice 7
2012 spring fMRI: theory & practice
Protons
Can measure nuclei with odd number of neutrons1H, 13C, 19F, 23Na, 31P
1H (proton)abundant: high concentration in human bodyhigh sensitivity: yields large signals
2012 spring fMRI: theory & practice 82012 spring fMRI: theory & practice
Protons align with fieldOutside magnetic field
Inside magnetic field
• randomly oriented
• spins tend to align parallel or anti-parallel to B0
• net magnetization (M) along B0
• spins precess with random phase• no net magnetization in transverse plane• only 0.0003% of protons/T align with field
Source: Mark Cohen’s web slides
M
M = 0Source: Robert Cox’s web slides
longitudinalaxis
transverseplane
Longitudinalmagnetization
2012 spring fMRI: theory & practice 92012 spring fMRI: theory & practice
Precession In and Out of Phase
Source: Mark Cohen’s web slides
• protons precess at slightly different frequencies because of (1) random fluctuations in the local field at the molecular level that affect both T2 and T2*; (2) larger scale variations in the magnetic field (such as the presence of deoxyhemoglobin!) that affect T2* only.
• over time, the frequency differences lead to different phases between the molecules (think of a bunch of clocks running at different rates – at first they are synchronized, but over time, they get more and more out of sync until they are random)
• as the protons get out of phase, the transverse magnetization decays
• this decay occurs at different rates in different tissues2012 spring fMRI: theory & practice 10
2012 spring fMRI: theory & practice
Radio Frequency
2012 spring fMRI: theory & practice 112012 spring fMRI: theory & practice
Larmor Frequency
Larmor equationf = B0
= 42.58 MHz/T
At 1.5T, f = 63.76 MHzAt 4T, f = 170.3 MHz
Field Strength (Tesla)
ResonanceFrequency for 1H
170.3
63.8
1.5 4.0
2012 spring fMRI: theory & practice 122012 spring fMRI: theory & practice
RF Excitation
Excite Radio Frequency (RF) field• transmission coil: apply magnetic field along B1 (perpendicular to B0) for ~3 ms• oscillating field at Larmor frequency• frequencies in range of radio transmissions• B1 is small: ~1/10,000 T• tips M to transverse plane – spirals down• analogies: guitar string (Noll), swing (Cox)• final angle between B0 and B1 is the flip angle
Source: Robert Cox’s web slides
Transversemagnetization
2012 spring fMRI: theory & practice 132012 spring fMRI: theory & practice
Relaxation and Receiving
Receive Radio Frequency Field• receiving coil: measure net magnetization (M)• readout interval (~10-100 ms)• relaxation: after RF field turned on and off, magnetization returns to normal
longitudinal magnetization T1 signal recoverstransverse magnetization T2 signal decays
Source: Robert Cox’s web slides
2012 spring fMRI: theory & practice 142012 spring fMRI: theory & practice
T1 and TR
Source: Mark Cohen’s web slides
T1 = recovery of longitudinal (B0) magnetization• used in anatomical images• ~500-1000 msec (longer with bigger B0)
TR (repetition time) = time to wait after excitation before sampling T1
2012 spring fMRI: theory & practice 152012 spring fMRI: theory & practice
T2 and TE
Source: Mark Cohen’s web slides
T2 = decay of transverse magnetizationTE (time to echo) = time to wait to measure T2 or T2* (after refocussing with spin echo or gradient echo)
2012 spring fMRI: theory & practice 162012 spring fMRI: theory & practice
T2*
Source: Jorge Jovicich
time
Mxy
Mo sinT2
T2*
T2* relaxation
• dephasing of transverse magnetization due to both:
- microscopic molecular interactions (T2)
- spatial variations of the external main field B
(tissue/air, tissue/bone interfaces)
• exponential decay (T2* 30 - 100 ms, shorter for higher Bo)
2012 spring fMRI: theory & practice 172012 spring fMRI: theory & practice
Echos
Source: Mark Cohen’s web slides
Echos – refocussing of signal
Spin echo:
use a 180 degree pulse to “mirror image” the spins in the transverse plane
when “fast” regions get ahead in phase, make them go to the back and catch up
-measure T2
-ideally TE = average T2
Gradient echo:
flip the gradient from negative to positive
make “fast” regions become “slow” and vice-versa
-measure T2*
-ideally TE ~ average T2*
pulse sequence: series of excitations, gradient triggers and readouts
Gradient echopulse sequence
t = TE/2
A gradient reversal (shown) or 180 pulse (not shown) at this point will lead to a recovery of transverse magnetization
TE = time to wait to measure refocussed spins
2012 spring fMRI: theory & practice 18
2012 spring fMRI: theory & practice
T1 vs. T2
Source: Mark Cohen’s web slides
2012 spring fMRI: theory & practice 192012 spring fMRI: theory & practice
Jargon Watch
• T1 = the most common type of anatomical image• T2 = another type of anatomical image• TR = repetition time = one timing parameter• TE = time to echo = another timing parameter• flip angle = how much you tilt the protons (90 degrees
in example above)
2012 spring fMRI: theory & practice 202012 spring fMRI: theory & practice
Step 4: Use Gradients to Encode Space
Remember that radio waves have to be the right frequency to excite protons.
The frequency is proportional to the strength of the magnetic field.
If we create gradients of magnetic fields, different frequencies will affect protons in different parts of space.
lower magnetic field;
lower frequencies
higher magnetic field;
higher frequencies
space
field strength
2012 spring fMRI: theory & practice 212012 spring fMRI: theory & practice
Spatial Coding:GradientsHow can we encode spatial position?
• Example: axial slice
Use other tricks to get other two dimensions
• left-right: frequency encode
• top-bottom: phase encode
excite only frequencies
corresponding to slice plane
Field Strength (T) ~ z position
Fre
q
Gradient coil
add a gradient to the main magnetic
field
Gradient switching – that’s what makes all the beeping & buzzing noises during imaging!
22
2012 spring fMRI: theory & practice
Step 5: Convert Frequencies to Brain Space
k-space contains information about
frequencies in image
We want to see brains, not frequencies
2012 spring fMRI: theory & practice 232012 spring fMRI: theory & practice
A Walk Through K-space
echo-planar imaging• sample k-space in a linear zig-zag trajectory
spiral imaging• sample k-space in a spiral trajectory
single shot imaging• sample k-space with one trajectory
multi-shot imaging• sample k-space with multiple (typically 2 or 4) trajectories
• Our technicians at RRI prefer spiral and multishot acquisitions because they’re more efficient
single shot EPI two shot EPI
Note: The above is k-space, not slices
single shot spiral two shot spiral
(forgive the hand drawn spirals)
2012 spring fMRI: theory & practice 242012 spring fMRI: theory & practice
Susceptibility Artifacts
-In addition to T1 and T2 images, there is a third kind, called T2* = “tee-two-star”-In T2* images, artifacts occur near junctions between air and tissue
• sinuses, ear canals
•In some ways this sucks, but in one way, it’s fabulous…
sinuses
earcanals
T1-weighted imageT2*-weighted image
2012 spring fMRI: theory & practice 252012 spring fMRI: theory & practice
K-Space
Source: Traveler’s Guide to K-space (C.A. Mistretta)
2012 spring fMRI: theory & practice 262012 spring fMRI: theory & practice
A Walk Through K-space
K-space can be sampled in many “shots”(or even in a spiral)
2 shot or 4 shot• less time between samples of slices• allows temporal interpolation
both halves of k-space in 1 sec
1st half of k-spacein 0.5 sec
2nd half of k-spacein 0.5 sec
vs.
single shot two shot
1st volume in 1 sec interpolatedimage
Note: The above is k-space, not slices
1st half of k-spacein 0.5 sec
2nd half of k-spacein 0.5 sec
2nd volume in 1 sec 27
2012 spring fMRI: theory & practice
Susceptibility
Source: Robert Cox’s web slides
Adding a nonuniform object (like a person) to B0 will make the total magnetic field nonuniform
This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field
For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming
Susceptibility Artifact-occurs near junctions between air and tissue
• sinuses, ear canals-spins become dephased so quickly (quick T2*), no signal can be measured
sinuses
earcanals
Susceptibility variations can also be seen around blood vessels where deoxyhemoglobin affects T2* in nearby tissue
2012 spring fMRI: theory & practice 282012 spring fMRI: theory & practice