1. 10 spring fMRI: theory & practice
Class 2: Basics of fMRI
10 spring fMRI: theory & practice
2009 spring fMRI: theory & practice

2. 2010 spring fMRI: theory & practice
fMRI Setup
2010 spring fMRI: theory & practice

3. 2010 spring fMRI: theory & practice
The Briefest Possible Explanation of MR Physics I Could Manage (while still covering important ideas and jargon)
2010 spring fMRI: theory & practice

4. 2010 spring fMRI: theory & practice
Necessary Equipment
4T magnet
RF Coil
gradient coil
(inside)
Magnet
Gradient Coil
RF Coil
Source for Photos: Joe Gati
2010 spring fMRI: theory & practice

5. 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.
2010 spring fMRI: theory & practice

6. 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.
2010 spring fMRI: theory & practice

7. 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
fat has low signal  dark
CSF has high signal  bright
CSF has low signal  dark
2010 spring fMRI: theory & practice
T2-WEIGHTED ANATOMICAL IMAGE
T1-WEIGHTED ANATOMICAL IMAGE

8. 2010 spring fMRI: theory & practice
Protons
Can measure nuclei with odd number of neutrons
1H, 13C, 19F, 23Na, 31P
1H (proton)
abundant: high concentration in human body
high sensitivity: yields large signals
2010 spring fMRI: theory & practice

9. Protons align with field
Outside magnetic field
Protons align with field
randomly oriented
Inside magnetic field
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 % of protons/T align with field M
longitudinal
axis
Longitudinal
magnetization
transverse
plane
2010 spring fMRI: theory & practice
Source: Mark Cohen’s web slides
M = 0
Source: Robert Cox’s web slides

10. Precession In and Out of Phase
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 tissues
2010 spring fMRI: theory & practice
Source: Mark Cohen’s web slides

11. Turn your dial to 4T fMRI -- Broadcasting at a frequency of 170.3 MHz!
Radio Frequency
Turn your dial to 4T fMRI --
Broadcasting at a frequency of MHz!
2010 spring fMRI: theory & practice

12. 2010 spring fMRI: theory & practice
Larmor Frequency
Larmor equation
f = B0
 = MHz/T
At 1.5T, f = MHz
At 4T, f = MHz
170.3
Resonance
Frequency for 1H
63.8
1.5
4.0
Field Strength (Tesla)
2010 spring fMRI: theory & practice

13. 2010 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
Transverse
magnetization
2010 spring fMRI: theory & practice
Source: Robert Cox’s web slides

14. Relaxation and Receiving
Receive Radio Frequency Field
receiving coil: measure net magnetization (M)
readout interval (~ ms)
relaxation: after RF field turned on and off, magnetization returns to normal
longitudinal magnetization  T1 signal recovers
transverse magnetization  T2 signal decays
2010 spring fMRI: theory & practice
Source: Robert Cox’s web slides

15. 2010 spring fMRI: theory & practice
T1 and TR
T1 = recovery of longitudinal (B0) magnetization
used in anatomical images
~ msec (longer with bigger B0)
TR (repetition time) = time to wait after excitation before sampling T1
2010 spring fMRI: theory & practice
Source: Mark Cohen’s web slides

16. 2010 spring fMRI: theory & practice
T2 and TE
T2 = decay of transverse magnetization
TE (time to echo) = time to wait to measure T2 or T2* (after refocussing with spin echo or gradient echo)
2010 spring fMRI: theory & practice
Source: Mark Cohen’s web slides

17. 2010 spring fMRI: theory & practice
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*  ms, shorter for higher Bo)
Mxy
Mo sin T2
T2*
time
2010 spring fMRI: theory & practice
Source: Jorge Jovicich

18. 2010 spring fMRI: theory & practice
Echos
pulse sequence: series of excitations, gradient triggers and readouts
Gradient echo
pulse sequence
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*
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
2010 spring fMRI: theory & practice
Source: Mark Cohen’s web slides

19. 2010 spring fMRI: theory & practice
T1 vs. T2
2010 spring fMRI: theory & practice
Source: Mark Cohen’s web slides

20. 2010 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)
2010 spring fMRI: theory & practice

21. Step 4: Use Gradients to Encode Space
field strength
space
lower magnetic field;
lower frequencies
higher magnetic field;
higher frequencies
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.
2010 spring fMRI: theory & practice

22. Spatial Coding:Gradients
Field Strength (T) ~ z position
Freq
Gradient coil
add a gradient to the main magnetic field
Spatial Coding:Gradients
How can we encode spatial position?
Example: axial slice
excite only frequencies corresponding to slice plane
Use other tricks to get other two dimensions
left-right: frequency encode
top-bottom: phase encode
Gradient switching – that’s what makes all the beeping & buzzing noises during imaging!
2010 spring fMRI: theory & practice

23. Step 5: Convert Frequencies to Brain Space
k-space contains information about frequencies in image
We want to see brains, not frequencies
2010 spring fMRI: theory & practice

24. 2010 spring fMRI: theory & practice
A Walk Through K-space
single shot EPI
two shot EPI
single shot spiral
two shot spiral
(forgive the hand drawn spirals)
Note: The above is k-space, not slices
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
2010 spring fMRI: theory & practice

25. Susceptibility Artifacts
T2*-weighted image
T1-weighted image
sinuses
ear
canals
-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…
2010 spring fMRI: theory & practice

26. 2010 spring fMRI: theory & practice
K-Space
2010 spring fMRI: theory & practice
Source: Traveler’s Guide to K-space (C.A. Mistretta)

27. 2010 spring fMRI: theory & practice
A Walk Through K-space
single shot
two shot
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
Note: The above is k-space, not slices
both halves of k-space in 1 sec
1st half of k-space
in 0.5 sec
2nd half of k-space
in 0.5 sec
1st half of k-space
in 0.5 sec
2nd half of k-space
2nd volume in 1 sec
vs.
interpolated
image
2010 spring fMRI: theory & practice
1st volume in 1 sec

28. 2010 spring fMRI: theory & practice
Susceptibility
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
ear
canals
Aha!
Susceptibility variations can also be seen around blood vessels where deoxyhemoglobin affects T2* in nearby tissue
2010 spring fMRI: theory & practice
Source: Robert Cox’s web slides