1. Section 2 Basic fMRI Physics

2. Other Resources
These slides were condensed from several excellent online sources. I have tried to give credit where appropriate.
If you would like a more thorough introductory review of MR physics, I suggest the following:
Robert Cox’s slideshow, (f)MRI Physics with Hardly Any Math, and his book chapters online.
See “Background Information on MRI” section
Mark Cohen’s intro Basic MR Physics slides
Douglas Noll’s Primer on MRI and Functional MRI
For a more advanced tutorial, see:
Joseph Hornak’s Web Tutorial, The Basics of MRI

3. Recipe for MRI 1) Put subject in big magnetic field (leave him there)
2) Transmit radio waves into subject [about 3 ms]
3) Turn off radio wave transmitter
4) Receive radio waves re-transmitted by subject
Manipulate re-transmission with magnetic fields during this readout interval [ ms: MRI is not a snapshot]
5) Store measured radio wave data vs. time
Now go back to 2) to get some more data
6) Process raw data to reconstruct images
7) Allow subject to leave scanner (this is optional)
Source: Robert Cox’s web slides

4. History of NMR NMR = nuclear magnetic resonance
Felix Block and Edward Purcell
1946: atomic nuclei absorb and re-emit radio frequency energy
1952: Nobel prize in physics
nuclear: properties of nuclei of atoms
magnetic: magnetic field required
resonance: interaction between magnetic field and radio frequency
Bloch
Purcell
NMR  MRI: Why the name change?
less likely but more amusing explanation:
subjects got nervous when fast-talking doctors suggested an NMR
most likely explanation:
nuclear has bad connotations

5. History of fMRI MRI -1971: MRI Tumor detection (Damadian)
-1973: Lauterbur suggests NMR could be used to form images
-1977: clinical MRI scanner patented
-1977: Mansfield proposes echo-planar imaging (EPI) to acquire images faster
fMRI
-1990: Ogawa observes BOLD effect with T2*
blood vessels became more visible as blood oxygen decreased
-1991: Belliveau observes first functional images using a contrast agent
-1992: Ogawa et al. and Kwong et al. publish first functional images using BOLD signal
Ogawa

6. Necessary Equipment Magnet Gradient Coil RF Coil 4T magnet RF Coil
(inside)
Magnet
Gradient Coil
RF Coil
Source: Joe Gati, photos

7. The Big Magnet B0 x 80,000 = Very strong 1 Tesla (T) = 10,000 Gauss
Source:
1 Tesla (T) = 10,000 Gauss
Earth’s magnetic field = 0.5 Gauss
x 80,000 =
4 Tesla = 4 x 10,000  0.5 = 80,000X Earth’s magnetic field
Robarts Research Institute 4T
Continuously on
Main field = B0 B0

8. Source: http://www.simplyphysics.com/
Magnet Safety
The whopping strength of the magnet makes safety essential.
Things fly – Even big things!
Source:
Source:
flying_objects.html
Screen subjects carefully
Make sure you and all your students & staff are aware of hazzards
Develop stratetgies for screening yourself every time you enter the magnet
Do the metal macarena!

9. Subject Safety
Anyone going near the magnet – subjects, staff and visitors – must be thoroughly screened:
Subjects must have no metal in their bodies:
pacemaker
aneurysm clips
metal implants (e.g., cochlear implants)
interuterine devices (IUDs)
some dental work (fillings okay)
Subjects must remove metal from their bodies
jewellery, watch, piercings
coins, etc.
wallet
any metal that may distort the field (e.g., underwire bra)
Subjects must be given ear plugs (acoustic noise can reach 120 dB)
This subject was wearing a hair band with a ~2 mm copper clamp. Left: with hair band. Right: without.
Source: Jorge Jovicich

10. 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

11. 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
Source: Mark Cohen’s web slides
M = 0
Source: Robert Cox’s web slides

12. 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!

13. Larmor Frequency Larmor equation f = B0  = 42.58 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)

14. 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 B1 B0
Source: Robert Cox’s web slides

15. Cox’s Swing Analogy
Source: Robert Cox’s web slides

16. 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
Source: Robert Cox’s web slides

17. 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
Source: Mark Cohen’s web slides

18. Spatial Coding:Gradients
Field Strength (T) ~ z position
Freq
Gradient coil
add a gradient to the main magnetic field
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!

19. 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
Source: Mark Cohen’s web slides

20. 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)
Source: Mark Cohen’s web slides

21. 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
Source: Mark Cohen’s web slides

22. T1 vs. T2
Source: Mark Cohen’s web slides

23. K-Space
Source: Traveler’s Guide to K-space (C.A. Mistretta)

24. A Walk Through K-space single shot two shot vs.
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
1st volume in 1 sec

25. 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*  ms, shorter for higher Bo)
Mxy
Mo sin T2
T2*
time
Source: Jorge Jovicich

26. 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
Source: Robert Cox’s web slides

27. Hemoglobin Hemoglogin (Hgb): - four globin chains
- each globin chain contains a heme group
- at center of each heme group is an iron atom (Fe)
- each heme group can attach an oxygen atom (O2)
- oxy-Hgb (four O2) is diamagnetic  no B effects
- deoxy-Hgb is paramagnetic  if [deoxy-Hgb]   local B 
Source: Jorge Jovicich

28. BOLD signal Blood Oxygen Level Dependent signal
neural activity   blood flow   oxyhemoglobin   T2*   MR signal
Mxy
Signal
Mo sin
T2* task
T2* control
Stask S
Scontrol
time
TEoptimum
Source: fMRIB Brief Introduction to fMRI
Source: Jorge Jovicich

29. BOLD signal
Source: Doug Noll’s primer

30. First Functional Images
Source: Kwong et al., 1992

31. Hemodynamic Response Function
% signal change
= (point – baseline)/baseline
usually 0.5-3%
initial dip
-more focal and potentially a better measure
-somewhat elusive so far, not everyone can find it
time to rise
signal begins to rise soon after stimulus begins
time to peak
signal peaks 4-6 sec after stimulus begins
post stimulus undershoot
signal suppressed after stimulation ends

32. (return to equilibrium state)
Review
Magnetic field
Tissue protons align
with magnetic field
(equilibrium state)
RF pulses
Protons absorb
RF energy
(excited state)
Relaxation
processes
Spatial encoding
using magnetic
field gradients
Relaxation
processes
Protons emit RF energy
(return to equilibrium state)
NMR signal
detection
Repeat
RAW DATA MATRIX
Fourier transform
IMAGE
Source: Jorge Jovicich