1. Basic fMRI Physics In BOLD fMRI, we are measuring:
the inhomogeneities introduced into the magnetic field of the scanner…
as a result of the changing ratio of oxygenated:deoxygenated blood…
via their effect on the rates of dephasing of hydrogen nuclei.
Ehhh???

2. History of MRI NMR = nuclear magnetic resonance
nuclear: properties of nuclei of atoms
magnetic: magnetic field required
resonance: magnetic field x radio frequency
1946: Block and Purcell
atomic nuclei absorb and re-emit radio frequency energy
1992: Ogawa and colleagues
first functional images using BOLD signal
NMR  MRI: Why the name change?
most likely explanation:
nuclear has bad connotations
less likely explanation:
NMR means Nouveau Mouvement Religieux
Bloch
Purcell
Ogawa

3. Necessary Equipment Magnet Gradient Coil RF Coil 3T magnet RF Coil
(inside)
Magnet
Gradient Coil
RF Coil
Source: Joe Gati, photos

4. 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]
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

5. The Big Magnet B0 x 60,000 = Main field = B0 Continuously on
Very strong :
Earth’s magnetic field = 0.5 Gauss / 1 Tesla (T) = 10,000 Gauss
3 Tesla = 3 x 10,000  0.5 = 60,000 x Earth’s magnetic field B0
x 60,000 =
Source:
Robarts Research Institute 3T

6. Source: http://www.simplyphysics.com/flying_objects.html
Safety
The strength of the magnet makes safety essential : things fly – even big things!
Source:
Source:
Anyone entering the magnet must be metal free
This subject was wearing a hair band with a ~2 mm copper clamp. Left: with hair band. Right: without.
Source: Jorge Jovicich
Develop screening strategies :
do the metal macarena!

7. 1H aligns with B0 randomly oriented
Protons are abundant: high concentration in human body have high sensitivity: yields large signals
longitudinal
axis
Outside magnetic field
randomly oriented
M = 0
transverse
plane
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
Source: Mark Cohen’s web slides M
Source: Robert Cox’s web slides
Longitudinal
magnetization

8. Larmor Frequency Larmor equation : resonance frequency f = B0/2π
for 1H = MHz/T
Frequency (MHz)
127.7
63.8
1.5
3.0
Field Strength (Tesla)
Turn your dial to 3T fMRI …
… broadcasting at a frequency of Mhz

9. Radio-Frequency Excitation
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
longitudinal
axis
Source: Robert Cox’s web slides

10. 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 (realignment)
transverse magnetization   T2 signal decays (dephasing)
Source: Robert Cox’s web slides

11. Why the dephasing ?
protons precess at slightly different frequencies because of
random fluctuations in the local field at the molecular level that affect both T2 and T2*;
larger scale variations in the magnetic field that affect T2* only.
over time, the frequency differences lead to different phases between the molecules
(clock analogy)
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

12. T1 and TR T1 = recovery of longitudinal magnetization (B0)
due to realignment of spins
TR (time to repetition) = time to wait after excitation before sampling T1
= time before next RF excitation
≈ M0(1-exp(-t/T1))
Source: Mark Cohen’s web slides

13. T2 and TE T2 = decay of transverse (B1) magnetization
due to dephasing of spins
TE (time to echo) = time to wait before sampling T2
(after refocusing of signal)
≈ exp(-t/T2))
Source: Mark Cohen’s web slides

14. T1 and T2 contrasts TISSUE T1(s) T2(s) grey matter 1.0 0.10
white matter
0.7
0.08
CSF
2.0
0.25
blood
1.2
water
4.7
3.50
Source: Mark Cohen’s web slides

15. T2* relaxation dephasing of transverse magnetization due to both:
- microscopic molecular interactions (as for 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

16. Spatial Coding: Gradients
How can we encode spatial position?
Add a gradient to the main magnetic field
Excite only frequencies corresponding to slice plane
Use other tricks to get other two dimensions
left-right: frequency encode
top-bottom: phase encode
Frequency
Field Strength ~ z position
Gradient switching – that’s what makes all the beeping & buzzing noises during imaging => EAR PLUGS !

17. Echos
pulse sequence: series of excitations, gradient triggers and readouts
Echos = refocusing of signal
Spin echo (not shown) – measure T2
Gradient echo (shown) - measure T2*
flip the gradient at t=TE/2
measure after refocusing at t=TE
(left-right)
(top-bottom)
t = TE/2
A gradient reversal at this point will lead to a recovery of transverse magnetization
TE = time to wait to measure refocused spins
Source: Mark Cohen’s web slides

18. A walk through the K-space
(inverse Fourier transform)
Source: Traveler’s Guide to K-space (C.A. Mistretta)

19. 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
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
Source: Robert Cox’s web slides
ear
canals
Aha!
Susceptibility variations can also be seen around blood vessels where deoxyhemoglobin affects T2* in nearby tissue

20. Hemoglobin A molecule to breathe with: - four globin chains
- each globin chain contains a heme group
- at center of each heme group is an iron atom (Fe)
- each iron ion Fe2+ can attach an oxygen molecule (O2)
- oxy-Hemoglobin (four O2) is diamagnetic  no B effects
- deoxy-Hemoglobin is paramagnetic  if [deoxy-Hgb]   local B 
Source: Jorge Jovicich

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

22. BOLD signal
Source: Doug Noll’s primer

23. (return to equilibrium state)
To take away
Tissue protons align
with magnetic field
(equilibrium state)
RF pulses
Protons absorb
RF energy
(excited state)
Relaxation
processes
Protons emit RF energy
(return to equilibrium state)
Spatial encoding
using magnetic
field gradients
NMR signal
detection
Repeat
RAW DATA MATRIX
Fourier transform
IMAGE
Magnetic field
Kwong et al., 1992
Source: Jorge Jovicich