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???
History of MRI
NMR = nuclear magnetic resonance
nuclear: properties of nuclei of atoms
magnetic: magnetic field required
resonance: magnetic field x radio frequency
NMR  MRI: Why the name change?
1946: Block and Purcell
atomic nuclei absorb and re-emit radio frequency energy
1992: Ogawa and colleagues
first functional images using BOLD signal
Bloch
Purcell
Ogawa
most likely explanation:
nuclear has bad connotations
less likely explanation:
NMR means Nouveau Mouvement Religieux
Necessary Equipment
3T magnet
RF Coil
gradient coil
(inside)
Magnet
Gradient Coil
RF Coil
Source: Joe Gati, photos
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
[10-100 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
The Big Magnet
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
x 60,000 =
Source: www.spacedaily.com
B0
Robarts Research Institute 3T
Safety
The strength of the magnet makes safety essential : things fly – even big things!
Source: www.howstuffworks.com
Source: http://www.simplyphysics.com/flying_objects.html
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!
1H
aligns with B0
Protons are abundant: high concentration in human body
have high sensitivity: yields large signals
Outside magnetic field
• randomly oriented
longitudinal
axis
transverse
plane
M=0
Inside magnetic field
Longitudinal
magnetization
• 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
M
Source: Mark Cohen’s web slides
Source: Robert Cox’s web slides
Larmor equation :
resonance frequency f = B0/2π
for 1H
= 42.58 MHz/T
Frequency (MHz)
Larmor Frequency
127.7
63.8
1.5
3.0
Field Strength (Tesla)
Turn your dial to 3T fMRI …
… broadcasting at a frequency of 127.7 Mhz
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
longitudinal
axis
Transverse
magnetization
Source: Robert Cox’s web slides
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 recovers (realignment)
transverse magnetization   T2 signal decays (dephasing)
Source: Robert Cox’s web slides
Why the dephasing ?
•
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 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
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
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
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
0.25
water
4.7
3.50
Source: Mark Cohen’s web slides
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*  30 - 100 ms, shorter for higher Bo)
Mxy
Mo sin
T2
T2 *
time
Source: Jorge Jovicich
Spatial Coding: Gradients
Frequency
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
Field Strength ~ z position
Gradient switching – that’s what makes
all the beeping & buzzing noises during
imaging => EAR PLUGS !
Echos
pulse sequence: series of excitations, gradient triggers and readouts
Echos = refocusing of signal
Spin echo (not shown) – measure T2
(left-right)
Gradient echo (shown) - measure T2*
flip the gradient at t=TE/2
measure after refocusing at t=TE
(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
A walk through the K-space
(inverse Fourier transform)
Source: Traveler’s Guide to K-space (C.A. Mistretta)
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
Susceptibility variations can also be seen around blood vessels
where deoxyhemoglobin affects T2* in nearby tissue
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: http://wsrv.clas.virginia.edu/~rjh9u/hemoglob.html, Jorge Jovicich
BOLD signal
Blood Oxygen Level Dependent signal
neural activity   blood flow   oxyhemoglobin   T2*   MR signal
Mxy
Signal
Mo
sin
T2* task
T2* control
Stask
Scontrol
S
TEoptimum
Source: Brief Introduction to fMRI by Irene Tracey
time
Source: Jorge Jovicich
BOLD signal
Source: Doug Noll’s primer
To take away
Magnetic field
Tissue protons align
with magnetic field
(equilibrium state)
RF pulses
Kwong et al., 1992
Relaxation
processes
Protons absorb
RF energy
(excited state)
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