Section 2
Basic fMRI Physics
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.
http://afni.nimh.nih.gov/afni/edu/
See “Background Information on MRI” section
Mark Cohen’s intro Basic MR Physics slides
http://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/MiscShared.html
Douglas Noll’s Primer on MRI and Functional MRI
http://www.bme.umich.edu/~dnoll/primer2.pdf
For a more advanced tutorial, see:
Joseph Hornak’s Web Tutorial, The Basics of MRI
http://www.cis.rit.edu/htbooks/mri/mri-main.htm
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: 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
History of NMR
NMR = nuclear magnetic resonance
Felix Block and Edward Purcell
1946: atomic nuclei absorb and reemit 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?
most likely explanation:
nuclear has bad connotations
less likely but more amusing explanation:
subjects got nervous when fast-talking doctors suggested an NMR
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
Necessary Equipment
4T magnet
RF Coil
gradient coil
(inside)
Magnet
Gradient Coil
RF Coil
Source: Joe Gati, photos
The Big Magnet
Very strong
1 Tesla (T) = 10,000 Gauss
Earth’s magnetic field = 0.5 Gauss
4 Tesla = 4 x 10,000  0.5 = 80,000X Earth’s magnetic field
Continuously on
Main field = B0
Robarts Research Institute 4T
x 80,000 =
Source: www.spacedaily.com
B0
Magnet Safety
The whopping strength of the magnet makes safety essential.
Things fly – Even big things!
Source: www.howstuffworks.com
Source: http://www.simplyphysics.com/
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!
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)
This subject was wearing a hair band with a ~2 mm
Subjects must remove metal from their bodies
copper clamp. Left: with hair band. Right: without.
• jewellery, watch, piercings
Source: Jorge Jovicich
• 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)
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
Outside magnetic field
Protons align with field
• randomly oriented
Inside magnetic field
M
• 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
longitudinal
axis
Longitudinal
magnetization
M=0
Source: Mark Cohen’s web slides
Source: Robert Cox’s web slides
transverse
plane
Larmor Frequency
Larmor equation
f = B0
 = 42.58 MHz/T
At 1.5T, f = 63.76 MHz
At 4T, f = 170.3 MHz
170.3
Resonance
Frequency for 1H
63.8
1.5
4.0
Field Strength (Tesla)
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
B0
B1
Source: Robert Cox’s web slides
Cox’s Swing Analogy
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
transverse magnetization  T2 signal decays
Source: Robert Cox’s web slides
T1 and TR
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
Source: Mark Cohen’s web slides
add a gradient to
the main magnetic
field
Spatial Coding:Gradients
How can we encode spatial position?
excite only
frequencies
corresponding to
slice plane
• Example: axial slice
Use other tricks to get other two dimensions
• left-right: frequency encode
• top-bottom: phase encode
Freq
Gradient switching – that’s what
makes all the beeping & buzzing
noises during imaging!
Field Strength (T) ~ z position
Gradient coil
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
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
Echos
pulse sequence: series of excitations, gradient triggers and readouts
Gradient echo Echos – refocussing of signal
pulse sequence
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
t = TE/2
A gradient reversal (shown) or
180 pulse (not shown) at this
point will lead to a recovery of
transverse magnetization
make “fast” regions become “slow” and
vice-versa
-measure T2*
-ideally TE ~ average T2*
TE = time to wait to
measure refocussed spins
Source: Mark Cohen’s web slides
T1 vs. T2
Source: Mark Cohen’s web slides
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)
Mxy
Mo sin
T2
T2*
time
Source: Jorge Jovicich
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
sinuses
ear
canals
Susceptibility Artifact
-occurs near junctions between air
and tissue
• sinuses, ear canals
-spins become dephased so quickly
(quick T2*), no signal can be
measured
Susceptibility variations can also be seen around
blood vessels where deoxyhemoglobin affects T2*
in nearby tissue
Source: Robert Cox’s web slides
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: 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: fMRIB Brief Introduction to fMRI
time
Source: Jorge Jovicich
BOLD signal
Source: Doug Noll’s primer
First Functional Images
Source: Kwong et al., 1992
Hemodynamic Response Function
% signal change
= (point – baseline)/baseline
usually 0.5-3%
time to rise
signal begins to rise soon after stimulus begins
time to peak
initial dip
signal peaks 4-6 sec after stimulus begins
-more focal and potentially a better
measure
post stimulus undershoot
-somewhat elusive so far, not
signal suppressed after stimulation ends
everyone can find it
Review
Magnetic field
Tissue protons align
with magnetic field
(equilibrium state)
RF pulses
Relaxation
processes
Protons absorb
Spatial encoding
RF energy
using magnetic
(excited state)
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