Section 2 Basic fMRI Physics
Other ResourcesThese 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 Coxs 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 Cohens intro Basic MR Physics slides
http://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/MiscShared.html
Douglas Nolls Primer on MRI and Functional MRI
http://www.bme.umich.edu/~dnoll/primer2.pdf
For a more advanced tutorial, see:Joseph Hornaks Web Tutorial,
The Basics of MRI
http://www.cis.rit.edu/htbooks/mri/mri-main.htm
Recipe for MRI1) 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 Coxs web slides
History of NMRNMR = 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 NMR
MRI: Why the name change? Purcell
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 fMRIMRI -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 Equipment4T magnet
RF Coil gradient coil (inside)
Magnet
Gradient Coil
RF Coil
Source: Joe Gati, photos
The Big MagnetVery strong 1 Tesla (T) = 10,000 Gauss Earths
magnetic field = 0.5 Gauss 4 Tesla = 4 x 10,000 0.5 = 80,000X
Earths magnetic field Continuously on Main field = B0Robarts
Research Institute 4T
x 80,000 =
B0
Source: www.spacedaily.com
The whopping strength of the magnet makes safety essential.
Things fly Even big things!
Magnet Safety
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 SafetyAnyone 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)
ProtonsCan measure nuclei with odd number of neutrons 1H, 13C,
19F, 23Na, 31P1H
(proton) abundant: high concentration in human body high
sensitivity: yields large signals
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
0.0003% of protons/T align with fieldlongitudinal axis
M
Longitudinal magnetization
M=0
Source: Mark Cohens web slides Source: Robert Coxs web
slides
transverse plane
Larmor FrequencyLarmor equationf = B0 = 42.58 MHz/T At 1.5T, f =
63.76 MHz At 4T, f = 170.3 MHz
170.3
Resonance Frequency for 1H63.8
1.5
4.0
Field Strength (Tesla)
RF ExcitationExcite 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 Coxs web slides
Coxs Swing Analogy
Source: Robert Coxs web slides
Relaxation and ReceivingReceive 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 normallongitudinal magnetization T1 signal recovers transverse
magnetization T2 signal decays
Source: Robert Coxs web slides
T1 and TRT1 = 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 Cohens web slides
add a gradient to the main magnetic field excite only
frequencies corresponding to slice planeFreq
Spatial Coding:GradientsHow can we encode spatial position?
Example: axial slice
Use other tricks to get other two dimensions left-right:
frequency encode top-bottom: phase encode Gradient switching thats
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 tissuesSource: Mark Cohens
web slides
T2 and TET2 = 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 Cohens web slides
Echospulse sequence: series of excitations, gradient triggers
and readoutsGradient 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 T2Gradient echo: flip the
gradient from negative to positivet = TE/2
make fast regions become slow and vice-versa
A gradient reversal (shown) or 180 pulse (not shown) at this
point will lead to a recovery of transverse magnetization
-measure T2* -ideally TE ~ average T2*TE = time to wait to
measure refocussed spinsSource: Mark Cohens web slides
T1 vs. T2
Source: Mark Cohens web slides
K-Space
Source: Travelers Guide to K-space (C.A. Mistretta)
A Walk Through K-spacesingle shot two shotK-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
vs.
both halves of k-space in 1 sec
1st half of k-space in 0.5 sec
2nd half of k-space 1st half of k-space in 0.5 sec in 0.5
sec
2nd half of k-space in 0.5 sec
1st volume in 1 sec
interpolated image
2nd volume in 1 sec
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*
timeSource: Jorge Jovicich
SusceptibilityAdding 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
shimmingSusceptibility 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
Susceptibility variations can also be seen around blood vessels
where deoxyhemoglobin affects T2* in nearby tissueSource: Robert
Coxs 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 signalBlood Oxygen Level Dependent signal neural activity
blood flow oxyhemoglobin T2*Mxy Signal
MR signal
Mo sin
T2* task T2* controlS time
Stask ScontrolTEoptimum
Source: fMRIB Brief Introduction to fMRI
Source: Jorge Jovicich
BOLD signal
Source: Doug Nolls primer
First Functional Images
Source: Kwong et al., 1992
Hemodynamic Response Function
% signal change= (point baseline)/baseline usually 0.5-3%
time to risesignal begins to rise soon after stimulus begins
initial dip
time to peak
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
ReviewMagnetic 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