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HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis
Fall 2008
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HST.583: Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2008
Harvard-MIT Division of Health Sciences and Technology
Course Director: Dr. Randy Gollub.
MR physics and safety
for fMRI
Lawrence L. Wald, Ph.D.
Massachusetts General Hospital
Athinoula A. Martinos Center
Wald, fMRI MR Physics
Outline:
Wed. Sept 24 (LLW):
MR signal, Gradient and spin echo
Basic image contrast
Mon. Sept 29 (LLW):
Encoding the image
Wed Oct 1 (LLW):
Fast imaging for fMRI, artifacts
fMRI BOLD
Wald, fMRI MR Physics
What is NMR?
NUCLEAR
MAGNETIC
RESONANCE
A magnet, a glass of water,
and a radio wave source and detector….
Wald, fMRI MR Physics
What is NMR?
Nuclear magnetism
M
=
Wald, fMRI MR Physics
E
B
ΔE= hυ
protons
(N↑ – N↓)/NTOT = 1 – exp(-ΔE/kT)
≈ 10-4
Earth’s
Field
N
E
W
S
Wald, fMRI MR Physics
compass
Compass needles
Earth’s
Field
υ
z
Main
Field
Bo
North
N
E
W
y
S
x
Freq = γ B
Wald, fMRI MR Physics
42.58 MHz/T
Gyroscopic motion
Main
Field
Bo
z
North
• Proton has magnetic moment
M
y
• Proton has spin (angular
momentum)
>>gyroscopic precession
x
Larmor precession freq. = 42.58 MHz/T
Wald, fMRI MR Physics
υ = γ Bo
EXCITATION : Displacing the spins
from Equilibrium (North)
Problem: It must be moving for us to detect it.
Solution: knock out of equilibrium so it oscillates
How? 1) Tilt the magnet or compass suddenly
2) Drive the magnetization (compass needle)
with a periodic magnetic field
Wald, fMRI MR Physics
Excitation: Resonance
Why does only one frequency efficiently tip
protons?
Resonant driving force.
It’s like pushing a child on a swing in time with
the natural oscillating frequency.
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z is "longitudinal" direction
x-y is "transverse" plane
RF Field (B1)
applies a torque
to the spins…
Static
Field, B0
z
y
Mo
Applied RF
Field (B1)
x
The RF pulse rotates Mo the about applied field
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"Exciting" the Magnetization:
tip angle
z
Static
Field, B0
45°
Wald, fMRI MR Physics
z
y
y
x
x
90°
Detecting the Magnetization:
Faraday’s Law
z
A moving bar magnet induces a
Voltage in a coil of wire.
(a generator…)
90°
y
x
υo
The RF coil design is the #1
determinant of the system SNR
V(t)= -dΦ/dt
Φ = n Bspins A
Wald, fMRI MR Physics
Detecting the NMR: the noise
Noise comes from electrical losses in
the resistance of the coil or
electrical losses in the tissue.
z
90°
For a resistor:
Pnoise = 4kTRB
y
x
υo
•
V(t)
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•
•
Noise is white.
>>Noise power α bandwidth
Noise is spatially uniform.
R is dominated by the tissue. >>
big coil is bad.
The NMR Signal
RF
time
Voltage
(Signal)
time
υ
υo
Bo
z
z
90°
z
y
Mo
y
y
x
x
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υo
V(t)
x
Signal to Noise Ratio in MRI
•
Most important piece of hardware is the RF coil.
•
SNR α voxel volume (# of spins)
•
SNR α SQRT( total time of data collection)
•
SNR depends on the amount of signal you throw away
to better visualize the brain (gain image contrast)
Wald, fMRI MR Physics
Physical Foundations of MRI
NMR: 60 year old phenomena that generates the
signal from water that we detect.
MRI:
using NMR signal to generate an image
Three magnetic fields (generated by 3 coils)
1) static magnetic field Bo
2) RF field that excites the spins B1
3) gradient fields that encode spatial info
Gx, Gy, Gz
Wald, fMRI MR Physics
Three Steps in MR:
0) Equilibrium (magnetization points along Bo)
1) RF Excitation (tip magn. away from equil.)
2) Precession induces signal,
dephasing (timescale = T2, T2*).
3) Return to equilibrium (timescale = T1).
Wald, fMRI MR Physics
Magnetization vector during MR
RF
encode
time
Voltage
(Signal)
Mz
Mxy
Wald, fMRI MR Physics
Three places in process to make a
measurement (image)
0) Equilibrium (magnetization points along Bo)
1) RF Excitation (tip magn. away from equil.)
2) Precession induces signal, allow to dephase
for time TE.
3) Return to equilibrium (timescale =T1).
proton
density
weighting
T2 or T2*
weighting
T1 Weighting
Wald, fMRI MR Physics
Contrast in MRI: proton density
Form image immediately after excitation
(creation of signal).
Tissue with more protons per cc give more
signal and is thus brighter on the image.
No chance to dephase, thus no
differences due to different tissue T2
values.
Magnetization starts fully relaxed (full Mz),
thus no T1 weighting.
Wald, fMRI MR Physics
T2*-Dephasing
Wait time TE after excitation before measuring M.
Shorter T2* spins have dephased
z
z
z
y
y
y
vector
sum
x
initially
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x
at t= TE
x
T2* Dephasing
Just the tips of the
vectors…
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T2* decay graphs
Transverse Magnetization
1.0
T2* = 200
0.8
Tissue #1
0.6
T2* = 60
0.4
0.2
0.0
0
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Tissue #2
20
40
60
Time (milliseconds)
80
100
T2* Weighting
Phantoms with
four different T2* decay
rates...
There is no contrast
difference immediately
after excitation, must wait
(but not too long!).
Choose TE for max.
inten. difference.
Wald, fMRI MR Physics
Gradient Echo (T2* contrast)
Dephasing is entirely from a spatial difference in the
applied static fields.
z
90°
y
t=0
x
B o + Gx x
z
y
x
t=T
Red arrows processes faster
due to its higher local field
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x
Gradient Echo (T2* contrast)
Dephasing is entirely from a spatial difference in the
applied static fields.
z
90°
y
t=0
x
z
z
y
t=T
z
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x
x
x
y
y
t=T
B o + Gx x
x
t = 2T
B o + Gx x
x
Gradient Echo
RF excitation
t
Gx
t
S
t
Boring!
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7T 32ch MGH array
2D FLASH, TR/TE=3 500/30
0.22 x 0.22 x 1mm (48nl) 8min acq
Wald, RSNA 2007
Courtesy of Dr. Christopher J. Wiggins. Used with permission.
A.A. Martinos Center, MGH Radiology
7T 32ch MGH array
Courtesy of Dr. Christopher J. Wiggins. Used with permission.
G. Wiggins,
C. Wiggins,
Martinos Center MGH
Wald, RSNA 2007
2D FLASH, TR/TE=3 500/30
0.22 x 0.22 x 1mm (48nl) 8min acq
A.A. Martinos Center, MGH Radiology
7 Tesla
230um
2D FLASH
3
0.23 x 0.23, x 1.5mm
8min acq
Courtesy of Dr. Christopher J. Wiggins.
Wald, Munich, 2008
Used with permission.
7 Tesla
230um
2D FLASH,
3
0.23 x 0.23 x 1.5mm
8min acq
Wald, Munich, 2008
Courtesy of Dr. Christopher J. Wiggins.
Used with permission.
7 T, 32ch 200um x 200um x 1mm
an
2D T2* weighted
200um x 200um x 1mm
(1024x1024
matrix)
Wald, Munich,
2008
“U-fiber” ??
Courtesy of Dr. Christopher J. Wiggins. Used with permission.
Spin Echo (T2 contrast)
Some dephasing can be refocused because its due to
static fields.
180°
z
90°
y
t=0
x
z
t=T
Echo!
z
z
y
y
y
x
x
x
t = T (+)
Blue arrows precesses faster due to local
field inhomogeneity than red arrow
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t = 2T
Spin Echo
180° pulse only helps cancel static inhomogeneity
The “runners” can have static speed distribution.
If a runner trips, he will not make it back in phase with the others.
Wald, fMRI MR Physics
NMR Signal
T2 weighed spin echo image
gray
white
Time to Echo , TE (ms)
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Other contrast for MRI
In brain: (gray/white/CSF/fat)
Proton density differ ~ 20%
T1 relaxation differ ~ 2000%
How to exploit for imaging?
Vary repetition rate - TR
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T1 weighting in MRI (w/ 90o excite)
TR
RF
encode
encode
encode
Voltage
(Signal)
Mz
grey matter (long T1)
Wald, fMRI MR Physics white matter (short T1)
time
T1-Weighting
1.0
white matter
T1 = 600
Signal
0.8
grey matter
T1 = 1000
0.6
CSF
T1 = 3000
0.4
0.2
0.0
0
1000
2000
TR (milliseconds)
Wald, fMRI MR Physics
3000
T1 weighting in MRI (w/ 30o excite)
TR
RF
encode
encode
encode
Voltage
(Signal)
Mz
white matter (short T1)
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time
Image contrast summary: TR, TE
Long
Proton
Density
T2
TR
Short
T1
poor!
Short
Wald, fMRI MR Physics
Long
TE
Source of T1 and T2 contrast in brain:
Myelin content
Layer 1: no cell bodies,
moderate myelination
Image removed due to copyright restrictions.
Diagram showing the arrangement of nerve cells
and fibers in layers and sublayers parallel to the
surface in a vertical section through the human
striate area or visual cortical center.
Determine
functional
Layer 4b: thick region
with myelination
(line on
boundaries
based
of Gennari)
MR strucure alone…
White matter: heavy
myelination
Myelin differences are the
primary source of T1 and T2
contrast of gray/white matter.
Nissel stain:
Weigert stain:
fMRI MR Physics
cellWald,
bodies
fibers
Cortical layers in Monkey at 7T
Intensity along line perpendicular To V1
MPRAGE 250um x 250um x 750um (4 hours)
Wald, fMRI MR Physics