Massachusetts General Hospital

1
MR physics and safety for fMRI
Lawrence L. Wald, Ph.D.

• Massachusetts General Hospital
• Athinoula A. Martinos Center

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Outline

• Monday Oct 18 (LLW)
• MR signal, Gradient and spin echo
• Basic image contrast

Wed. Oct 20 (JJ) Encoding the image
Monday Oct 25 (LLW) Fast imaging for fMRI,
artifacts
Wed. Oct 25 (LLW) fMRI BOLD contrast
Mon. Nov. 1 (JJ) Review, plus other contrast
mechanisms for fMRI (CBV, CBF)
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What is NMR?

• NUCLEAR
• MAGNETIC
• RESONANCE

A magnet, a glass of water, and a radio wave
source and detector.
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What is NMR? Nuclear magnetism
M

5
E
B
DE hu
protons
(N? N?)/NTOT 1 exp(-DE/kT) 10-4
Earths Field
compass
6
Compass needles
Main Field Bo
Earths Field
u
z
North
y
x
Freq g B
42.58 MHz/T
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Gyroscopic motion
Main Field Bo
z
North

• Proton has magnetic moment
• Proton has spin (angular momentum)
• gtgtgyroscopic precession

M
y
x
? ? Bo
Larmor precession freq. 42.58 MHz/T
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EXCITATION Displacing the spinsfrom
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

9
Excitation Resonance

• Why does only one frequency efficiently tip
  protons?
• Resonant driving force.
• Its like pushing a child on a swing in time with
  the natural oscillating frequency.

10
z is "longitudinal" direction x-y is "transverse"
plane
Static Field, B0
z
RF Field (B1) applies a torque to the spins
Applied RF Field (B1)
y
x
Mo
The RF pulse rotates Mo the about applied field
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"Exciting" the Magnetization tip angle
z
z
Static Field, B0
y
y
x
x
45
90
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Detecting the Magnetization Faradays Law
A moving bar magnet induces a Voltage in a coil
of wire. (a generator) The RF coil design is
the 1 determinant of the system SNR
V(t) -dF/dt
F n Bspins A
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Detecting the NMR the noise

• Noise comes from electrical losses in the
  resistance of the coil or electrical losses in
  the tissue.
• For a resistor
• Pnoise 4kTRB
• Noise is white.
• gtgtNoise power a bandwidth
• Noise is spatially uniform.
• R is dominated by the tissue. gtgt big coil is
  bad.

V(t)
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The NMR Signal
RF
time
Voltage (Signal)
time
Bo
Mo
V(t)
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Signal to Noise Ratio in MRI

• Most important piece of hardware is the RF coil.
• SNR a voxel volume ( of spins)
• SNR a SQRT( total time of data collection)
• SNR depends on the amount of signal you throw
  away to better visualize the brain (gain image
  contrast)

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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
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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).
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Magnetization vector during MR
RF
encode
time
Voltage (Signal)
Mxy
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Three places in process to make ameasurement
(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
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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.

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T2-Dephasing

• Wait time TE after excitation before measuring M.
  
• Shorter T2 spins have dephased

z
z
z
y
y
y
vector sum
x
x
x
initially at t TE
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T2 Dephasing

• Just the tips of the vectors

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T2 decay graphs
1.0
T2 200
0.8
Tissue 1
0.6
Transverse Magnetization
T2 60
0.4
0.2
Tissue 2
0.0
100
80
60
40
20
0
Time (milliseconds)
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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.
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Gradient Echo (T2 contrast)

• Dephasing is entirely from a spatial difference
  in the applied static fields.

Bo Gx x
z
z
90
y
y
x
x
x
t 0
t T
Red arrows processes faster due to its higher
local field
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Gradient Echo (T2 contrast)

• Dephasing is entirely from a spatial difference
  in the applied static fields.

Bo Gx x
x
Bo Gx x
z
z
y
y
x
x
x
t T
t 2T
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Gradient Echo
RF excitation
t
Gx
t
S
t
Boring!
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Spin Echo (T2 contrast)

• Some dephasing can be refocused because its due
  to static fields.

180
Echo!
z
z
z
z
90
y
y
y
y
x
x
x
x
t T ()
t 0
t 2T
t T
Blue arrows precesses faster due to local field
inhomogeneity than red arrow
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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.

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T2 weighed spin echo image
gray
NMR Signal
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
time
grey matter (long T1) white matter (short T1)
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T1-Weighting
1.0
white matter T1 600
0.8
grey matter T1 1000
0.6
Signal
CSF T1 3000
0.4
0.2
0.0
3000
2000
1000
0
TR (milliseconds)
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T1 weighting in MRI (w/ 30o excite)
TR
RF
encode
encode
encode
Voltage (Signal)
Mz
time
white matter (short T1)
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Image contrast summary TR, TE
Proton Density
Long
T2
TR
Short
T1
poor!
Short
Long
TE
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Source of T1 and T2 contrast in brain Myelin
content
Layer 1 no cell bodies, moderate myelination
Determine functional boundaries based on MR
strucure alone
Layer 4b thick region with myelination (line of
Gennari)
White matter heavy myelination
Myelin differences are the primary source of T1
and T2 contrast of gray/white matter.
Nissel stain Weigert stain cell bodies fibers
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Cortical layers in Monkey at 7T
Intensity along line perpendicular To V1
MPRAGE 250um x 250um x 750um (4 hours)