Basic MR image encoding
MGH-NMR Center
HST.583: Functional Magnetic Resonance Imaging: Data Acquisition and Analysis
Harvard-MIT Division of Health Sciences and Technology
Dr. Larry Wald
MGH-NMR Center
Review: the NMR Signal
RF
time
Voltage
(Signal)
time
X
Xo
Bo
z
z
90°
z
y
Mo
y
y
x
x
Xo
V(t)
x
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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 durning MR
RF
encode
time
Voltage
(Signal)
Mz
time
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Three places in process to make a
measurement (image)
0) Equilibrium (magnetization points along Bo)
1) RF Excitation (tip magn. away from equil.)
proton
density
weighting
2) Precession induces signal, allow to dephase
for time
T2 or T2*
TE.
weighting
3) Return to equilibrium (timescale =T1).
T1 Weighting
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T2*-Weighting
Wait time TE after excitation before measuring M.
Shorter T2* spins have dephased
z
z
z
y
y
y
vector
sum
x
initially
x
x
at t= TE
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Aside: Magnetic field gradient
Bo
Gx x
Uniform magnet
z
x
Field from
gradient
coils
Bo + Gx x
Total field
Gx wBz wx
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A gradient causes a spread of frequencies
Bo
y
Xo
X
z
B o + Gz z
B
o
z
# of spins
v = JBTOT = J(Bo + Gz z)
B Field
MR frequency of the protons in
a given location is proportional to
the local applied field.
resonance frequency
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A gradient causes dephasing
I caused it, I can reverse it…
Gradient echo
X = JBTOT = J%R Gz z
RF
'X = J'BTOT = J Gz z
Gx
'T = 'X W = J Gz z W
Gratuitous manipulation…
(?)
a1
a2
t
S(t)
What happens if the spin moves?
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Spin Echo
Some dephasing can be refocused because its
due to static fields.
z
90°
y
z
x
t=T
z
z
y
x
t=0
Echo!
y
y
180°
x
t = T (+)
x
t = 2T
Blue/Green arrows precesses faster due to local
field inhomogeneity than red/orange 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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Other contrast for MRI
In brain: (gray/white/CSF/fat)
Proton density differ ~ 20%
T1 relaxation differ ~
2000%
How to exploit for imaging?
Answer:
Vary repetition rate - TR
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T1 weighting in MRI
TR
RF
encode
encode
encode
Voltage
(Signal)
Mz
grey matter (long T1)
white matter (short T1)
time
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T1-Weighting
1.0
Signal
0.8
white matter
T1 = 600
grey matter
T1 = 1000
0.6
CSF
T1 = 3000
0.4
0.2
0.0
0
1000
2000
TR (milliseconds)
3000
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T1-Weighting
Very long TR, Signal ~ Proton
Density
Shortening TR o long T1 darker
"Best" T1 contrast, TR near T1
Contrast comes at expense of
throw away some
Signal:
magnetization
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Summarizing Contrast
Two knobs: TE and TR
Effects tend to compete, most tissue with long
T1 also has long T2 and contrast goes opposite
ways.
T1-weighting: short T1 is bright
T2-weighting:
long T2 bright
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Image contrast through choices of TR, TE
Long
Proton
Density
T2
T1
poor!
TR
Short
Short
Long
TE
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1D projection image
Bo
y
Xo
X
z
B o + Gz z
B
o
z
# of spins
v = JBTOT = J(Bo + Gz z)
B Field
MR frequency of the protons in
a given location is proportional to
the local applied field.
resonance frequency
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Step one: excite a slice
Bo
y
While the grad. is on,
excite only band of
frequencies.
NMR signal inten.
B Field
(w/ z gradient)
z
B o + Gz z
z
B
RF
o
t
Gz
t
'v
v
Why?
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Step two: encode spatial info. in-plane
B
along
o
z
y
“Frequency encoding”
B
BTOT = Bo + Gz
x
o
x
Signal
B Field
(w/ x gradient)
x
X
Freq.
with gradient
X
o
without gradient
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‘Pulse sequence’ so far
RF
t
“slice select”
Gz
“freq. encode”
(read-out)
Gx
t
t
S(t)
Sample points
t
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“Phase encoding”
RF
“slice select”
“phase encode”
“freq. encode”
(read-out)
Gz
Gy
Gx
t
t
t
t
S(t)
t
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How does blipping on a grad. encode
spatial info?
Bo
y
W
Gy
y2
z
B Field
(w/ z gradient)
y1
all y locs
process at
same freq.
B
all y locs
process at
same freq.
o
y
y1
y2
spins in
forehead
precess
faster...
Xy = JBTOT = JBo 'y Gy
Ty = XyW= JBo 'y (Gy W
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How does blipping on a grad. encode
spatial info?
y
Bo
y2
Ty = XyW= JBo 'y (Gy W
z
y1
after RF
After the blipped y gradient...
z
z
z
z
90°
y
x
Xo
x
position y1
y
x
position 0
y
x
y
position y2
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How does blipping on a grad. encode
spatial info?
y
The magnetization vector
in the xy plane is wound into
a helix directed along y axis.
Phases are ‘locked in’ once
the blip is over.
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The bigger the gradient blip area, the tighter the helix Ty = XyW= JBo 'y (Gy W
y
small blip
medium blip
large blip
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What have you measured?
uniform water
Consider 2 samples:
no signal observed
1 cm
signal is as big as if no gradient
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Measurement intensity at a spatial frequency...
ky
1/1.2mm = 1/Resolution
10 mm
1/2.5mm
1/5mm
1/10 mm
kx
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Fourier transform
ky
1 / Resx
kx
FOVx = matrix * Resx
1 / FOVx
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Frequency encoding revisited
RF
t
Gz
Gx
t
t
S(t)
t
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“Spin-warp” encoding
ky
RF
t
“slice select”Gz
t
“phase enc”Gy
“freq. enc”
(read-out)
Gx
t
a2
a1
kx
t
S(t)
t
one excitation, one line of kspace...
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“Spin-warp” encoding mathematics
The “image” is the spin density function: U(x)
Phase due to readout:
T(t) = Zo t + JGx x t
Phase due to P.E.
T(t) = Zo t + JGy y W
RF
t
Gz
t
Gy
Gx
t
a2
a1
t
S(t)
'T(t) = Zo t + JGx x t + JGy y W
t
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“Spin-warp” encoding mathematics
Signal at time t from location (x,y)
S(t) U (x, y)e
iJGx xtiJ Gy yW
The coil integrates over object:
S(t )
³³ U( x, y)e
iJG x xt iJ G y yW
dxdy
object
Substituting kx = -J Gx t and kx = -J Gx t :
S(kx , k y )
³³ U(x, y)e
ik x xik y y
dxdy
object
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“Spin-warp” encoding mathematics
View signal as a matrix in kx, ky…
S(kx , k y )
³³ U(x, y)e
ik x xik y y
dxdy
object
:
Solve for U(x,y,)
U(x, y) FT 1 >S(k x ,k y ) @
U(x, y)
³³ S(k x ,ky )e
ik x x ik y y
dk x dk
y
kspace
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Fourier transform
ky
1 / Resx
kx
FOVx = matrix * Resx
1 / FOVx
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Kspace facts
Resolution is determined by the largest spatial
freq sampled.
FOV = matrix * resolution
If the object is real, half the information in
kspace matrix is redundant. We only need to
record half of it.
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kspace
Image space (magnitude)
kspace (magnitude)
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kspace artifacts: spike
One “white pixel” in kspace from a electric spark
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Kspace artifacts: Symmetric N/2 ghost
Even numbered lines got
exp(iI)
Odd numbered lines got
exp(-iI)
I = 12 degrees
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kspace artifacts: subject motion
ky
Yellow = position1
Orange = moved 2 pixels
kx
Movement in real space =
linear phase shift across
kspace.
=> Orange points have
linear phase T = a ky
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T1-Weighting
Very long TR, Signal ~ Proton
Density
Shortening TR o long T1 darker
"Best" T1 contrast, TR near T1
Contrast comes at expense of
throw away some
Signal:
magnetization
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Fast Imaging
“Dost thou love life?
Then do not squander time,
for that’s the stuff
life is made of.”
- Benjamin Franklin
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Requirements for brain mapping
Considerations:
• Signal increase = 0 to 5% (small)
• Motion artifact on conventional image is 0.5% - 3%
• Need to see changes on timescale of hemodynamic
changes (seconds)
Requirement: Fast, “single shot” imaging, image in 80ms,
set of slices every 1-3 seconds.
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What’s the difference? conventional MRI
echoplanar imaging
RF
t
“slice select”Gz
“freq. enc”
(read-out)
RF
t
G
z
G
y
Gy
G
x
Gx
S(t)
S(t)
etc...
T2*
t
ky
ky
kx
kx
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“Echo-planar” encoding
ky
RF
t
t
Gz
Gy
t
Gx
S(t)
kx
etc...
T2*
(no
grads)
t
T2*
one excitation, many lines of kspace...
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“Echo-planar” encoding
Observations:
• Adjacent points along kx are taken
with short 't (= 5 us). (high bandwidth)
ky
• Adjacent points along ky are taken
with long 't (= 500us). (low bandwidth)
• A given line is read quickly, but the total
encode time is longer than conventional
Imaging.
kx
• Adjacent lines are traversed in opposite
directions.
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Bandwidth is asymmetric in EPI
• Adjacent points in kx have short
't = 5 us (high bandwidth)
ky
• Adjacent points along ky are
taken
with long 't (= 500us). (low
bandwidth)
The phase error (and thus
distortions) are in the phase
encode direction.
kx
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EPI problems: N/2 ghost
Asymmetry in alternate lines gives N/2 image ghost.
Asymmetry from:
Eddy currents
receiver filter
receiver timing
head coil tuning.
object
N/2 ghost
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EPI problems: frequency offset
If one object has a different NMR frequency (e.g. fat and water) it gets shifted in PE
direction. (why?)
fat
water
fat
True location
water
Echoplanar image
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Enemy #1 of EPI:
local susceptibility gradients
Bo field maps in the head
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What do we mean by “susceptibility”?
In physics, it refers to a material’s
tendency to magnetize when placed in
an external field.
In MR, it refers to the effects of
magnetized material on the image
through its local distortion of the static
magnetic field Bo.
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Ping-pong ball in water…
Susceptibility effects occur
near magnetically dis-similar
materials
Field disturbance around air surrounded by water (e.g. sinuses)
Bo
Field map (coronal image) 1.5T
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Bo map in head: it’s the air tissue
interface…
Sagittal Bo field maps at 3T
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Susceptibility field (in Gauss) increases w/ Bo
Ping-pong ball in H20:
Field maps ('TE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T)
1.5T
3T
7T
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Local susceptibility gradients: 2 effects
1) Local dephasing of the signal (signal
loss) within a voxel, mainly from thruplane gradients
2) Local geometric distortions, (voxel
location improperly reconstructed)
mainly from local in-plane gradients.
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1) Non-uniform Local Field Causes Local Dephasing
Sagittal Bo field map at 3T
5 water
protons in
different
parts of the
voxel…
z
z
90°
y
slowest
x
T=0
fastest
T = TE
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Local susceptibility gradients:
thru-plane dephasing
Bad for thick slice above frontal sinus…
3T
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Thru-plane dephasing gets worse
at longer TE
3T, TE = 21, 30, 40, 50, 60ms
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Problem #2 Susceptibility Causes Image Distortion in EPI
y
Field near sinus
y
To encode the image, we control phase evolution as a
function of position with
applied gradients.
Local suscept. Gradient causes unwanted phase evolution.
The phase encode error
builds up with time. 'T = J
Blocal 't
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Susceptibility Causes Image Distortion
y
Field near
sinus
y
Conventional grad. echo,
'T D encode time D 1/BW
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Susceptibility Causes Image Distortion
Echoplanar Image,
'T D encode time D 1/BW
z
3T head gradients
Field near
sinus
Encode time = 34, 26, 22, 17ms MGH-NMR Center
Characterization of grad.
performance
• length of readout train for given
resolution
RF
Gz
or echo spacing (esp) or freq of readout…
t
t
Gy
t
Gx
‘echo spacing’ (esp) esp = 500 us for whole body grads, readout length = 32 ms
esp = 270us for 3T, readout length = 17 ms
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What is important in EPI performance?
Short image encoding time.
Parameters related to total encoding time:
1) echo spacing.
2) frequency of readout waveform.
Key specs for achieving short encode times:
1) gradient slew rate.
2) gradient strength.
3) ability to ramp sample.
Good shimming (second order shims)
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Ramp-sampling of EPI is key to
reducing encode time
ky
Area under samples
D 1 / Resolution
kx
ky
kx
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With fast gradients, add parallel imaging
'k
2S
FOV
{
Acquisition:
SENSE
SMASH
Reduced k-space
sampling
Folded images in
each receiver channel
Reconstruction:
Folded datasets
+
Coil sensitivity
maps
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(iPAT) GRAPPA for EPI susceptibility
3T Trio, MRI Devices Inc. 8 channel array
b=1000 DWI images
iPAT (GRAPPA) = 0, 2x, 3x
Fast gradients are the foundation, but EPI
still suffers distortion
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Enemy #1 of EPI:
local susceptibility gradients
Bo field maps in the head
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EPI: Local susceptibility gradients
Local susceptibility gradients have 2 effects:
1) Local dephasing of the signal (signal loss) mainly from thru plane gradients
2) Local geometric distortions, mainly from local in-plane gradients.
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Susceptibility: thru plane dephasing
1
2
3
Signal from whole slice comes from adding together
the MR vectors.
When in phase,
add constructively,
SNR increases like
slice thickness.
4
5
6
Magnetic
Field Uniform
+
+
+
+
+
=
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Susceptibility Artifact and
Slice Thickness
1
2
Signal from whole slice comes from adding together
the MR vectors,
which get out of
phase when the
magnetic field is
not uniform
3
4
5
6
Magnetic
Field NONUniform
+
+
+
+
+
=
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Local susceptibility gradients:
thru-plane dephasing
Bad for thick slice above frontal sinus…
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Local gradients: geometric distortion
Local gradient alters the helix of phase we have so
carefully wound.
Phase error accumulates over entire kspace.
(conventional imaging phase is reset every
line)
>> faster encoding is better.
Readout points are taken close together (~5us)
Phase encode points are taken farther apart (~500us)
>> distortion occurs in P.E. direction.
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Characterization of grad. performance
• length of readout train for given resolutio
(requires fast slew and high grad amplitude)
RF
Gz
Gy
t
t
t
Gx
‘echo spacing’ (esp)= 512 us for 1.5T, readout length = 32 ms
= 366us for 3T, readout length = 23 ms
S(t)
(no
grads)
t
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EPI and Spirals
ky
ky
kx
kx
Gx
Gx
Gy
Gy
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EPI
Spirals
Eddy currents:
ghosts
blurring
Susceptibility:
distortion,
dephasing
blurring
dephasing
k = 0 is sampled:
1/2 through
1st
Corners of kspace:
yes
no
Gradient demands:
very high
pretty high
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EPI and Spirals
EPI at 3T
Spirals at 3T
(from G. Glover)
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