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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.
Lawrence L. Wald, Ph.D.
Massachusetts General Hospital
Athinoula A. Martinos Center
Wald, fMRI MR Physics

• Why, introduction
• How: Review of k-space trajectories
Different techniques (EPI, Spiral)
• Problems from B0 Susceptibility artifacts
Wald, fMRI MR Physics

Wald, fMRI MR Physics
Capture time course,
(e.g. hemodynamic) eliminate artifact from motion
(during encode.)

RF encode time
Voltage
(Signal)
Mz time
Wald, fMRI MR Physics

Two questions:
1) What does blipping on a gradient do to the water magnetization.
2) Why does measuring the signal amplitude after a blip tell you info about the spatial frequency composition of the image
(k-space).
Wald, fMRI MR Physics

B o
G x x B o +
G x x
Uniform magnet z x
Wald, fMRI MR Physics
Field from gradient coils
G x
=
B z
Total field
x

Step two: encode spatial info. in-plane
B o along z y
“Frequency encoding”
B o x
B
TOT
= B o
+ G z x v =
γ
B
TOT
=
γ
(B o
+ G x x) x with gradient
Wald, fMRI MR Physics
Freq.
υ o
υ without gradient

y
2 y
1 y
B o
How does blipping on a grad. encode spatial info?
B o
τ
G y z all y locs process at same freq.
all y locs process at same freq.
y y
1 y
2 spins in forehead precess faster...
υ( y
)
=
γ
B
TOT
=
γ
B o
θ ( y
)
=
υ( y
) τ
=
γ
B o
Δ y G y
Δ y (G y
τ)
Wald, fMRI MR Physics

y
2 y
1 y
How does blipping on a grad. encode spatial info?
B o z
θ ( y
)
=
υ( y
) τ
=
γ
B o
Δ y (G y
τ) after RF z
90° z
After the blipped y gradient...
z z x
υ o y
Wald, fMRI MR Physics x position y
1 y x y x y position 0 position y
2

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.
Wald, fMRI MR Physics

The bigger the gradient blip area, the tighter the helix
θ ( y
)
=
υ( y
) τ
=
γ
B o
Δ y (G y
τ) y
G y small blip
Wald, fMRI MR Physics medium blip large blip

Consider 2 samples:
1 cm no signal observed
Wald, fMRI MR Physics signal is as big as if no gradient

Measurement intensity at a spatial frequency...
10 mm k y
1/1.2mm = 1/Resolution
1/2.5mm
1/5mm
1/10 mm k x
Wald, fMRI MR Physics

k y
1 / Res x
Fourier transform k x
FOV x
= matrix * Res x
Wald, fMRI MR Physics
1 / FOV x

G y
G y
t
1/1.2mm = 1/Resolution
1/2.5mm
1/5mm
1/10 mm k x t
More efficient!
Frequency and phase encoding are the same principle!
Wald, fMRI MR Physics

Conventional “Spin-warp” encoding k y
RF
“slice select” G z
“phase enc” G y
“freq. enc”
(read-out)
G x
S(t) a
1 a
2 t t t t t k x one excitation, one line of kspace...
Wald, fMRI MR Physics

Image encoding,
“Journey through kspace”
The Movie…
Wald, fMRI MR Physics

k y
1 / Res x
Fourier transform k x
FOV x
= matrix * Res x
Wald, fMRI MR Physics
1 / FOV x

Conventional “Spin-warp” encoding k y
RF
“slice select” G z
“phase enc” G y
“freq. enc”
(read-out)
G x
S(t) a
1 a
2 t t t t k x t one excitation, one line of kspace...
Wald, fMRI MR Physics

RF
G z
G y
G x
S(t)
(no grads)
k y t t t
T2* etc...
t
T2* one excitation, many lines of kspace...
Wald, fMRI MR Physics k x

Bandwidth is asymmetric in EPI k y
• Adjacent points in k x have short
Δ t = 5 us (high bandwidth)
• Adjacent points along k y are taken with long
Δ t (= 500us). (low bandwidth)
The phase error (and thus distortions) are in the phase encode direction.
k x
Wald, fMRI MR Physics

Characterization of EPI performance length of readout train for given resolution or echo spacing (esp) or freq of readout…
RF
G z
G y
G x t t t
‘echo spacing’ (esp) esp = 500 us for whole body grads, readout length = 32 ms esp = 270us for head gradients, readout length = 17 ms
Wald, fMRI MR Physics

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)
Wald, fMRI MR Physics

The good.
The bad.
The ugly.
Wald, fMRI MR Physics

Wald, fMRI MR Physics
B o field maps in the head

Wald, fMRI MR Physics
B o field maps in the head

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 B o
.
Wald, fMRI MR Physics

Susceptibility effects occur near magnetically dis-similar materials
Field disturbance around air surrounded by water
(e.g. sinuses)
Wald, fMRI MR Physics
B o
Field map
(coronal image)
1.5T

o
Wald, fMRI MR Physics
Sagittal Bo field maps at 3T

o
Ping-pong ball in H
2
0:
Field maps (
Δ
TE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T)
1.5T
Wald, fMRI MR Physics
3T 7T

Other Sources of Susceptibility You
Should Be Aware of…
Those fillings might be a problem…
Wald, fMRI MR Physics

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.
Wald, fMRI MR Physics

Sagittal B o field map at 3T
5 water protons in different parts of the voxel… z
90° y z slowest x
T = 0 fastest
T = TE
Wald, fMRI MR Physics

Local susceptibility gradients: thru-plane dephasing in grad echo EPI
Bad for thick slice above frontal sinus…
Wald, fMRI MR Physics
3T

Solution: high resolution
1mm isotropic
TE=30ms, GRAPPA =2
6/8 part-Fourier
Minimal OFC drop-out issues with 3T 1mm isotropic
3T 32ch EPI
Wald, Zhengzhou 2008

Thru-plane dephasing gets worse at longer TE
Wald, fMRI MR Physics
3T, TE = 21, 30, 40, 50, 60m s

Field near sinus
Problem #2 Susceptibility Causes
Image Distortion in EPI y
To encode the image, we control phase evolution as a function of position with applied gradients.
y
Local suscept. Gradient causes unwanted phase evolution.
The phase encode error builds up with time.
Δθ
=
γ
B local
Δ t
Wald, fMRI MR Physics

y
Field near sinus y
Conventional grad. echo,
Δθ α encode time
α
1/BW
Wald, fMRI MR Physics

Susceptibility in EPI can give either a compression or expansion
Altering the direction kspace is transversed causes either local compression or expansion.
choose your poison…
3T whole body gradients
Wald, fMRI MR Physics

Susceptibility Causes Image Distortion
Echoplanar Image,
Δθ α encode time
α
1/BW z
Field near sinus
Wald, fMRI MR Physics
3T head gradients
Encode time = 34, 26, 22, 17ms

k y
k y k x
G x
G y
Wald, fMRI MR Physics
G x
G y k x

Susceptibility:
EPI distortion, dephasing
Eddy currents: ghosts k = 0 is sampled: 1/2 through 1st
Corners of kspace:
Gradient demands: yes very high
Wald, fMRI MR Physics
Spirals blurring, dephasing blurring no pretty high

Nasal Sinus
B
0
Wald, fMRI MR Physics

Nasal Sinus + mouth shim
B
0
Wald, fMRI MR Physics

B
0
Effect of Ear & Mouth Shim on EPI
Wald, fMRI MR Physics
Courtesy of Peter Jezzard. Used with permission.

With fast gradients, add parallel imaging
Δ k
=
2
π
FOV
Acquisition:
Reconstruction:
Folded datasets
+
Coil sensitivity maps
Wald, fMRI MR Physics
Reduced k-space sampling
Folded images in each receiver channel

Using the detector array to encode image
Wald, RSNA 2007 A.A. Martinos Center, MGH Radiology

90 Channel
Uncombined
Images
Wald, RSNA 2007 A.A. Martinos Center, MGH Radiology

Parallel acquisition: noise penalties
Calculating the g-factor map
SNR accel
=
SNR
G R map of 1/G noise correlation matrix coil sensitivity profiles
Wald, RSNA 2007
Rate = 4
Gmax=2.17

R=2
1/G-factor Maps, 3 Tesla
R=3 R=4 R=5 R=6
MGH
96 Ch
Gmax=1.01
Gmax=1.04
Gmax=1.17
Gmax=1.42
Gmax=1.86
MGH
32 Ch
Gmax=1.02
Gmax=1.26
Gmax=2.6
Gmax=4.1
Gmax=6.0
12 Ch
Wald, RSNA 2007
Gmax=1.1
Gmax=1.52
Gmax=2.67
Gmax=4.78
Gmax=6.6
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.0
0.9
0.8

MGH
96 Ch
MGH
32 Ch
2X2 2X3 4X3 4X4 5X4
Gmax=1.02
Gmax=1.05
Gmax=1.4
Gmax=1.6
Gmax=2.0
Gmax=1.05
Gmax=1.3
Gmax=2.3
Gmax=3.6
Gmax=8.6
12 Ch
Wald, RSNA 2007 Gmax=1.26
Gmax=2.8
Gmax=36
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

3D encoding power of the array: eigenmodes of the sensitivity maps
Analysis following:
Univ. Würzburg
Breuer et al.
ISMRM 2005 p2668
MGH brain arrays
The 90ch coil still has significant components over 32ch.
Wald, RSNA 2007 A.A. Martinos Center, MGH Radiology

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
Wald, fMRI MR Physics

Encoding with RF…
4 fold acceleration of single shot submillimeter SE-EPI: 23 channel array
23 Channel array at 1.5T
With and without 4x Accel.
Single shot EPI,
256x256, 230mm FOV
TE = 78ms
Wald, fMRI MR Physics

Extending the phased array to more channels:
23 channel “Bucky” array for 1.5T

9 Fold GRAPPA acceleration 3D
FLASH
9 minute scan down to 1 minute…
23 Channel array at 1.5T
Can speed up encoding by an order of magnitude!
Wald, fMRI MR Physics
3D Flash, 1mm x 1mm x 1.5mm, 256x256x128

12 channel coil
32 channel coil improves fMRI
32 channel coil
1 run 3 run
3T Retinotopic mapping
Wald, Beijing 2008
5 run 1 run
Triantafyllou, Hinds, MIT

90 ch 1.5T
96 ch 3T
Wald, Boston 2008
Graham Wiggins
A.A. Martinos Center, MGH Radiology

96 Ch
32 Ch
12 Ch
3T SNR Maps
150
100
50
0

3T SNR Profiles agn
Wald, Munich 2008
Position
Order of magnitude!

Larry Wald
Wald, fMRI MR Physics