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E. Wong, BE278, UCSD Winter 2013!
Bioengineering 278"Magnetic Resonance Imaging"
"Winter 2013"
Lecture 6!
• Phase Contrast and Diffusion Imaging!• Motion Encoding!• Phase Contrast MRA!• Elastography!• Diffusion in a Gradient Field!• Anisotropic Diffusion!• Fiber Tract Mapping!
!
E. Wong, BE278, UCSD Winter 2013!
Motion Encoding!
RF!Gz!
GY!
Gx!
Modify Mxy!• Phase Contrast MRA!• Elastography!• Diffusion Imaging !
Excitation!Mz->Mxy!!
Image!Acquisition!
Modify MZ!• Time of Flight MRA!• Arterial Spin Labeling!• Myocardial Tagging!
E. Wong, BE278, UCSD Winter 2013!
Phase from Motion:!
€
φ(t) = γB(t)dt∫= γ
G (t) •
r (t)dt∫= γ
G (t)( r 0 +
V t + ...)dt∫
= r 0 • γ
G (t)dt∫ +
V • γ
G (t)tdt∫ + ...
Zeroth!Moment (m0)!
=k!
First (flow)!Moment (m1)!
m0=1!m1=1!
m0=0!m1=-2!
m0=0!m1=0!
€
2 +1( ) :1
m0=!m1=0!
€
2
G!
Bipolar Gradient:!
δ"
Δ"
€
m1 = γGδΔ
Encoding MXY for Motion: Phase Contrast!
How Big can m1 be?!For: !G=4G/cm!
!δ=Δ=50ms!• π per 6µm!• VENC=velocity for φ=π"• =6µm/50ms=0.12mm/s !
E. Wong, BE278, UCSD Winter 2013!
Phase Contrast MRA!RF!
GZ!
GY!
GX!
• One image with velocity encoding positive!• One image with velocity encoding negative!• Vector sum of gradients determines direction of encoding!• Display phase difference between images!• Phase difference subtracts out off-resonance and other phase effects!
E. Wong, BE278, UCSD Winter 2013!
Phase Contrast MRA!• Phase is proportional to velocity!• Quantitate velocity from phase images and/or:!• Construct angiograms by MIP of velocity maps!
MIP!
Bushberg: The Essential Physics of Medical Imaging, 2002.!
E. Wong, BE278, UCSD Winter 2013!
Muthupillai et al, Nature Medicine 2 (5) 1996!
MR Elastography!
Taouli et al, AJR 2009; 193:14–27!
Anatomy! Acoustic Waves!
Stiffness!Velocity!
Gradient!
E. Wong, BE278, UCSD Winter 2013!
Signal Attenuation by Diffusion!
RF!Excitation!
Diffusion Weighting Gradients!
t!x!
A!
B!
C!
D!
A! B! C! D!t!
Diffusion:!• Random walk!• No net displacement -> No net phase shift!
E. Wong, BE278, UCSD Winter 2013!
Image Space K-space !
Flow @1mm/s ~100µm!
Diffusion!@10-3mm2/s!
~15µm!Δx!
Encoding MXY for Motion: Diffusion!
In 100ms:!
Diffusion:!• RMS displacement in time dt !• Convolution with Gaussian in image space!• Multiplication by Gaussian in K-space!
= 2Ddt
FT!
€
S /S0 = e−D k 2dt∫ = e−bD
G!
Bipolar Gradient:!
δ"
Δ"
€
e−x2 /Ddt
€
e−k2Ddt
Total Attenuation:!
€
b ≡ k 2dt∫where:!
E. Wong, BE278, UCSD Winter 2013!
Diffusion Imaging!• Quantitative measure of local self diffusion coefficient!• Measurement in multiple directions gives information on
diffusion anisotropy and fiber orientation!
• Uses:!• Clinical applications in
stroke and white matter disease!
• White matter fiber tract mapping (anatomical connectivity)!
E. Wong, BE278, UCSD Winter 2013!
Diffusion Imaging in Stroke!Na+ H2O ATP
ADP Cell
Na+ H2O ATP
ADP Cell
E. Wong, BE278, UCSD Winter 2013!
Anisotropic Diffusion!
Slide credit: L. Frank!
E. Wong, BE278, UCSD Winter 2013!
Anisotropic Diffusion!
Slide credit: L. Frank!
E. Wong, BE278, UCSD Winter 2013!
Comparison with anatomical preparation!
S. Mori - JHU!
E. Wong, BE278, UCSD Winter 2013!
Detail fiber structures !
S. Mori - JHU!
E. Wong, BE278, UCSD Winter 2013!
Anatomical guidance:!Example: Anatomical deformation due to tumor growth "
S. Mori - JHU!
E. Wong, BE278, UCSD Winter 2013!
Diffusion - Fiber Crossings!
Relative Anisotropy! Directional Variance!
Corpus Callosum! Corona Radiata!
Slide credit: L. Frank!
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