KAIST 2011년 2학기 영상공학특강 (김대식 교수) 수업 발표자료

1. Diffusion MRI
2011. 9. 29.
KAIST 바이오및뇌공학과
이정원
1

2. What is diffusion?
• Fick’s Law (1855, Adolf Fick)
J : diffusion flux (mol/m2s)
D : diffusion coefficient or diffusivity (m2/s)
Φ : Concentration in dimensions (mol/m3)
x : the position (m)
t : time (s)
2

3. What is diffusion?
• Brownian motion (Robert Brown, 1827)
– the presumably random drifting of particles suspended in a fluid
The characteristic bell-shaped curves of
the diffusion of Brownian particles.
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4. What is diffusion?
• Einstein recognized that Brownian motion was associated with diffusion
– No macroscopic concentration gradient is needed.
– Self-diffusion arising from local concentration fluctuations
• Einstein derived the self-diffusion coefficient of the Brownian particle
– Einstein expressed the energy change as the total work done by the particles contained within
the volume
– Diffusion coefficient
• Einstein rewrote Fick’s laws for the diffusion
– in terms of diffusion under probability gradients
𝐷 =
𝑘 𝐵 𝑇
6𝜋𝜂𝑅
: Sutherland-Einstein relation (1905)
𝑘 𝐵 ∶ 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛′
𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝜂 ∶ viscosity
T ∶ absolute temperature
R ∶ radius of the spherical particle
𝐾𝑛
𝜁
− 𝐷
𝛿𝑛
𝛿𝑥
= 0
𝐾 ∶ 𝑛𝑒𝑡 𝑓𝑜𝑟𝑐𝑒
𝑛 ∶ the number of Brownian particles per unit volume
𝜁 ∶ friction
D ∶ diffusion coefficient
X ∶ position
𝑃 𝑟 𝑟′
, 𝑡 : 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑝𝑟𝑜𝑏𝑎𝑏𝑙𝑖𝑡𝑦 𝑡ℎ𝑎𝑡 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 𝑎𝑡 𝑟 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑧𝑒𝑟𝑜 𝑤𝑖𝑙𝑙 𝑚𝑜𝑣𝑒 𝑡𝑜 𝑟′
𝑎𝑓𝑡𝑒𝑟 𝑎 𝑡𝑖𝑚𝑒 𝑡
: Einstein equation for diffusion
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5. Why diffusion?
• Tissue cellularity • Connectivity
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DW-MRI DTI

6. How to measure the diffusion in MRI
• A review of MR imaging sequences
Gradient Echo
sequence
Spin Echo
sequence
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7. How to measure the diffusion in MRI
7
Allen W. Song, Brain Imaging and Analysis Center, Duke University,
“Principles of MRI Physics and Engineering”
Gradient Echo DW-MRI Spin Echo DW-MRI
• Almost any MR imaging sequence can be designed to be sensitive to diffusion
– By adding magnetic field gradients
• To magnetically label spins carried by diffusing molecules
• Only parallel component has an effect

8. How to measure the diffusion in MRI
Stationary
water
Mobile
water
Stationary
water
Mobile
water
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9. How to measure the diffusion in MRI
• The first gradient pulse
– Alters the phase shift of each proton
– By an amount dependent on the water molecule’s spatial location relative to the gradient
• The second gradient pulse
– if the water molecule does not move between the application of the first and second
gradient pulses
• Reverse this phase shift
– If there is movement of the water molecule between application of the first and second
gradient pulses
• Complete rephasing cannot happen, causing signal loss from this spatial location
• The amount of signal loss is directly proportional to the degree of water motion (the protons’
mean diffusional path length)
• Two components measured
– Magnitude: the extent to which protons are free to diffuse
• Signal loss ∝ degree of water motion (the protons’ mean diffusional path length)
– Direction: preferential diffusion direction
• Signal loss is proportional to the motion component in the same direction as the diffusion
gradient. No signal loss would occur if the motion was perpendicular to the gradient direction.
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10. How to measure the diffusion in MRI
Gradient and spin
90
RF
Dephasing
Rephasing
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11. Imperfect refocusing
=Signal loss!
How to measure the diffusion in MRI
If spin moves
90
RF
Dephasing
Rephasing
G
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12. Equation of diffusion attenuation, and b-value
• There is a particular problem
– The combination of the imaging and the diffusion gradient pulses produce attenuation
effects
• So, b-value is suggested
– To summarize all gradient effects (diffusion and imaging pulses)
– The diffusion sensitivity of the sequence
– Without additional gradients, SE imaging sequences has very low b-values (around 1 s/mm2)
𝐴 𝑇𝐸 : ln
𝑆
𝑆𝑜
= −𝛾2 𝐺2 𝛿2 ∆ −
𝛿
3
𝑫 = −𝑏𝑫
b-value
SignalIntensity
D
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13. Various sequences of diffusion-weighted MRI
• Pulsed field gradient spin echo (PFGSE)
• Double pulsed gradient spin echo
– Two gradient pulse pairs on the same spin magnetization
– To compensate flow
• Stimulated echo
• Gradient echo
𝐴 𝑇𝐸 = exp(−𝛾2 𝐺2 𝛿2 ∆ −
𝛿
3
𝐷)
𝐴 𝑇𝐸 = exp(−𝛾2 𝐺2 𝛿2 ∆ −
𝛿
3
+
𝜀3
30
−
𝛿𝜀3
6
𝐷)
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14. We can get diffusion-weighted MR images
• Among various MRI images
– T1-weighted MRI
– T2-weighted MRI
– FLAIR (Fluid attenuated inversion recovery)
– Proton Density weighted MRI
– Diffusion-weighted MRI
– Diffusion Tensor Imaging
– Susceptibility Weighted Imaging (SWI)
– Dynamic Susceptibility Contrast (DSC) MRI
– Magnetic Resonance Spectroscopy (MRS)
– Functional MRI
CT T1
weighted
T2-
weighted
Diffusion
weighted
ADC map
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15. Diffusion-weighted image vs. Diffusion map
• Diffusion-weighted image
– Darkness: high diffusion
– Brightness: low diffusion
– Intensity is affected by many other parameters than diffusion
• Diffusion map (ADC map)
– To obtain pure maps of the diffusion coefficient
– By acquiring two images with different b-values, b and b0
– Darkness: low, slow diffusion
– Brightness: high, fast diffusion
𝐴 = [1 − exp −
TR
𝑇1
]exp −
𝑇𝐸
𝑇2
exp(−𝑏𝑫)
𝑫 𝑥,𝑦,𝑧 = −ln[
𝐴 𝑥,𝑦,𝑧 𝑏
𝐴 𝑥,𝑦,𝑧 𝑏0
]/(𝑏 − 𝑏0)
Diffusion-weighted image ADC map
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16. Diffusion map
• Two b-value acquisitions
– Best precision: b-b0 = 1/D (in the brain b-b0 = 1000 to 1500 s/mm2)
• More than two b-value acquisitions
– Better accuracy
– To get further information on tissue microstructure and dynamics
16b-value
SignalIntensity
D

17. IVIM
• IVIM (intravoxel incoherent motion)
– Pseudo-diffusion process from movement of the blood in the microvasculature
– A means to cover all molecular displacements to which “diffusion” MRI could be sensitive
– Diffusion measurements with MRI may include perfusion effects and not just true diffusion
• Perfusion effects at very low b-values (<200 s/mm2)
– Only two b-values (0 and 1000 s/mm2) could include perfusion effect
• Overestimation of the true diffusion coefficient D
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18. ADC (apparent diffusion coefficient)
• ADC map
– Describes microscopic water diffusibility in the presence of factors that restrict diffusion
within tissues.
– ADC is measured by combining two diffusion-weighted images
• typically with (Sb) and without (So) diffusion weighting
• or using two b-values
– Multiple b-values are needed
• To differentiate between perfusion and diffusion
– The area of high diffusion is represented as a bright area; a high ADC value
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19. ADC (apparent diffusion coefficient)
• To take into account diffusion and pseudo-diffusion processes
• By replacing the microscopic diffusion coefficient D with a global parameter, ADC
• In the brain, as larger b-values can generally be used and f is very small (2~4%)
ADC ≡ −ln[
𝐴(𝑏)
𝐴(𝑏0)
]/(𝑏 − 𝑏0)
𝐴𝐷𝐶 ≈ 𝐷 + 𝑓/𝑏 f : perfusion fraction
Diffusion-weighted image ADC map
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20. Fast and slow diffusion pool
• The biexponential model
𝐴 = 𝑓𝑠𝑙𝑜𝑤 exp −𝑏𝐷𝑠𝑙𝑜𝑤 + 𝑓𝑓𝑎𝑠𝑡exp(−𝑏𝐷𝑓𝑎𝑠𝑡)
f: the volume fraction (fslow + ffast = 1)
D: the diffusion coefficient
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21. Clinical applications of DW-MRI
• Clinical applications
– Tissue characterization (differentiating benign from malignant lesions)
– Tumor staging
– Predicting treatment outcomes (before and soon after starting therapy)
– Monitoring treatment response after chemotherapy or radiation
– Differentiating post-therapeutic changes from residual active tumor
– Detecting recurrent cancer
– Detecting lymph node involvement by cancer
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22. Biological processes
involved in therapy induced changes in tumor ADC
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식세포 활동

23. Primary brain tumor in DW-MRI
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Charles-Edwards, E.M. and deSouza, N.M. (2006). “Diffusion-weighted magnetic
resonance imaging and its application to cancer.” Cancer imaging : the official
publication of the International Cancer Imaging Society, 6, pp. 135-43.
B-value = 0 B-value = 500 B-value = 1000 ADC map
Edema
Tumor

24. Treatment response prediction
• Functional diffusion map (fDM) as a biomarker
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25. Summary
• Fick’s law of diffusion → Einstein equation
• Why diffusion?
– Tissue cellularity : DW-MRI
– Connectivity : DTI
• How to measure diffusion in MRI
– By adding a pair of magnetic field gradients (diffusion gradient)
– Diffusivity → signal attenuation
• High signal : low diffusion
• Low signal : high diffusion
• The b-value
– the diffusion sensitivity of the sequence (correlated with G, ∆, 𝛿)
• ADC map: tissue cellularity
– From (more than) two DW-MRI with different b-value → ADC map
– High intensity : high diffusion
– Low intensity : low diffusion
• IVIM
– Blood flow effect analysis
• Biexponential model
– Slow and fast diffusion pool
– Intra-cellular and extra-cellular compartment
• Clinical application
– Tissue characterization
– Tumor staging
– prediction and monitoring of treatment response
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𝐴 = 𝑓𝑠𝑙𝑜𝑤 exp −𝑏𝐷𝑠𝑙𝑜𝑤 + 𝑓𝑓 𝑎𝑠𝑡exp(−𝑏𝐷𝑓𝑎𝑠𝑡)

26. References
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