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Diffusion Weighted MRI (2011-09-29 이정원)

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

Published in: Health & Medicine, Technology

Diffusion Weighted MRI (2011-09-29 이정원)

  1. 1. Diffusion MRI 2011. 9. 29. KAIST 바이오및뇌공학과 이정원 1
  2. 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. 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. 3
  4. 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 4
  5. 5. Why diffusion? • Tissue cellularity • Connectivity 5 DW-MRI DTI
  6. 6. How to measure the diffusion in MRI • A review of MR imaging sequences Gradient Echo sequence Spin Echo sequence 6
  7. 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. 8. How to measure the diffusion in MRI Stationary water Mobile water Stationary water Mobile water 8
  9. 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. 9
  10. 10. How to measure the diffusion in MRI Gradient and spin 90 RF Dephasing Rephasing 10
  11. 11. Imperfect refocusing =Signal loss! How to measure the diffusion in MRI If spin moves 90 RF Dephasing Rephasing G 11
  12. 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 12
  13. 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) 13
  14. 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 14
  15. 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 15
  16. 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. 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 17
  18. 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 18
  19. 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 19
  20. 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 20
  21. 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 21
  22. 22. Biological processes involved in therapy induced changes in tumor ADC 22 식세포 활동
  23. 23. Primary brain tumor in DW-MRI 23 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. 24. Treatment response prediction • Functional diffusion map (fDM) as a biomarker 24
  25. 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 25 𝐴 = 𝑓𝑠𝑙𝑜𝑤 exp −𝑏𝐷𝑠𝑙𝑜𝑤 + 𝑓𝑓 𝑎𝑠𝑡exp(−𝑏𝐷𝑓𝑎𝑠𝑡)
  26. 26. References 26

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