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Diffusion MRI

2011. 9. 29.KAIST 바이오및뇌공학과

이정원

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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)

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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. 

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 con-

tained within the volume

– Diffusion coefficient

• Einstein rewrote Fick’s laws for the diffusion– in terms of diffusion under probability gradients

𝐷=𝑘𝐵𝑇6𝜋𝜂 𝑅

: Sutherland-Einstein relation (1905) viscosityT absolute temperatureR radius of the spherical particle

𝐾𝑛𝜁−𝐷

𝛿𝑛𝛿𝑥

=0 the number of Brownian particles per unit volume frictionD diffusion coefficientX position

𝑃 (𝑟|𝑟 ′ , 𝑡 ) :𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑝𝑟𝑜𝑏𝑎𝑏𝑙𝑖𝑡𝑦 h𝑡 𝑎𝑡 𝑎𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔𝑎𝑡 𝑟 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑧𝑒𝑟𝑜𝑤𝑖𝑙𝑙𝑚𝑜𝑣𝑒𝑡𝑜𝑟 ′ 𝑎𝑓𝑡𝑒𝑟 𝑎 𝑡𝑖𝑚𝑒𝑡

: Einstein equation for diffusion

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Why diffusion?

• Tissue cellularity • ConnectivityDW-MRI DTI

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How to measure the diffusion in MRI

• A review of MR imaging sequences

Gradient Echo se-quence

Spin Echo sequence

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How to measure the diffusion in MRI

Allen W. Song, Brain Imaging and Analysis Center, Duke Uni-versity,

“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

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How to measure the diffusion in MRI

Stationary water

Mobilewater

Stationary water

Mobilewater

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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 pro-

tons’ 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 di-rection.

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How to measure the diffusion in MRIGradient and spin

90

RF

Dephasing

Rephasing

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Imperfect refocusing

=Signal loss!

How to measure the diffusion in MRIIf spin moves

90

RF

Dephasing

Rephasing

G

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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( 𝑆𝑆𝑜 )=−𝛾 2𝐺2 𝛿2 (∆− 𝛿

3 )𝑫=−𝑏𝑫

b-value

Sig

na

l In

ten

sity

D

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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 (−𝛾 2𝐺2𝛿2(∆− 𝛿3 )𝐷)

𝐴 (𝑇𝐸 )=exp (−𝛾 2𝐺2𝛿2([∆− 𝛿3 ]+ 𝜀3

30−

𝛿𝜀3

6 )𝐷)

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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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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(− TR𝑇1)]exp (− 𝑇𝐸

𝑇 2)exp (−𝑏𝑫)

𝑫𝑥 , 𝑦 , 𝑧=− ln [𝐴𝑥 ,𝑦 , 𝑧 (𝑏 )𝐴𝑥 ,𝑦 , 𝑧 (𝑏0 )

] /(𝑏−𝑏0)

Diffusion-weighted image ADC map

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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

b-value

Sig

na

l In

ten

sity

D

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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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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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ADC (apparent diffusion coefficient)

• To take into account diffusion and pseudo-diffusion processes• By replacing the microscopic diffusion coefficient D with a global parame-

ter, 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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Fast and slow diffusion pool

• The biexponential model

𝐴= 𝑓 𝑠𝑙𝑜𝑤 exp (−𝑏𝐷𝑠𝑙𝑜𝑤 )+ 𝑓 𝑓𝑎𝑠𝑡exp (−𝑏𝐷 𝑓𝑎𝑠𝑡)f:thevolumefraction(fslow+ffast=1)D:thediffusioncoefficient

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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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Biological processes involved in therapy induced changes in tumor ADC

식세포 활동

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Primary brain tumor in DW-MRI

Charles-Edwards, E.M. and deSouza, N.M. (2006). “Diffusion-weighted magnetic resonance imaging and its application to cancer.” Cancer imag-ing : 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

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Treatment response prediction

• Functional diffusion map (fDM) as a biomarker

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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, )

• 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

𝐴= 𝑓 𝑠𝑙𝑜𝑤exp (−𝑏𝐷𝑠𝑙𝑜𝑤 )+ 𝑓 𝑓𝑎𝑠𝑡exp (−𝑏𝐷 𝑓𝑎𝑠𝑡)

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References