The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus...

The Danish National Research Foundation’s

Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital

Diffusion weighted MRI

Brian Hansen, [email protected]



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• Background: The physics of diffusion Fickian diffusion Brownian motion Self diffusion

• Diffusion measurements PGSE pulse sequence and spin dynamics Interpreting the diffusion weighted signal Diffusion in biological tissues

• Diffusion MRI in neuroimaging / neuroscience Diffusion weighted MRI and the ADC map Other applications: Fibre tracking

Lecture outline



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Background and motivation

• Diffusion processes are everywhere in Nature Gases Solids (semi-conductors, alloys) Liquids (chemical reactions, biology, physiology)

• Diffusion Weighted (DW) MRI is a non-invasive method for measuring diffusion: Diffusion coefficient (physical or apparent) Direction of diffusion (preferred direction)

• From these parameters the state of e.g. tissue can be estimated.



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Clinical Application

• Ischemic infarction is not visible on conventional MRI (T1,T2, PD)

• DW MRI introduces new sensitivity:



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Physical Principles



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Fickian diffusion

Fick’s two laws describe diffusion driven by a difference in concentration.

Fick’s 1st:

Fick’s 2nd:

C(x,t)

x



Self-diffusion

• All water molecules perform a thermally driven random walk.

• We can only describe this motion statistically:

H2O

For Brownian motion z = 2



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Brownian Motion

• Named after scottish botanist Robert Brown (1773-1858).

• Explained by Einstein in 1905.

• The thermal motion of the molecules cause them to collide. Random motion follows.

Described by the Stokes-Einstein relation:

D is diffusion coefficient, kB is the Boltzmann constant, T is absolute temperature, is liquid viscosity and r is particle radius.



Diffusion in biological tissue

Diffusion in tissue is resticted by cell membranes, organelles etc:

These random trajectories will in time fill the plane and reveal the structure.



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Measuring Diffusion

• The Pulsed Gradient Spin Echo (PGSE) sequence

90

180

time

g



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No diffusion:

x

Spin 1 Spin 2 Spin 3

B

Stationary spins are unaffected by diffusion gradient.

time



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With diffusion:

x

Spin 1 Spin 2 Spin 3

B

time



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Vector sum

+ + =

+ + =

No loss of signal in areas with no diffusion.

Diffusion introduces a signal loss.

High diffusion gives strong signal attenuation.



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DW MRI parameters

Parameters g, , are combined in the b-factor:

Here is the proton gyromagnetic ratio.

The b-factor can be varied by varying one of g, and .

For the PGSE sequence the case b = 0 corresponds to the simpel SE sequence.

A large b-factor gives a large signal loss in areas with high diffusion. This is called strong diffusion weighting.

90

180

g



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Signal and b-factor I

The DWMR signal from simple free diffusion is described by:

By ”simple free diffusion” we mean that

applies for all times.



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Signal and b-factor IIOn a log-plot this yields a straight line:

log(S(b)/S(b=0)) = -bD

The slope of the curve gives us the physical diffusion coefficient.



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Measuring D

Remember:



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Diffusion in tissue

Diffusion in biological tissue is not free:

Cell membranes, organelles etc. restrict the diffusion of the water molecules.

Simple signal behaviour

breaks down due to complex tissue structure:

Grey matter, ECS in red.

This means that

no longer applies for all times.



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The Apparent Diffusion Coefficient

• The value we measure is no longer the physical diffusion coefficient: Instead we get an average over many restricted random walks

• We introduce the term Apparent Diffusion Coefficient (ADC)

• Two measurements at b = 0 and b = 1000 s/mm2 are made:

The slope gives the ADC – not the physical diffusion coefficient.

Typical ADC values in brain (mm2/s):

Normal gray matter: 0.8-1.010-3

Normal white matter: 0.2-1.0 10-3

Free water (CSF): 2.9 10-3

Review and references in Journal of Computer Assisted Tomography 25(4):515-519.



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Increasing b-values

b = 2000 b = 4000 b = 7000



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DWI and ADC maps

DW MRI provides two new image types:

The Diffusion Weighted Image (DWI) The ADC map (a calculated image)



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Stroke DWI

Acute

DWI

tPA + 2h tPA + 24h

DWIDWI



Possible cause of the bright areas in the DWI:

Cells in normal tissue

Cells in infarct (stroke)



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Summary: Strength of DWI

T2 MRI:

• Infarct is not visible – brain appears normal

DWI:

• Infarct clearly visible

• Scan time: 30 sec, EPI

• No IV contrast agent needed

• Infarct detectable after few minutes



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Summary: Image types

Two image types: DWI and ADC map:

DWI:

• Signal is diffusion weighted.

• High diffusion: signal loss

• Low diffusion: no signal loss

• Infarcts are bright

ADC map:

• Calculated image

• Contrast opposite to DWI

• Low intensity: low ADC value (low diffusion)

• High intensity: high ADC (high diffusion)



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DWI

ADC

MTT

Osvd



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Diffusion Tensor Imaging

Diffusion is often directional – e.g. along fibers:

Instead of measuring many b-values we measure along many different directions.

Instead of the ADC we obtain the Diffusion Tensor which describes the diffusion coefficient in space.

This is the basis of fibre tracking.



Images courtesy of Jesper Frandsen, CFIN



Image courtesy of Jesper Frandsen, CFIN

The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus...

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