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Diffusion weighted MRI. Brian Hansen, PhD brianh@phys.au.dk. Lecture outline. Background: The physics of diffusion Fickian diffusion Brownian motion Self diffusion Diffusion measurements PGSE pulse sequence and spin dynamics Interpreting the diffusion weighted signal
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Diffusion weighted MRI Brian Hansen, PhD brianh@phys.au.dk
Lecture outline • 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
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.
Clinical Application • Ischemic infarction is not visible on conventional MRI (T1,T2, PD) • DW MRI introduces new sensitivity:
Fickian diffusion Fick’s two laws describe diffusion driven by a difference in concentration. C(x,t) Fick’s 1st: Fick’s 2nd: x
H2O Self-diffusion • All water molecules perform a thermally driven random walk. • We can only describe this motion statistically: For Brownian motion z = 2
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, m 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.
Measuring Diffusion • The Pulsed Gradient Spin Echo (PGSE) sequence 180 90 g time D
No diffusion: Stationary spins are unaffected by diffusion gradient. time Spin 1 Spin 2 Spin 3
With diffusion: time Spin 1 Spin 2 Spin 3
Vector sum No loss of signal in areas with no diffusion. + + = Diffusion introduces a signal loss. High diffusion gives strong signal attenuation. + + =
180 90 g D DW MRI parameters Parameters g, d, D are combined in the b-factor: Here g is the proton gyromagnetic ratio. The b-factor can be varied by varying one of g, d and D. 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.
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.
Signal and b-factor II On 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.
Measuring D Remember:
Diffusion in tissue Diffusion in biological tissue is not free: This means that no longer applies for all times. Simple signal behaviour breaks down due to complex tissue structure: Cell membranes, organelles etc. restrict the diffusion of the water molecules. Grey matter, ECS in red. 18
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. 19
Increasing b-values b = 4000 b = 7000 b = 2000 20
DWI and ADC maps DW MRI provides two new image types: The Diffusion Weighted Image (DWI) The ADC map (a calculated image)
Stroke DWI Acute tPA + 2h tPA + 24h DWI DWI DWI
Possible cause of the bright areas in the DWI: Cells in normal tissue Cells in infarct (stroke)
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
Summary: Image types • 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) Two image types: DWI and ADC map:
DWI ADC MTT Osvd
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.
