Anisotropic Molecules diffuse more freely along one direction Isotropic Molecules diffuse

equally in all directions Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves... Brownian Motion 1827 Pollen MOVES!?

Water molecules are in constant thermal agitation

Diffusion is an essential physical process for the functioning of living systems. "De Rerum Natura" Lucretius 60BC In DW MRI we look at the mean displacement of water molecules within each voxel (what is a voxel?!)

Diffusion is affected by tissue microstructures!

Displacement of molecules is reduced and compared to their mean displacement in free water Diffusion Weighted MRI Apparent Diffusion Coefficient A bit of history.. “Einstein’s diffusion equation” 1905

Squared displacement is proportional to time

In an homogeneous, barrier-free medium, the distribution of displacement takes a Gaussian form with the peak at zero displacement and the same probability of displacing a given distance from the origin. > ADC

< signal < ADC

> signal Tensor The tensor is a 3D model of the diffusion in each voxel.

Eigenvectors - Direction of the major axes

Eigenvalues - Magnitude of the displacements along the axes

The principal axis of the ellipsoid is oriented towards

the direction with highest diffusion. Diffusion Imaging Einstein 1905 The end?? How do we measure diffusion? Eigenvector Eigenvalue magniture of the tensor as a whole Variance of the eigenvalues from the mean Fractional Anisotropy

(Fraction of the tensor that can be assigned to anisotropic diffusion) Deterministic - TrackVis Tractography

Use local diffusion orientation at each voxel to determine pathway between distant brain regions. Infer major trajectory of WM pathways by following a path from one voxel to the other.

+ non invasive - low resolution (large bundles)

+ whole brain - indirect (diffusion paths)

- error prone (MR noisy) Probabilistic - FMRIB's Diffusion Toolbox (FDT) > Use the major axis of the DTI ellipsoid as a fibre orientation estimate. A single pathway propagates from a seedpoint by moving in a direction that is parallel to the main eigenvector.

(ONE ORIENTATION FOR EACH VOXEL)

- Only one trajectory per voxel

- No confidence/uncertainty of trajectory Many pathway s are propagated from a seedpoint. The direction of the pathway in each voxel is the result of distributions of probable orientations.

(DISTRIBUTION OF ORIENTATIONS AT EACH VOXEL)

> Repeat an acquisition many times and repeat streamline tracking. Due to uncertainty in v1, curves will not perfectly overlap

> Create a map that shows the degree of overlap across the trials. + Uncertainty of the measurement (noise, incomplete modelling of diffusion signal, )

+ Multiple trajectory per voxel

-Accumulated error problem (uncertainty (error) accumulates along the tract) - false positives Uncertainty in orientation of principal eigenvector

in repepated scans (Jones at al 2002) ......but already pretty beautiful Still a lot to do... http://www.fmrib.ox.ac.uk/analysis/research/fdt/ http://trackvis.org/ Assumption: The direction of maximum diffusivity (in anisotropic voxels) is an estimate of the major fibre orientation DWI: what cause anisotropy? The axonal membrane is the main determinant of anisotropy Beaulieu C et al., 2001, NMR in Biomedicine Clinical relevance!

Pre surgical Tractography

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# Diffusion Tensor Imaging of the brain

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