Home Computer Science Computational Diffusion MRI: MICCAI Workshop, Athens, Greece, October 2016
Diffusion MR Model
We use a single restricted compartment of unknown orientation as a model for our phantoms. All microcapillaries (representing axons) are parallel and non-abutting cylinders, with equal radii and impermeable walls. The parameters of the model are (1) intrinsic diffusivity, Dj, (2) microcapillary diameter, a and (3) microcapillary direction, n.
The restricted diffusion signal, Sr, can be written as the product of components arising from displacements parallel, Sry, and perpendicular, Sr?, to the long axis of the microcapillary as described in . The model for Sr? is calculated using the Gaussian phase distribution approximation (GPD)  for a diffusion gradient perpendicular to the microcapillary with strength |G| sin в, where в is the angle between n and G. Sr|| describes free diffusion with Dj for a diffusion gradient parallel to the microcapillary with strength |G| cos в, and is calculated using Sr|| = exp(—b cos2 вDj/, where the b-value for trapezoidal OGSE is from .
The total signal accounting for both components (Sr|| and Sr?) is:
where So is the MR signal without diffusion weighting.
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