Generative statistical models of white matter microstructure for MRI simulations in virtual tissue blocks

Leandro Beltrachini^{1} and Alejandro Frangi^{1}

We based our analysis in axonal structures only, which were considered as generalised cylinders, i.e. non-straight cylinders with arbitrary cross-sections [4]. To do so, we create random instances of their axes by means of a random walk algorithm based on a multivariate von Mises-Fisher distribution [5]. This allows to consider a global axonal direction (i.e. the direction from one end of the axon to the other) and a local axonal dispersion (needed for representing local changes in the direction, i.e. tortuosity). We model the global axonal direction (i.e. the overall orientation considering all the axons passing through the voxel) using either parametric (e.g. Watson) or an arbitrary orientation density function (ODF), the latter described by the corresponding spherical harmonic decomposition [8]. Such representation is flexible enough to account for voxels belonging to different parts of the WM. Once the axes are defined, we assign a mean radii value for each axon according to a gamma distribution [6].

Then, we model each axon as a B-spline generalised cylinder using swept surfaces over the simulated axes [4]. This is a general technique providing flexibility for further generation of surface and volumetric meshes needed for numerical simulations (e.g. [3, 7]). Once the cylinders are built, we pack them avoiding intersections by random placement. The procedure is repeated until reaching a specific volume ratio. All computations were performed in MATLAB 2015a programming environment (The Mathworks, Natick, MA).

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Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

2005