Abstract #4408

# General tools for diffusion tensor distributions, and matrix-variate Gamma approximation for multidimensional diffusion MRI data

Alexis Reymbaut1,2
1Physical Chemistry, Lund University, Lund, Sweden, 2Random Walk Imaging AB, Lund, Sweden

Either on the voxel scale or within sub-voxel diffusion compartments, tissue microstructure can be described using a diffusion tensor distribution $$\mathcal{P}(\mathbf{D})$$$. One way to resolve microstructural heterogeneity relies on choosing a plausible parametric functional form to approximate $$\mathcal{P}(\mathbf{D})$$$. However, such a high-dimensional mathematical object is usually intractable. Here, we define matrix moments enabling the computation of diffusion metrics for any arbitrary functional choice approximating $$\mathcal{P}(\mathbf{D})$$\$. Applying these general tools to the matrix-variate Gamma distribution on the voxel scale, we obtain a new signal representation, the matrix-variate Gamma approximation, that we validate in vivo and in silico.

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