A Fourth Order Tensor Statistical Model for Diffusion Weighted MRI

In this communication, we propose an original statistical model for diffusion-weighted magnetic resonance imaging, in order to determine new biomarkers. Second order tensor (T2) modeling of Orientation Distribution Functions (ODFs) is popular and has benefited of specific statistical models, incorporating appropriate metrics. Nevertheless, the shortcomings of T2s, for example for the modeling of crossing fibers, are well identified. We consider here fourth order tensor (T4) models for ODFs, thus alleviating the T2 shortcomings. We propose an original metric in the T4 parameter space. This metric is incorporated in a nonlinear dimension reduction procedure. In the resulting reduced space, we represent the probability density of the two populations, normal and abnormal, by kernel density estimation with a Gaussian kernel, and propose a permutation test for the comparison of the two populations. Application of the proposed model on synthetic and real data is achieved. The relevance of the approach is shown.