Characterizing Complex White Matter Structure from Cube and Sphere Diffusion Imaging with a Multi-Fiber Model (CUSP- MFM)

Introduction. Multi-tensor models are of great interest for clinical applications because they enable the assessment of the white matter microstructure of individual fiber bundles in addition to the brain connectivity. In this work we propose a novel acquisition scheme and a novel fitting procedure for estimating the parameters of a multi-compartment model with two tensors and free water diffusion. Our acquisition scheme combines spherical and cubic sampling. It incorporates multiple non-zero b-values, necessary to fully estimate two-tensor models [1]. It enables high b-values to be acquired while achieving the same low TE as a single-shell HARDI scheme, and thus does not increase the geometric and intensity distortion. In conjunction with our acquisition scheme, which requires only short duration scans compatible with routine clinical use, our optimization algorithm incorporates a novel spatial regularization and ensures we fully estimate positive definite tensors, thus enabling the characterization of complex white matter microstructure. Our CUSP-MFM (CUbe+SPhere Multi-Fiber Model) is evaluated on both synthetic and clinical data. We demonstrate the ability of CUSP-MFM to characterize complex fiber structures from short duration acquisitions. Material and methods. Novel optimization for multi-fiber model (MFM). We consider in each voxel two anisotropic compartments representing two fiber bundles and one isotropic compartment modeling the diffusion of free water. We ensure the positive definite property of each tensor by parameterizing them in the log-Euclidean framework. We simultaneously estimate and regularize the multi-compartment model via a variational formulation, by minimizing: