Why multiple b-values are required for multi-tensor models. evaluation with a constrained log-euclidean model

Multi-tensor models have been proposed to assess multiple fiber orientations but are known to be numerically challenging. We show that the estimation cannot be performed with a single-shell HARDI acquisition because the fitting procedure leads to an infinite number of solutions ; multiple-shell HARDI acquisitions are required. Additionally, we propose a new log-euclidean constrained two-tensor model capable of assessing crossing fibers configurations with a relative limited number of DW acquisitions. We provide numerical experiments with this model to verify experimentally the necessity of multiple-shell HARDI acquisitions schemes for multitensor models.