Can AxCaliber be extended to estimate axonal radius and orientation at the same time?

Introduction One of the key ideas behind diffusion tensor (DT) imaging that explains its wide applicability, is the assumption that the diffusion of water molecules in live tissues, both inside and outside cells, is hindered in an anisotropic manner by the presence of membranes, and that mean displacement scales with square root of time. This assumption is obviously a simplification: diffusion is restricted by impermeable barriers [1] and the simple scaling doesn't hold in general. This limitation of DT can actually be used as a sign of the presence of finite scales in the tissue. Several models have been recently proposed that combine hindered and restricted diffusion and can measure direct axonal features such as density and diameter [2,3]. In particular, AxCaliber proposes a white-matter model made up of two compartments: (i) extracellular space where diffusion is hindered, and (ii) intracellular space where diffusion is restricted inside a population of impermeable cylinders of different diameters as described in [1]. AxCaliber requires previous knowledge of the axon orientation and assumes a Gamma distribution for the radii. In this work we extend AxCaliber in a non-parametric way, using a population of axons of different radii and orientations. Instead of using the computationally demanding Markov Chain Monte Carlo, we posed the estimation problem as a standard Quadratic Program, that can always be solved by fast and reliable algorithms. The feasibility of recovering multiple radii and orientations from noisy MR data is assessed using simulations.