Non Parametric Approach for Axon Diameter Distribution Estimation from Diffusion Measurements

Introduction Diffusion imaging enables microscopic assessment of tissue structure by measuring the displacement of water molecules. Several models have been proposed to relate diffusion weighted MR signals and various structural features of the tissue. One recent model, the composite hindered and restricted model of diffusion (CHARMED), was shown to be able to extract white matter fiber orientation (even in areas with complex white matter architecture) . An extension of this framework (AxCaliber) provides an estimate of the axon diameter distribution of fascicles within white matter . This distribution is obtained by performing diffusion weighted MR experiments with multiple diffusion times and multiple diffusion weighting. Previously, it was assumed that the axon diameter distribution was given by a known parametric function, a γ-variate distribution. Yet this approach is problematic in diagnostic applications, and more generally, when one does not know the parametric form of the diameter distribution beforehand. In this work we have developed a non-parametric approach for estimating the axon diameter distribution, extending the range of applications of the AxCaliber framework.