Return-to-Axis Probability Calculation from Single-Shell Acquisitions

Abstract

The Ensemble Average diffusion Propagator (EAP) provides relevant microstructural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like the Diffusion Tensor. The direct estimation of the EAP requires a dense sampling of the ${\mathbf {q}}$-space data. Although alternative techniques have been proposed, all of them require a high number of gradients and several b-values to be calculated. Once the EAP is calculated scalar measures must be directly derived. In this work, we propose a method to drastically reduce the number of points needed for the estimation of one of the measures, the return-to-axis probability (RTAP), efficiently estimating the ${\mathbf {q}}$-space diffusion measure from a single shell acquisition. The proposal avoids the calculation of the EAP assuming that the diffusion does not depend on the radial direction. By applying this assumption locally, we achieve closed-form expressions of the measure using information from only one b-value, compatible with acquisitions protocols used for HARDI. Results have shown that the measures are highly correlated with the same measures calculated with state-of-the-art EAP estimators and highly accelerated execution times.