Return-to-the-origin probability calculation in single shell acquisitions (ISMRM 2018)

Abstract: The ensamble average diffusion propagator (EAP) provides relevant microstructural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques. Due to the huge amount of samples needed for an accurate reconstruction of the EAP, more efficient alternative techniques have been proposed in the last decade. All of them require a high number of gradients and several b-values to be calculated. In order to use the EAP in practical studies, scalar measures must be directly derived, being the most common the return-to-origin probability (RTOP), the mean-squared displacement (MSD) and the return to plane and return to axis probabilities (RTPP, RTAP).

In this work, we propose an alternative method to estimate the return to axis probability (RTOP) from a single shell acquisition using a prior assumption over the diffusion signal. By applying that assumption locally, we achieve closed-form expressions of the measures using information from a only one b-value, compatible with acquisition protocols used for HARDI. Results have shown that the proposed method is highly correlated with the same measures calculated with state-of-the-art EPA estimators. In addition, due to the avoidance of EAP calculation, the execution times are highly accelerated.