Apparent Propagator Anisotropy from reduced Diffusion MRI acquisitions

The Propagator Anisotropy (PA) is a measurement of the orientational variability inside a tissue estimated from diffusion MRI using the Ensemble Average diffusion Propagator (EAP). It is based on the quantification of the angular difference between the propagator in a specific voxel and its isotropic counterpart. The PA has shown the ability to reveal microstructural information of interest and meaningful descriptive maps inside the white matter. However, the use of PA is not generalized among the clinical community, due to the great amount of data needed for its calculation, together with the associated long processing times. In order to calculate the PA, the EAP must also be properly estimated. This task would require a dense sampling of the Cartesian q-space. Alternatively, more efficient techniques have been proposed in the last decade. Even so, all of them imply acquiring a large number of diffusion gradients with different b-values and long processing times.In this work, we propose an alternative implementation to drastically reduce the number of samples needed, as well as boosting the estimation procedure. We avoid the calculation of the whole EAP by assuming that the diffusion anisotropy is roughly independent from the radial direction. With such an assumption, we achieve a closed-form expression for a measure similar to the PA but using information from one single shell: the Apparent Propagator Anisotropy (APA). The new measure remains compatible with standard acquisition protocols commonly used for HARDI (based on just one b-value). The intention of the APA is not to exactly replicate the PA but inferring microstructural information with comparable discrimination power as the PA but using a reduced amount of data.We report extensive results showing that the proposed measures present a robust behavior in clinical studies and they are computationally efficient and robust when compared with PA and other anisotropy measures.