Extracting quantitative measures from EAP: a small clinical study using BFOR

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents, and hence providing rich information about complex tissue microstructure properties. Bessel Fourier orientation reconstruction (BFOR) is one of several analytical, non-Cartesian EAP reconstruction schemes employing multiple shell acquisitions that have recently been proposed. Such modeling bases have not yet been fully exploited in the extraction of rotationally invariant q-space indices that describe the degree of diffusion anisotropy/restrictivity. Such quantitative measures include the zero-displacement probability (P(o)), mean squared displacement (MSD), q-space inverse variance (QIV), and generalized fractional anisotropy (GFA), and all are simply scalar features of the EAP. In this study, a general relationship between MSD and q-space diffusion signal is derived and an EAP-based definition of GFA is introduced. A significant part of the paper is dedicated to utilizing BFOR in a clinical dataset, comprised of 5 multiple sclerosis (MS) patients and 4 healthy controls, to estimate P(o), MSD, QIV, and GFA of corpus callosum, and specifically, to see if such indices can detect changes between normal appearing white matter (NAWM) and healthy white matter (WM). Although the sample size is small, this study is a proof of concept that can be extended to larger sample sizes in the future.