Spatially Regularized Reconstruction of Fibre Orientation Distributions in the Presence of Isotropic Diffusion
The connectivity and structural integrity of the white matter of the brain is nowadays known to be implicated into a wide range of brain-related diseases and injuries. However, it was not before the advent of diffusion magnetic resonance imaging (dMRI) that researchers have been able to probe the miscrostructure of white matter in vivo.
Presently, among a range of various methods of dMRI, high angular resolution diffusion imaging (HARDI) is known to excel in its ability to provide reliable information about the local orientations of neural fasciculi (aka fibre tracts). It preserves the high angular resolution property of diffusion spectrum imaging (DSI) but requires fewer measurements. Meanwhile, as opposed to the more traditional diffusion tensor imaging (DTI), HARDI is capable of distinguishing the orientations of multiple fibres passing through a given spatial voxel.
Unfortunately, the ability of HARDI to discriminate neural fibres that cross each other at acute angles is always limited. The limitation becomes the motivation to develop numerous post-processing tools, aiming at the improvement of the angular resolution of HARDI. Among all methods, spherical deconvolution (SD) is the shining one which attracts more and more attentions. Due to its ill-posed nature, however, SD standardly relies on a number of a priori assumptions which are to render its results unique and stable.
In this work, we propose a novel approach to the problem of SD in HARDI, which accounts for the spatial continuity of neural fibres as well as the presence of piece-wise smooth isotropic diffusion.
Subsequently, we demonstrate how the proposed solution can be used to successfully overcome the effect of partial voluming, while preserving the spatially coherency of cerebral diffusion at moderate-to-severe noise levels. In a series of both in silico and in vivo experiments, the performance of the proposed method is compared with that of several available alternatives, with the comparative results clearly supporting the viability and usefulness of our approach. Moreover, the results reveal and prove the power of applied spatial regularization terms.