Constrained spherical deconvolution of nonspherically sampled diffusion MRI data

Constrained spherical deconvolution (CSD) of diffusion-weighted MRI (DW-MRI) is a popular analysis method that extracts the full white matter (WM) fiber orientation density function (fODF) in the living human brain, noninvasively. It assumes that the DW-MRI signal on the sphere can be represented as the spherical convolution of a single-fiber response function (RF) and the fODF, and recovers the fODF through the inverse operation. CSD approaches typically require that the DW-MRI data is sampled shell-wise, and estimate the RF in a purely spherical manner using spherical basis functions, such as spherical harmonics (SH), disregarding any radial dependencies. This precludes analysis of data acquired with nonspherical sampling schemes, for example, Cartesian sampling. Additionally, nonspherical sampling can also arise due to technical issues, for example, gradient nonlinearities, resulting in a spatially dependent bias of the apparent tissue densities and connectivity information. Here, we adopt a compact model for the RFs that also describes their radial dependency. We demonstrate that the proposed model can accurately predict the tissue response for a wide range of b-values. On shell-wise data, our approach provides fODFs and tissue densities indistinguishable from those estimated using SH. On Cartesian data, fODF estimates and apparent tissue densities are on par with those obtained from shell-wise data, significantly broadening the range of data sets that can be analyzed using CSD. In addition, gradient nonlinearities can be accounted for using the proposed model, resulting in much more accurate apparent tissue densities and connectivity metrics.