Mesh-based spherical deconvolution: A flexible approach to reconstruction of non-negative fiber orientation distributions

Diffusion-weighted MRI has enabled the imaging of white matter architecture in vivo. Fiber orientations have classically been assumed to lie along the major eigenvector of the diffusion tensor, but this approach has well-characterized shortcomings in voxels containing multiple fiber populations. Recently proposed methods for recovery of fiber orientation via spherical deconvolution utilize a spherical harmonics framework and are susceptible to noise, yielding physically-invalid results even when additional measures are taken to minimize such artifacts. In this work, we reformulate the spherical deconvolution problem onto a discrete spherical mesh. We demonstrate how this formulation enables the estimation of fiber orientation distributions which strictly satisfy the physical constraints of realness, symmetry, and non-negativity. Moreover, we analyze the influence of the flexible regularization parameters included in our formulation for tuning the smoothness of the resultant fiber orientation distribution (FOD). We show that the method is robust and reliable by reconstructing known crossing fiber anatomy in multiple subjects. Finally, we provide a software tool for computing the FOD using our new formulation in hopes of simplifying and encouraging the adoption of spherical deconvolution techniques.