Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution

Abstract

Diffusion-weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers. The diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel. However, this model has been shown to fail in regions containing several fiber populations with distinct orientations. A number of alternative models have been suggested, such as multiple tensor fitting, q-space, and Q-ball imaging. However, each of these has inherent limitations. In this study, we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion-weighted MR data without the need for prior assumptions regarding the number of fiber populations present. We assume that all white matter fiber bundles in the brain share identical diffusion characteristics, thus implicitly assigning any differences in diffusion anisotropy to partial volume effects. The diffusion-weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function (the diffusion-weighted attenuation profile for a typical fiber bundle) with the fiber orientation density function (ODF). The fiber ODF (the distribution of fiber orientations within the voxel) can therefore be obtained using spherical deconvolution. The properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1.5-T clinical scanner. The technique can recover the fiber ODF in regions of multiple fiber crossing and holds promise for applications such as tractography.