Spatial Characterisation of Fibre Response Functions for Spherical Deconvolution in Multiple Sclerosis

Brain tractography based on diffusion-weighted (DW) MRI data has been increasingly used to investigate crucial pathophysiological aspects of several neurological conditions, including multiple sclerosis (MS). The advent of fibre tracking methods based on constrained spherical deconvolution (CSD), which recovers the fibre orientation distribution function (fODF) by performing a single-kernel (or uniform-kernel) deconvolution of the measured DW signals with non-negativity constraints, has meant an important breakthrough. However, it is unclear whether using a uniform kernel deconvolution of the measured DW signals for the whole brain is appropriate, especially in pathology. In this study, our main aim was to explore the validity of using a uniform fibre kernel for spherical deconvolution in a cohort of 19 patients with a first inflammatory-demyelinating attack of the central nervous system suggestive of MS and 12 age-matched healthy controls. In particular, considering that the number of peaks is a key feature the fODF and is known to impact directly on downstream fibre tracking, we assessed the association between patient-wise mean number of (fODF) peaks in the non-lesional white matter obtained with a uniform kernel and the bias or differences in the estimation of local diffusion properties when a uniform kernel (instead of a locally-fitted voxel-wise kernel) was used. Finally, in order to support our in-vivo results, we performed a simulation analysis to further assess the theoretical impact of using a uniform kernel. Our in-vivo results showed non-significant trends towards an influence of the bias in the estimation of the local diffusion properties when a uniform kernel was used on the number of peaks. In the simulation analysis, a clear association was observed between such bias and the number of peaks. All this suggests that the use of a uniform kernel to estimate the fODFs at the voxel level may not be adequate. However, we acknowledge that the approach followed here has some limitations, mainly derived from the methods used to estimate the voxel-wise local diffusion properties. Further investigations using larger in-vivo data sets and performing more comprehensive simulation analyses are therefore warranted.