Modelling uncertainty in brain fibre orientation from diffusion-weighted magnetic resonance imaging
Diffusion-weighted magnetic resonance imaging (DW-MRI) permits in-vivo measurements of water diffusion, from which we can infer the orientation of white matter fibres in the brain. We show that by ordering the measurements, we can improve the reproducibility of the fibre-orientation estimate from partially-completed DW-MRI scans, without altering the complete data set. Tractography methods reconstruct entire fibre pathways from the local fibre-orientation estimates. Because the local fibre-orientation measurements are subject to uncertainty, the reconstructed fibre pathways are best described with a probabilistic algorithm. One way to estimate the connection probabilities is by defining a probability density function (PDF) in each voxel, and sampling from the PDF in a Monte-Carlo fashion. We propose new models of the PDF based on standard spherical statistical methods. The models improve previous work by closely modelling the dispersion of repeated noisy estimates of the fibre orientation. We compare a simple PDF (the Watson PDF) that models circular cluster of axes to a more general PDF (the Bingham PDF) that models circular or elliptical clusters of axes. We also propose models of the PDF in regions of crossing fibres, where there are two distinct fibre populations in the voxel. We validate the PDFs by comparing them to the uncertainty in fibre orientation calculated from bootstrap resampling of a repeated brain MR acquisition. We find mat the Bingham PDF produces connection probabilities that are closer to the bootstrap results man the Watson PDF. We use the new PDF models to perform a connectivity-based segmentation of the corpus callosum in eight different subjects. The results are similar to those of previous studies on corpus callosum connectivity, despite the use of finer cortical labelling, suggesting that the dominant connections from the corpus callosum project to the superior frontal gyrus, the superior parietal gyrus and the occipital gyrus.