A Bayesian random effects model for enhancing resolution in diffusion MRI

i u i |, , ~ ( , / ) ≠ 2 , that is, a normal distribution with mean ( i u ) given by the average of the neighbouring voxel values, and variance i u m w / 2 , where i and j are voxel labels, 2 u w is a scaling parameter and mi is the number of voxels adjacent to the ith voxel. A gamma distribution was assigned to the inverse of the normal variance. The set of neighbours included all those voxels with one or more corners in common with the ith voxel. The remaining parameters were assigned exchangeable prior distributions. Posterior distributions were sampled using Markov chain Monte Carlo (MCMC) implemented in WinBUGS/GeoBUGS (5) together with the WinBUGS development interface (6). Results The figure shows the results obtained for one of the three subjects in the region of the junction between the cingulum and corpus callosum. Similar results were obtained in the other subjects. The lower half of the figure shows an array of vector cluster plots, as obtained when the signal intensity data were modelled at the resolution provided by the native dMRI data. The upper half of the figure shows the corresponding results generated by modelling the signal intensity data in each voxel as a mixture of signals from 3 vertically resolved sub-voxels. The analysis was performed on a native 5-by-5 ROI, a 3-by-5 portion of which is shown in the figure. At the native resolution the boundary between the cingulum and corpus callosum gives rise to a row of crossing fibres. A largely successful separation of the two structures has been achieved by using the latent variables random effects model. In particular, the row of voxels at the junction between the two structures is partitioned into a single row of subvoxels assigned to the corpus callosum and two rows assigned to the cingulum. The resulting pattern of subvoxel fibre orientations is entirely consistent with the underlying white matter structure at the junction between the cingulum and corpus callosum. Discussion Spatial resolution is a limiting factor in diffusion tractography and other dMRI applications. The concept that an increase in resolution can be achieved through post-acquisition data processing has been investigated previously (7- 9), motivated by the need for methods that can deal with bending, fanning and partial volume problems that occur due to poor spatial resolution. The results presented here show that the Bayesian random effects model provides a plausible separation of components at the subvoxel level, despite the relatively low information content of the 20-directions dMRI data and moderate b-value (1000 s mm -2 ) used in this study. In particular, the model has the potential to offer a solution to the crossing fibre problem that arises due to partial volume effects.