The self-diffusion of water molecules in the brain is a sensitive probe of biological tissue microstructure and micro-biophysics. Amongst the tissue properties which contribute to the local diffusion characteristics is the local orientational structure of the tissue; most interestingly, diffusion is anisotropic in white matter, being greater in the direction of white matter tracts. By sensitising the magnitude of the NMR spin-echo to local diffusion and by making assumptions about the structure of local diffusion it is possible to recover the dominant orientation of diffusion in each MR imaging voxel [12], known as the principal diffusion direction (PDD). Under the assumption that these PDDs correspond well with the mean local fibre orientation in white matter voxels, it has been possible to trace pathways through the vector field of PDDs to reconstruct major white matter pathways in the living human brain [37]. However, the sensitivity of this ``diffusion tractography'' process to, for example, image noise, partial volume effects and incomplete signal modelling has meant that, in general, tractography has been limited to major white matter pathways which are easily found in post-mortem dissection. Furthermore, the deterministic nature of tractography approaches to date have meant that the descriptions of the estimated fibre trajectories have been entirely qualitative. With no measure of either confidence in or strength of the recovered connections, the interpretation of the trajectories as true fibre pathways has been limited and it has not been possible to compare results between subjects in a quantitative fashion.
Research at FMRIB has concentrated on developing a statistical framework in which to address the tractography problem. By considering the fitting of voxel-wise models of diffusion in the presence of image noise and incomplete signal modelling we are able to construct probability density functions (pdfs) on the voxelwise PDD (local mean fibre orientation) [7]. With these local pdfs on fibre direction it is no longer sensible to perform tractography by tracing deterministic pathways through the data field. Instead, we have developed a generalisation of diffusion tractography to the case where there is uncertainty in local fibre orientation [7]. We estimate a pdf on the location of the fibre trajectory (a connectivity distribution). We are able to quantify our belief in the location of the pathway and hence quantify our belief in the existence of axonal connections between brain regions. By removing the need to make a deterministic decision at every step in the tractography process, we are able to trace beyond regions of low diffusion anisotropy and deep into grey matter structures (see fig. 10a) [8]. This methodology has been implemented as FDT (FMRIB's Diffusion Toolbox).
The availability of such a rich source of connectivity information has allowed us to address new questions with diffusion tractography. It is possible, by examining connectivity patterns derived from diffusion tractography, to identify functionally distinct subunits in the brain. For example, by generating connectivity distributions from every voxel in thalamus we have been able to compute the probability of connection from every thalamic voxel to each of seven predefined cortical zones. We have used this information to segment thalamus into putative thalamic nuclei on the basis of connectivity information alone [8] (fig. 10b,c). These connectivity-defined regions form the basis of an atlas of thalamo-cortical connectivity (www.fmrib.ox.ac.uk/connect) which we have used to provide the first functional/anatomical validation of diffusion tractography [26]. For example, in fig. 10d, the thalamic region defined by a high probability of connection with prefrontal cortex corresponds well with the location of previously reported (FMRI/PET) activation centres in executive memory tasks.
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