The use of the null distribution to determine the statistical significance of connections observed using probabilistic fibre tracking

Probabilistic tractography methods that use Monte Carlo sampling of voxelwise fibre orientation probabilitydensity functions suffer from distance-related artefacts due to the propagation of uncertainty along the tractpath. These are manifested as a preferential weighting of regions close to the tracking start point at theexpense of more distant regions — an effect that can mask genuine anatomical connections. We propose amethodology based on comparison of the conventional connection probability map with a null connectionmap that defines the distribution of connections expected by a random tracking process and that isdominated by the same distance effects. When the connection probability is significantly greater than theresult of the null tracking result this identifies voxels where the diffusion information is providing moreevidence of connection than that expected from random tracking. We show that the null connectionprobability map used is governed by Poisson statistics within each voxel, allowing analytical estimation ofconnection values that are significantly different to the null connection values. The resultant significantconnection maps can be combined with the conventional probabilistic tractography output to produce mapsof significant connections which reduce distance-related artefacts by removing areas where the observedfrequency of connection is dominated simply by distance effects and not the diffusion information. This isachieved by applying an objective statistical interpretation of observed patterns of connection which cannotbe achieved by simple thresholding of conventional probabilistic tractography maps due to the distanceeffect.