Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?

Abstract

We present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations. Using automatic relevance determination, we are able to perform online selection of the number of fibre orientations supported by the data at each voxel, simplifying the problem of tracking in a multi-orientation field. We then apply the identical probabilistic algorithm to tractography in the multi- and single-fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single-fibre tractography. We show that multi-fibre tractography offers significant advantages in sensitivity when tracking non-dominant fibre populations, but does not dramatically change tractography results for the dominant pathways.

Figure 1

(a) Marginal posterior distribution on μ for true model averaging (red), and ARD approximation (black). (b) Effective prior distribution given by standard Gaussian ARD (red), and range-limited Beta ARD (black) in the range [0 1]

Figure 2

Probabilistic multi-orientation fitting a) Axial slice showing regions where more than a single orientation were supported (thresholded at f_i 0.5 after ARD-based estimation). b) and c) axial and sagittal close ups of crossing fibre bundles with dominant fibre orientation in red and second in blue. Directions shown are the mean vectors of the posterior distribution samples. d) Samples from the posterior distributions on the first two fibre orientation in a voxel (green dot in a)) where the lateral motor projections (red) cross the longitudinal SLF projections (blue). The right hand-side is a 90° rotation of the left

Figure 3

Thalamic parcellation with single fibre (a) and crossing-fibre (b) tractography. Key to cortical projections is as follows. Prefrontal cortex in burgundy, premotor cortex in red, primary motor cortex in light blue, primary sensory cortex in dark blue, posterior parietal cortex in orange, occipital cortex in mid-blue and temporal cortex in yellow.

Figure 4

Tracking the cortico-spinal tract from the internal capsule to the primary motor cortex with single fibre (left) and multi-fibre (right) tractography. A coronal maximum intensity projection is shown. Voxels are colour coded from 25 (red) to 200 (yellow) samples passing through the voxel. Single fibre results are shown as the leftmost nine (3x3) subjects, and multi-fibre results are the rightmost nine subjects. Each subject is displayed in the same location in the two grids.

Figure 5

Tracking of the Parietal-Premotor connections of the medial portion of the superior longitudinal fasciculus in nine subjects with single fibre (3x3 on left) and multi-fibre (3x3 on right) tractography. A sagittal maximum intensity projection is shown. Voxels are colour coded from 25 (red) to 200 (yellow) samples passing through the voxel. Note that the single fibre tractography was not able to find any connections that reached the target in any subject.

Figure 6

Tracking of the acoustic radiations between medial geniculate nucleus of thalamus and primary auditary cortex with single fibre (left) and multi-fibre (right) tractography. An axial maximum intensity projection is shown. Voxels are colour coded from 10 (red) to 50 (yellow) samples passing through the voxel. Note that the single fibre tractography was not able to find any connections that reached the target in any subject.

Figure 7

Tracking the projection from the sub-genual white matter to amygdala using single fibre (left) and multi-fibre (right) tractography. An coronal maximum intensity projection is shown. Voxels are colour coded from 10 (red) to 100 (yellow) samples passing through the voxel.

Figure 8

Simulations of two crossing fibres with different number of diffusion encoding orientations (main x-axis), SNR (main y-axis), b-values (individual x-axes), and separation angle (individual y-axes). Simluations were repeated 5 times. Greyscale shows the average number of fibres recovered by the estimation technique.

Figure 9

Simulations of three fibres crossing at 90° with different number of diffusion encoding orientations (main x-axis), b-values (individual x-axes),and SNR (individual y-axes). Simluations were repeated 5 times. Greyscale shows the average number of fibres recovered by the estimation technique.