Demonstrate a PCA-based method for tract shape comparison and then, using that method, explore evidence of differences in tract shape in first episode psychosis.

Imaging: Subjects were imaged according to a 60 direction, 6 b0, b = 1200 s/mm², 2.4mm isotropic resolution protocol. Images were corrected for motion, eddy current and EPI distortions using the ExploreDTI software toolbox. Damped Richardson-Lucy deconvolution tractography was then performed with 1mm step size, 45^o/0.05 angular/fODF thresholds, 3mm isotropic seeding and [30 300]mm streamline length limits.

Shape Categorisation: Subject whole brain tractography results were (affinely, preserving shape but eliminating variance in position/orientation within the bore) normalised to a standard MNI template. Streamlines were then re-parameterised to 30 knot-points (spline interpolation), translated to the origin (center of mass subtraction) and reduced to a 1d feature vector through coordinate concatenation. PCA was then applied to determine principal modes of feature vector variation and, by extension, variation of streamline shape. Following decomposition of the feature vectors onto the first seven PCA eigenvectors (representing a set of streamline shape basis functions encapsulating ~98% of observed shape variation), the resultant weight vectors were clustered (k-means, k=800) and, for each subject, histograms of streamline cluster membership recorded.

“Whole brain” Tract Shape Categorisation: Each cluster represents a narrow subset of streamline shapes which, by definition, can only occur within an accordingly narrow subset (often only one) of white matter tracts. Importantly, however, those same white matter tracts, because of both inter-subject variations in morphology and the different paths streamlines might take within and individual tract, can be represented by more than one cluster. Examining changes in the fraction of streamlines assigned to each of the 800 clusters allows us to narrow down our search to tracts of interest.

Determining Specific Modes of Variation: The framework as described serves as a useful preliminary tool. However, while one could manually inspect each cluster and determine the shape changes required to force streamlines from one to the other (thus building up an understanding of cluster relationships and the factors behind the observed change), this is a difficult task and produces results that are potentially difficult to interpret. Instead, we segment the tracts, or portions of tract, highlighted by the above 'Whole Brain' characterisation and subject those to a more tailored shape analysis. As before, tracts are (rigidly) normalised and reduced to 1d feature vectors. Then, for each white matter tract, we conduct a separate PCA, generating a set of shape basis functions that are specific to tract in question. For each subject we then calculate the mean feature vector and, following basis decomposition, examine group differences. The advantage of using a tailored basis set is that the shape changes that drove any observed difference are easily understood by examining their effect on the (across subject) mean streamline.

Figure 1 demonstrates the results of conducting a series of 800 (unpaired) t-tests comparing the frequency of streamlines belonging to a given cluster across the two subject groups. Examining the contents of the most significant clusters (Figure 2), we observe streamlines belonging to the genu of the corpus callosum, corticospinal tract and anterior thalamic radiations, all of which have known associations with psychosis/schizophrenia^2,3,6,7, though only the corpus callosum result survives multiple comparison correction, indicating a significant increase in that form of fibre shape within the genu in first episode psychosis. Figure 3 demonstrates modes of variation derived through genu specific modelling which, following statistical analysis of projected mean shapes (Figure 4), indicates significant differences (post multiple comparison correction) in the 5^th mode of shape variation. This indicates a 'narrowing' of the mean shape in which the termination points in the right and left frontal lobe close inwards with a slight torsion that, were the ends to cross, would cause the right to pass slightly over the left.Using the proposed methods, and with no additional assumptions, we identified changes in the shape of genu of the corpus callosum – an area for which there is a great deal of evidence for links with psychosis/schizophrenia. Moreover, the indicated method of change – a narrowing and/or twist – is potentially consistent with developmental theories of schizophrenia that suggest reduced brain symmetry⁸ that may, if equivalent cortical connections are to be preserved, necessitate such deformations of the corpus callosum as the relative position/morphology of connected cortical regions is altered – an avenue of investigation that is the subject of ongoing work.