Explore the effects of varying both streamline and parcellation densities on the group wise separability of graph theoretical metrics using, as an example dataset, a cohort (n=30) of subjects with first episode psychotic experiences compared to 30 age/sex matched controls.

Imaging: Diffusion: 60 direction, 6 b0, b=1200s/mm², 2.4mm isotropic resolution, twice refocused spin-echo sequence. mcDESPOT²: SPGR images acquired at TE=2.1ms, TR=4.7ms, flip angles = [3, 4, 5,6,7,9, 13, 18] degrees; bSSFP acquititions at TE=1.6ms, TR=3.2ms, flip angles = [10.6, 14.1, 18.5, 23.8, 29.1, 35.3, 40, 60] degrees. bSSFP acquisitions were repeated with and without 180 RF phase alteration to remove SSFP banding artefacts and SPGR and IRSPGE acquisitions were used to correct B0 and B1-induced myelin water fraction errors. All data were acquired on a GE 3T Signal HDx system.

Tractography: Damped Richardson-Lucy (dRL)³ deconvolution based tractography was performed with 45^o/0.05 angular/fODF magnitude thresholds and 0.5mm step size. Seed points were randomly generated until 1 million streamlines were produced (according to previous criteria) within a 30mm to 300mm length range. Matrix operations, e.g. those required for dRL fibre orientation density function estimation (fODF) were re-implemented using the CUBLAS software library (NVidia, Santa Clara, California, USA), while other operations, e.g. trilinear interpolation were achieved using in-house CUDA implementations.

Graph Construction\Measurements: Cortical parcellation templates ranging from 180 to 1080 parcellations (at 90 parcellation intervals calculated by successive subdividing the AAL template⁴) were non-linearly co-registered to each subject. Weighted graphs were then generated using randomly selected samples of 200 thousand to 1 million streamlines (at 200 thousand streamline intervals) at each parcellation step, creating 55 possible streamline/parcellation density combinations. Edge weights were defined as the mean parameter value integrated along streamline segments connecting the relevant node pair. Weighting parameters were fractional anisotropy (FA), mean diffusivity (MD), myelin water fraction (MWF), quantitative T1, R1 (1/T1) and binarized streamline count. Graph metrics considered were mean strength (or degree for binarized streamline strength), global efficiency and clustering coefficient. For these operations significant use was made of CUDA atomic operations that, through intelligent memory management, reduce complications related to parallelised graph construction (i.e. race conditions).

Figure 1 shows example of the scale of speed increases achieved through switching key components of the tractography algorithm to CUDA based implementations. Note, for example, significant improvements in fODF calculation speed – a matrix based operation to which GP-GPU technology is ideally suited. For reference tested hardware was a single Nvidia GTX Titan Black vs. Intel E5-2603, with multi-threaded CPU implementations written in MATLAB/MEX C adapted from ExploreDTI software toolkit⁵). Figures 2, 3 and 4 display, respectively, p-value maps (individual values obtained through unpaired t-tests) for mean strength, clustering coefficient and global efficiency metrics.Our results indicate significant (patient vs. control) reductions in mean connection strength (FA, T1 and binary), FA-weighted global efficiency and FA-weighted mean clustering coefficient; all of which are consistent with previous observations linking psychotic experiences/schizophrenia to reduced global connectivity⁶. Patterns in the significance across these weighting parameter/graph metric combinations reveal interesting trends. Firstly, increasing streamline density reduces separability. While this may at first seem counter-intuitive, we must consider that the initial 200k streamline density is already high and, as such, it is unlikely that under sampling artefacts are occurring. Increasing the number of streamlines beyond this point, therefore, only increases the probability of observing artefactual (false positive) connections and, as those connections then increasingly obscure the true connectome, reduces group separability. The second variable, cortical parcellation density, has more nuanced effects. Trends in global efficiency and mean strength indicate increased separation with increased parcellation density, whereas clustering coefficient varies by weighting parameter; FA-weighted graphs (the only measure reaching significance), for example, provideoptimal separability between 360 and 630 parcellations while MWF-weighted graphs provide most separability at lower parcellation numbers.While increasing streamline densities has little effect, it is perhaps unsurprising that reducing the size of cortical parcellations below that of the standard AAL template can begin to yield more informative differences in connectivity since, as many FMRI studies have shown, cortical activity is generally more localised than the large regions defined by the AAL template. With improving computational techniques, such as GP-GPU technology, the (computational) convenience afforded by “big” region templates is no longer required. Thus, for future work (and even re-examination of existing null results in the literature), there is little reason not to consider a denser cortical parcellation, or a range of parcellations, when searching for differences in structural connectomes.