Highly accelerated graph theory implementations show benefits of finer cortical parcellations for group connectomic analyses

Greg D Parker^{1}, Mark Drakesmith^{1,2}, and Derek K Jones^{1,2}

**Imaging:**
Diffusion: 60 direction, 6 b0,
b=1200s/mm^{2}, 2.4mm isotropic resolution, twice refocused spin-echo
sequence. mcDESPOT^{2}:
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 template^{4})
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).

1. Rubinov M, and Sporns O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage. 2009;52(3):1059-1069

2. Deoni SCL, et al. Gleaning multicomponent T1 and T2 information from steady-state imaging data. Magnetic Resonance in Medicine. 2008;60(6):1372-1387.

3. Dell'Acqua F, et al. A modified damped Richardson-Lucy algorithm to reduce isotropic background effects in spherical deconvolution. Neuroimage. 2009;49(2):1446-48

4. Tzourio-Mazoyer N, et al. Automated anatomical labelling of activations in SPM using macroscopic anatomical parcellations of the MNI MRI single-subject brain. Neuroimage. 2002;15:273-2989

5. Leemans A, et al. ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data. Proc. ISMRM 17. 2009; abstract 3537

6. Drakesmith M, et al. Schizophrenia-Like Topological Changes in the Structural Connectome of Individuals With Subclinical Psychotic Experiences. Human Brain Mapping. 2015;36:2629-2643

Units: CPU processing time divided by GPU processing times for a
given number (x axis) of datapoints processed. (A) dRL fODF estimation
improvements. (B) Trilinear interpolation performance improvement.
(C) fODF peak finding (Newton-Raphson method) improvements.

Mean
strength. (A) p-values originating from unpaired t-tests. (B)
Binarisation of (A) where red indicates (uncorrected) p < 0.05. X
axis scale, N x 90 cortical parcellations. Y axis scale, N x 200k
streamlines.

Clustering
Coefficient. (A) p-values originating from unpaired t-tests. (B)
Binarisation of (A) where red indicates (uncorrected) p < 0.05. X
axis scale, N x 90 cortical parcellations. Y axis scale, N x 200k
streamlines.

Global Efficiency. (A) p-values originating from unpaired t-tests.
(B) Binarisation of (A) where red indicates (uncorrected) p <
0.05. X axis scale, N x 90 cortical parcellations. Y axis scale, N x
200k streamlines.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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