Abdol Aziz O. Ould Ismail^{1,2}, Ghoncheh Amouzandeh^{1,3}, and Samuel Colles Grant^{1,2}

Diffusion
tensor imaging (DTI) provides a unique contrast based on the restricted
directionality of water movement in an anisotropic environment. As such, DTI-based
tractography can be used to characterize and quantify the structural
connectivity within neural tissue. Here, structural connectivity within
isolated abdominal neural ganglia of *Aplysia
californica* (ABG) is assessed by integrating DTI and network theoretical
analysis. For ABG, findings demonstrate a default structural network with
preferential specific small-world properties when compared to simulated lattice
and random networks that are equivalent in order and degree.

Diffusion
data were acquired for ten samples (N = 10) at 11.75T using a 500-MHz widebore
vertical magnet operated by a Bruker Avance spectrometer (Bruker BioSpin Corp.,
Billerica MA). After localizing images, DTI was acquired with the following
acquisition parameters: Δ=21ms, δ=3ms, matrix = 100×100, TE = 30 ms, TR=2 s,
FOV=5x5 mm, and slice thickness = 150 μm. DTI data were collected over a total
acquisition time of 19.5 h using a multi-slice, diffusion-weighted 2D spin echo
sequence at a resolution of 50×50×150 µm (Fig.1 A-G). A total of 22 pulsed
field experiments were used to encode diffusion, including four equally
dispersed unweighted b_{0} images having an effective b value of 73 s/mm^{2}. The
nominal b value for the remaining 18 diffusion weighted scans was 1000 s/mm^{2}.
For tractography analysis using DSI Studio^{2}, 16 ROI-based nodes in each ganglion were used to
establish a track network with the following cutoffs and thresholds: Track
Counts = 10^{6}, FA threshold = 0.2 and Angular Threshold = 30°. The graph properties of experimental data were extracted using MATLAB
R2015b (Mathworks, Natick, MA) to obtain the clustering coefficients, local and
global efficiency, and characteristic path lengths of the binary matrices^{3}.

Experimental networks were compared to two Watts–Strogatz (WS) networks that were generated to include 16 local communities while maintaining the same rewiring probability as the experimental data. WS networks were assigned rewiring probabilities of 0 and 1 corresponding to lattice and random networks, respectively. In order to assess the intensity of the traffic through individual vertices in experimental data, the weighted clustering coefficient for each node was measured. Additionally, the centrality was investigated to define the most connected hubs in the selected ROIs. Finally, the graph properties reconstructed by the connectivity between nodes were assessed against the mean FA and ADC measurements for the ROIs as a function of the immediate geometrical node neighbors (the k number) for k=3, 5 and 8.

Significant
differences in FA measurements were found between the ganglion body and
branchial nerves (Fig. 2). The experimental networks exhibit small-world
properties when quantitatively evaluated using novel small world metric^{4} ω and
small worldness^{5} σ (Fig. 3). FA and ADC maps were obtained for the isolated
abdominal ganglia to investigate the correlations of these measurements with
the graph properties of their corresponding nodes. More critically, the lack of
significance between immediate geometric neighbors with respect to the weighted
clustering coefficient demonstrates the graph’s preference for more critical
hubs on the periphery of the ganglion that have a higher number of
interconnections within closed clusters even though there exists a lower
centrality (Fig. 4). This finding is supported by immunohistology, which
demonstrates a well-known higher distribution of large neurons in the periphery
of the ganglion with more axon density in central regions. The graph theory
here applied would suggest that the information circulated among these
peripheral hubs is critical for network robustness.

1. Ould Ismail, A. A. O, Amouzandeh, G., & Grant, S. C. 2016. Structural connectivity within neural ganglia: A default small-world network. Neuroscience 337: 276-284.

2. Yeh F, Verstynen TD, Wang Y, Fernández-Miranda JC, Tseng WI. 2013. Deterministic diffusion fiber tracking improved by quantitative anisotropy. PLoS One. 8(11): e80713.

3. Watts DJ, Strogatz SH. 1998. Collective dynamics of ‘small-world’ networks. Nature 393: 440-442.

4. Telesford QK, Joyce KE, Hayasaka S, Burdette JH, Laurienti PJ. 2011. The ubiquity of small-world networks. Brain Connectivity 1: pp. 367-375.

5. Humphries MD, Gurney K (2008) Network ‘small-world-ness’: a quantitative method for determining canonical network equivalence. PLoS One 3(4): e0002051.