Graph analysis is frequently applied to assess whole-brain structural and functional network features. However, graph analysis may not be adequate for comparison of overall network characteristics between subjects or groups with different network sizes and edge densities [1]. Furthermore, graph analysis is hampered by the lack of an appropriate generic null model and a unifying framework. We therefore propose an alternative framework based on Bayesian generative modeling, which may overcome these limitations. We aimed to characterize 1) the relative contribution of local substructures underlying the anatomical whole-brain network topology and its changes across the human lifespan and 2) the impact of simulated lesions on these underlying structures.

We used standardized high quality, diffusion tensor imaging (DTI) and T1-weighted datasets from 382 healthy adults (age 20.2 to 86.2 years), freely available on http://biomedic.doc.ic.ac.uk/brain-development/. Subjects were scanned once at 1.5T (N = 205) or 3T (N = 177). DTI parameters: 15 diffusion-weighted images, b = 1000 s/mm², 2 b₀ images, 56 axial slices, 2.35-mm slice-thickness, 128 × 128 acquisition matrix, 1.75 × 1.75 mm voxels; repetition time (TR)/echo time (TE) 9.1 s/80 ms (at 1.5 T) or 11.9 s/51 ms (at 3T). Images were non-rigidly aligned to the Harvard-Oxford atlas (96 bilateral cortical network regions) after motion and b-matrix correction. Whole-brain tractography was executed from voxel seeds with fractional anisotropy > 0.2 using the interpolated streamline algorithm implementation (step size 0.5 mm, 70° maximum angle) (DTIStudio software). Tractography data were converted for each subject into a binary undirected network, with edges for regions with one or more connecting streamlines. Average networks were constructed for four age-categories (20-34, 35-50, 51-70 and >70 years). To investigate effects of plausible network injury, we simulated random and hub damage by eliminating 5-25% of total nodes or hubs (i.e. 5-25% of nodes with highest betweenness centrality), respectively.

Networks were fitted with a generative Bayesian exponential random graph model (based on a Markov chain Monte Carlo approach) [2]. The underlying assumption of these fits is that the topological structure of an observed network can be explained in terms of the relative prevalence of a set of overlapping local substructures. Our model included four substructures, based on previous literature [3], representing density, global efficiency, local clustering and topology (Figure 1A).

Networks were successfully generated by using the four local network parameters. Goodness-of-fit data demonstrated great overlap and fractional deviances between descriptive network parameters of simulated and real networks (Figure 2). Despite clear effects on network topologies across age and due to hub damage (Figure 1B), no significant changes were detected in relative contributions of substructures. Networks tended to be less dense and more clustered with increasing age and damage. Global efficiency tended to increase with age, whereas a decreasing trend was seen with increasing hub-damage.Although most trends were in line with previous literature, in contrast global efficiency tended to increase with age. Interestingly, this latter result is consistent with previous research using the same approach, which might indicate methodological reasons for increased global efficiency [3]. The effect of hub-damage on decreased global efficiency seems to increase across age, probably indicating that older people are more vulnerable to hub damage then younger people.Generative Bayesian exponential random graph models are applicable to moderate to large brain networks. Their use, potentially combined with other recent approaches such as minimum spanning tree or motif count [1], may shed new light on the complex organization and dynamics of neural networks in health and disease [1, 3].