A Predictive Network Model of Cerebral Cortical Connectivity Based on a Distance Rule

Abstract

SUMMARY Recent advances in neuroscience have engendered interest in large-scale brain networks. Using a consistent database of corticocortical connectivity, generated from hemisphere-wide, retrograde tracing experiments in the macaque, we analyzed interareal weights and distances to reveal an important organizational principle of brain connectivity. Using appropriate graph theoretical measures, we show that although very dense (66%), the interareal network has strong structural specificity. Connection weights exhibit a heavy-tailed lognormal distribution spanning five orders of magnitude and conform to a distance rule reflecting exponential decay with interareal separation. A single-parameter random graph model based on this rule predicts numerous features of the cortical network: (1) the existence of a network core and the distribution of cliques, (2) global and local binary properties, (3) global and local weight-based communication efficiencies modeled as network conductance, and (4) overall wire-length minimization. These findings underscore the importance of distance and weight-based heterogeneity in cortical architecture and processing.

The Brain in Space

“…This behavior is reminiscent of the rich-club behavior observed in low-density networks but, in fact, on our dense graph, the rich-club index is barely significant (demonstrated below). Thirdly, EDR graphs display local and global communication efficiencies (measured as network conductances; see Ercsey-Ravasz et al 2013) similar to those computed on our edge-complete graph G 29 Â 29 . We computed these efficiencies for our G 29 Â 29 and evaluated their evolution as a function of the removal of weak and strong edges, respectively.…”

“…The behavior observed was qualitatively similar to that obtained from EDR graphs but not CDR graphs. Fourthly, we found that the EDR model positions areas in a way that minimize total wire length whereas CDR graphs do not (Ercsey-Ravasz et al 2013). Thus, the EDR and the spatial positioning of the areas appear to represent two fundamental constraints on cortical connectivity.…”

“…The observed weight-distance relations are described by an EDR that accounts for a surprising number of characteristics of the cortical network (Ercsey-Ravasz et al 2013). First, given that the observed inter-areal distances are normally distributed, the EDR predicts that FLN will follow a log normal distribution.…”

“…We introduced a novel method to detect core-periphery structures in dense graphs based on a clique distribution analysis (Ercsey-Ravasz et al 2013). A clique is a subset of nodes that have all the possible connections between them.…”

Connectome Networks: From Cells to Systems

“…Numerous new (and mostly relatively weak) projections were uncovered, and the overall connectivity profile for each area was best approximated by a lognormal distribution (Markov et al 2011), with a few strong projections and a large admixture of medium or weak pathways. Graph analysis provided evidence for a relatively high proportion of unidirectional links (Markov et al 2014), a strong contribution of long-distance projections towards areal specificity (Markov et al 2013a), significant distance-dependence of connection densities (Ercsey-Ravasz et al 2013), and hierarchical arrangement of areas into "counter-streams" (Markov et al 2013b). Several of these characteristic topological features are also found in other mammalian species, e.g., the cat or rodent brain.…”