Small-world connectivity, motif composition, and complexity of fractal neuronal connections.

Connection patterns of the cerebral cortex consist of pathways linking neuronal populations across multiple levels of scale, from whole brain regions to local minicolumns. This nested interconnectivity suggests the hypothesis that cortical connections are arranged in fractal or self-similar patterns. We describe a simple procedure to generate fractal connection patterns that aim at capturing the potential self-similarity and hierarchical ordering of neuronal connections. We examine these connection patterns by calculating a broad range of structural measures, including small-world attributes and motif composition, as well as some global measures of functional connectivity, including complexity. As we vary fractal patterns by changing a critical control parameter, we find strongly correlated changes in several structural and functional measures, suggesting that they emerge together and are mutually linked. Measures obtained from some modeled fractal patterns closely resemble those of real neuroanatomical data sets, supporting the original hypothesis.