Hierarchy, Fractality, Small-World and Resilience of Haversian Bone Structure: A Complex Network Study

This article describes the application of recently introduced complex networks concepts and methods to the characterization and analysis of cortical bone structure. Three-dimensional reconstructions of the system of channels underlying bone structure are obtained by using histological and computer graphics methods and then represented in terms of complex networks. Confluences of two or more channels are represented as nodes, while the interconnecting channels are expressed as edges. The hierarchical backbone (the tree with maximum depth) of such a network is obtained and understood to correspond to the main structure underlying the channel system. The remainder of the network is shown to correspond to geographical communities, suggesting that the bone channel structure involves a number of regular communities appended along the hierarchical backbone. It is shown that such additional edges play a crucial role in enhancing the network resilience and in reducing the shortest paths in both topology and geometry.The recently introduced concept of fractal dimension of a network (cond-mat/0503078) is then correlated with the resilience of the several components of the bone channel structure to obstruction and failure, with important implications for the understanding of the organization and robustness of cortical bone structure.