Topographical maps as complex networks

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Abstract
The neuronal networks in the mammalian cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of organization implies special demands on developing systems in order to achieve precise maps preserving spatial adjacencies, even at the expense of isometry. Although the object of intensive biological research, the elucidation of the main anatomic-functional purposes of the ubiquitous topographical connections in the mammalian brain remains an elusive issue. The present work reports on how recent results from complex network formalism can be used to quantify and model the effect of topographical connections between neuronal cells over the connectivity of the network. While the topographical mapping between two cortical modules is achieved by connecting nearest cells from each module, four kinds of network models are adopted for implementing intramodular connections, including random, preferential-attachment, short-range, and long-range networks. It is shown that, though spatially uniform and simple, topographical connections between modules can lead to major changes in the network properties in some specific cases, depending on intramodular connections schemes, fostering more effective intercommunication between the involved neuronal cells and modules. The possible implications of such effects on cortical operation are discussed.