Structural Determinants of Functional Brain Dynamics

Neural connections of the mammalian cerebral cortex exhibit specific patterns ranging in scale from interconnections linking whole brain regions to intra-areal patterns of connections between cell populations or individual cortical neurons (Cajal, 1909; Brodmann, 1909; Zeki, 1993; Salin and Bullier, 1995; Swanson, 2003). Detailed anatomical and physiological studies have revealed many of the basic components and interconnections of cortical microcircuitry (Douglas and Martin, 1991), and of their arrangement into columns and minicolumns (Mountcastle, 1978; 1997). Columns and other localized populations of neurons maintain connections within and between brain regions, constituting large-scale patterns of anatomical connectivity. While the large-scale networks of human cortex remain largely unmapped (Sporns et al., 2005), comprehensive descriptions of anatomical patterns of cortical connectivity have been collated for several other mammalian species (e.g. Felleman and Van Essen, 1991; Scannell et al., 1999). Closer analysis has revealed that these patterns are neither completely regular nor completely random, but combine structural aspects of both of these extremes (reviewed in Sporns et al., 2004). This basic insight has sparked significant interest in characterizing the structure of brain networks, using methods that are also applied in parallel efforts to map and describe other biological networks, e.g. those of cellular metabolism, gene regulation, or ecology. This chapter is intended as an overview of recent quantitative approaches to brain networks (see also Sporns, 2005), with an emphasis on theoretical and computational studies that inform us about the structural features that determine functional brain dynamics.