Analysis of Complex Networks

10.3 Functional Dynamics

The previous section looked at changes in network topology but as an information processing system the brain also shows functional changes regarding the activity levels of nodes and to information transfer and processing. We now look how activity spreads in neural systems starting with simple systems that exhibit local neighborhood but no global long-distance connections.

10.3.1 Spreading in Excitable Media

In some cases, a network may be more simply connected than described for neural systems in that only direct spatial neighbors are connected as in lattice or regular networks. A simple model for activation spreading is that of excitable media where waves can propagate but cannot pass another wave until a certain amount of time (the refractory time) has passed. Such a model can be implemented using either partial differential equations or cellular automata.

One example of excitable media studies in neuroscience is the phenomenon of spreading depression over the cortical surface. Whereas most models only study a flat two-dimensional surface [67], some models start to take into account the three-dimensional folding structure of the cortex and the mapping of area function [19].

An earlier field, and in fact the first application of excitable media [73], was the study of spreading activation in cardiac tissue. For cardiac tissue, muscle cells are linked by electric synapses (gap junctions) so that changes in the internal cellular potential can quickly spread ...