(217f) Coarse-Graining of Heterogeneous Neural Dynamics

In biology, the structure of networks plays an important role in the resulting dynamics both intracellularly and in the interactions between cells, especially in the nervous system. The realism of simulations of large networks of neurons can be enhanced by introducing cell heterogeneity: neurons are characterized by different values of physiological parameters, as well as by different connectivities in the network. In this case, we find that the (evolving) system state often quickly becomes a smooth function of these parameters. We make use of this phenomenon to express the system state through a significantly reduced number of variables, allowing for acceleration of several computational tasks.

The problem of coarse-graining a large heterogeneous network of neurons thus becomes that of finding the appropriate basis functions (the appropriate "observables") given the (multidimensional) distribution of the parameters. We use nonparameteric techniques to generate such basis function sets which are orthogonal with respect to arbitrary multidimensional parameter spaces. For high-dimensional spaces of heterogeneous parameters, we use analysis of variance (ANOVA) as an alternative coarsening technique.

With a coarse description, we show how to accelerate tasks such as finding coherent steady states and synchronized limit cycles. We demonstrate applications of these techniques both for networks of simple coupled oscillators, and for a much more complicated simulation of circadian dynamics in the suprachiasmatic nucleus of the mammal hypothalamus.