Efficient models of cortical activity via local dynamic equilibria and coarse-grained interactions.

Biologically detailed models of brain circuitry are challenging to build and simulate due to the large number of neurons, their complex interactions, and the many unknown physiological parameters. Simplified mathematical models are more tractable, but harder to evaluate when too far removed from neuroanatomy/physiology. We propose that a multiscale model, coarse-grained (CG) while preserving local biological details, offers the best balance between biological realism and computability. This paper presents such a model. Generally, CG models focus on the interaction between groups of neurons-here termed "pixels"-rather than individual cells. In our case, dynamics are alternately updated at intra- and interpixel scales, with one informing the other, until convergence to equilibrium is achieved on both scales. An innovation is how we exploit the underlying biology: Taking advantage of the similarity in local anatomical structures across large regions of the cortex, we model intrapixel dynamics as a single dynamical system driven by "external" inputs. These inputs vary with events external to the pixel, but their ranges can be estimated