The Simplification of Biological Models using Voronoi Tiling of the Phase Plane

A novel approach to simplifying biological models has been suggested by Hetherington and Saffrey, involving a Voronoi tiling of the phase plane, then following the flow vector (dx/dt dy/dt, where x and y are the variables undergoing phase plane analysis), to create a directed graph of nodes within the phase plane. Closed loops of the graph will correspond to stable limit cycles. In this way a complicated model may be more simply expressed as the traversal of a set of states in the phase plane of the model. This essay discusses the results of this process as applied to the Morris-Lecar model and a hepatocyte calcium oscillation model, and finds that the phase plane patterns generated by the algorithm closely resemble those found in the literature (obtained by numerical integration methods). The generation of bifurcation diagrams requires a little more tuning to increase reliability, however overall the algorithm seems to work well for the models described.