Why do atherosclerotic plaques only occur at specific sites in the arteries? Does the surface geometry of the brain affect the way waves move through the cortex? These questions and many others in the physiological sphere contain implicitly a real difficulty for modellers. How do we contend with the multiple scale lengths. Plaques are quite large compared to cells making up the vascular wall, waves in the brain (cortical spreading depression) move slowly but cover huge numbers of neocons and other cells. Our knowledge of single cell physiology is reasonably mature as is our knowledge of say how blood flows in the heart arteries. But how do we couple these phenomena together to understand the interaction of cells and large scale geometry.

The talk will present work done over the last two years on numerical models of coupled cells from both a discrete methodology to that of the use of homogenisation to produce reaction-diffusion equations simulating the complex dynamics that emerge from relatively simple reaction mechanisms. The talk will show results from simulating millions of smooth muscle and endothelial cells lining the bifurcation of a coronary artery requiring supercomputing resources (Blue Gene and IBM Power 6). In addition it will present the both 1D and 2D diffusion examples ranging from a simple linear coupling of cells to that imposed on a toroidal geometry showing the influence of curvature induced diffusion.