Intercellular communication via gap junctions between arterial cells plays an important role in coordinating the events in neighborhood cells. This can form the basis of the transmission of signals in an organized cluster of cells in both longitudinal and radial dimensions. Changing the strength of intercellular gap junction coupling coefficients in the microscale has noticeable effects on the macroscale behavior. We have shown that there exists a complex structure to the solution of coupled arterial endothelial cell (EC) and smooth muscle cell (SMC) over large length scales. These simulations are the solution to a complex coupled cell model. This has been done using a discrete method whereby a unit of coupled EC and SMCs have been mapped to a single MPI task onto Blue Gene/L, /P and finally /Q architectures and with each task communicating with neighboring nodes and thus simulating the coupling of IP3, membrane voltage and calcium (Ca2+) over length scales much larger than a single cell. Up to 64,000 MPI tasks have been used to investigate the calcium concentration over both time and space. The solution shows that with each EC/SMC set, as a spatially varying oscillatory unit, waves of Ca2+ on scales much larger than the cell length propagate upstream. These waves grow in complexity as time progresses with what seems to be spontaneous oscillations of EC/SMC units far from the propagating wavefront.

We are currently simulating on Blue Gene/Q at VLSCI and Argonne (Mira) the Ca2+ dynamics through a single coronary artery consisting of up to 100 million cells. We will show results of the simulations along with scaling data and discuss the difficulties of I/O and rising above the 64,000 task limit. It is interesting to note that by allowing the cell length δl to contract to zero and the number of cells to tend to infinity a form of the reaction diffusion equations evolves through the use of homogenization theory. The talk will present results from both the massively parallel simulation as well as a continuum model based on the work of Gonzalez-Fernandez and Ermentrout.

BIO
Professor David has a BSc and a PhD in mathematics from the University of Leeds in the UK. He was awarded the Foxwell Award from the Department of Energy in 1986. Professor David is currently the director of BlueFern Supercomputing Unit at Canterbury. His "Brains Trust" Research group is one of the leading teams in the world for numerical simulations of cerebral perfusion.