Large-scale Modeling of Cardiac Electrophysiology JB Pormann , JA Board , DJ Rose , CS Henriquez Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA Department of Computer Science, Duke University, Durham, NC, USA Department of Biomedical Engineering, Duke University, Durham, NC, USA Abstract Simulation of wavefront propagation in the whole heart requires significant computational resources. The growth of cluster computing has made it possible to simulate very large scale problems in a lab environment. In this work, we present computational results of simulating a reaction diffusion system of equations of various sizes on a Beowulf cluster. To facilitate comparisons at different spatial resolutions, an idealized ventricular geometry was used. The model incorporates anisotropy, fiber rotation, and realistic membrane dynamics to determine the computational constraints for the most detailed situations of interest. Three meshes with mesh spacings of , , and , corresponding to roughly , , and nodes in the computational domain, were considered. The results show that good parallel performance is possible on a cluster up to 32 processors. 1. Introduction Sophisticated computer simulations are being used to investigate the factors that generate and sustain life- threatening heart rhythms such as ventricular fibrillation. For models with domain sizes that approach the size of the human heart, the computational resources required to perform the simulation can exceed that found on a typical workstation. A domain comprising only 16M nodes with a membrane model of 5-8 state variables can use over 8GB of memory. To overcome these computational constraints, investigators have made use of commercial- class supercomputers such as the Cray YMP/T90 series and the IBM SP. While these supercomputers still provide outstanding performance, they are expensive and not always available to the average investigator. An alternative to using commercial supercomputers is a Beowulf cluster that involves several closely networked workstations. Such clusters have become increasingly popular, but have been viewed as being too experimental to handle the algorithmic and communication demands involved in solving the reaction-diffusion equations used to model electrical dynamics in cardiac muscle. Recent advances in hardware and software, however, have made cluster computing attractive for large scale simulations. In this paper, we describe the computational performance of a model of wavefront propagation in domain size approximating the human heart. To investigate the computational needs and test the cluster environment, an idealized ventricular geometry, with non-uniform, rotational ansiotropy and various models of cardiac membrane ionic fluxes was used. The idealized geometry permitted different grids with the same shape but different elements sizes to be studied. The simulations were performed using CardioWave, a modular simulation system for the Bidomain Equations [1], developed in our laboratory. The results show that when using a distributed memory parallel approach, the computational and memory resources of multiple but otherwise independent workstations can be used efficiently up to 32 processors for a domain size of 16 million computational nodes. 2. Methods CardioWave was developed to solve the system of bidomain equations on a parallel computer. The specific have been described previously [1]. Unlike other simulators of wavefront dynamics in the heart, Cardiowave is not a single, monolithic program, but rather a set of program modules related to time integration, output, membrane kinetics, matrix solvers etc, from which the user selects to create a custom executable for the problem of interest. In the typical simulation described in this work, the explicit- monodomain time-integrator module, the LR-1 membrane dynamics module, the simple stimulus and output modules were selected to create simulator. An additional module was selected to instruct the simulator that the execution would be performed in parallel. As such, the same set of modules can be selected and compiled on any distributed parallel computer without modification. To test the parallel performance, an idealized geometry with anisotropic properties was used such that diffferent grid spacings could be considered while minimizing the 0276-6547/02 $17.00 © 2002 IEEE 259 Computers in Cardiology 2002;29:259-262.