CARP User Meeting Edward J. Vigmond (University of Calgary), Gernot Plank (Medical University of Graz) September 5–7, 2008 1 Overview of the Field Heart disease is the number one killer in the industrialized world. Modelling cardiac electrical phenomena is attractive since it allows complete control of the system and one has full knowledge of all components in the system, unlike animal experiments. Cardiac bioelectricity is described by the bidomain equations[1] which links current flow in the extracellular space to current flow within cells through current flowing through the cell membranes: ∇· (¯ σ i +¯ σ e )∇φ e = -∇ · ¯ σ i ∇V m - I e (1) ∇· ¯ σ i ∇V m = -∇ · ¯ σ i ∇φ e + βI m (V m ,ζ ) (2) which is a parabolic and an elliptical equation which depend on the voltage across the cell membrane, V m , and the extracellular electric potential, φ e . While the media are linear, a highly nonlinear source source term, I m , links solutions in the two media. Simulations of cardiac electrophysiology are becoming increasingly sophisticated and more quantitative. This has arisen as a result of faster computing hardware, better imaging and experimental methodology, and advances in scientific computation. However, simulation of a human heart at a near real time performance is still a challenge as the size of the system is currently prohibitive. Solving the bidomain equations is an inherently expensive procedure since the involved space constants are small (some tens of μm up to 1 mm) and the time scales are very fast. At the same time, domain sizes which are sufficiently large to maintain arrhythmias or to observe wavefront propagation free of boundary effects, is large, at the order of centimetres, and the observation periods are long (some hundreds of milliseconds up to minutes). The dynamics of charge transport across the membrane and between intracellular compartments is described by a set of non-linear ODEs. In general, the set of ODEs is quite stiff. This is particularly true for very recent formulations that rely on Markov state models to describe the cellular dynamics. In these models, the intrinsic time scales vary from the sub-microsecond scale for the fastest processes up to hundreds of milliseconds for the slowest processes. The fast onset of the cellular excitation process, referred to as upstroke of the action potential, leads to potential variations over fairly small spatial domains when electrical wavefronts are traversing the heart (within less than 1 mm the transmembrane voltage covers the full physiological range). That is, discretizations of the bidomain equations using anatomically realistic representations of the whole heart together with recent mechanistically realistic models of the cellular dynamics typically lead to systems of millions of degrees of freedom and hundreds of thousands of time steps. Therefore, even when simulations are executed using the most powerful HPC hardware available today, execution times impede fine-grained explorations of the parameter space of interest. 1