A Clustering Method for Calculating Membrane Currents in Cardiac Electrical Models

Many studies into cardiac electrical rhythm and disturbances use computer modeling as a valuable tool for testing hypotheses. Computer modeling is often limited by tractability and the availability of computing resources. Some of these limitations can be overcome by efficient numerical schemes that solve the equations modeling cardiac electrical activation. This work presents a new numerical method, the piecewise phase space approximation (PPSA), for the time advancement of the coupled systems of ordinary differential equations (ODEs) that are used to describe cardiac cell membrane currents. Using novel metrics, data structures and approximations, state variables are discretely clustered in the phase space of the ODEs. Extreme points of each cluster are advanced through time by an appropriate solver and the remainder of the cluster points are reconstructed using a predictor function. This new method can contribute additional efficiency to many other established and emerging techniques for discretizing and solving cardiac electrical activation problems. The PPSA is assessed by a two-variable problem and a suite of one and two-dimensional cardiac electrical activation models of varying complexity. Less computational operations are required for comparable results with methods where all points are solved independently. Electrical activation in a detailed model of canine ventricles confirms these results. The performance of the PPSA will continue to improve with further investigation into alternative predictor functions, relaxation of phase space discretizations and parallelization of the algorithm.