Ionic charge conservation and long-term steady state in the Luo-Rudy dynamic cell model

It has been postulated that cardiac cell models accounting for changes in intracellular ion concentrations violate a conservation principle, and, as a result, computed parameters (e.g., ion concentrations and transmembrane potential, V(m)) drift in time, never attaining steady state. To address this issue, models have been proposed that invoke the charge conservation principle to calculate V(m) from ion concentrations ("algebraic" method), rather than from transmembrane current ("differential" method). The aims of this study are to compare model behavior during prolonged periods of pacing using the algebraic and differential methods, and to address the issue of model drift. We pace the Luo-Rudy dynamic model of a cardiac ventricular cell and compare the time-dependent behavior of computed parameters using the algebraic and differential methods. When ions carried by the stimulus current are taken into account, the algebraic and differential methods yield identical results and neither shows drift in computed parameters. The present study establishes the proper pacing protocol for simulation studies of cellular behavior during long periods of rapid pacing. Such studies are essential for mechanistic understanding of arrhythmogenesis, since cells are subjected to rapid periodic stimulation during many arrhythmias.