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 i ntracellular ion concentrations violate a conservation principle, and, as a result, computed parameters (e.g., ion concentrations and transmembrane po tential, V,) drift in time, never attaining steady state. To address this i ssue, models have been proposed that invoke the charge conservation princip le to calculate Vm from ion concentrations ("algebraic" method), rather tha n from transmembrane current ("differential" method). The aims of this stud y are to compare model behavior during prolonged periods of pacing using th e algebraic and differential methods, and to address the issue of model dri ft. We pace the Luo-Rudy dynamic model of a cardiac ventricular cell and co mpare the time-dependent behavior of computed parameters using the algebrai c and differential methods. When ions carried by the stimulus current are t aken into account, the algebraic and differential methods yield identical r esults and neither shows drift in computed parameters. The present study es tablishes the proper pacing protocol for simulation studies of cellular beh avior during long periods of rapid pacing. Such studies are essential for m echanistic understanding of arrhythmogenesis, since cells are subjected to rapid periodic stimulation during many arrhythmias.