Time-dependent transients in an ionically based mathematical model of the canine atrial action potential

Abstract

. Time-dependent transients in an ionically based mathematical model of the canine atrial action potential. Am J Physiol Heart Circ Physiol 282: H1437-H1451, 2002. First published November 29, 2001 10.1152/ajpheart.00489.2001.-Ionically based cardiac action potential (AP) models are based on equations with singular Jacobians and display time-dependent AP and ionic changes (transients), which may be due to this mathematical limitation. The present study evaluated transients during long-term simulated activity in a mathematical model of the canine atrial AP. Stimulus current assignment to a specific ionic species contributed to stability. Ionic concentrations were least disturbed with the K ϩ stimulus current. All parameters stabilized within 6-7 h. Inward rectifier, Na , respectively. Time-dependent AP shortening was largely due to the outward shift of Na ϩ /Ca 2ϩ exchange related to intracellular Na ϩ (Na i ϩ ) accumulation. AP duration (APD) reached a steady state after ϳ40 min. AP transients also occurred in canine atrial preparations, with the APD decreasing by ϳ10 ms over 35 min, compared with ϳ27 ms in the model. We conclude that model APD and ionic transients stabilize with the appropriate stimulus current assignment and that the mathematical limitation of equation singularity does not preclude meaningful long-term simulations. The model agrees qualitatively with experimental observations, but quantitative discrepancies highlight limitations of long-term model simulations. ionic drift; action potential transients; atrial fibrillation; electrophysiology; ion channels and transporters THE ESTABLISHMENT of the original DiFrancesco-Noble (DN) model of cardiac myocyte electrophysiology spawned the development of numerous other dynamic models patterned after the DN formulation (5). These models explicitly include transmembrane ion channels and pumps, the intracellular calcium sequestering and release activity of the sarcoplasmic reticulum (SR), and changing intracellular ionic concentrations. The incorporation of concentration changes into the cardiac electrical model was an important development because such changes occur rapidly in the small volume of the cardiac cell and can have profound effects on action potential (AP) properties.Dynamic models are finely tuned to reproduce electrophysiological behavior observed experimentally during observation periods of short duration. However, the original DN model was noted to produce a continual cycle-by-cycle (transient) accumulation (K ϩ ) or depletion (Na ϩ , Ca 2ϩ ) of intracellular ionic species (5). AP morphology and the pre-and postcycle values of the ionic concentrations were not constant as would be expected of steady-state behavior. Transient changes were negligible over a few cardiac cycles, but departures from the prestimulus initial concentrations were cumulative and became substantial over many cycles. Guan et al. (9) noted that the original DN equations are mathematically dependent (Jacobian is singular), and therefore that model fixed points are unsta...

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