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

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⁺ stimulus current. All parameters stabilized within 6-7 h. Inward rectifier, Na⁺/Ca²⁺ exchanger, L-type Ca²⁺, and Na⁺ -Cl^- cotransporter currents made the greatest contributions to stabilization of intracellular [K⁺], [Na⁺], [Ca²⁺], and [Cl^-], respectively. Time-dependent AP shortening was largely due to the outward shift of Na⁺/Ca²⁺ exchange related to intracellular Na⁺ (Na_i⁺) accumulation. AP duration (APD) reached a steady state after ∼40 min. AP transients also occurred in canine atrial preparations, with the APD decreasing by ∼10 ms over 35 min, compared with ∼27 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.