Time-dependent transients in an ionically based mathematical model of the canine atrial action potential
James Kneller, Rafael J. Ramirez, Denis Chartier, Marc Courtemanche, Stanley Nattel
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Source: Crossref
Published: Apr 1, 2002
DOI: 10.1152/ajpheart.00489.2001
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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 + /Ca 2+ exchanger, L-type Ca 2+ , and Na + -Cl − cotransporter currents made the greatest contributions to stabilization of intracellular [K + ], [Na + ], [Ca 2+ ], and [Cl − ], respectively. Time-dependent AP shortening was largely due to the outward shift of Na + /Ca 2+ exchange related to intracellular Na + (Na[Formula: see text]) 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.
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