Steady State During Ultra-long Term Continuous Pacing

We carefully checked that the model reaches stable quiescence as well as a steady state response to periodic pacing. However, for continuous pacing of extremely long duration, beyond 2 hours of simulation time, small numerical errors could appear as a result of machine precision. These numerical errors are completely eliminated by using an analytical expression for the calculation of subspace Ca²⁺ (Zeng J, Laurita KR, Rosenbaum DS, Rudy Y. Circ Res. 1995;77:140-152), which amounts to replacing the differential equations for buffering and subspace Ca²⁺ with the equations below. The Hund-Rudy model code available on this website already computes analytically subspace Ca²⁺, and has been tested to reach a stable steady-state for all (short and long) pacing conditions.

Definitions are as follows (concentrations given in mmol/L): [Ca²⁺]_ss indicates free [Ca²⁺]_ss in the subspace; BSL, concentration of Ca²⁺ buffered by anionic sarcolemmal binding sites for Ca²⁺ in the subspace; , maximum concentration of Ca²⁺ buffered by anionic sarcolemmal binding sites for Ca²⁺ in the subspace; BSR, concentration of Ca²⁺ buffered by anionic binding sites for Ca²⁺ in the subspace; , maximum concentration of Ca²⁺ buffered by anionic binding sites for Ca²⁺ in the subspace; K_m,BSL and K_m,BSR , equilibrium constants of buffering by BSL and BSR respectively; and [Ca²⁺]_ss, change in total Ca²⁺ amount during one time step. The subscripts ss , new , and old indicate subspace, present time step, and previous time step, respectively.