Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this problem through the theory of dynamical systems, bifurcation analysis and continuation methods; under which a converged action potential is a stable limit cycle. Various attempts have been made to improve the efficiency of identifying these limit cycles, with limited success. We demonstrate that continuation methods can more efficiently infer the converged action potential as proposed model parameter sets change during optimization or inference routines. In an example electrophysiology model this reduces parameter inference computation time by 70%. We also discuss theoretical considerations and limitations of continuation method use in place of time-consuming model simulations. The application of continuation methods allows more robust optimization by making extra runs from multiple starting locations computationally tractable, and facilitates the application of inference methods such as Markov Chain Monte Carlo to gain more information on the plausible parameter space.

翻译：在生物系统的数学建模中，参数化过程通常需要拟合稳定的周期性数据。在心脏电生理学中，这通常需要通过长时间模拟收敛至稳定的动作电位。我们通过动力系统理论、分岔分析和延拓方法来探讨这一问题；在此框架下，收敛的动作电位对应稳定的极限环。尽管已有多种尝试旨在提高识别这些极限环的效率，但成效有限。我们证明，当优化或推断过程中提出的模型参数集发生变化时，延拓方法能够更高效地推断收敛的动作电位。在一个电生理学模型示例中，该方法将参数推断计算时间减少了70%。我们还讨论了使用延拓方法替代耗时模型模拟的理论考量与局限性。延拓方法的应用使得从多个起始位置进行额外计算在计算上可行，从而实现更稳健的优化，并促进如马尔可夫链蒙特卡罗等推断方法的应用，以获取关于合理参数空间的更多信息。