Estimation of Parameters for an Archetypal Model of Cardiomyocyte Membrane Potentials

Abstract

Contemporary realistic mathematical models of single-cell cardiac electrical excitation are immensely detailed. Model complexity leads to parameter uncertainty, high computational cost and barriers to mechanistic understanding. There is a need for reduced models that are conceptually and mathematically simple but physiologically accurate. To this end, we consider an archetypal model of single-cell cardiac excitation that replicates the phase-space geometry of detailed cardiac models, but at the same time has a simple piecewise-linear form and a relatively low-dimensional configuration space. In order to make this archetypal model practically applicable, we develop and report a robust method for estimation of its parameter values from the morphology of single-stimulus action potentials derived from detailed ionic current models and from experimental myocyte measurements. The procedure is applied to five significant test cases and an excellent agreement with target biomarkers is achieved. Action potential duration restitution curves are also computed and compared to those of the target test models and data, demonstrating conservation of dynamical pacing behaviour by the fine-tuned archetypal model. An archetypal model that accurately reproduces a variety of wet-lab and synthetic electrophysiology data offers a number of specific advantages such as computational efficiency, as also demonstrated in the study. Open-source numerical code of the models and methods used is provided.

Keywords

• mathematical model
• cardiac action potential
• electrophysiology
• parameter estimation