A Parsimonious Model of the Rabbit Action Potential Elucidates the Minimal Physiological Requirements for Alternans and Spiral Wave Breakup

Richard A Gray and Pras Pathmanathan

PLOS Computational Biology, 2016, vol. 12, issue 10, 1-21

Abstract: Elucidating the underlying mechanisms of fatal cardiac arrhythmias requires a tight integration of electrophysiological experiments, models, and theory. Existing models of transmembrane action potential (AP) are complex (resulting in over parameterization) and varied (leading to dissimilar predictions). Thus, simpler models are needed to elucidate the “minimal physiological requirements” to reproduce significant observable phenomena using as few parameters as possible. Moreover, models have been derived from experimental studies from a variety of species under a range of environmental conditions (for example, all existing rabbit AP models incorporate a formulation of the rapid sodium current, INa, based on 30 year old data from chick embryo cell aggregates). Here we develop a simple “parsimonious” rabbit AP model that is mathematically identifiable (i.e., not over parameterized) by combining a novel Hodgkin-Huxley formulation of INa with a phenomenological model of repolarization similar to the voltage dependent, time-independent rectifying outward potassium current (IK). The model was calibrated using the following experimental data sets measured from the same species (rabbit) under physiological conditions: dynamic current-voltage (I-V) relationships during the AP upstroke; rapid recovery of AP excitability during the relative refractory period; and steady-state INa inactivation via voltage clamp. Simulations reproduced several important “emergent” phenomena including cellular alternans at rates > 250 bpm as observed in rabbit myocytes, reentrant spiral waves as observed on the surface of the rabbit heart, and spiral wave breakup. Model variants were studied which elucidated the minimal requirements for alternans and spiral wave break up, namely the kinetics of INa inactivation and the non-linear rectification of IK.The simplicity of the model, and the fact that its parameters have physiological meaning, make it ideal for engendering generalizable mechanistic insight and should provide a solid “building-block” to generate more detailed ionic models to represent complex rabbit electrophysiology.Author Summary: Understanding and preventing life-threatening irregular electrical heart rhythms includes basic experimental, numerical, and theoretical research. Computer models of the electrical dynamics of cardiac cells and impulse propagation throughout the heart are essential tools of this research. For example, simulations of electrical activity such as rotating ‘spiral waves’ have been used to understand how irregular heart rhythms are maintained. However, existing models are derived exclusively from sub-cellular data under a variety of environmental conditions and species. These models tend to be exceedingly complex including hundreds of variables and parameters which make them difficult to validate and analyze. Using experimental data from one species (rabbit) under nearly identical physiological conditions, we developed a simple model of the electrical activity of a cardiac cell derived from sub-cellular, cellular, and tissue experimental data. This model reproduces cellular excitability and its recovery as well as several important “emergent” phenomena including beat-to-beat cellular alterations and unstable spiral waves. Under some conditions, unstable spiral waves in this model give rise to continuous formation of new spiral waves (i.e., “spiral wave breakup”) which is thought to be the underlying cause of cardiac fibrillation and sudden cardiac death.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1005087

DOI: 10.1371/journal.pcbi.1005087

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