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

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, I(Na), 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 I(Na) with a phenomenological model of repolarization similar to the voltage dependent, time-independent rectifying outward potassium current (I(K)). 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 I(Na) 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 I(Na) inactivation and the non-linear rectification of I(K).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.