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

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.

Cardiac strength-interval curves calculated using a bidomain tissue with a parsimonious ionic current

“…The strength interval curves for both cathodal and anodal stimuli applied through a unipolar electrode for a 2 ms pulse are shown in Fig 1 , using the standard model parameters [ 12 , 13 ]. The S 1 -S 2 interval is defined as the time between the start of the S 1 stimulus pulse (at time 0) and the start of the S 2 pulse.…”

“…The values for k r are chosen to show the effect of the I K current when it is linear ( k r = ∞) and nonlinear ( k r = 21.28 and 40 mV). The value k r = 21.28 mV corresponds to that used in Gray’s original model [ 12 , 13 ]. When g K and E K are fixed (0.3 mS cm -2 and -83 mV), the current-voltage curves have the same intercept and slope for I K = 0.…”

“…A recently developed parsimonious ionic model [ 12 , 13 ] reproduces many experimentally measured characteristics of ventricular action potentials using only three variables, two ion currents, and eleven parameters. The advantage of a parsimonious model is that it highlights essential features of the membrane kinetics while not getting bogged down in nonessential details.…”

Advancing Regulatory Science With Computational Modeling for Medical Devices at the FDA's Office of Science and Engineering Laboratories

“…Computational models of anatomy or physiology include improved drug delivery in the cornea with ultrasound energy ( 24 ); physiological models of heart cells ( 25 ), renal circulation ( 26 ), hemodynamic responses to blood volume perturbations ( 27 ), left bundle branch block ( 28 ), gas dynamics in the retina ( 29 ), coupled electrical and mechanical activity in the heart ( 30 ); energy absorption in patients with deep-brain stimulators ( 31 – 34 ), breast tissue expanders ( 35 ), in pregnant women and fetus during MRI exams ( 36 ); subthalamic nucleus ( 37 ), the breast ( 38 ), cancellous bone ( 39 ), the head ( 40 ) and whole body models ( 41 , 42 ).…”

Personalization of Cellular Electrophysiology Models: Utopia?

“…But how much of their data is human, and how do we go about replacing it with fresh patient-specific data? Analyses such as [1,6,7] partially address the first question, and show that AP models are almost exclusively multi-species -in fact, while Hodgkin and Huxley's model was entirely squid, the first cardiac AP model already mixed species [8] and this has continued largely unchanged, the only exception perhaps being the rabbit model by Gray et al [9]. A secondary (and solvable) problem that these analyses highlight is that AP model history is so complex that tracing the origins of model parameters is a challenging and time-consuming task.…”