A mathematical model for electrical activity in pig atrial tissue
Authors: Peris-Yagüe Víctor , Rubio Tony , Fakuade Funsho E. , Voigt Niels , Luther Stefan , Majumder Rupamanjari 
Published: October 2021

Atrial fibrillation (AF) is the most common sustained form of cardiac arrhythmia occurring in humans. Its effective treatment requires a detailed understanding of the underlying mechanisms at the genetic, molecular, cellular, tissue and organ levels. To study the complex mechanisms underlying the development, maintenance and termination of cardiac arrhythmias, we need preclinical research models. These models range from in vitro cell cultures to in vivo small and large animal hearts. However, translational research requires that the results of these animal experiments are understood in the context of human subjects. Currently, this is achieved through simulations with state-of-the-art mathematical models for human and animal heart tissue. In the context of AF, a model that is extensively used by experimentalists, is that of the pig atria. However, until now, an ionically detailed mathematical model for pig atrial tissue has been lacking, and researchers have been forced to rely on mathematical models from other animal species to understand their experimental observations.

In this paper, we present the first ionically detailed mathematical model of porcine atrial electrophysiology. To build the model, we first fitted experimental patch-clamp data from literature to describe the individual currents flowing across the cell membrane. Later, we fine-tuned the model by fitting action potential duration restitution (APDR) curves for different repolarisation levels. The experimental data for the APDR studies was produced in N. Voigt’s lab.

We extended our model to the tissue level and demonstrated the ability to maintain stable spiral waves. In agreement with previous experimental results, our model shows that early repolarisation is primarily driven by a calcium-mediated chloride current, IClCa, which is completely inactivated at high pacing frequencies. This is a condition found only in porcine atria. The model shows spatiotemporal chaos with reduced repolarisation.

Author summary

State-of-the-art mathematical models of cardiac electrophysiology play an important role in bridging the gap between animal research conducted in the laboratory and preclinical research being considered for translation into the clinic. Using computer simulations, these models enable detailed studies of the behaviour of ion channels and ion transfer at the cellular level, the propagation of electrical waves at the tissue level and the visualisation of the excitation pattern within the heart wall at the organ level. Thus, they contribute to a better understanding of the mechanisms underlying cardiac arrhythmias.

Here, we present the first ionically detailed mathematical model for porcine atrial electrophysiology. The individual membrane currents were modelled by fitting experimental data obtained from literature. The overall electrical response of the tissue was adjusted by fitting action potential duration restitution (APDR) curves obtained from in-house patch-clamp measurements. Our model accounts for an early repolarisation phase of the AP that is primarily Ca2+-dependent, a feature that is consistent with experiments and is identified to be unique to pigs. In extended media, our model is capable of sustaining stable spiral waves, and spatiotemporal chaos, when the repolarisation reserve is reduced.