# A Mathematical Model for Electrical Activity in Pig Atrial Tissue

### Abstract

State of the art mathematical models are currently used to bridge the gap between basic research conducted in the laboratory and preclinical research conducted on large animals, which ultimately paves the way for clinical translation. In this regard, there is a great need for models that can be used alongside experiments for in-depth investigation and validation. One such experimental model is the porcine atrium, which is commonly used to study the mechanisms of onset and control of atrial fibrillation in the context of its surgical management. However, a mathematical model of pig atria is lacking. In this paper, we present the first ionically detailed mathematical model of porcine atrial electrophysiology, at body temperature. The model includes 12 ionic currents, 4 of which were designed based on experimental patch-clamp data directly obtained from literature. The formulations for the other currents are adopted from the human atrial model, and modified for porcine specificity based on our measured restitution data for different action potential characteristics: resting membrane potential, action potential amplitude, maximum upstroke velocity and action potential duration and different levels of membrane voltage repolarization. The intracellular Ca2+ dynamics follows the Luo-Rudy formulation for guinea pig ventricular cardiomyocytes. The resulting model represents “normal” cells which are formulated as a system of ordinary differential equations. We extend our model to two dimensions to obtain plane wave propagation in tissue with a velocity of 0.58 m/s and a wavelength of 8 cm. The wavelength reduces to 5 cm when the tissue is paced at 200 ms. Using S1-S2 cross-field protocol, we demonstrate in an 11.26 cm square simulation domain, the ability to initiate single spiral waves(rotation period $∼eq$ 180 ms) that remain stable for more than 40 s. The spiral tip exhibits hypermeander. In agreement with previous experimental results using pig atria, our model shows that early repolarization is primarily driven by a calcium-mediated chloride current, IClCa, which is completely inactivated at high pacing frequencies. This is a condition that occurs only in porcine atria. Furthermore, the model shows spatiotemporal chaos with reduced repolarization.

Publication
Frontiers in Physiology 13: 812535