Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations

• Main Authors: Roberto Barrio, M. Angeles Martínez, Lucía Pérez, Esther Pueyo
• Format: Article
• Language: English
• Published: MDPI AG 2020-06-01
• Series: Mathematics
• Subjects: cardiac dynamics; early afterdepolarizations (EADs); bifurcations; isolas; fast–slow decomposition
• Online Access: https://www.mdpi.com/2227-7390/8/6/880

In this study, we teased out the dynamical mechanisms underlying the generation of arrhythmogenic early afterdepolarizations (EADs) in a three-variable model of a mammalian ventricular cell. Based on recently published studies, we consider a 1-fast, 2-slow variable decomposition of the system describing the cellular action potential. We use sweeping techniques, such as the spike-counting method, and bifurcation and continuation methods to identify parametric regions with EADs. We show the existence of isolas of periodic orbits organizing the different EAD patterns and we provide a preliminary classification of our fast–slow decomposition according to the involved dynamical phenomena. This investigation represents a basis for further studies into the organization of EAD patterns in the parameter space and the involved bifurcations.