Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model

Barrio Gil, Roberto (Universidad de Zaragoza) ; Martinez Carballo, María Ángeles (Universidad de Zaragoza) ; Pueyo Paules, Esther (Universidad de Zaragoza) ; Serrano Pastor, Sergio (Universidad de Zaragoza)

Resumen: Arrhythmogenic early afterdepolarizations (EADs) are investigated in a biophysically detailed mathematical model of a rabbit ventricular myocyte, providing their location in the parameter phase space and describing their dynamical mechanisms. Simulations using the Sato model, defined by 27 state variables and 177 parameters, are conducted to generate electrical action potentials (APs) for different values of the pacing cycle length and other parameters related to sodium and calcium concentrations. A detailed study of the different AP patterns with or without EADs is carried out, showing the presence of a high variety of temporal AP configurations with chaotic and quasiperiodic behaviors. Regions of bistability are identified and, importantly, linked to transitions between different behaviors. Using sweeping techniques, one-, two-, and three-parameter phase spaces are provided, allowing ascertainment of the role of the selected parameters as well as location of the transition regions. A Devil’s staircase, with symbolic sequence analysis, is proposed to describe transitions in the ratio between the number of voltage (EAD and AP) peaks and the number of APs. To conclude, the obtained results are linked to recent studies for low-dimensional models and a conjecture is made for the internal dynamical structure of the transition region from non-EAD to EAD behavior using fold and cusp bifurcations and maximal canards.
In a healthy heart, the sinoatrial node sends out an electrical impulse that spreads throughout the heart activating all cardiac myocytes to produce an electrical response called the action potential (AP). The AP follows a sequence of AP phases corresponding to the inflow and outflow of ions through the membrane of cardiac myocytes. Under some circumstances, that sequence of AP phases can be disrupted by the presence of the so-called early afterdepolarizations (EADs), which are secondary voltage depolarizations that can appear during phase 2 or 3 of the AP. Side effects of drugs, ion channel dysfunction, or oxidative stress, among others, can lead to the genesis of EADs.1–3 In heart failure, long QT syndrome, and other pathological conditions, EADs have been reported to be a relevant cause of fatal ventricular arrhythmias,4–6 but more knowledge is required to understand the theoretical mechanisms underlying their generation. During the last few decades, computational models of cardiac electrical activity have been instrumental in shedding light on various cardiac phenomena, including EADs. Biophysically detailed models of high dimension, i.e., with a large number of state variables, allow more faithful reproduction of experimental observations and facilitate biophysical interpretation. Here, we use the high-dimensional electrophysiological model of a rabbit ventricular myocyte developed by Sato et al.6 with 27 state variables and 177 model parameters. By combining different techniques for dynamical system analysis, we investigate the parameter phase space using three parameters reported to highly influence model dynamics.7 We identify regions in the phase space showing transitions from absence to presence of EADs through different temporal sequences of EADs. In these processes, dynamical phenomena are present, including bistability, chaos, fold, and cusp bifurcations. Putting all this information together and taking into account recent findings using low-dimensional models, we provide a conjecture about the internal dynamical structure of the transition region from absence to presence of EADs in the parameter phase space studied for the Sato model.

Idioma: Inglés

DOI: 10.1063/5.0055965

Año: 2021

Publicado en: CHAOS 31 (2021), 073137 [20 pp.]
ISSN: 1054-1500

Factor impacto JCR: 3.741 (2021)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 7 / 56 = 0.125 (2021) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 17 / 267 = 0.064 (2021) - Q1 - T1

Factor impacto CITESCORE: 5.8 - Mathematics (Q1) - Physics and Astronomy (Q1)

Factor impacto SCIMAGO: 1.009 - Applied Mathematics (Q1) - Statistical and Nonlinear Physics (Q1) - Physics and Astronomy (miscellaneous) (Q1) - Mathematical Physics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/T39-17R-BSICoS
Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-20R
Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/LMP124-18
Financiación: info:eu-repo/grantAgreement/EC/H2020/638284/EU/Is your heart aging well? A systems biology approach to characterize cardiac aging from the cell to the body surface/MODELAGE
Financiación: info:eu-repo/grantAgreement/ES/MICINN-FEDER/PID2019-105674RB-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-096026-B-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)
Área (Departamento): Área Teoría Señal y Comunicac. (Dpto. Ingeniería Electrón.Com.)