Using delay differential equations to induce alternans in a model of cardiac electrophysiology.
Cardiac electrical alternans is a period-2 dynamical behavior with alternating long and short action potential durations (APD) that often precedes dangerous arrhythmias associated with cardiac arrest. Despite the importance of alternans, many current ordinary differential equations models of cardiac electrophysiology do not produce alternans, thereby limiting the use of these models for studying the mechanisms that underlie this condition. Because delay differential equations (DDEs) commonly induce complex dynamics in other biological systems, we investigate whether incorporating DDEs can lead to alternans development in cardiac models by studying the Fox et al. canine ventricular action potential model. After suppressing the alternans in the original model, we show that alternans can be obtained by introducing DDEs in the model gating variables, and we quantitatively compare the DDE-induced alternans with the alternans present in the original model. We analyze the behavior of the voltage, currents, and gating variables of the model to study the effects of the delays and to determine how alternans develops in that setting, and we discuss the mathematical and physiological implications of our findings. In future work, we aim to apply our approach to induce alternans in models that do not naturally exhibit such dynamics.
Department of Mathematics, Millersville University, P.O. Box 1002, Millersville, PA 17551, USA.
Justin
J
Eastman
Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA.
Julian
J
Sass
Graduate Program on Computational Modeling, Federal University of Juiz de Fora, 36036-900 Juiz de Fora, MG, Brazil.
Johnny M
JM
Gomes
Graduate Program on Computational Modeling, Federal University of Juiz de Fora, 36036-900 Juiz de Fora, MG, Brazil.
Rodrigo Weber
RW
Dos Santos
School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, NY 14623, USA.
Elizabeth M
EM
Cherry
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D020746:Calcium Channels, L-Type / Q000378:metabolism; D004285:Dogs; D004594:Electrophysiology; D006321:Heart / Q000502:physiology*; D015640:Ion Channel Gating / Q000502:physiology; D008954:Models, Biological; D008959:Models, Neurological; D013997:Time Factors
D020746:Calcium Channels, L-Type
Cardiac arrhythmia mechanisms; Ion channel modeling; Period-doubling