Predicting the onset of period-doubling bifurcations in noisy cardiac systems

Abstract

Biological, physical, and social systems often display qualitative changes in dynamics. Developing early warning signals to predict the onset of these transitions is an important goal. The current work is motivated by transitions of cardiac rhythms, where the appearance of alternating features in the timing of cardiac events is often a precursor to the initiation of serious cardiac arrhythmias. We treat embryonic chick cardiac cells with a potassium channel blocker, which leads to the initiation of alternating rhythms. We associate this transition with a mathematical instability, called a period-doubling bifurcation, in a model of the cardiac cells. Period-doubling bifurcations have been linked to the onset of abnormal alternating cardiac rhythms, which have been implicated in cardiac arrhythmias such as T-wave alternans and various tachycardias. Theory predicts that in the neighborhood of the transition, the system's dynamics slow down, leading to noise amplification and the manifestation of oscillations in the autocorrelation function. Examining the aggregates' interbeat intervals, we observe the oscillations in the autocorrelation function and noise amplification preceding the bifurcation. We analyze plots-termed return maps-that relate the current interbeat interval with the following interbeat interval. Based on these plots, we develop a quantitative measure using the slope of the return map to assess how close the system is to the bifurcation. Furthermore, the slope of the return map and the lag-1 autocorrelation coefficient are equal. Our results suggest that the slope and the lag-1 autocorrelation coefficient represent quantitative measures to predict the onset of abnormal alternating cardiac rhythms.early warning signals | period-doubling bifurcations | cardiac arrhythmias | dynamical systems

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

“…The emergence of spatial chaos, furthermore, suggests that the disease is difficult to eliminate and will persist as an endemic [17,46]. If a mathematical model for a given disease exists, analytical methods provide the critical point(s) of the model and show when to expect sudden shift(s) towards a contrasting dynamical regime [191][192][193][194][195] (see Appendix A.3). This regime shifting is of considerable interest in other fields, including ecosystem management, population ecology, financial risk assessment, etc.…”

George Ralph Mines (1886–1914): the dawn of cardiac nonlinear dynamics

“… in this issue) and administration of a potassium channel blocker (Quail et al . ). In a perspective on the former article in this issue, Vandenberg & Hill () suggest that analysis of cardiac alternans might be useful in improving management of patients at risk for sudden cardiac death.…”

“…In a similar vein, in this issue Trayanova & Chang (2016) describe how one can use MRI mapping, combined with computer simulation, to determine the risk for ventricular tachycardia and fibrillation and to help guide ablations in the clinic, while Jacquemet (2016) discusses modelling of six different targets for ablation in atrial fibrillation. The increased fluctuations seen as one approaches a period-doubling bifurcation have been very recently considered in two situations using interventions that are capable of provoking arrhythmias: fast pacing (Prudat et al 2016 in this issue) and administration of a potassium channel blocker (Quail et al 2015). In a perspective on the former article in this issue, Vandenberg & Hill (2016) suggest that analysis of cardiac alternans might be useful in improving management of patients at risk for sudden cardiac death.…”

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“…This problem is discussed extensively in [22,23,31]; 2. the analysis presented sets bounds for the robustness of a model, and it is straightforward enough to be implemented in any algorithm that creates a template out of a time series. It is noted that low-dimensional, noisy discrete-time mappings are still widely used as models in several fields of science and engineering [32,33,34].…”