The inverse problem for cardiac arrhythmias.

A cardiac arrhythmia is an abnormality in the rate or rhythm of the heart beat. We study a type of arrhythmia called a premature ventricular complex (PVC), which is typically benign, but in rare cases can lead to more serious arrhythmias or heart failure. There are three known mechanisms for PVCs: reentry, an ectopic focus, and triggered activity. We develop minimal models for each mechanism and attempt the inverse problem of determining which model (and therefore which mechanism) best describes the beat dynamics observed in an ambulatory electrocardiogram. We demonstrate our approach on a patient who exhibits frequent PVCs and find that their PVC dynamics are best described by a model of triggered activity. Better identification of the PVC mechanism from wearable device data could improve risk stratification for the development of more serious arrhythmias.

Long ECGs reveal rich and robust dynamical regimes in patients with frequent ectopy.

We have analyzed the electrocardiographic data collected during continuous 7-day ambulatory recordings in patients with frequent premature ventricular complexes (PVCs). We analyze the dependence of the frequency and patterns of PVCs on the heart rate and the time of the day. Patients display rhythms of a complex yet consistent structure. In a given patient, the pattern remains robust over different days and particular repetitive patterns appear at specific heart rates, suggesting the appearance of bifurcations in the dynamics. Over the course of 24 h, we find that in some patients, patterns appear to depend only on the heart rate, whereas in others, both the time of the day and the heart rate play a role in controlling the dynamics. Identifying parameter values at which bifurcations occur facilitates the development of dynamical models for arrhythmia. The use of powerful recording and analysis techniques will enable improved analysis of data and better understanding of mechanisms of arrhythmia in individual patients.

Detecting and distinguishing tipping points using spectral early warning signals.

Theory and observation tell us that many complex systems exhibit tipping points-thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical transitions that could help prevent undesirable events such as ecosystem collapse. However, conventional EWS do not indicate the type of transition, since they are based on the generic phenomena of critical slowing down. For instance, they may fail to distinguish the onset of oscillations (e.g. Hopf bifurcation) from a transition to a distant attractor (e.g. Fold bifurcation). Moreover, conventional EWS are less reliable in systems with density-dependent noise. Other EWS based on the power spectrum (spectral EWS) have been proposed, but they rely upon spectral reddening, which does not occur prior to critical transitions with an oscillatory component. Here, we use Ornstein-Uhlenbeck theory to derive analytic approximations for EWS prior to each type of local bifurcation, thereby creating new spectral EWS that provide greater sensitivity to transition proximity; higher robustness to density-dependent noise and bifurcation type; and clues to the type of approaching transition. We demonstrate the advantage of applying these spectral EWS in concert with conventional EWS using a population model, and show that they provide a characteristic signal prior to two different Hopf bifurcations in data from a predator-prey chemostat experiment. The ability to better infer and differentiate the nature of upcoming transitions in complex systems will help humanity manage critical transitions in the Anthropocene Era.