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

@article{Quail2015PredictingTO,
title={Predicting the onset of period-doubling bifurcations in noisy cardiac systems},
author={Thomas Quail and Alvin Shrier and Leon Glass},
journal={Proceedings of the National Academy of Sciences},
year={2015},
volume={112},
pages={9358 - 9363}
}
• Published 13 July 2015
• Biology
• Proceedings of the National Academy of Sciences
Significance Predicting the onset of transitions in the qualitative dynamics of complex systems remains a challenging problem, with relevance in diverse fields. This study focuses on the development of early warning signals that can predict the onset of alternating cardiac rhythms. We treat cardiac cells with a potassium channel blocker, which induces the initiation of alternating rhythms. Based on these experiments, we develop a quantitative measure that can detect how far the system is from…
45 Citations

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## References

SHOWING 1-10 OF 51 REFERENCES
Chaotic dynamics in cardiac aggregates induced by potassium channel block.
• Biology
Chaos
• 2012
A Hodgkin-Huxley-style cardiac ionic model captured the different types of complex dynamics following blockage of the hERG mediated potassium current.
Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics.
• Biology
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2004
It is shown that the gain gamma necessary to establish control may vary significantly depending on the value of the slope of the so-called standard restitution curve, but that the product gammaS12 stays approximately in the same range.
Spatiotemporal intracellular calcium dynamics during cardiac alternans.
• Biology
Chaos
• 2009
The results demonstrate that ion channel stochasticity at the level of single calcium release units can influence the whole-cell alternans dynamics by causing phase reversals over many beats during fixed frequency pacing close to the alternans bifurcation.
Calcium alternans is due to an order-disorder phase transition in cardiac cells.
• Biology
Physical review letters
• 2015
It is shown that alternans occurs via an order-disorder phase transition which exhibits critical slowing down and a diverging correlation length, and is characterized by critical exponents consistent with the Ising universality class.
Amplitude equation approach to spatiotemporal dynamics of cardiac alternans.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2007
These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative predictions that can be compared to ionic model simulations or experiments.
Human seizures self-terminate across spatial scales via a critical transition
• Biology, Psychology
Proceedings of the National Academy of Sciences
• 2012
Evidence is presented that seizures self-terminate via a discontinuous critical transition or bifurcation, which constrains the specific biophysical mechanisms underlying seizure termination, suggests a dynamical understanding of status epilepticus, and demonstrates an accessible system for studying critical transitions in nature.
Effects of Pacing Site and Stimulation History on Alternans Dynamics and the Development of Complex Spatiotemporal Patterns in Cardiac Tissue
• Biology
Front. Physiol.
• 2013
Alternans in canine ventricles not only exhibit larger amplitudes and persist for longer cycle length regimes compared to those found in smaller mammalian hearts, but also show novel dynamics not previously described that enhance dispersion and show high sensitivity to initial conditions.
Stochastic and spatial influences on drug-induced bifurcations in cardiac tissue culture.
• Biology
Physical review letters
• 2009
A stochastic partial differential equation model based on discrete ionic currents recorded in chick heart cells demonstrates that drug diffusion and noise can induce the coupled beats and bursting rhythms observed.
Period-doubling instability and memory in cardiac tissue.
• Biology
Physical review letters
• 2002
A return map memory model is compared to action potential data from an ionic model and it is found that the memory model reproduced dynamics that could not be explained by a unidimensional restitution relation.