Nonlinear Dynamics in Cardiology

Krogh‐Madsen, Trine; Christini, David J.

doi:10.1146/annurev-bioeng-071811-150106

Cited by 67 publications

(43 citation statements)

References 160 publications

(207 reference statements)

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“…V m dynamics can potentially become more random in conditions where Ca 2+ waves are present, and SCR generates global spikes of [Ca] i causing DADs. It is well appreciated that the coupling of Ca 2+ cycling and excitation can potentiate arrhythmias (4,(38)(39)(40)(41)(42). However, how TA emerges from the interplay of a nearly deterministic V m subsystem and a highly stochastic Ca 2+ cycling subsystem remains largely unknown.…”

Section: +mentioning

confidence: 99%

Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes

Song

2017

Proc. Natl. Acad. Sci. U.S.A.

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Cardiac myocytes normally initiate action potentials in response to a current stimulus that depolarizes the membrane above an excitation threshold. Aberrant excitation can also occur due to spontaneous calcium (Ca 2+ ) release (SCR) from intracellular stores after the end of a preceding action potential. SCR drives the Na + /Ca 2+ exchange current inducing a "delayed afterdepolarization" that can in turn trigger an action potential if the excitation threshold is reached. This "triggered activity" is known to cause arrhythmias, but how it is initiated and terminated is not understood. Using computer simulations of a ventricular myocyte model, we show that initiation and termination are inherently random events. We determine the probability of those events from statistical measurements of the number of beats before initiation and before termination, respectively, which follow geometric distributions. Moreover, we elucidate the origin of randomness by a statistical analysis of SCR events, which do not follow a Poisson process observed in other eukaryotic cells. Due to synchronization of Ca 2+ releases during the action potential upstroke, waiting times of SCR events after the upstroke are narrowly distributed, whereas SCR amplitudes follow a broad normal distribution with a width determined by fluctuations in the number of independent Ca 2+ wave foci. This distribution enables us to compute the probabilities of initiation and termination of bursts of triggered activity that are maintained by a positive feedback between the action potential upstroke and SCR. Our results establish a theoretical framework for interpreting complex and varied manifestations of triggered activity relevant to cardiac arrhythmias.calcium wave | delayed afterdepolarization | triggered activity | bistability | arrhythmias V entricular arrhythmias, the leading cause of sudden death (1), tend to occur unexpectedly. Understanding their initiation mechanisms remains a major challenge for clinical cardiologists (2). Lethal arrhythmias can occur without any abnormal sign in the ECG, or can be preceded by multiple premature ventricular complexes (PVCs) or short runs of ventricular tachycardia (3). There are many possible sources of randomness that can be responsible for the seemingly unpredictable nature of arrhythmias, such as environmental stresses via neural or metabolic regulations, chaotic dynamics (4, 5), or fluctuations associated with the intrinsic stochasticity of ion channel kinetics (6, 7).During normal contraction, calcium (Ca 2+ ) release from the sarcoplasmic reticulum (SR)-the intracellular Ca 2+ store of a ventricular myocyte-is triggered by Ca 2+ entry into the cell via L-type calcium channels (LCCs), a mechanism known as Ca 2+ -induced Ca 2+ -release (CICR). However, SR Ca 2+ release can also occur spontaneously, as observed in a variety of pathological conditions ranging from heart failure (8, 9) to ischemia (10) to catecholaminergic polymorphic ventricular tachycardia (11)(12)(13)(14). Spontaneous Ca 2+ release (SCR) transi...

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Section: +mentioning

confidence: 99%

Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes

Song

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…Many tools of nonlinear dynamics and chaos theory have been used in the study of cardiac dynamics [45]. The Floquet theory (also known as Bloch's theorem in solid-state physics) [46][47][48] is a convenient tool to study for instance, in Fig.…”

Section: Floquet Stability Analysismentioning

confidence: 99%

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Collet

Bragard

Dauby

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This article characterizes the cardiac autonomous electrical activity induced by the mechanical deformations in the cardiac tissue through the mechano-electric feedback (MEF). A simplified and qualitative model is used to describe the system and we also account for temperature effects. The analysis emphasizes a very rich dynamics for the system, with periodic solutions, alternans, chaotic behaviors, etc. The possibility of self-sustained oscillations is analyzed in detail, particularly in terms of the values of important parameters such as the dimension of the system and the importance of the stretch-activated currents. It is also shown that high temperatures notably increase the parameters ranges for which self-sustained oscillations are observed and that several attractors can appear, depending on the location of the initial excitation of the system. Finally, the instability mechanisms by which the periodic solutions are destabilized have been studied by a Floquet analysis, which has revealed period-doubling phenomena and transient intermittencies.

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“…However, due to the highly interdisciplinary nature of this research, it is nontrivial for physicists and mathematicians to understand the complex biology and physiology of the heart, and, conversely, for biologists and cardiologists to grasp the nonlinear electrical and mechanical dynamics. The short reviews by Glass [4] and by Karma and Gilmour [5] are excellent introductory articles for physicists and mathematicians, as well as other more detailed recent reviews [6–8] that cover aspects of nonlinear dynamics in the heart.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear and stochastic dynamics in the heart

et al. 2014

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In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

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Nonlinear Dynamics in Cardiology

Cited by 67 publications

References 160 publications

Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes

Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Nonlinear and stochastic dynamics in the heart

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