Global coupling in excitable media provides a simplified description of mechanoelectrical feedback in cardiac tissue

Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.

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

This article characterizes the cardiac autonomous electrical activity induced by the mechanical deformations in the cardiac tissue through the mechano-electric feedback. 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 parameter 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.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Transient and periodic spatiotemporal structures in a reaction-diffusion-mechanics system

We study transient spatiotemporal structures induced by a weak space-time localized stimulus in an excitable contractile fiber within a two-component globally coupled reaction-diffusion model. The model which we develop allows us to analyze various regimes of excitation spreading and determine origin of the induced structures for various contraction types (defined by the fiber fixation) and global coupling strengths. One of the most notable effects we observed is the after-excitation effect. It leads to emergence of multiple excitation pulses excited by a single external stimulus and can result in long-lasting transient activity and appearance of new oscillatory attractor regimes, including the ones with multiple phase clusters.

Control of cardiac alternans in an electromechanical model of cardiac tissue

Electrical alternations in cardiac action potential duration have been shown to be a precursor to arrhythmias and sudden cardiac death. Through the mechanism of excitation-contraction coupling, the presence of electrical alternans induces alternations in the heart muscle contractile activity. Also, contraction of cardiac tissue affects the process of cardiac electric wave propagation through the mechanism of the so-called mechanoelectrical feedback. Electrical excitation and contraction of cardiac tissue can be linked by an electromechanical model such as the Nash-Panfilov model. In this work, we explore the feasibility of suppressing cardiac alternans in the Nash-Panfilov model which is employed for small and large deformations. Several electrical pacing and mechanical perturbation feedback strategies are considered to demonstrate successful suppression of alternans on a one-dimensional cable. This is the first attempt to combine electrophysiologically relevant cardiac models of electrical wave propagation and contractility of cardiac tissue in a synergistic effort to suppress cardiac alternans. Numerical examples are provided to illustrate the feasibility and the effects of the proposed algorithms to suppress cardiac alternans.

Exact coherent structures and chaotic dynamics in a model of cardiac tissue

Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low- and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are referred to as exact coherent structures (ECS) and play an important role in both initiating and sustaining turbulence. The nature of ECS and their role in organizing spatiotemporally chaotic dynamics, however, is reasonably well understood only for systems on relatively small spatial domains lacking continuous Euclidean symmetries. Construction of ECS on large domains and in the presence of continuous translational and/or rotational symmetries remains a challenge. This is especially true for models of excitable media which display spiral turbulence and for which the standard approach to computing ECS completely breaks down. This paper uses the Karma model of cardiac tissue to illustrate a potential approach that could allow computing a new class of ECS on large domains of arbitrary shape by decomposing them into a patchwork of solutions on smaller domains, or tiles, which retain Euclidean symmetries locally.

Cardiac contraction induces discordant alternans and localized block

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e., alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be proarrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e., from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.

Control of cardiac alternans by mechanical and electrical feedback

A persistent alternation in the cardiac action potential duration has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. A coupling between these cardiac alternans and the intracellular calcium dynamics has also been identified in previous studies. In this paper, the system of PDEs describing the small amplitude of alternans and the alternation of peak intracellular Ca(2+) are stabilized by optimal boundary and spatially distributed actuation. A simulation study demonstrating the successful annihilation of both alternans on a one-dimensional cable of cardiac cells by utilizing the full-state feedback controller is presented. Complimentary to these studies, a three variable Nash-Panfilov model is used to investigate alternans annihilation via mechanical (or stretch) perturbations. The coupled model includes the active stress which defines the mechanical properties of the tissue and is utilized in the feedback algorithm as an independent input from the pacing based controller realization in alternans annihilation. Simulation studies of both control methods demonstrate that the proposed methods can successfully annihilate alternans in cables that are significantly longer than 1 cm, thus overcoming the limitations of earlier control efforts.

Swing, release, and escape mechanisms contribute to the generation of phase-locked cluster patterns in a globally coupled FitzHugh-Nagumo model

We investigate the mechanism of generation of phase-locked cluster patterns in a globally coupled FitzhHugh-Nagumo model where the fast variable (activator) receives global feedback from the slow variable (inhibitor). We identify three qualitatively different mechanisms (swing-and-release, hold-and-release, and escape-and-release) that contribute to the generation of these patterns. We describe these mechanisms and use this framework to explain under what circumstances two initially out-of-phase oscillatory clusters reach steady phase-locked and in-phase synchronized solutions, and how the phase difference between these steady state cluster patterns depends on the clusters relative size, the global coupling intensity, and other model parameters.

Dynamic mechanisms of generation of oscillatory cluster patterns in a globally coupled chemical system

We use simulations and dynamical systems tools to investigate the mechanisms of generation of phase-locked and localized oscillatory cluster patterns in a globally coupled Oregonator model where the activator receives global feedback from the inhibitor, mimicking experimental results observed in the photosensitive Belousov-Zhabotinsky reaction. A homogeneous two-cluster system (two clusters with equal cluster size) displays antiphase patterns. Heterogenous two-cluster systems (two clusters with different sizes) display both phase-locked and localized patterns depending on the parameter values. In a localized pattern the oscillation amplitude of the largest cluster is roughly an order of magnitude smaller than the oscillation amplitude of the smaller cluster, reflecting the effect of self-inhibition exerted by the global feedback term. The transition from phase-locked to localized cluster patterns occurs as the intensity of global feedback increases. Three qualitatively different basic mechanisms, described previously for a globally coupled FitzHugh-Nagumo model, are involved in the generation of the observed patterns. The swing-and-release mechanism is related to the canard phenomenon (canard explosion of limit cycles) in relaxation oscillators. The hold-and-release and hold-and-escape mechanisms are related to the release and escape mechanisms in synaptically connected neural models. The methods we use can be extended to the investigation of oscillatory chemical reactions with other types of non-local coupling.

Cardiac alternans annihilation by distributed mechano-electric feedback (MEF)

The presence of the electrical alternans induces, through the mechanism of the excitation-contraction coupling, an alternation in the heart muscle contractile activity. In this work, we demonstrate the cardiac alternans annihilation by applied mechanical perturbation. In particular, we address annihilation of alternans in realistic heart size tissue by considering ionic currents suggested by Luo-Rudy-1 (LR1) model, in which the control algorithm involves a combined electrical boundary pacing control and a spatially distributed calcium based control which perturbs the calcium in the cells. Complimentary to this, we also address a novel mechanism of alternans annihilation which uses a Nash Panfilov model coupled with the stress equilibrium equations. The coupled model includes an additional variable to represent the active stress which defines the mechanical properties of the tissue.

[One-dimensional time-dependent model of the cardiac pacemaker activity induced by the mechanoelectric feedback in a thermo-electro-mechanical background]

AIM OF THE STUDY

In a healthy heart, the mechanoelectric feedback (MEF) process acts as an intrinsic regulatory mechanism of the myocardium which allows the normal cardiac contraction by damping mechanical perturbations in order to generate a new healthy electromechanical situation. However, under certain conditions, the MEF can be a generator of dramatic arrhythmias by inducing local electrical depolarizations as a result of abnormal cardiac tissue deformations, via stretch-activated channels (SACs). Then, these perturbations can propagate in the whole heart and lead to global cardiac dysfunctions. In the present study, we qualitatively investigate the influence of temperature on autonomous electrical activity generated by the MEF.

METHOD

We introduce a one-dimensional time-dependent model containing all the key ingredients that allow accounting for the excitation-contraction coupling, the MEF and the thermoelectric coupling.

RESULTS

Our simulations show that an autonomous electrical activity can be induced by cardiac deformations, but only inside a certain temperature interval. In addition, in some cases, the autonomous electrical activity takes place in a periodic way like a pacemaker. We also highlight that some properties of action potentials, generated by the mechanoelectric feedback, are significantly influenced by temperature. Moreover, in the situation where a pacemaker activity occurs, we also show that the period is heavily temperature-dependent.

CONCLUSIONS

Our qualitative model shows that the temperature is a significant factor with regards to the electromechanical behavior of the heart and more specifically, with regards to the autonomous electrical activity induced by the cardiac tissue deformations.

Emergence of spiral wave activity in a mechanically heterogeneous reaction-diffusion-mechanics system

We perform a numerical study of emergent spiral wave activity in a two-dimensional reaction-diffusion-mechanics medium with a regional inhomogeneity in active and passive mechanical properties. We find that self-sustaining spiral wave activity emerges for a wide range of mechanical parameters of the inhomogeneity via five mechanisms. We classify these mechanisms, relate them to parameters of the inhomogeneity, and discuss how these results can be applied to understand the onset of cardiac arrhythmias due to regional mechanical heterogeneity.

Delay-enhanced coherent chaotic oscillations in networks with large disorders

We study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all-to-all (global) topology in the presence of impurities (disorder). We find that the coupling delay is capable of inducing phase-coherent chaotic oscillations in both types of networks, thereby enhancing the spatiotemporal complexity even in the presence of 50% of symmetric disorders of both fixed and random types. Furthermore, the coupling delay increases the robustness of the networks up to 70% of disorders, thereby preventing the network from acquiring periodic oscillations to foster disorder-induced spatiotemporal order. We also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated Kuramoto order parameter. We also explain a possible mechanism for the phenomenon of delay-induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications.