Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue

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 are 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 and their application 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 in cardiac arrhythmias.Peer ReviewedPreprin

Induced Drift of Scroll Waves in the Aliev-Panfilov Model and in an Axisymmetric Heart Left Ventricle

The low-voltage cardioversion-defibrillation is a modern sparing electrotherapy method for such dangerous heart arrhythmias as paroxysmal tachycardia and fibrillation. In an excitable medium, such arrhythmias relate to appearance of spiral waves of electrical excitation, and the spiral waves are superseded to the electric boundary of the medium in the process of treatment due to high-frequency stimulation from the electrode. In this paper we consider the Aliev-Panfilov myocardial model, which provides a positive tension of three-dimensional scroll waves, and an axisymmetric model of the left ventricle of the human heart. Two relations of anisotropy are considered, namely, isotropy and physiological anisotropy. The periods of stimulation with an apical electrode are found so that the electrode successfully entrains its rhythm in the medium, the spiral wave is superseded to the base of the ventricle, and disappears. The results are compared in two-dimensional and three-dimensional media. The intervals of effective stimulation periods are sufficiently close to each other in the two-dimensional case and in the anatomical model. However, the use of the anatomical model is essential in determination of the time of superseding. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.The work was supported by the Russian Science Foundation (project No. 17–71–20024). The work was performed with the use of the ‘URAN’ supercomputer of IMM UB RAS

Scroll wave with negative filament tension in a model of the left ventricle of the human heart and its overdrive pacing

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev-Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10-20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10 s. © 2021 American Physical Society.Russian Science Foundation, RSF: 17-71-20024Our work involved simulations at the “Uran” cluster of IMM UB RAS (Ekaterinburg). Our research is supported by a Russian Science Foundation grant (Project 17-71-20024)

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation

Optogenetic Control of Cardiac Arrhythmias

The regular, coordinated contraction of the heart muscle is orchestrated by periodic waves generated by the heart’s natural pacemaker and transmitted through the heart’s electrical conduction system. Abnormalities occurring anywhere within the cardiac electrical conduction system can disrupt the propagation of these waves. Such dis- ruptions often lead to the development of high frequency spiral waves that override normal pacemaker activity and compromise cardiac function. The occurrence of high frequency spiral waves in the heart is associated with cardiac rhythm disorders such as tachycardia and fibrillation. While tachycardia may be terminated by rapid periodic stimulation known as anti-tachycardia pacing (ATP), life-threatening ventricular fibril- lation requires a single high-voltage electric shock that resets all the activity and restore the normal heart function. However, despite the high success rate of defibrillation, it is associated with significant side effects including tissue damage, intense pain and trauma. Thus, extensive research is conducted for developing low-energy alternatives to conventional defibrillation. An example of such an alternative is the low-energy anti-fibrillation pacing (LEAP). However, the clinical application of this technique, and other evolving techniques requires a detailed understanding of the dynamics of spiral waves that occur during arrhythmias. Optogenetics is a tool, that has recently gained popularity in the cardiac research, which serves as a probe to study biological processes. It involves genetically modifying cardiac muscle cells such that they become light sensitive, and then using light of specific wavelengths to control the electrical activity of these cells. Cardiac optogenetics opens up new ways of investigating the mechanisms underlying the onset, maintenance and control of cardiac arrhythmias. In this thesis, I employ optogenetics as a tool to control the dynamics of a spiral wave, in both computer simulations and in experiments.In the first study, I use optogenetics to investigate the mechanisms underlying de- fibrillation. Analogous to the conventional single electric-shock, I apply a single globally-illuminating light pulse to a two-dimensional cardiac tissue to study how wave termination occurs during defibrillation. My studies show a characteristic transient dynamics leading to the termination of the spiral wave at low light intensities, while at high intensities, the spiral waves terminate immediately. Next, I move on to explore the use of optogenetics to study spiral wave termina- tion via drift, theoretically well-known mechanism of arrhythmia termination in the context of electrical stimulation (e.g. ATP). I show that spiral wave drift can be induced by structured illumination patterns using lights of low intensity, that result in a spatial modulation of cardiac excitability. I observe that drift occurs in the positive direction of light intensity gradient, where the spiral also rotates with a longer period. I further show how modulation of the excitability in space can be used to control the dynamics of a spiral wave, resulting in the termination of the wave by collision with the domain boundary. Based on these observations, I propose a possible mechanism of optogenetic defibrillation. In the next chapter, I use optogenetics to demonstrate control over the dynamics of the spiral waves by periodic stimulation with light of different intensities and pacing frequencies resulting in a temporal modulation of cardiac excitability. I demonstrate how the temporal modulation of excitability leads to efficient termination of arrhythmia. In addition, I use computer simulations to identify mechanisms responsible for arrhyth- mia termination for sub- and supra-threshold light intensities. My numerical results are supported by experimental studies on intact hearts, extracted from transgenic mice. Finally, I demonstrate that cardiac optogenetics not only allows control of excita- tion waves, but also by generating new waves through the induction of wave breaks. We demonstrate the effects of high sub-threshold illumination on the morphology of the propagating wave, leading to the creation of new excitation windows in space that can serve as potential sites for re-entry initiation. In summary, this thesis investigates several approaches to control arrhythmia dy- namics using optogenetics. The experimental and numerical results demonstrate the potential of feedback-induced resonant pacing as a low-energy method to control arrhythmia.2022-01-1

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities