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

Dynamika modelu lidské buňky

The heart is a complex organ on its continuous work is dependending life of every human. It is a hollow muscular organ whose mechanical work is controlled by electrical signals. These signals are produced by the heart itself and are propagated at different speeds at its individual parts. Violations of this system can lead to life threatening states. It is therefore very important to describe this system in detail, examine its changes and the effects of these changes on the function of heart. In this work, improved Fenton-Karma model is used for approximation cardiac muscle cell. This model is stimulated on various stimulation frequencies and amplitudes. Responses of this model are studied from the dynamical point of view using phase portraits, the Fourier spectra, Poincaré section, bifurcation diagram and the 0-1 test for chaos.Srdce je komplexní orgán na jehož průběžné práci je závislý život každého člověka. Jedná se o dutý svalový orgán, jehož mechanická práce je řízena elektrickými signály. Tyto signály jsou produkovány samotným srdcem a jsou šířeny různou rychlostí v jeho jednotlivých částech. Porušení tohoto systému může vést k život ohrožujícím stavům. Je proto velmi důležité podrobně popsat tento systém, zkoumat jeho změny a účinky těchto změn na jeho funkci. V této práci je pro aproximaci buněk srdečního svalu použit vylepšený model Fenton-Karma. Tento model je stimulován různou stimulační frekvencí a amplitudou. Odpovědi tohoto modelu jsou studovány z dynamického hlediska pomocí fázových portrétů, Fourierových spekter, Poincarého řezu, bifurkačního diagramu a testu 0-1 chaosu.470 - Katedra aplikované matematikyvýborn

Dynamika modelů srdeční elektrofyziologie

Cardiac arrhythmias are a widespread disease in the developed world, especially in the elderly population, and a leading cause of death. Their origin is very complex and difficult to predict. The causes of this disease are various. Irregular propagation of control signals in heart tissue can occur due to scarring of heart tissue after a heart attack, clogging of arteries in the heart, infection with COVID-19, etc. This work analyses the dynamic properties of cardiac electrophysiology and their changes during the pathophysiological propagation of electrical signals in the heart. Using nonlinear analysis of mathematical models of heart cells are found combinations of stimulation frequencies and amplitudes, at which chaotic responses of cardiac electrophysiology occur. Furthermore, the possibilities of using artificial intelligence to detect dangerous sites based on the spatial arrangement of scars in the heart are presented.Srdeční arytmie jsou ve vyspělém světě rozšířeným onemocněním, zejména u starší populace, a hlavní příčinou úmrtí. Jejich původ je velmi složitý a těžko předvídatelný. Příčiny tohoto onemocnění jsou různé. K nepravidelnému šíření řídících signálů v srdeční tkáni může dojít v důsledku zjizvení srdeční tkáně po infarktu, ucpání tepen v srdci, infekce COVID-19 atd. V této práci jsou analyzovány dynamické vlastnosti srdeční elektrofyziologie a jejich změny při patofyziologickém šíření elektrických signálů v srdci. Nelineární analýzou matematických modelů srdečních buněk jsou nalezeny kombinace stimulačních frekvencí a amplitud, při kterých dochází k chaotických odpovědím srdeční elektrofyziologie. Dále jsou prezentovány možnosti využití umělé inteligence k detekci nebezpečných míst na základě prostorového uspořádání jizev v srdci.96210 - Laboratoř pro náročné datové analýzy a simulacevyhově

Modeling Action Potential Propagation During Hypertrophic Cardiomyopathy Through a Three-Dimensional Computational Model

Hypertrophic cardiomyopathy (HCM) is the most common monogenic disorder and the leading cause of sudden arrhythmic death in children and young adults. It is typically asymptomatic and first manifests itself during cardiac arrest, making it a challenge to diagnose in advance. Computational models can explore and reveal underlying molecular mechanisms in cardiac electrophysiology by allowing researchers to alter various parameters such as tissue size or ionic current amplitudes. The goal of this thesis is to develop a computational model in MATLAB and to determine if this model can accurately indicate cases of hypertrophic cardiomyopathy. This goal is achieved by combining a three-dimensional network of the bidomain model with the Beeler-Reuter model and then by manually varying the thickness of that tissue and recording the resulting membrane potential with respect to time. The results of this analysis demonstrated that the developed model is able to depict variations in tissue thickness through the difference in membrane potential recordings. A one-way ANOVA analysis confirmed that the membrane potential recordings of the different thicknesses were significantly different from one another. This study assumed continuum behavior, which may not be indicative of diseased tissue. In the future, such a model might be validated through in vitro experiments that measure electrical activity in hypertrophied cardiac tissue. This model may be useful in future applications to study the ionic mechanisms related to hypertrophic cardiomyopathy or other related cardiac diseases

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, has made it extremely difficult to pinpoint the detailed mechanisms of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w

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 pro-arrhythmic. 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

Determination of myocardial energetic output for cardiac rhythm pacing

This research is aimed to the determination of the changes in the cardiac energetic output for three different modes of cardiac rhythm pacing. The clinical investigation of thirteen patients with the permanent dual-chamber pacemaker implantation was carried out. The patients were taken to echocardiography examination conducted by way of three pacing modes (AAI, VVI and DDD). The myocardial energetic parameters—the stroke work index (SWI) and the myocardial oxygen consumption (MVO2) are not directly measurable, however, their values can be determined using the numerical model of the human cardiovascular system. The 24-segment hemodynamical model (pulsating type) of the human cardiovascular system was used for the numerical simulation of the changes of myocardial workload for cardiac rhythm pacing. The model was fitted by well-measurable parameters for each patient. The calculated parameters were compared using the two-tailed Student’s test. The differences of SWI and MVO2 between the modes AAI and VVI and the modes DDD and VVI are statistically significant (P < 0.05). On the other hand, the hemodynamic effects for the stimulation modes DDD and AAI are almost identical, i.e. the differences are statistically insignificant (P > 0.05)

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction–diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters’ space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.ELKARTEK KK-2020/0000

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (ICaL) plays a critical role in cardiac electrophysiology, and models of ICaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modeling ICaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalian ICaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model of ICaL. // This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiolog

A new approach to modelling the dynamics of cardiac action potentials

This thesis is concerned with the development of a new approach to the modelling of cardiac action potentials. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behaviour of cardiac cells well, the models are computationally demanding for numerical simulations and are very difficult to analyse from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. However, from a physiological viewpoint these equations are unrealistic and often fail to reproduce important quantitative properties of the tissue. In this thesis we introduce a different approach to the mathematical modelling of cardiac action potentials with the aim of gaining a clearer insight into the origin of the dynamics of electrophysiological models. Chapter 1 contains an introduction to the research and outlines the main aims of the work. In Chapter 2 various background material is introduced. This includes some basic electrophysiology, ideas currently used in mathematical modelling of excitable media, and details of models previously developed for the study of cardiac tissue. In Chapter 3, following a detailed analysis of an early physiological model, we develop a mathematical model based on the currents involved. This model reproduces, to good accuracy, action potentials of heart tissue and we discuss the essential ideas behind the dynamics. In Chapter 4 the mathematical model developed in the previous chapter is analysed in more detail and simpler equations using similar ideas are introduced. Various types of action potentials of varying behaviours are studied. In Chapter 5 we investigate some spatial simulations of the new mathematical models. We principally concentrate on one-dimensional studies but towards the end of the chapter we look at some two-dimensional simulations. Finally, in Chapter 6, we discuss our conclusions and some possible ideas for further related work. Details of our methods of numerical simulation are included in Appendix A