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

Influence of cardiac tissue anisotropy on re-entrant activation in computational models of ventricular fibrillation

The aim of this study was to establish the role played by anisotropic diffusion in (i) the number of filaments and epicardial phase singularities that sustain ventricular fibrillation in the heart, (ii) the lifetimes of filaments and phase singularities, and (iii) the creation and annihilation dynamics of filaments and phase singularities. A simplified monodomain model of cardiac tissue was used, with membrane excitation described by a simplified 3-variable model. The model was configured so that a single re-entrant wave was unstable, and fragmented into multiple re-entrant waves. Re-entry was then initiated in tissue slabs with varying anisotropy ratio. The main findings of this computational study are: (i) anisotropy ratio influenced the number of filaments Sustaining simulated ventricular fibrillation, with more filaments present in simulations with smaller values of transverse diffusion coefficient, (ii) each re-entrant filament was associated with around 0.9 phase singularities on the surface of the slab geometry, (iii) phase singularities were longer lived than filaments, and (iv) the creation and annihilation of filaments and phase singularities were linear functions of the number of filaments and phase singularities, and these relationships were independent of the anisotropy ratio. This study underscores the important role played by tissue anisotropy in cardiac ventricular fibrillation

Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles

Early Afterdepolarizations, EADs, are defined as the reversal of the action potential before completion of the repolarization phase, which can result in ectopic beats. However, the series of mechanisms of EADs leading to these ectopic beats and related cardiac arrhythmias are not well understood. Therefore, we aimed to investigate the influence of this single cell behavior on the whole heart level. For this study we used a modified version of the Ten Tusscher-Panfilov model of human ventricular cells (TP06) which we implemented in a 3D ventricle model including realistic fiber orientations. To increase the likelihood of EAD formation at the single cell level, we reduced the repolarization reserve (RR) by reducing the rapid delayed rectifier Potassium current and raising the L-type Calcium current. Varying these parameters defined a 2D parametric space where different excitation patterns could be classified. Depending on the initial conditions, by either exciting the ventricles with a spiral formation or burst pacing protocol, we found multiple different spatio-temporal excitation patterns. The spiral formation protocol resulted in the categorization of a stable spiral (S), a meandering spiral (MS), a spiral break-up regime (SB), spiral fibrillation type B (B), spiral fibrillation type A (A) and an oscillatory excitation type (O). The last three patterns are a 3D generalization of previously found patterns in 2D. First, the spiral fibrillation type B showed waves determined by a chaotic bi-excitable regime, i.e. mediated by both Sodium and Calcium waves at the same time and in same tissue settings. In the parameter region governed by the B pattern, single cells were able to repolarize completely and different (spiral) waves chaotically burst into each other without finishing a 360 degree rotation. Second, spiral fibrillation type A patterns consisted of multiple small rotating spirals. Single cells failed to repolarize to the resting membrane potential hence prohibiting the Sodium channel gates to recover. Accordingly, we found that Calcium waves mediated these patterns. Third, a further reduction of the RR resulted in a more exotic parameter regime whereby the individual cells behaved independently as oscillators. The patterns arose due to a phase-shift of different oscillators as disconnection of the cells resulted in continuation of the patterns. For all patterns, we computed realistic 9 lead ECGs by including a torso model. The B and A type pattern exposed the behavior of Ventricular Tachycardia (VT). We conclude that EADs at the single cell level can result in different types of cardiac fibrillation at the tissue and 3D ventricle level

Dynamical mechanism of atrial fibrillation: a topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure

Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system

Spatiotemporal Organization of Electromechanical Phase Singularities during High-Frequency Cardiac Arrhythmias

Ventricular fibrillation (VF) is a lifethreatening electromechanical dysfunction of the heart associated with complex spatiotemporal dynamics of electrical excitation and mechanical contraction of the heart muscle. It has been hypothesized that VF is driven by three-dimensional (3D) rotating electrical scroll waves, which can be characterized by filament-like electrical phase singularities (EPS). Recently, it was shown that rotating excitation waves during VF are associated with rotating waves of mechanical deformation. 3D mechanical scroll waves and mechanical filaments describing their rotational core were observed in the ventricles by using high-resolution ultrasound. The findings suggest that the spatiotemporal organization of cardiac fibrillation may be assessed from waves of mechanical deformation. However, the complex relationship between excitation and mechanical waves during VF is currently not understood. Here, we study the fundamental nature of mechanical phase singularities (MPS), their spatiotemporal organization and relation with EPS. We demonstrate the existence of two fundamental types of MPS: "paired singularities", which are co-localized with EPS, and "unpaired singularities", which can form independently. We show that the unpaired singularities emerge due to the anisotropy of the active force field, generated by fiber anisotropy in cardiac tissue, and the non-locality of elastic interactions, which jointly induce strong spatiotemporal inhomogeneities in the strain fields. The inhomogeneities lead to the breakup of deformation waves and create MPS, even in the absence of EPS, which are typically associated with excitation wave break. We exploit these insights to develop an approach to discriminate paired and unpaired MPS. Our findings provide a fundamental understanding of the complex spatiotemporal organization of electromechanical waves in the heart.Comment: 23 pager, 17 figure

Effect of Tissue Structure (and) Disease on Simulated Arrhythmias in the Human Heart

Ventricular Fibrillation (VF) is a severe cardiac arrhythmia. Early experiments provided evidence that the mechanism of VF is consistent with re-entry. In 3D the sources of re-entrant waves are lines of phase singularity called ‘filaments’. Filament interactions and filament numbers can be used to quantify the complexity of activation patterns in simulated VF. The aim of this thesis is to study the effect of tissue structure, shape, initial conditions, and region of scar on filament dynamics using computational modelling. Transmural heterogeneity in 3D slab tissue representing the ventricular wall did not show important difference in the number of filaments. Configuration of filaments were influenced by transmural heterogeneity. With transmural heterogeneity, clustering of filaments were observed near slow conducting border resulting in increase of filament life time. To study the effect on the shape of the tissue on filaments, filament dynamics in 3D slab tissue was compared with filament dynamics in an idealized human left ventricle (LV) with similar apex base dimension and wall thickness. The volume of idealized LV is about twice the volume of 3D slab. Results showed idealized LV had twice the number of filaments compared to slab geometry especially with steeper restitution dynamics. This thesis highlights non-linear behaviour of activation patterns during VF in 3D where small changes had a large influence on the number of filaments in both 3D slab and idealized LV especially with steeper restitution dynamics. Pre-existing scar tissue in VF patients can act as a source of anatomical re-entry and pin re-entrant filaments to the scar boundary. However, the interaction of scar with complex activation during VF is not well understood. This thesis investigated how simulated scars (circumferential, transmural and sub-endo transmural) with varying size and with either regular or with irregular scar boundary, influenced re-entrant filaments in simplified computational models of 3D slab and idealized LV. Circumferential scar did not show any influence on filament dynamics and clustering of filaments to scar boundary. Increased radius of transmural and sub-endocardial transmural scar had more clustering of filaments to the scar boundary especially with steeper restitution dynamics. Sub- endocardial transmural scar with increased radius had more clustering of filaments compared to transmural scar. Region of scar with irregular boundary had more clustering compared to scar with regular boundary. Generally transmural scar and sub-endocardial transmural scar with regular or irregular boundary did not increase the number of filaments much but increased the length and lifetime of filaments due to clustering of filaments to the scar boundary. Since filaments pin to the boundary of the scar region, it can be hard to remove them using defibrillation techniques. It might be necessary to measure the radius and the depth of pre-existing scar tissue accurately in VF patients, as the bigger scar is likely to have more complex activation in VF. In this way it might be easier to predict the strength of defibrillation to use, in order to stop VF