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

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

Optics and Fluid Dynamics Department annual progress report for 2001

research within three scientific programmes: (1) laser systems and optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The department has core competences in: optical sensors, optical materials, optical storage, biooptics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM, by Danish research councils and by industry. A summary of the activities in 2001 is presented. ISBN 87-550-2993-0 (Internet

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

Fluctuations and Oscillatory Instabilities of Intracellular Fiber networks

Biological systems with their complex biochemical networks are known to be intrinsically noisy. The interplay between noise and dynamical behavior is particularly relevant in the case of chemotactic amoeboid cells as their cytoskeleton operates close to an oscillatory instability. Here, we investigate the oscillatory dynamics in the actin system of chemotactic amoeboid cells. We show that the large phenotypic variability in the polymerization dynamics can be accurately captured by a generic nonlinear oscillator model, in the presence of noise. The relative role of the noise is fully determined by a single dimensionless parameter, experimentally measurable, and whose distribution completely characterizes the possible cellular behavior. We find that cells operate either below or above the threshold of self-oscillation, always in a regime where noise plays a very substantial role. To test the limits of this phenomenological description, we perturbed experimentally the cytoskeletal dynamics by a short chemoattractant pulse and measured the spatio-temporal response of filamentous actin reporter, LimE, and depolymerization regulators Coronin1 and Aip1. After pulsing, we observed self oscillating cells to relax back to their oscillatory state after a noisy transient. Particularly long transients were observed for cells initially displaying highly correlated oscillations. The observation of a slow recovery time of the actin polymerizing network provides a link to the long times scales, characteristic of chemotactic cell motility. In the second part of this work, we have characterized the response of LimE, Aip1, and Coronin to cAMP in non oscillating cells. We have used a proposed method that transforms the observed time series into symbolic dynamics, that gives partial information on the interactions between these proteins. We tested the predictions by studying the LimE response in mutant cells that either lacked Aip1 or Coronin. Finally, a model is proposed where Aip1 and Coronin synergizes to control actin polymerization

Network Dynamics, Synchronization, and Self-Propelled Particles in Chemical Systems

Neural networks are a class of biological networks of great importance. They are a key component of the central nervous system that coordinates body functions. The exploration of the detailed mechanism of biological neural networks remains extremely active. Inspired by the structure of biological neural networks, artificial neural networks have been designed to solve a variety of problems in pattern recognition, prediction, optimization and control. However, few studies have been reported that explore the dynamics of biological neural networks using chemical systems. As part of this thesis, an experimentally trainable network based on the photosensitive Belousov-Zhabotinsky reaction is developed, where the individual node is a catalyst loaded micro-particle. The interactions between nodes in the network are created by arranging links with different weights, similar to the excitable and inhibitory synapses in biological neural networks. The distribution of the weights of the excitable links has been studied. The results indicate that a stable distribution of the weights is exhibited.;Synchronization in coupled nonlinear oscillators is a remarkable and ubiquitous phenomenon in nature. Application of periodic global feedback to oscillators allows the creation of new kinds of wave patterns with the coexistence of stable phase states. In experiments with the photosensitive BZ reaction, periodic global feedback is implemented by varying the illumination intensity. In a 1:1 frequency-locked entrainment, 2pi phase fronts called phase kinks have been observed in the photosensitive BZ reaction. Generally, a phase kink represents the existence of stable phase differences, propagating as an analog of traveling waves in 2D excitable media. By modifying the conditions of local forcing, the experiments show that a phase kink can be trapped to form a closed pattern.;Self-propulsion is an essential feature of many living systems. There are numerous realizations of self-propelled particles in biological systems, such as the bacteria Listeria monocytogenes in cells. Such biological phenomena inspire the creation of artificial self-propelled particles. Recently, nonbiological micro- to nanoscale particles, that convert chemical energy into translational motion, have been investigated. Studies show that Pt-coated polystyrene particles, coated on one hemisphere with Pt, exhibit self-propulsion in dilute H2O2 solutions. Here, we experimentally study the dynamical behavior of silica particles that are asymmetrically coated with Pt in H2O2 solutions, similar to Pt-coated polystyrene particles. The focus of our study is on the particle orientation with respect to the direction of motion. This is investigated using velocity autocorrelation and propulsion direction analyses