Complete dynamical analysis of myocardial cell exposed to magnetic flux

The heart is the essential, yet complex, component of the human cardiovascular system. In the past few decades, researchers have taken giant steps toward better understanding of the cardiac system and there have been proposed some mathematical models to describe the heart's function. In this paper, a new Fitzhugh-Nagumo neuron (FNN) model is proposed to model the electrical activity of the heart in which the effect of magnetic flux is considered. Magnetic field can greatly affect the heart's function. The dynamical analyses of the model, including quantitative assessment of the system's equilibria and its stability, phase portraits analysis, bifurcation and Lyapunov exponents analysis, and basin of attraction analysis, are carried out. In addition, a model of cardiac tissue is designed to study the electrical spatiotemporal activity of heart tissue under the electromagnetic effects. Our numerical simulations confirm that the electromagnetic excitation can change the normal rhythm of the heart. It can initiate the reentrant excitations leading to emergence of spiral seeds. This study highlights the role of electromagnetic induction in dynamical instability of the action potential duration, and thus the chaotic dynamics in the cardiac tissue.     

Molecular dynamics studies of slow dynamics in random media: Type A-B and reentrant transitions

Molecular dynamics simulations of mobile particles confined in disordered immobile particles are carried out. Slow dynamics in random media are characterized by two types of dynamics: Type B dynamics for large mobile particle density and Type A dynamics for small mobile particle density. The crossover from Type A to B dynamics is studied by the mean square displacement and the density correlation function. Our results are qualitatively consistent with the results of recent numerical and theoretical studies on relevant spatially heterogeneous systems. We also investigate the effect of random matrix generation on the dynamics of mobile particles in order to examine the reentrant transition predicted by the recent mode-coupling theory. Our simulations demonstrate that the diffusion of the mobile particles largely depends on the protocol of the random matrix generation and that the reentrant transition is observed for a particular protocol.     

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 reentrant waves, i.e., electrical wave(s) that recirculate 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, have made it extremely difficult to pinpoint the detailed dynamics 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. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. 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. (c) 2002 American Institute of Physics.     

Mechanisms for initiation of cardiac discordant alternans

Electrical alternans, defined as a beat-to-beat change in the duration of the excited phase of cardiac cells, is among the known precursors of sudden cardiac death. It may appear as concordant (all the tissue presenting the same phase of oscillation) or discordant (with out-of-phase regions distributed among tissue). Spatially discordant alternans can lead to unidirectional block that initiates reentry and ventricular fibrillation. The role played by tissue heterogeneities and heart rate changes in their initiation remains, however, unclear. We study the mechanisms for initiation of spatially discordant alternans by numerical simulations of an ionic model spatially distributed in a one-dimensional cable and in an anatomical model of the rabbit heart. The effects of CV-restitution, ectopic beats, and the role of spatial gradients of electrical restitution properties are investigated. In homogeneous tissue, the origin of discordant alternans may be dynamical, through CV-restitution, or due to a localized change in the pacing period. We also find that a sudden change of stimulation rate can initiate discordant alternans in the presence of a spatial gradient of APD-restitution without necessitating CV-restitution. The mechanism of, and the conditions for, initiation are determined based on an iterated map analysis of beat to beat changes of APD. This analysis leads to the definition of a vulnerable window for initiation of discordant alternans. Moreover, the pattern of spatially discordant alternans is found to change slowly over several beats following initiation, as reflected in ECG recordings.     

Active dynamics of filaments in motility assays

We study the active dynamics of single and interacting cytoskeletal filaments in motility assays, in which immobilized motor proteins bind the filaments to a surface and actively pull them along this surface. We present a model which couples the overdamped dynamics of filaments, the active dynamics of motor heads, and the elasticity of motor stalks and which can be used for Langevin dynamics simulations. Single filaments perform a persistent random walk, which we characterize by several simulation results. For interacting filaments with a repulsive interaction of filaments, the motor-driven dynamics of filaments leads to a non-equilibrium phase transition which generalizes the isotropic-nematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations and analytical theory show that the motor activity enhances the tendency for nematic ordering.     

Spatially hybrid computations for streamer discharges : II. Fully 3D simulations

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air. Future applications of the hybrid model lie in effects of electron density fluctuations on inception, propagation and branching of streamers, and in accurate calculations of electron energies at and of electron run-away from the streamer head. The last is relevant for hard radiation from streamer-leader systems and possibly for Terrestrial Gamma-Ray Flashes.     

Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity

This study presents computations and analysis of the dynamics of reentrant spiral waves in a realistic model of cardiac electrical activity, incorporating the Beeler-Reuter equations into a two-dimensional cable model. In this medium, spiral waves spontaneously break up, but may be stabilized by shortening the excitation pulse duration through an acceleration of the dynamics of the calcium current. We describe the breakup of reentrant waves based on the presence of slow recovery fronts within the medium. This concept is introduced using examples from pulse circulation around a ring and extended to two-dimensional propagation. We define properties of the restitution and dispersion relations that are associated with slow recovery fronts and promote spiral breakup. The role of slow recovery fronts is illustrated with concrete examples from numerical simulations. (c) 1996 American Institute of Physics.     

Death,dynamics and disorder: Terminating reentry in excitable media by dynamically-induced inhomogeneities

Formation of feedback loops of excitation waves (reentrant circuit) around non-conducting ventricular scar tissue is a common cause of cardiac arrhythmias, such as ventricular tachycardia, often leading to death. This is typically treated by rapid stimulation from an implantable device (ICD). However, the mechanisms of reentry termination success and, more importantly, failure, are poorly understood. To study such mechanisms, we simulated pacing termination of reentry in a model of cardiac tissue having significant restitution and dispersion properties. Our results show that rapid pacing dynamically generates conduction inhomogeneities in the reentrant circuit, leading to successful pacing termination of tachycardia. The study suggests that more effective pacing algorithms can be designed by taking into account the role of such dynamical inhomogeneities.     

Cooperative motions in a finite size model of liquid silica: an anomalous behavior

Finite size effects on dynamical heterogeneity are studied in liquid silica with Molecular Dynamics simulations using the BKS potential model. When the system size decreases relaxation times are found to increase in accordance with previous results in finite-size simulations and confined liquids. It has been suggested that this increase may be related to a modification of the spatially heterogeneous dynamics in confined liquids. In agreement with this hypothesis we observe a decrease of the spatially heterogeneous dynamics when the size decreases. The spatially heterogeneous dynamics is usually characterized by the dynamical aggregation of the most or the least mobile atoms. However we find that the decrease of the dynamical aggregation associated to the least mobile atoms is much more important than the decrease associated to the most mobile atoms when the size decreases. This result associated with a slowing down of the liquid is surprising as it is expected that the dynamical aggregation of the least mobile atoms should increase the slowing down of the liquid dynamics. The decrease of the heterogeneous behaviour is also in contradiction with the increase of the spatially heterogeneous dynamics observed in liquids confined inside nanopores. However, an increase of the non-Gaussian parameter appears both for the confinement inside nanopores and for the finite size simulations. As the non-Gaussian parameter is usually associated with the heterogeneous dynamics, the increase of the non-Gaussian parameter together with a decrease of the spatially heterogeneous dynamics is also surprising.     

Atomistic and lattice model of a grain boundary defaceting phase transition

Recent calculations have shown that grain boundary (GB) stress is too small to stabilize finite GB facets, suggesting that the existing theory of GB defaceting phase transitions is incomplete. We perform molecular dynamics calculations, which show a reversible phase transition at approximately 400 K with a concerted shuffle of two atoms at the facet junction as the elementary excitation. Based on this excitation we formulate an appropriate lattice model, perform Monte Carlo simulations, and establish an analytical relationship between the elementary excitation energy and the transition temperature.     

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter S?1. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity, which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.     

Coupled Iterated Map Models of Action Potential Dynamics in a One-dimensional Cable of Cardiac Cells

Low-dimensional iterated map models have been widely used to study action potential dynamics in isolated cardiac cells. Coupled iterated map models have also been widely used to investigate action potential propagation dynamics in one-dimensional (1D) coupled cardiac cells, however, these models are usually empirical and not carefully validated. In this study, we first developed two coupled iterated map models which are the standard forms of diffusively coupled maps and overcome the limitations of the previous models. We then determined the coupling strength and space constant by quantitatively comparing the 1D action potential duration profile from the coupled cardiac cell model described by differential equations with that of the coupled iterated map models. To further validate the coupled iterated map models, we compared the stability conditions of the spatially uniform state of the coupled iterated maps and those of the 1D ionic model and showed that the coupled iterated map model could well recapitulate the stability conditions, i.e., the spatially uniform state is stable unless the state is chaotic. Finally, we combined conduction into the developed coupled iterated map model to study the effects of coupling strength on wave stabilities and showed that the diffusive coupling between cardiac cells tends to suppress instabilities during reentry in a 1D ring and the onset of discordant alternans in a periodically paced 1D cable.     

随机反应扩散格气模型上钙动力学的粗粒化模拟

发展了一种基于随机格气模型的粗粒化方法,该方法能有效模拟内质网表面钙动力学信息. 首先将相邻的微观节点合并成粗粒化节点,再根据局域平均场近似推导出粗粒化反应速率,然后执行粗粒化动力学蒙特卡洛模拟. 发现粗粒化动力学蒙特卡洛模拟结果和微观模拟结果非常吻合. 有趣的是,存在一个最佳的粗粒化比m,使得粗粒化模拟与微观模拟的相变点偏差最小. 固定m,发现临界点随体系尺度增加而单调增加,而且相变点的偏差与体系尺度存在一个标度关系.此外,该粗粒化方法大大地加快了蒙特卡洛模拟速率,并且与微观模拟直接相关. 该方法可以广泛用来研究体系尺度效应,而节省大量计算时间.     

Computerized mapping of fibrillation in normal ventricular myocardium

It is well known that the ability to fibrillate is intrinsic to a normal ventricle that exceeds a critical mass. The questions we address are how is ventricular fibrillation (VF) initiated and perpetuated in normal myocardium, and why is VF not seen more often in the general population if all ventricles have the ability to fibrillate. To study the mechanisms of VF, we used computerized mapping techniques with up to 512 channels of simultaneous multisite recordings for data acquisition. The data were then processed for dynamic display of the activation patterns and for mathematical analyses of the activation intervals. The results show that in normal ventricles, VF can be initiated by a single strong premature stimulus given during the vulnerable period of the cardiac cycle. The initial activations form a figure-eight pattern. Afterward, VF will perpetuate itself without any outside help. The self-perpetuation itself is due to at least two factors. One is that single wave fronts spontaneously break up into two or more wavelets. The second is that when two wavelets intersect perpendicular to each other, the second wavelet is broken by the residual refractoriness left over from the first wavelet. Mathematical analyses of the patterns of activation during VF revealed that VF is a form of chaos, and that transition from ventricular tachycardia (VT) to VF occurs via the quasiperiodic route. In separate experiments, we found that we can convert VF to VT by tissue size reduction. The physiological mechanism associated with the latter transition appears to be the reduction of the number of reentrant wave fronts and wandering wavelets. Based on these findings, we propose that the reentrant wave fronts and the wandering wavelets serve as the physiological equivalent of coupled oscillators. A minimal number of oscillators is needed for VF to perpetuate itself, and to generate chaotic dynamics; hence a critical mass is required to perpetuate VF. We conclude that VF in normal myocardium is a form of reentrant cardiac arrhythmia. A strong electrical stimulus initiates single or dual reentrant wave fronts that break up into multiple wavelets. Sometimes short-lived reentry is also generated during the course of VF. These organized reentrant and broken wavelets serve as coupled oscillators that perpetuate VF and maintain chaos. Although the ability to support these oscillators exists in a normal ventricle, the triggers required to generate them are nonexistent in the normal heart. Therefore, VF and sudden death do not happen to most people with normal ventricular myocardium. (c) 1998 American Institute of Physics.     

Unidirectional pinning and hysteresis of spatially discordant alternans in cardiac tissue

Spatially discordant alternans is a widely observed pattern of voltage and calcium signals in cardiac tissue that can precipitate lethal cardiac arrhythmia. Using spatially coupled iterative maps of the beat-to-beat dynamics, we explore this pattern's dynamics in the regime of a calcium-dominated period-doubling instability at the single-cell level. We find a novel nonlinear bifurcation associated with the formation of a discontinuous jump in the amplitude of calcium alternans at nodes separating discordant regions. We show that this jump unidirectionally pins nodes by preventing their motion away from the pacing site following a pacing rate decrease but permitting motion towards this site following a rate increase. This unidirectional pinning leads to strongly history-dependent node motion that is strongly arrhythmogenic.     

Moment equations for a spatially extended system of two competing species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.     

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.     

Hybrid modeling of electrical and optical behavior in the heart

Optical mapping of transmembrane potential using voltage-sensitive dyes has revolutionized cardiac electrophysiology by enabling the visualization of electrical excitation waves in the heart. However, the interpretation of the optical mapping data is complicated by the fact that the optical signal arises not just from the surface, but also from some depth into the heart wall. Here, we review modeling efforts, in which the diffusion of photons is incorporated into the computer simulations of cardiac electrical activity (“hybrid” modeling), with the goal of improving our understanding of optical signals. We discuss the major accomplishments of hybrid modeling which include: (i) the explanation of the optical action potential upstroke morphology and prediction of its dependence on the subsurface wave front angle, (ii) the unexpectedly low magnitudes of optically recorded surface potentials during electrical shocks, and (iii) the “depolarization” of the core of the spiral wave and odd dual-humped optical action potentials during reentrant activation. We critically examine current optical mapping techniques and controversies in our understanding of electroporation during defibrillation. Finally, we provide a brief overview of recent theoretical studies aimed at extending optical mapping techniques for imaging intramural excitation to include transillumination imaging of scroll wave filaments and depth-resolved optical tomographic methods.