Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.     

心脏磁场分布电流源重构及其精度分析

用测量到的心脏磁场信号重构其电流源是一种无创揭示心脏电活动的方法. 心脏电活动的时空信息可视化, 将有助于心脏功能的研究和心脏疾病诊断. 本文通过仿真实验研究了一种减时窗波束形成器对分布时变电流源的重构能力, 以及源重构结果与心室兴奋传播的关系. 采用元胞自动机模拟心室的兴奋传播, 产生分布随时间变化的电流源, 并用边界元法构建了一个心脏-躯干模型, 模拟体电导的作用. 仿真结果表明, 这种减时窗波束形成器能够重构分布时变电流源, 并达到较好的精度. 将该方法和无穷大均匀介质导联矩阵用于一例正常人的心脏磁场信号分析, 其结果可以反映心室兴奋传播的基本特征. 关键词： 心磁图 源重构 边界元 波束形成器     

Effect of the architecture of the left ventricle on the speed of the excitation wave in muscle fibers

It is known that preferential paths for the propagation of an electrical excitation wave in the human ventricular myocardium are associated with muscle fibers in tissue. The speed of the excitation wave along a fiber is several times higher than that across the direction of the fiber. To estimate the effect of the architecture and anisotropy of the myocardium of the left ventricle on the process of its electrical activation, we have studied the relation between the speed of the electrical excitation wave in a one-dimensional isolated myocardial fiber consisting of sequentially coupled cardiomyocytes and in an identical fiber located in the wall of a threedimensional anatomical model of the left ventricle. It has been shown that the speed of a wavefront along the fiber in the three-dimensional myocardial tissue is much higher than that in the one-dimensional fiber. The acceleration of the signal is due to the rotation of directions of fibers in the wall and to the position of the excitation wavefront with respect to the direction of this fiber. The observed phenomenon is caused by the approach of the excitable tissue with rotational anisotropy in its properties to a pseudoisotropic tissue.     

Models of defibrillation of cardiac tissue

Heterogeneities, such as gap junctions, defects in periodical cellular lattices, intercellular clefts and fiber curvature allow one to understand the effect of an electric field in cardiac tissue. They induce membrane potential variations even in the bulk of the myocardium, with a characteristic sawtooth shape. The sawtooth potential, induced by heterogeneities at large scales (tissue strands) can be more easily observed, and lead to stronger effects than the one induced at the cellular level. In the generic model of propagation in cardiac tissue (FitzHugh), 4 mechanisms of defibrillation were found, two mechanisms based on excitation (E(A),E(M)), and two-on de-excitation (D(A),D(M)). The lowest electric field is required by an E(M) mechanism. In the Beeler-Reuter ionic model, mechanism D(M) is impossible. We critically review the experimental basis of the theory and propose new experiments. (c) 1998 American Institute of Physics.     

Curvature-dependent excitation propagation in cultured cardiac tissue

The geometry of excitation wave front may play an important role on the propagation block and spiral wave formation. The wave front which is bent over the critical value due to interaction with the obstacles may partially cease to propagate and appearing wave breaks evolve into rotating waves or reentry. This scenario may explain how reentry spontaneously originates in a heart. We studied highly curved excitation wave fronts in the cardiac tissue culture and found that in the conditions of normal, non-inhibited excitability the curvature effects do not play essential role in the propagation. Neither narrow isthmuses nor sharp corners of the obstacles, being classical objects for production of extremely curved wave front, affect non-inhibited wave propagation. The curvature-related phenomena of the propagation block and wave detachment from the obstacle boundary were observed only after partial suppression of the sodium channels with Lidocaine. Computer simulations confirmed the experimental observations. The explanation of the observed phenomena refers to the fact that the heart tissue is made of finite size cells so that curvature radii smaller than the cardiomyocyte size loses sense, and in non-inhibited tissue the single cell is capable to transmit excitation to its neighbors.     

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.     

Elasticity and active force generation of cochlear outer hair cells.

The cochlear outer hair cell is described by a cylindrical membrane model, characterized by area and shear moduli for a passive elastic element and an active tension element dependent on the membrane potential. In passive experiments, these moduli are determined from the pressure-strain relations. The area modulus obtained is 0.07 N m-1, similar to a lipid bilayer and the shear modulus is 0.007 N m-1. These moduli combined with previous active experiments show that the active tension is nearly isotropic and is about 1.6 x 10(-2) N m-1 V-1, resulting in a 0.5 nN/mV force per cell. This implies that the receptor potential for acoustical stimulation produces an active force comparable to the acoustic force applied to the basilar membrane per outer hair cell. This finding supports the hypothesis that the outer hair cell acts as feedback motor in the fine tuning mechanism of the mammalian ear.     

Enhanced self-termination of re-entrant arrhythmias as a pharmacological strategy for antiarrhythmic action

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional virtual ventricular tissues based on the Oxsoft family of cell models, with membrane excitation parameters simulating the inherited long Q-T syndromes has been shown to be consistent with this hypothesis: the largest meander is seen in the syndrome with the lowest probability of death per arrhythmic episode. Here we extend our previous results to virtual tissues based on the Luo-Rudy family of models. Consistent with our hypothesis, for both families of models, whose different ionic mechanisms produce different patterns of meander, the LQT virtual tissue with the larger meander simulates the syndrome with the lower probability of death per episode. Further, we search the parameter space of the repolarizing currents to find their conductance parameter values that give increased meander of spiral waves. These parameters may provide targets for antiarrhythmic drugs designed to act by increasing the likelihood of self-termination of re-entrant arrhythmias. (c) 2002 American Institute of Physics.     

An investigation into the role of the optical detection set-up in the recording of cardiac optical mapping signals: A Monte Carlo simulation study

Photon scattering is known to distort the fluorescence signals recorded from optically mapped cardiac tissue. However, the contribution of the parameters which define the optical detection set-up has not been assessed. In this study, Monte Carlo (MC) simulations of photon scattering within ventricular tissue are combined with a detailed model of a tandem-lens optical detection apparatus to characterise (i) the spatial origin upon emission of photons recorded in voltage-sensitive fluorescence measurements of cardiac electrical activity (using the fluorescent dye di-4-ANEPPS) and how this affects signal distortion, and (ii) the role the detector characteristics could play in modulating signal distortion during uniform illumination and photon emission from tissue depth. Results show that, for the particular excitation/emission wavelengths considered (488 nm and 669 nm, respectively), the dimensions of the scattering volume during uniform illumination extend around 3 times further in the surface recording plane than in depth. As a result, fluorescence recordings during electrical propagation are more distorted when transmembrane potential levels differ predominantly in the surface plane than in depth. In addition, MC simulation results show that the spatial accuracy of the fluorescence signal is significantly limited due to photon scattering, with only a small fraction of the recorded signal intensity originating from tissue beneath the pixel (approximately 11% for a 0.25×0.25 mm pixel). Increasing pixel size increases this fraction, however, it also results in an increase in the scattering volume dimensions, thus reducing the spatial resolution of the optical system, and increasing signal distortion. MC simulations also demonstrate that photon scattering in cardiac tissue limits the ability of optical detection system tuning in accurately locating fluorescent emission from depth. Specifically, our results prove that the focal plane depth that yields maximum signal intensity provides an underestimation of the emission depth. In conclusion, our study demonstrates the potential of MC simulations of photon scattering in guiding the design of optical mapping set-ups to optimise performance under diverse experimental conditions.     

Sensor design for development of tribo-electric tomography system with increased number of sensors

Electrodynamic sensor, which can also be called as tribo-electric sensor, senses the electrostatic charge carried by the particle. The tomography system using electrodynamic sensor is called as tribo-electric tomography system. Source of the signal induced on the electrodynamic sensor is brought by the object to be measured and no excitation circuit is necessary. This electrodynamic sensing is a passive sensing and the fast and light weighted tomography system is expected. On the other hand, most of tomography system, like capacitance tomography or resistance tomography, demands excitation circuit and is an active sensing. The number of measurements with the passive sensing is equal to the number of sensors and that of active sensing is the number of the combinations of two sensors. The passive sensing tomography system demands more sensors to be settled. We plan to improve in reconstructed images by increasing the number of the electrodynamic sensors in tribo-electric tomography system. We investigate the influence of surface area to signal intensity solving the electrical field in the sensing zone using finite element method.     

被动方式产生近似无衍射贝塞尔光技术

无衍射光束具有中心光斑小且不随传播距离变化、自再现、产生局域空心光等特点,由于这些特殊的光束特性而在许多领域,如计量学,经典光学,非线性光学和生命科学等领域中得到广泛的应用。无衍射光束的产生与变换是目前的一个研究热点。通过衍射理论、干涉理论和几何光学方法可对无衍射光进行描述。实现无衍射贝塞尔光束的方法可分为主动式和被动式。本文主要综述地介绍了几种被动式产生近似无衍射贝塞尔光束的最新技术,通过分析其优缺点,给出了这些技术的适用范围。     

Reentrant excitation in an analog-digital hybrid circuit model of cardiac tissue

We propose an analog-digital hybrid circuit model of one-dimensional cardiac tissue with hardware implementation that allows us to perform real-time simulations of spatially conducting cardiac action potentials. Each active nodal compartment of the tissue model is designed using analog circuits and a dsPIC microcontroller, by which the time-dependent and time-independent nonlinear current-voltage relationships of six types of ion channel currents employed in the Luo-Rudy phase I (LR-I) model for a single mammalian cardiac ventricular cell can be reproduced quantitatively. Here, we perform real-time simulations of reentrant excitation conduction in a ring-shaped tissue model that includes eighty nodal compartments. In particular, we show that the hybrid tissue model can exhibit real-time dynamics for initiation of reentries induced by uni-directional block, as well as those for phase resetting that leads to annihilation of the reentry in response to impulsive current stimulations at appropriate nodes and timings. The dynamics of the hybrid model are comparable to those of a spatially distributed tissue model with LR-I compartments. Thus, it is conceivable that the hybrid model might be a useful tool for large scale simulations of cardiac tissue dynamics, as an alternative to numerical simulations, leading toward further understanding of the reentrant mechanisms.     

Formation of virtual isthmus: A new scenario of spiral wave death after a decrease in excitability

Termination of rotating (spiral) waves or reentry is crucial when fighting with the most dangerous cardiac tachyarrhythmia. To increase the efficiency of the antiarrhythmic drugs as well as finding new prospective ones it is decisive to know the mechanisms how they act and influence the reentry dynamics. The most popular view on the mode of action of the contemporary antiarrhythmic drugs is that they increase the core of the rotating wave (reentry) to that extent that it is not enough space in the real heart for the reentry to exist. Since the excitation in cardiac cells is essentially change of the membrane potential, it relies on the functioning of the membrane ion channels. Thus, membrane ion channels serve as primary targets for the substances, which may serve as antiarrhythmics. At least, the entire group of antiarrhythmics class I (modulating activity of sodium channels) and partially class IV (modulating activity of calcium channels) are believed to destabilize and terminate reentry by decreasing the excitability of cardiac tissue. We developed an experimental model employing cardiac tissue culture and photosensitizer (AzoTAB) to study the process of the rotating wave termination while decreasing the excitability of the tissue. A new scenario of spiral wave cessation was observed: an asymmetric growth of the rotating wave core and subsequent formation of a virtual isthmus, which eventually caused a conduction block and the termination of the reentry.     

Outer hair cell active force generation in the cochlear environment

Outer hair cells are critical to the amplification and frequency selectivity of the mammalian ear acting via a fine mechanism called the cochlear amplifier, which is especially effective in the high-frequency region of the cochlea. How this mechanism works under physiological conditions and how these cells overcome the viscous (mechanical) and electrical (membrane) filtering has yet to be fully understood. Outer hair cells are electromotile, and they are strategically located in the cochlea to generate an active force amplifying basilar membrane vibration. To investigate the mechanism of this cell's active force production under physiological conditions, a model that takes into account the mechanical, electrical, and mechanoelectrical properties of the cell wall (membrane) and cochlear environment is proposed. It is shown that, despite the mechanical and electrical filtering, the cell is capable of generating a frequency-tuned force with a maximal value of about 40 pN. It is also found that the force per unit basilar membrane displacement stays essentially the same (40 pNnm) for the entire linear range of the basilar membrane responses, including sound pressure levels close to hearing threshold. Our findings can provide a better understanding of the outer hair cell's role in the cochlear amplifier.     

Nonlinear discharge dynamics in small bore current channels

General properties of current and voltage dynamics for discharges having narrow current channels are studied using a generic transmission-line model with active parameters. The line parameters for the inductance and capacitance per unit length are, except for positivity and some physically motivated monotonicity conditions, left as unspecified functions of local line current and voltage. The resistance per unit length is taken to vary inversely with current, thereby assuring dynamical properties common to transient electrical discharges. Emphasis is placed on determining global properties of current front dynamics, i.e., the speed and direction of motion of the free boundary interfaces between instantaneously active (current-carrying) and passive (current-free) regions of the discharge current channel, and the space-time paths across which current reversal occurs. The results are applied to surface electrical discharges initiated at a charge spot     

Cardiac Excitation Waves under Strong Hyperkalemia Condition

Normal blood levels of potassium are critical for maintaining normal heart electrical rhythm. Both low blood potassium levels (hypokalemia) and high blood potassium levels (hyperkalemia) can lead to abnormal heart rhythms. The aim of the work presented is to study the effect of potassium concentration on the excitation wave in the cardiac tissue. Results have been obtained both in the experimental model, which is a monolayer of neonatal rat cardiomyocytes, and in the modified Korhonen computer model, designed for ventricular rat neonatal cardiomyocytes. The existence of non-sodium excitation waves under a strong hyperkalemia (more than 10 mM K + in the extracellular environment) in the cardiomyocyte monolayer has been found and has also be confirmed by inactivation of sodium channels with a specific channel blocker.     

Evolution of nonclassical light propagating through passive optical coupled waveguides: Entanglement dynamic

In this paper, nonclassical light propagation through passive optical coupler is investigated. On the other hand, passive optical device design for nonclassical light is analyzed in this work. Effect of mode mismatching including mismatching in propagation constant on operation of the considered device is studied. We investigate different separable and entangled input excitations with single photons in this case. We specially study the measure of entanglement and effect of propagation constant mismatch on it. The simultaneous effect of loss and mismatch is also studied. Obtained results for different excitation states illustrate that there is a possibility to design such that the system operation can be immune versus fabrication imperfections.     

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.     

Virtual cell and tissue dynamics of ectopic activation of the ventricles

Cardiac ventricular cells and tissues are normally excitable, and are activated by propagating waves of excitation that are initiated in the specialized pacemaking region of the heart. However, isolated or repetitive activity can be initiated at abnormal (ectopic) sites in the ventricles. To trigger an endogenous ectopic beat, there must be a compact focus of cells with changed membrane excitation parameters and kinetics, which initiate activity by after-depolarizations triggered by propagating activity, or that have bifurcated into autorhythmicity. This ectopic focus needs to be large enough, and adequately coupled, to drive the surrounding tissue. We investigate the initiation of ectopic excitation in computational models of human ventricular cells triggered by after-depolarizations and by up/down regulation of specific membrane conductance systems, and the propagation and evolution of ectopic activity in homogeneous or heterogeneous and isotropic, anisotropic, or orthotropic tissues.