Electrical turbulence as a result of the critical curvature for propagation in cardiac tissue

In cardiac tissue, the propagation of electrical excitation waves is dependent on the active properties of the cell membrane (ionic channels) and the passive electrical properties of cardiac tissue (passive membrane properties, distribution of gap junctions, and cell shapes). Initiation of cardiac arrhythmias is usually associated with heterogeneities in the active and/or passive properties of cardiac tissue. However, as a result of the effect of wave front geometry (curvature) on propagation of cardiac waves, inexcitable anatomical obstacles, like veins and arteries, may cause the formation of self-sustained vortices and uncontrolled high-frequency excitation in normal homogeneous myocardium. (c) 1998 American Institute of Physics.     

Effects of reduced discrete coupling on filament tension in excitable media

Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.     

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.     

Characterization of patterned irregularity in locally interacting,spatially extended systems: Ventricular fibrillation

The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviors can be described by solutions of reaction-diffusion equation excitable medium models. The direct comparison of such solutions with existing experimental observations is virtually impossible as there are too many factors to be taken into account, including not only the complicated dynamics of the re-entrant waves of excitation in the tissue, but also the way the appearance of these waves on the surface is modified by the inhomogeneity, anisotropy and three-dimensional nature of heart tissue. One way of indirect comparison is to compare characteristics of the complexity of the model and the real data, that are invariant under these modifications of the signal. Karhunen-Loeve decomposition is a standard tool for evaluating the complexity of multidimensional signals. A comparison of the separate and conjoint complexities of the signals on the opposite sides of the preparation can be considered as an indicator how much three-dimensional effects are essential in the preparation behavior. (c) 2001 American Institute of Physics.     

Stimulus-induced response patterns of medium-embedded neurons

Neuronal ensembles in living organisms are often embedded in a media that provides additional interaction pathways and autoregulation. The underlying mechanisms include but are not limited to modulatory activity of some distantly propagated neuromediators like serotonin, variation of extracellular potassium concentration in brain tissue, and calcium waves propagation in networks of astrocytes. Interaction of these diverse processes can lead to formation of complex spatiotemporal patterns, both self-sustained or triggered by external signal. Besides network effects, many dynamical features of such systems originate from reciprocal interaction between single neuron and surrounding medium. In the present paper we study the response of such systems to the application of a single stimulus pulse. We use a minimal mathematical model representing a forced excitable unit that is embedded in a diffusive or (spatially inhomogeneous) excitable medium. We illustrate three different mechanisms for the formation of response patterns: (i) self-sustained depolarization, (ii) propagation of depolarization due to “nearest-neighbor” networks, and (iii) re-entrant waves.     

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.     

Conduction block in one-dimensional heart fibers

We present a nonlinear dynamical systems analysis of the transition to conduction block in one-dimensional cardiac fibers. We study a simple model of wave propagation in heart tissue that depends only on the recovery of action potential duration and conduction velocity. If the recovery function has slope >or=1 and the velocity recovery function is nonconstant, rapid activation causes dynamical heterogeneity and finally conduction block away from the activation site. This dynamical mechanism may play a role in the initiation and breakup of spiral waves in excitable media.     

Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria

The maintenance of multiple wavelets appears to be a consistent feature of atrial fibrillation (AF). In this paper, we investigate possible mechanisms of initiation and perpetuation of multiple wavelets in a computer model of AF. We developed a simplified model of human atria that uses an ionic-based membrane model and whose geometry is derived from a segmented magnetic resonance imaging data set. The three-dimensional surface has a realistic size and includes obstacles corresponding to the location of major vessels and valves, but it does not take into account anisotropy. The main advantage of this approach is its ability to simulate long duration arrhythmias (up to 40 s). Clinically relevant initiation protocols, such as single-site burst pacing, were used. The dynamics of simulated AF were investigated in models with different action potential durations and restitution properties, controlled by the conductance of the slow inward current in a modified Luo-Rudy model. The simulation studies show that (1) single-site burst pacing protocol can be used to induce wave breaks even in tissue with uniform membrane properties, (2) the restitution-based wave breaks in an atrial model with realistic size and conduction velocities are transient, and (3) a significant reduction in action potential duration (even with apparently flat restitution) increases the duration of AF. (c) 2002 American Institute of Physics.     

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.     

Suppressing arrhythmias in cardiac models using overdrive pacing and calcium channel blockers

Recent findings indicate that ventricular fibrillation might arise from spiral wave chaos. Our objective in this computational study was to investigate wave interactions in excitable media and to explore the feasibility of using overdrive pacing to suppress spiral wave chaos. This work is based on the finding that in excitable media, propagating waves with the highest excitation frequency eventually overtake all other waves. We analyzed the effects of low-amplitude, high-frequency pacing in one-dimensional and two-dimensional networks of coupled, excitable cells governed by the Luo-Rudy model. In the one-dimensional cardiac model, we found narrow high-frequency regions of 1:1 synchronization between the input stimulus and the system's response. The frequencies in this region were higher than the intrinsic spiral wave frequency of cardiac tissue. When we paced the two-dimensional cardiac model with frequencies from this region, we found that spiral wave chaos could, in some cases, be suppressed. When we coupled the overdrive pacing with calcium channel blockers, we found that spiral wave chaos could be suppressed in all cases. These findings suggest that low-amplitude, high-frequency overdrive pacing, in combination with calcium channel inhibitors (e.g., class II or class IV antiarrhythmic drugs), may be useful for eliminating fibrillation. (c) 2002 American Institute of Physics.     

用低通滤波方法终止心脏组织中的螺旋波和时空混沌

通过让心肌细胞钠离子通道的触发门变量延迟打开, 使介质具有激发延迟能力, 介质延迟激发时间随控制电压和刺激频率增加而增加, 当控制电压超过一个阈值时, 延迟激发介质具有低通滤波作用:低频波可以连续通过, 而高频波不能连续通过. 本文用Luo-Rudy相I模型研究了介质延迟激发对螺旋波和时空混沌的影响, 数值模拟结果表明: 当控制电压超过阈值时, 介质的延迟激发可有效消除螺旋波和时空混沌; 从小逐渐增大控制电压, 在钙最大电导率较小情况下, 延迟激发会导致介质激发性降低, 使螺旋波漫游幅度增大, 直至传导障碍导致螺旋波消失; 当钙最大电导率较大时, 延迟激发会导致螺旋波失稳变弱, 这样当控制电压增加到一定值时, 时空混沌可以演化成漫游螺旋波, 当控制参数被适当选取时, 观察到漫游幅度大的螺旋波漫游出系统边界消失现象, 继续增大控制电压将导致时空混沌直接消失.     

Digital photocontrol of the network of live excitable cells

Recent development of tissue engineering techniques allows creating and maintaining almost indefinitely networks of excitable cells with desired architecture. We coupled the network of live excitable cardiac cells with a common computer by sensitizing them to light, projecting a light pattern on the layer of cells, and monitoring excitation with the aid of fluorescent probes (optical mapping). As a sensitizing substance we used azobenzene trimethylammonium bromide (AzoTAB). This substance undergoes cis-trans-photoisomerization and trans-isomer of AzoTAB inhibits excitation in the cardiac cells, while cis-isomer does not. AzoTAB-mediated sensitization allows, thus, reversible and dynamic control of the excitation waves through the entire cardiomyocyte network either uniformly, or in a preferred spatial pattern. Technically, it was achieved by coupling a common digital projector with a macroview microscope and using computer graphic software for creating the projected pattern of conducting pathways. This approach allows real time interactive photocontrol of the heart tissue.     

Wave propagation in heterogeneous bistable and excitable media

Two examples for the propagation of traveling waves in spatially non-uniform media are studied: (a) bistable media with periodically varying excitation threshold and (b) bistable and excitable media with randomly distributed diffusion coefficient and excitation properties. In case (a), we have applied two different singular perturbation techniques, namely averaging (first and second order) and a projection method, to calculate the averaged front velocity as a function of the spatial period L of the heterogeneity for the Schlögl model. Our analysis reveals a velocity overshoot for small values of L and propagation failure for large values of L. The analytical predictions are in good agreement with results of direct numerical simulations. For case (b), effective medium properties are derived by a self-consistent homogenization approach. In particular, the resulting velocities found by direct numerical simulations of the random medium are reproduced well as long as the diffusion lengths in the medium are larger than the heterogeneity scale. Simulations reveal also that complex irregular dynamics can be triggered by heterogeneities.     

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.     

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.     

Nonlocal control of pulse propagation in excitable media

We study the effects of nonlocal control of pulse propagation in excitable media. As ageneric example for an excitable medium the FitzHugh-Nagumo model with diffusion in theactivator variable is considered. Nonlocal coupling in form of an integral term with aspatial kernel is added. We find that the nonlocal coupling modifies the propagatingpulses of the reaction-diffusion system such that a variety of spatio-temporal patternsare generated including acceleration, deceleration, suppression, or generation of pulses,multiple pulses, and blinking pulse trains. It is shown that one can observe these effectsfor various choices of the integral kernel and the coupling scheme, provided that thecontrol strength and spatial extension of the integral kernel is appropriate. In addition,an analytical procedure is developed to describe the stability borders of the spatiallyhomogeneous steady state in control parameter space in dependence on the parameters of thenonlocal coupling.     

Spontaneous spiral wave breakup caused by pinning to the tissue defect

The work presents a mechanism of spiral wave initiation due to the specific boundary conditions on a border of cardiac tissue defect. There are known scenarios when anatomical or functional defects in cardiac tissue may provoke the spiral wave origination, including unidirectional blockage while passing through the narrow gates, bent over critical curvature wave fronts, inhomogeneous recovery of the tissue, etc. We show a new scenario of spiral wave breakup on a small defect, which is unexcitable but permeable for ionic currents supporting the excitation wave. It was believed that such defects stabilize the rotating wave; however, as shown, instead of stabilizing it leads to the spiral breakup and subsequent multiplication of the rotating waves.     

Regular wave propagation out of noise in chemical active media

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.     

Characteristics of quantum conductance in a quasi-one-dimension quantum wire containing cavity structures

Quantum-mechanical calculations of the conductance for model devices, consisting of dual semi-infinite quantum wires connected in series by a cavity, are carried out with use of the coupled-mode transfer method and mode matching technique. The effects of the mode-mode coupling and geometry-induced scattering on the quantum conductance are in detail studied by varying the geometric structure of the cavity. There are no traces of quantization conductance. The pattern of the conductance displays many peaks and dips. The threshold energy of the first onset of the conductance is lower than the normal value for opening the propagation channel of the lowest subband in the quantum wire. The overall character of the conductance exhibits heavy fluctuations around the classical conductance for the relevant point contact. The fluctuation amplitude is of order of 2e ²/h, similar to universal conductance fluctuations. The oscillatory structure becomes rich and dense as the scale of the cavity increases. There is a global trend for the conductance to rise as the cavity is compressed. The structures of resonant peaks and antiresonance dips in the conductance are originated from the mode coupling among the subbands in the cavity and quantum wires. The heavy conductance fluctuation may be caused by the quantum interference of the electron waves due to the multiple scattering (reflections) of electrons by the cavity boundaries.