Self-organization and the dynamical nature of ventricular fibrillation

This article reviews recent data supporting the conjecture that, in the structurally and electrophysiologically normal heart, cardiac fibrillation is not a totally random phenomenon. Experimental and numerical studies based on the theory of excitable media suggest that fibrillation in the mammalian ventricles is the result of self-organized three-dimensional (3-D) electrical rotors giving rise to scroll waves that move continuously (i.e., drift) throughout the heart at varying speeds. A brief review of studies on the dynamics of rotors in two-dimensional (2-D) and 3-D excitable media is presented with emphasis on the experimental demonstration of such dynamics in cardiac muscle of various species. The discussion is centered on rotor dynamics in the presence and the absence of structural heterogeneities, and in the phenomena of drifting and anchoring, which in the electrocardiogram (ECG) may manifest as life-threatening cardiac rhythm disturbances. For instance, in the rabbit heart, a single electrical rotor that drifts rapidly throughout the ventricles gives rise to complex patterns of excitation. In the ECG such patterns are indistinguishable from ventricular fibrillation. On the other hand, a rotor that anchors to a discontinuity or defect in the muscle (e.g., a scar, a large artery or a bundle of connective tissue) may result in stationary rotating activity, which in the ECG is manifested as a form of so-called "monomorphic" ventricular tachycardia. More recent data show that ventricular fibrillation occurs in mammals irrespective of size or species. While in small hearts, such as those of mice and rabbits, a single drifting or meandering rotor can result in fibrillation, in larger hearts, such as the sheep and possibly the human, fibrillation occurs in the form of a relatively small number of coexisting but short-lived rotors. Overall, the work discussed here has paved the way for a better understanding of the mechanisms of fibrillation in the normal, as well as diseased human heart. (c) 1998 American Institute of Physics.     

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.     

基于ANEP染料荧光光谱迁移的单波长心脏光学标测系统

近几年来,光学标测技术已经成为心脏电生理研究中一种非常重要的手段。它利用对嵌在细胞膜上的电压敏感染料随着膜电位变化而产生的荧光光谱迁移进行成像,来进行心律失常与电击除颤等电生理研究。文章测量了常用的电压敏感染料di-4-ANEPPS的荧光光谱,并根据该染料的光谱迁移,设计了一套包括一个通用CCD相机的单波长光学标测系统,可以达到较高的时空分辨率。记录心肌细胞中的电兴奋传导过程,从而可以为今后国内心律失常作用机制的研究工作提供一个有力的工具。     

Ventricular fibrillation and atrial fibrillation are two different beasts

Although the mechanisms of fibrillation are no doubt multi-faceted, the geometry of the heart may play a major role in the dynamics of wave propagation during fibrillation [A. T. Winfree, Science 266, 1003-1006 (1994)]. The ventricles are thick chambers made up of sheets of parallel muscle fibers with the direction of fibers rotating across the ventricular walls (rotational anisotropy). The thick walls of the ventricles allow reentry to develop transmurally, provided the wavelength is sufficiently small. Depending on the kinetics of heart cells, the dynamics of rotating waves in three dimensions may be fundamentally different than in two dimensions, leading to destabilization of reentry and ventricular fibrillation (VF) in thick ventricles. The atria have an intricate geometry comprised of a thin sheet of cardiac tissue attached to a very complex network of pectinate muscles. The branching geometry of the pectinate muscles may lead to destabilization of two-dimensional reentry via "long-distance" electrical connections giving rise to atrial fibrillation (AF). Therefore, although fibrillation occurs via complex three-dimensional wave propagation in the ventricles and the atria, the underlying mechanisms and factors that sustain VF and AF are probably different.(c) 1998 American Institute of Physics.     

Spatiotemporal dynamics of damped propagation in excitable cardiac tissue

Compared to steadily propagating waves (SPW), damped waves (DW), another solution to the nonlinear wave equation, are seldom studied. In cardiac tissue after electrical stimulation in an SPW wake, we observe DW with diminished amplitude and velocity that either gradually decrease as the DW dies, or exhibit a sharp amplitude increase after a delay to become an SPW. The cardiac DW-SPW transition is a key link in understanding defibrillation and stimulation close to the refractory period, and is ideal for a general study of DW dynamics.     

Suppress Winfree turbulence by local forcing excitable systems

The occurrence of Winfree turbulence is currently regarded as one of the principal mechanisms underlying cardiac fibrillation. We develop a local stimulation method that suppresses Winfree turbulence in three-dimensional excitable media. We find that Winfree turbulence can be effectively suppressed by locally injecting periodic signals to only a very small subset (around some surface region) of total space sites. Our method for the first time demonstrates the effectiveness of local low-amplitude periodic excitations in suppressing turbulence in 3D excitable media and has fundamental improvements in efficiency, convenience, and turbulence suppression speed compared with previous strategies. Therefore, it has great potential for developing into a practical low-amplitude defibrillation approach.     

用晚钠电流终止心脏中的螺旋波和时空混沌

采用人类心脏模型研究了用晚钠电流控制二维心脏组织中的螺旋波和时空混沌,我们提出这样的控制策略来产生晚钠电流:让慢失活门变量j始终等于0.7,同时实时调节钠电流的快失活门变量h的阈值电压V_I,即先让阈值电压V_I经过T_1时间从71.55 mV均匀减少到50.55 mV,然后经过T_2时间再从50.55 mV均匀增加到71.55 mV,当阈值电压V_I回到71.55 mV,钠电流的快、慢失活门变量恢复正常变化.数值模拟结果表明:只要适当选择控制时间,不论心肌细胞是否存在自发的晚钠电流,控制产生的晚钠电流都可以有效抑制螺旋波和时空混沌,而且需要的晚钠电流都很小,且控制时间都很短,因为螺旋波和时空混沌消失主要是通过传导障碍消失,少数情况下时空混沌是通过转变为靶波消失.我们希望这种控制方法能为室颤控制提供新的思路.     

The role of cardiac tissue structure in defibrillation

The purpose of this paper is to investigate the relationship between cardiac tissue structure, applied electric field, and the transmembrane potential induced in the process of defibrillation. It outlines a general understanding of the structural mechanisms that contribute to the outcome of a defibrillation shock. Electric shocks defibrillate by changing the transmembrane potential throughout the myocardium. In this process first and foremost the shock current must access the bulk of myocardial mass. The exogenous current traverses the myocardium along convoluted intracellular and extracellular pathways channeled by the tissue structure. Since individual fibers follow curved pathways in the heart, and the fiber direction rotates across the ventricular wall, the applied current perpetually engages in redistribution between the intra- and extracellular domains. This redistribution results in changes in transmembrane potential (membrane polarization): regions of membrane hyper- and depolarization of extent larger than a single cell are induced in the myocardium by the defibrillation shock. Tissue inhomogeneities also contribute to local membrane polarization in the myocardium which is superimposed over the large-scale polarization associated with the fibrous organization of the myocardium. The paper presents simulation results that illustrate various mechanisms by which cardiac tissue structure assists the changes in transmembrane potential throughout the myocardium. (c) 1998 American Institute of Physics.     

基于符号相对熵的心电信号时间不可逆性分析

心电图(ECG)信号的时间不可逆性能够反映出心脏的生理功能和健康状态.从短时ECG信号中探测时间不可逆性特征具有重要的现实意义. 文章提出符号相对熵方法(先进行符号化处理,再分别计算它们的时间不可逆性),研究了从MIT-BIH标准数据库中提取的正常窦性心律(normal sinus rhythm,NSR)、心室纤颤(ventricular fibrillation,VF)、心脏猝死(sudden cardiac death,SCD)三种信号.结果表明,这三种信号的时间不可逆性有所不同:NSR信号的时间不可 关键词： 心电信号 相对熵 时间不可逆性     

Shock-induced arrhythmogenesis in the myocardium

The focus of this article is the investigation of the electrical behavior of the normal myocardium following the delivery of high-strength defibrillation shocks. To achieve its goal, the study employs a complex three-dimensional defibrillation model of a slice of the canine heart characterized with realistic geometry and fiber architecture. Defibrillation shocks of various strengths and electrode configurations are delivered to the model preparation in which a sustained ventricular tachycardia is induced. Instead of analyzing the post-shock electrical events as progressions of transmembrane potential maps, the study examines the evolution of the postshock phase singularities (PSs) which represent the organizing centers of reentry. The simulation results demonstrate that the shock induces numerous PSs the majority of which vanish before the reentrant wavefronts associated with them complete half of a single rotation. Failed shocks are characterized with one or more PSs that survive the initial period of PS annihilation to establish a new postshock arrhythmia. The increase in shock strength results in an overall decrease of the number of PSs that survive over 200 ms after the end of the shock; however, the exact behavior of the PSs is strongly dependent on the shock electrode configuration. (c) 2002 American Institute of Physics.     

多腔体心脏磁场模型的研究与应用

利用核磁共振图像(MRI)中提取的人体和心脏边界,根据边界元方法(BEM)建立了一个考虑左、右心房和心室的多腔体心脏磁场模型.分析了用该模型得到的36通道心脏磁场数据和特定时刻的磁场图.并在此基础上,研究了完全性右束支传导阻滞(CRBBB)和完全性左束支传导阻滞(CLBBB)病人ST-T段的心脏电活动.结果显示,用移动单电流偶极子模拟的单束支电兴奋传导所产生的磁场图与用超导量子干涉器(SQUID)测量的CRBBB/CLBBB病人数据绘制的心脏复极时的心磁图(MCG)十分相似.结果表明,该多腔体心脏BEM模型可用于CLBBB/CRBBB病人心脏磁场逆问题的研究.此外,文中给出了两个评价指标:测量平面上多腔体与单腔体的心脏磁场强度极大值之比,以及两种模型的36个测量点上磁场强度均方根之比.分析表明,多腔体心脏模型更贴近人体心脏的实际情况.该模型中心脏组织电导率参数的取值,以及等效电流偶极子的位置和个数决定了磁场的强度和分布.     

Termination of spiral wave breakup in a Fitzhugh-Nagumo model via short and long duration stimuli

Rotating spiral waves have been observed in a variety of nonlinear biological and physical systems. Spiral waves are found in excitable and oscillatory systems and can be stationary, meander, or even degenerate into multiple unstable rotating waves (a process called "spiral wave breakup"). In the heart, spiral wave breakup is thought to be the underlying mechanism of cardiac fibrillation. The spatiotemporal complexity of multiple unstable spiral waves is difficult to control or terminate. Here, the mechanisms of the termination of spiral wave breakup in response to global stimulation are investigated. A modified Fitzhugh-Nagumo model was used to represent cellular kinetics to study the role of the fast (activation) and slow (recovery) variables. This simplified model allows a theoretical analysis of the termination of spiral wave breakup via both short and long duration pulses. Simulations were carried out in both two-dimensional sheets and in a three-dimensional geometry of the heart ventricles. The short duration pulses affected only the fast variable and acted to reset wave propagation. Monophasic pulses excited tissue ahead of the wave front thus reducing the amount of excitable tissue. Biphasic shocks did the same, but they also acted to generate new wave fronts from the pre-existing wave tails by making some active regions excitable. Thus, if the short duration stimuli were strong enough, they acted to fill in excitable tissue via propagating wave fronts and terminated all activity. The long duration wave forms were selected such that they had a frequency spectrum similar to that of the pseudoelectrocardiograms recorded during fibrillation. These long duration wave forms affected both the recovery and activation variables, and the mechanism of unstable multiple spiral wave termination was different compared to the short duration wave forms. If the long duration stimuli were strong enough, they acted to alter the "state" (i.e., combination of fast and slow variables) of the tissue throughout 1.5 cycles, thus "conditioning" the tissue such that by the end of the stimuli almost no excitable tissue remained. The peak current, total energy, and average power of stimuli required to terminate spiral wave breakup were less for the long duration wave forms compared to the short duration wave forms. In addition, closed loop feedback via stimulation with a wave form that was the difference of the pseudoelectrocardiogram and a strongly periodic chaotic signal was successful at terminating spiral wave breakup. These results suggest that it may be possible to improve cardiac defibrillation efficacy by using long duration wave forms to affect recovery variables in the heart as opposed to the traditional brief duration wave forms that act only on the fast variables. (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.     

Progress toward controlling in vivo fibrillating sheep atria using a nonlinear-dynamics-based closed-loop feedback method

We describe preliminary experiments on controlling in vivo atrial fibrillation using a closed-loop feedback protocol that measures the dynamics of the right atrium at a single spatial location and applies control perturbations at a single spatial location. This study allows investigation of control of cardiac dynamics in a preparation that is physiologically close to an in vivo human heart. The spatial-temporal response of the fibrillating sheep atrium is measured using a multi-channel electronic recording system to assess the control effectiveness. In an attempt to suppress fibrillation, we implement a scheme that paces occasionally the cardiac muscle with small shocks. When successful, the inter-activation time interval is the same and electrical stimuli are only applied when the controller senses that the dynamics are beginning to depart from the desired periodic rhythm. The shock timing is adjusted in real time using a control algorithm that attempts to synchronize the most recently measured inter-activation interval with the previous interval by inducing an activation at a time projected by the algorithm. The scheme is "single-sided" in that it can only shorten the inter-activation time but not lengthen it. Using probability distributions of the inter-activation time intervals, we find that the feedback protocol is not effective in regularizing the dynamics. One possible reason for the less-than-successful results is that the controller often attempts to stimulate the tissue while it is still in the refractory state and hence it does not induce an activation. (c) 2002 American Institute of Physics.     

The effect of gap junctional distribution on defibrillation

We summarize a mathematical theory for direct activation and defibrillation of cardiac tissue. We show that the direct stimulus and defibrillation thresholds are likely to be strongly affected by the gap junctional distribution and density, suggesting an indirect experimental test of the theory. (c) 1998 American Institute of Physics.     

用于心脏电活动成像的空间滤波器输出噪声抑制方法

利用人体表面测量的心脏磁场数据无创成像心脏电活动,需要解决的关键问题是提高其重建分布电流源偶极矩强度的分辨率.本文在最小方差波束成形(MVB)方法的基础上,提出了一种可抑制空间滤波器输出噪声功率增益(SONG)的波束成形方法,目的是通过构造一种新的滤波器权矩阵,约束空间滤波器的输出噪声功率增益,提高重建分布电流源偶极矩强度的分辨率,即分布电流源空间谱估计的源分辨能力,从而增强心脏电活动磁成像的分辨率.文中给出了电流源重建的理论分析和仿真结果;比较了该方法与MVB方法的差别;并给出了两个健康人36通道心脏磁场数据的电活动成像.结果表明,SONG方法分辨电流源的能力较强,能够观察到心脏电磁场信号R峰时刻健康人的心室电活动较强,心房电活动较弱等特征.     

Vulnerability to ventricular fibrillation

One of the factors that favors the development of ventricular fibrillation is an increase in the dispersion of refractoriness. Experiments will be described in which an increase in dispersion in the recovery of excitability was determined during brief episodes of enhanced sympathetic nerve activity, known to increase the risk of fibrillation. Whereas in the normal heart ventricular fibrillation can be induced by a strong electrical shock, a premature stimulus of moderate intensity only induces fibrillation in the presence of regional ischemia, which greatly increases the dispersion of refractoriness. One factor that is of importance for the transition of reentrant ventricular tachycardia to ventricular fibrillation during acute regional ischemia is the subendocardial Purkinje system. After selective destruction of the Purkinje network by lugol, reentrant tachycardias still develop in the ischemic region, but they do not degenerate into fibrillation. Finally, attempts were made to determine the minimal mass of thin ventricular myocardium required to sustain fibrillation induced by burst pacing. This was done by freezing of subendocardial and midmural layers. The rim of surviving epicardial muscle had to be larger than 20 g. Extracellular electrograms during fibrillation in both the intact and the "frozen" left ventricle were indistinguishable, but activation patterns were markedly different. In the intact ventricle epicardial activation was compatible with multiple wavelet reentry, in the "frozen" heart a single, or at most two wandering reentrant waves were seen. (c) 1998 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.     

Artifacts,assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart

Insidious experimental artifacts and invalid theoretical assumptions complicate the comparison of numerical predictions and observed data. Such difficulties are particularly troublesome when studying electrical stimulation of the heart. During unipolar stimulation of cardiac tissue, the artifacts include nonlinearity of membrane dyes, optical signals blocked by the stimulating electrode, averaging of optical signals with depth, lateral averaging of optical signals, limitations of the current source, and the use of excitation-contraction uncouplers. The assumptions involve electroporation, membrane models, electrode size, the perfusing bath, incorrect model parameters, the applicability of a continuum model, and tissue damage. Comparisons of theory and experiment during far-field stimulation are limited by many of these same factors, plus artifacts from plunge and epicardial recording electrodes and assumptions about the fiber angle at an insulating boundary. These pitfalls must be overcome in order to understand quantitatively how the heart responds to an electrical stimulus. (c) 2002 American Institute of Physics.     

Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates

Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF.