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.     

The induction of reentry in cardiac tissue. The missing link: How electric fields alter transmembrane potential

This review examines the initiation of reentry in cardiac muscle by strong electric shocks. Specifically, it concentrates on the mechanisms by which electric shocks change the transmembrane potential of the cardiac membrane and create the physiological substrate required by the critical point theory for the initiation of rotors. The mechanisms examined include (1) direct polarization of the tissue by the stimulating current, as described by the one-dimensional cable model and its two- and three-dimensional extensions, (2) the presence of virtual anodes and cathodes, as described by the bidomain model with unequal anisotropy ratios of the intra- and extracellular spaces, (3) polarization of the tissue due to changing orientation of cardiac fibers, and (4) polarization of individual cells or groups of cells by the electric field ("sawtooth potential"). The importance of these mechanisms in the initiation of reentry is examined in two case studies: the induction of rotors using successive stimulation with a unipolar electrode, and the induction of rotors using cross-field stimulation. These cases reveal that the mechanism by which a unipolar stimulation induces arrhythmias can be explained in the framework of the bidomain model with unequal anisotropy ratios. In contrast, none of the examined mechanisms provide an adequate explanation for the induction of rotors by cross-field stimulation. Hence, this study emphasizes the need for further experimental and theoretical work directed toward explaining the mechanism of field stimulation. (c) 1998 American Institute of Physics.     

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.     

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。     

Modeling the effect of external electric field and current on the stochastic dynamics of ATPase nano-biomolecular motors

The rotary motion of the F₀ part of the F₀F₁-ATPase motor that synthesizes the ATP molecules used by the intracellular stepping motors, such as kinesins, is modeled within a stochastically fluctuating medium via the application of the Langevin dynamics wherein the random intramembrane fluctuations are represented by a white noise. We have investigated the influence of an applied electric field and an applied electric current on this rotary motion, and the subsequent production rate of the ATP molecules. It is seen that the application of a field, or a current, changes both the elastic behavior of the cell membrane and the transmembrane potential. These changes in turn transform the dynamics of the F₀ part of the motor. We have found that at low fields, the role of transmembrane potential becomes significant in the production rate of the ATP molecules, whereas at high fields the changes induced in the surface tension of the membrane also contribute to the production rate of the ATP.     

Defibrillation via the elimination of spiral turbulence in a model for ventricular fibrillation

Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart make it incapable of any concerted pumping action. Methods of controlling ventricular fibrillation include electrical defibrillation as well as injected medication. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often counterproductive, electrical shocks. We propose a defibrillation method that uses a very low-amplitude shock (of order mV) applied for a brief duration (of order 100 ms) and over a coarse mesh of lines on our model ventricle.     

用同步复极化终止心脏中的螺旋波和时空混沌

为了模拟电击除颤导致动作电位持续时间缩短, 在Luo-Rudy相I心脏模型中引入了同步复极化. 研究了同步复极化对螺旋波和时空混沌动力学的影响. 数值结果表明: 在控制周期比较小的情况下, 同步复极化可以有效消除螺旋波和时空混沌, 在有一些控制参数下, 同步复极化只能消除螺旋波, 或者只能消除时空混沌. 当螺旋波不被控制时, 观察到螺旋波转变为长周期和长波长的螺旋波或破碎成时空混沌的现象. 并对控制机制进行了分析. 关键词： 螺旋波 时空混沌 同步复极化 控制     

Turbulence control with local pacing and its implication in cardiac defibrillation

In this review article, we describe turbulence control in excitable systems by using a local periodic pacing method. The controllability conditions of turbulence suppression and the mechanisms underlying these conditions are analyzed. The local pacing method is applied to control Winfree turbulence (WT) and defect turbulence (DT) induced by spiral-wave breakup. It is shown that WT can always be suppressed by local pacing if the pacing amplitude and frequency are properly chosen. On the other hand, the pacing method can achieve suppression of DT induced by instabilities associated with the motions of spiral tips while failing to suppress DT induced by the instabilities of wave propagation far from tips. In the latter case, an auxiliary method of applying gradient field is suggested to improve the control effects. The implication of this local pacing method to realistic cardiac defibrillation is addressed.     

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.     

A virtual instrumentation based protocol for the automated implementation of the inner field compensation method

One influential parameter which mediates interactions between many types of molecules and biological membranes stems from the lumped contributions of the transmembrane potential, dipole potential and the difference in the surface potentials on both sides of a membrane. With relevance to cell physiology, such electrical features of a biomembrane are prone to undergoing changes as a result of interactions with the aqueous surrounding. Among the most useful tools devoted to exploring changes of electrical parameters of a lipid membrane induced by certain extracellular ions, lipid composition, and embedded membrane peptides and proteins, are spectroscopic imaging and the inner field compensation (IFC) method. In this work we layout the principles of a fully computerized version of the IFC method, which makes it more readily available to users. As a direct application, we deployed this improved version of the IFC method to time-resolve changes induced by alamethicin monomers upon membrane dipole potential, following their aggregation within an artificial lipid membrane. Intriguingly, even prior crossing the membrane core, the membrane-bound alamethicin monomers are shown to significantly increase the dipole potential of the monolayer they reside in. Such data further emphasize the yet less-explored interplay between membrane-based protein and peptides, and the membrane dipole potential.     

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.     

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.     

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.     

The extracellular matrix is an important source of ultrasound backscatter from myocardium

Ultrasound tissue characterization with measurement of backscatter has been employed in numerous experimental and clinical studies of cardiac pathology, yet the cellular components responsible for scattering from cardiac tissues have not been unequivocally identified. This laboratory has proposed a mathematical model for myocardial backscatter that postulates the fibrous extracellular matrix (ECM) as a significant determinant of backscatter. To demonstrate the importance of ECM, this group sought to determine whether measurements of backscatter from the isolated ECM could reproduce the known directional dependence, or anisotropy of backscatter, from intact cardiac tissues in vitro. Segments of left ventricular free wall from ten formalin fixed porcine hearts were insonified at 50 MHz, traversing the heart wall from endo- to epicardium to measure the anisotropy of myocardial backscatter, defined as the difference between peak (perpendicular to fibers) and trough (parallel to fibers) backscatter amplitude. The tissue segments were then treated with 10% NaOH to dissolve all of the cellular components, leaving only the intact ECM. Scanning electron micrographs (SEM) were obtained of tissue sections to reveal complete digestion of the cellular elements. The dimensions of the residual voids resulting from cell digestion were approximately the diameter of the intact myocytes (10-30 microm). These samples were reinsonified after seven days of treatment to compare the anisotropy of integrated backscatter. The magnitude of anisotropy of backscatter changed from 15.4 +/- 0.8 to 12.6 +/- 1.1dB for intact as compared with digested specimens. Because digestion of the myocardium leaves only extracellular sources of ultrasonic scattering, and because the isolated ECM exhibits similar ultrasonic anisotropy as does the intact myocardium, it is concluded that there is a direct association between the ECM and the anisotropy of backscatter within intact tissue. Thus, it is suggested that ultrasonic tissue characterization represents a potentially clinically applicable method for delineating the structure and function of the ECM.     

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.     

压缩应变载荷下氮化镓隧道结微观压电特性及其巨压电电阻效应

电子器件可控性研究在日益追求器件智能化和可控化的当今社会至关重要. 基于第一性原理和量子输运计算, 本文研究了压缩应变载荷对氮化镓(GaN)隧道结基态电学性质和电流输运的影响, 在原子尺度上窥视了氮化镓隧道结的微观压电性, 验证了其内在的巨压电电阻(GPR)效应. 计算结果表明, 压缩应变载荷可以调节隧道结内氮化镓势垒层的电势能降、内建电场、电荷密度和极化强度, 进而实现对隧道结电流输运和隧穿电阻的调控. 在-1.0 V的偏置电压下, -5%的压缩应变载荷将使氮化镓隧道结的隧穿电阻增至4倍. 本研究展现了氮化镓隧道结在可控电子器件中的应用潜力, 也展现了应变工程在调控电子器件性能方面的光明前景.     

Stimulation of bone repair with ultrasound: A review of the possible mechanic effects

In vivo and in vitro studies have demonstrated the positive role that ultrasound can play in the enhancement of fracture healing or in the reactivation of a failed healing process. We review the several options available for the use of ultrasound in this context, either to induce a direct physical effect (LIPUS, shock waves), to deliver bioactive molecules such as growth factors, or to transfect cells with osteogenic plasmids; with a main focus on LIPUS (or Low Intensity Pulsed Ultrasound) as it is the most widespread and studied technique. The biological response to LIPUS is complex as numerous cell types respond to this stimulus involving several pathways. Known to-date mechanotransduction pathways involved in cell responses include MAPK and other kinases signaling pathways, gap-junctional intercellular communication, up-regulation and clustering of integrins, involvement of the COX-2/PGE2, iNOS/NO pathways and activation of ATI mechanoreceptor. The mechanisms by which ultrasound can trigger these effects remain intriguing. Possible mechanisms include direct and indirect mechanical effects like acoustic radiation force, acoustic streaming, and propagation of surface waves, fluid-flow induced circulation and redistribution of nutrients, oxygen and signaling molecules. Effects caused by the transformation of acoustic wave energy into heat can usually be neglected, but heating of the transducer may have a potential impact on the stimulation in some in-vitro systems, depending on the coupling conditions. Cavitation cannot occur at the pressure levels delivered by LIPUS. In-vitro studies, although not appropriate to identify the overall biological effects, are of great interest to study specific mechanisms of action. The diversity of current experimental set-ups however renders this analysis very complex, as phenomena such as transducer heating, inhomogeneities of the sound intensity in the near field, resonances in the transmission and reflection through the culture dish walls and the formation of standing waves will greatly affect the local type and amplitude of the stimulus exerted on the cells. A future engineering challenge is therefore the design of dedicated experimental set-ups, in which the different mechanical phenomena induced by ultrasound can be controlled. This is a prerequisite to evaluate the biological effects of the different phenomena with respect to particular parameters, like intensity, frequency, or duty cycle. By relating the variations of these parameters to the induced physical effects and to the biological responses, it will become possible to derive an ‘acoustic dose’ and propose a quantification and cross-calibration of the different experimental systems. Improvements in bone healing management will probably also come from a combination of ultrasound with a ‘biologic’ components, e.g. growth factors, scaffolds, gene therapies, or drug delivery vehicles, the effects of which being potentiated by the ultrasound.     

A solid-state NMR index of helical membrane protein structure and topology

The secondary structure and topology of membrane proteins can be described by inspection of two-dimensional (1)H-(15)N dipolar coupling/(15)N chemical shift polarization inversion spin exchange at the magic angle spectra obtained from uniformly (15)N-labeled samples in oriented bilayers. The characteristic wheel-like patterns of resonances observed in these spectra reflect helical wheel projections of residues in both transmembrane and in-plane helices and hence provide direct indices of the secondary structure and topology of membrane proteins in phospholipid bilayers. We refer to these patterns as PISA (polarity index slant angle) wheels. The transmembrane helix of the M2 peptide corresponding to the pore-lining segment of the acetylcholine receptor and the membrane surface helix of the antibiotic peptide magainin are used as examples.     

Spatial Characteristics of the Beam Plasma Discharge in Crossed Electric and Magnetic Fields

The paper presents the results of the experimental investigation of the beam plasma discharge spatial structure in crossed fields induced by adding a high ionization potential gas to the discharge. Direct experimental evidence of the polarization mechanism of the radial current in a device with this type of discharge has been obtained.     

Maxwell Equations without a Polarization Field,Using a Paradigm from Biophysics

When forces are applied to matter, the distribution of mass changes. Similarly, when an electric field is applied to matter with charge, the distribution of charge changes. The change in the distribution of charge (when a local electric field is applied) might in general be called the induced charge. When the change in charge is simply related to the applied local electric field, the polarization field P is widely used to describe the induced charge. This approach does not allow electrical measurements (in themselves) to determine the structure of the polarization fields. Many polarization fields will produce the same electrical forces because only the divergence of polarization enters Maxwell’s first equation, relating charge and electric forces and field. The curl of any function can be added to a polarization field P without changing the electric field at all. The divergence of the curl is always zero. Additional information is needed to specify the curl and thus the structure of the P field. When the structure of charge changes substantially with the local electric field, the induced charge is a nonlinear and time dependent function of the field and P is not a useful framework to describe either the electrical or structural basis-induced charge. In the nonlinear, time dependent case, models must describe the charge distribution and how it varies as the field changes. One class of models has been used widely in biophysics to describe field dependent charge, i.e., the phenomenon of nonlinear time dependent induced charge, called ‘gating current’ in the biophysical literature. The operational definition of gating current has worked well in biophysics for fifty years, where it has been found to makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that the operational definition of gating current be used to define voltage and time dependent induced charge, although other definitions may be needed as well, for example if the induced charge is fundamentally current dependent. Gating currents involve substantial changes in structure and so need to be computed from a combination of electrodynamics and mechanics because everything charged interacts with everything charged as well as most things mechanical. It may be useful to separate the classical polarization field as a component of the total induced charge, as it is in biophysics. When nothing is known about polarization, it is necessary to use an approximate representation of polarization with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.