Periodic conductivity as a mechanism for cardiac stimulation and defibrillation

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Effects of high-frequency biphasic shocks on ventricular vulnerability and defibrillation outcomes through synchronized virtual electrode responses

Electrical defibrillation is a well-established treatment for cardiac dysrhythmias. Studies have suggested that shock-induced spatial sawtooth patterns and virtual electrodes are responsible for defibrillation efficacy. We hypothesize that high-frequency shocks enhance defibrillation efficacy by generating temporal sawtooth patterns and using rapid virtual electrodes synchronized with shock frequency. High-speed optical mapping was performed on isolated rat hearts at 2000 frames/s. Two defibrillation electrodes were placed on opposite sides of the ventricles. An S1-S2 pacing protocol was used to induce ventricular tachyarrhythmia (VTA). High-frequency shocks of equal energy but varying frequencies of 125–1000 Hz were used to evaluate VTA vulnerability and defibrillation success rate. The 1000-Hz shock had the highest VTA induction rate in the shorter S1-S2 intervals (50 and 100 ms) and the highest VTA defibrillation rate (70%) among all frequencies. Temporal sawtooth patterns and synchronous shock-induced virtual electrode responses could be observed with frequencies of up to 1000 Hz. The improved defibrillation outcome with high-frequency shocks suggests a lower energy requirement than that of low-frequency shocks for successful ventricular defibrillation.

Response of single cell with acute angle exposed to an external electric field

It is known that the electric field incurs effects on the living cells. Predicting the response of single cell or multilayer cells to induced alternative or static eclectic field has permanently been a challenge. In the present study a first order single cell with acute angle under the influence of external electric field is considered. The cell division stage or the special condition of reshaping is modelled with a cone being connected. In the case of cell divisions, anaphase, it can be considered with two cones that connected nose-to-nose. Each cone consists of two regions. The first is the membrane modelled with a superficial layer, and the second is cytoplasm at the core. A Laplace equation is written for this model and the distribution of its electric field is a sharp point in the single cell for which an acute angle model is calculated.

Termination of reentrant cardiac action potential propagation using far-field electrical pacing

Several different types of rapid cardiac rhythm disorders, including atrial and ventricular fibrillation, are likely caused by multiple, rapidly rotating, action potential (AP) waves. Thus, an electrical pacing therapy, whose effectiveness is based on being delivered with a particular timing relative to one of these waves, is unlikely to be useful in terminating the remaining waves. Here, we develop pacing protocols that are designed to terminate rotating waves independently of when the sequences of stimuli are imposed or where each wave is in its rotation at the time the sequences are initiated. These protocols are delivered as far-field stimuli, and therefore are capable of simultaneously influencing all the waves present. The pacing intervals for these protocols are, in general, of unequal duration and are determined through examination of the dynamics of AP propagation in a 1-D ring model. Series of two or three stimuli with interstimulus intervals chosen in this way are shown to be effective in terminating these waves over a wide range of ring circumferences and AP dynamical parameters. Stimulus sequences of this type may form the basis for developing new defibrillation protocols to test in experiments or more realistic models of the electrical heart.

Increased interstitial loading reduces the effect of microstructural variations in cardiac tissue

Electrical propagation in diseased and aging hearts is strongly influenced by structural changes that occur in both the intracellular and interstitial spaces of cardiac tissue; however, very few studies have investigated how interactions between the two spaces affect propagation at the microscale. In this study, we used one-dimensional microstructural computer models of interconnected ventricular myocytes to systematically investigate how increasing the effective interstitial resistivity (rho(oeff)) influences action potential propagation in fibers with variations in intracellular properties such as cell coupling and cell length. Changes in rho(oeff) were incorporated into a monodomain model using a correction to the intracellular properties that was based on bidomain simulations. The results showed that increasing rho(oeff) in poorly coupled one-dimensional fibers alters the distribution of electrical load at the microscale and causes propagation to become more continuous. In the poorly coupled fiber, this continuous state is characterized by decreased gap junction delay, sustained conduction velocity, increased sodium current, reduced maximum upstroke velocity, and increased safety factor. Long, poorly coupled cells experience greater loading effects than short cells and show the greatest initial response to changes in rho(oeff). In inhomogeneous fibers with adjacent well-coupled and poorly coupled regions, increasing rho(oeff) in the poorly coupled region also reduces source-load mismatch, which delays the onset of conduction block and reduces the dispersion of repolarization at the transition between the two regions. Increasing the rho(oeff) minimizes the effect of cell-to-cell variations and may influence the pattern of activation in critical regimes characterized by low intercellular coupling, microstructural heterogeneity, and reduced or abnormal membrane excitability.

A mechanism for the upper limit of vulnerability

BACKGROUND

The strongest shock that induces reentry in the heart is the upper limit of vulnerability (ULV). In order to understand defibrillation, one must know what causes the ULV.

OBJECTIVE

The goal of this study was to examine the mechanism of the upper limit of vulnerability.

METHODS

Numerical simulations of cardiac tissue were performed using the bidomain model. An S2 shock was applied during the refractory period of the S1 action potential, and results using a smooth curving fiber geometry were compared with results using a smooth plus random fiber geometry.

RESULTS

When using a smooth fiber geometry only, no ULV was observed. However, when a random fiber geometry was included, the ULV was present. The difference arises from the fate of the shock-induced break wave front when it reaches the edge of the tissue hyperpolarized by the shock (the virtual anode).

CONCLUSION

Our numerical simulations suggest that local heterogeneities throughout the tissue may be crucial for determining the fate of the shock-induced wave front at the edge of the virtual anode, and therefore play an important role in the mechanism underlying the ULV.

The role of mechanoelectric feedback in vulnerability to electric shock

Experimental and clinical studies have shown that ventricular dilatation is associated with increased arrhythmogenesis and elevated defibrillation threshold; however, the underlying mechanisms remain poorly understood. The goal of the present study was to test the hypothesis that (1) stretch-activated channel (SAC) recruitment and (2) geometrical deformations in organ shape and fiber architecture lead to increased arrhythmogenesis by electric shocks following acute ventricular dilatation. To elucidate the contribution of these two factors, the study employed, for the first time, a combined electro-mechanical simulation approach. Acute dilatation was simulated in a model of rabbit ventricular mechanics by raising the LV end-diastolic pressure from 0.6 (control) to 4.2 kPa (dilated). The output of the mechanics model was used in the electrophysiological model. Vulnerability to shocks was examined in the control, the dilated ventricles, and in the dilated ventricles that also incorporated currents through SAC as a function of local strain, by constructing vulnerability grids. Results showed that dilatation-induced deformation alone decreased upper limit of vulnerability (ULV) slightly and did not result in increased vulnerability. With SAC recruitment in the dilated ventricles, the number of shock-induced arrhythmia episodes increased by 37% (from 41 to 56) and the lower limit of vulnerability (LLV) decreased from 9 to 7 V/cm, while ULV did not change. The heterogeneous activation of SAC caused by the heterogeneous fiber strain in the ventricular walls was the main reason for increased vulnerability to electric shocks since it caused dispersion of electrophysiological properties in the tissue, resulting in postshock unidirectional block and establishment of reentry.

Construction of a computer model to investigate sawtooth effects in the Purkinje system

The sawtooth effect refers to how one end of a cardiac cell is depolarized, while the opposite end is hyperpolarized, upon exposure to an exogenous electric field. Although hypothesized, it has not been observed in tissue. The Purkinje system is a one-dimensional (1-D) cable-like system residing on the endocardial surface of the heart and is the most obvious candidate for the manifestation of this phenomenon. This paper describes a computer modeling study of the effect of electric fields on the Purkinje system. Starting with a three-dimensional geometrically realistic, finite element, ventricular description, a Purkinje system is constructed which adheres to general physiological principles. Electrical activity in the Purkinje is described by use of 1-D cubic Hermite finite elements. Such a formulation allows for accurate modeling of loading effects at the Purkinje-myocyte junctions, and for preserving the discrete nature of the system. The response of a strand of Purkinje cells to defibrillation strength shocks is computed under several conditions. Also, the response of the isolated Purkinje network is illustrated. Results indicate that the geometry of the Purkinje system is the greatest determinant for far field excitation of the system. Given parameters within the plausible physiological range, the 1-D nature of the Purkinje system may lead to sawtooth potentials which are large enough to affect excitation. Thus, the Purkinje system is capable of affecting the defibrillation process, and warrants further experimentation to elucidate its role.

Quantification of shock-induced microscopic virtual electrodes assessed by subcellular resolution optical potential mapping in guinea pig papillary muscle

INTRODUCTION

The primary objective of this study was the quantitative description of shock-induced, locally occurring virtual electrodes in natural cardiac tissue.

METHODS AND RESULTS

Multiscale optical potential mapping using 10x, 20x, and 40x magnifying objectives, achieving resolutions of 0.13, 0.065, and 0.033 mm, was performed when applying uniform shocks (+/-10 V/cm, 5 ms) during diastole and action potential plateau. A procedure was developed to identify local potential deviations as depolarizing or hyperpolarizing peaks and to quantify their occurrence and characteristic amplitudes, lateral extents, and dynamics. At shock onset, peaks of either polarity developed significantly faster (tau = 0.92 +/- 0.65 ms, N = 64) than the average bulk polarization (tau = 2.25 +/- 0.96 ms, P < 0.001) and appeared locally fixed, changing their polarity at shock reversal. The mean peak magnitude (21.2 +/- 12 mV) and the amplitude distribution were essentially independent from the magnification. The peak density continuously increased with decreasing peak extent (taken at 70% of the amplitude), reaching a maximum of approximately 3 peaks/mm2 in the range of approximately 30-65 microm. There was no correlation between peak amplitude and size throughout. Potentially exciting peaks were found with a density of 0.04-0.2 peaks/mm2 corresponding to estimated 1-5 peaks/mm3.

CONCLUSIONS

Our results suggest that microscopic inhomogeneities form a substantial substrate for far-field excitation in natural cardiac tissue. Here, we effectively bridged the gap between the extensively studied myocyte cultures and larger heart preparations.

Simulations of optical mapping during electroporation

Experiments using optical mapping suggest that electroporation occurs in cardiac tissue when the transmembrane potential, Vm, is observed to be significantly less than +/- 400 mV. Our hypothesis, which we test by numerical simulation, is that Vm is greater than +/- 400 mV at the tissue surface, but optical mapping underestimates Vm because it averages over depth. Results indicate a significant underestimation of Vm. Experimental studies indicate a depolarization of the resting transmembrane potential, Vrest, after a strong shock. In a homogeneous model, electroporation only occurs near the tissue surface. Just as Vm during the stimulus is underestimated due to averaging, we hypothesize that the depolarization of Vrest is also underestimated.

Cardiac resynchronization therapy and phase resetting of the sinoatrial node: a conjecture

Congestive heart failure is a severe chronic disease often associated with disorders that alter the mechanisms of excitation-contraction coupling that may result in an asynchronous left ventricular motion which may further impair the ability of the failing heart to eject blood. In recent years a therapeutic approach to resynchronize the ventricles (cardiac resynchronization therapy, CRT) has been performed through the use of a pacemaker device able to provide atrial-based biventricular stimulation. Atrial lead senses the spontaneous occurrence of cells depolarization and sends the information to the generator which, in turn, after a settled delay [atrioventricular (AV) delay], sends electrical impulses to both ventricles to stimulate their synchronous contraction. Recent studies performed on heart rate behavior of chronically implanted patients at different epochs after implantation have shown that CRT can lead to sustained overall improvement of heart function with a reduction in morbidity and mortality. At this moment, however, there are no studies about CRT effects on spontaneous heart activity of chronically implanted patients. We performed an experimental study in which the electrocardiographic signal of five subjects under chronic CRT was recorded during the activity of the pacemaker programmed at different AV delays and under spontaneous cardiac activity after pacemaker deactivation. The different behavior of heart rate variability during pacemaker activity and after pacemaker deactivation suggested the hypothesis of a phase resetting mechanism induced by the pacemaker stimulus on the sinoatrial (SA) node, a phenomenon already known in literature for aggregate of cardiac cells, but still unexplored in vivo. The constraints imposed by the nature of our study (in vivo tests) made it impossible to plan an experiment to prove our hypothesis directly. We therefore considered the best attainable result would be to prove the accordance of our data to the conjecture through the use of models and physical considerations. We first used the data of literature on far-field effects of cardiac defibrillators to prove that the pacemaker impulses delivered to the two ventricles were able to induce modifications in membrane voltage at the level of the SA node. To simulate a phase resetting mechanism of the SA node, we used a Van der Pol modified model to allow the possibility of changing the refractory period and the firing frequency of the cells separately. With appropriate parameters of the model we reproduced phase response curves that can account for our experimental data. Furthermore, the simulated curves closely resemble the functional form proposed in literature for perturbed aggregate of cardiac cells. Despite the small sample of subjects investigated and the limited number of ECG recordings at different AV delays, we think we have proved the plausibility of the proposed conjecture.

Role of intramural virtual electrodes in shock-induced activation of left ventricle: Optical measurements from the intact epicardial surface

BACKGROUND

According to one hypothesized mechanism of defibrillation, shocks directly excite the bulk of ventricular myocardium in the excitable state due to intramural virtual electrodes; however, this hypothesis has not been examined in intact myocardium.

OBJECTIVES

The purpose of this study was examine the role of intramural virtual electrodes in shock-induced activation of intact left ventricular (LV) tissue.

METHODS

Twelve isolated porcine LV preparations were stained with a transmembrane potential (V(m))-sensitive dye by two methods: (1) surface staining and (2) global staining via coronary perfusion. Shocks (E approximately 0.8-48 V/cm, duration = 10 ms) were applied across the wall from epicardium to endocardium during diastole via transparent electrodes. Shock-induced V(m) responses were measured optically from the intact epicardial surface after surface staining and global staining.

RESULTS

Surface-staining recordings demonstrated different V(m) responses to cathodal and anodal shocks. Whereas cathodal shocks caused depolarization and rapid activation of the epicardial surface, anodal shocks induced hyperpolarization and delayed surface activation. In contrast, global-staining V(m) responses to cathodal and anodal shocks were qualitatively similar. Both responses were characterized by activation with small latency and rapid propagation. Weak shocks of both polarities induced monotonic action potential upstrokes; stronger shocks induced nonmonotonic upstrokes with two rising phases at shock onset and end. Such features of global-staining V(m) responses as make activation of the epicardium by anodal shocks and the nonmonotonic action potential upstrokes can be explained by the presence of subepicardial intramural virtual electrodes.

CONCLUSION

These data suggest that shocks induce intramural virtual electrodes that directly excite LV tissue and account for the shape of optical V(m) responses recorded from the epicardial surface.

Role of microscopic tissue structure in shock-induced activation assessed by optical mapping in myocyte cultures

INTRODUCTION

Termination of ventricular fibrillation by electric shocks is believed to be due to the direct activation of large tissue mass that may be caused by microscopic virtual electrodes formed at discontinuities in tissue structure. Here, microscopic shock-induced activation was measured optically in myocyte cultures; spatially averaged microscopic Vm measurements were compared with macroscopic measurements from left ventricular (LV) tissue.

METHODS AND RESULTS

Experiments were performed in linear cell strands of different width (approximately 0.1 and 0.8 mm) and isolated porcine LV preparations. Uniform field shocks were applied across strands or LV preparations during diastole and action potential (AP) plateau. Depending on shock strength, three different types of activation were observed in cell strands. Weakest shocks produced "delayed make" activation that started on the cathodal strand side after long latency and rapidly spread to the anodal side. Stronger shocks caused "make" activation with short latency and rapid spread across strands. Strongest shocks caused nonuniform "make-break" activation where the cathodal side was activated with a short latency but activation of the anodal side was delayed until after the shock end due to a large negative shock-induced polarization. Spatial averaging of Vm responses across 0.1-mm (but not 0.8-mm) strands resulted in AP upstrokes and plateau polarizations that closely resembled the Vm responses measured in LV myocardium. The shock strength for the transition between fast and delayed activation in 0.1-mm cell strands and LV myocardium was similar as well.

CONCLUSION

These data provide evidence that microscopic tissue structures with dimensions of approximately hundred microns are responsible for shock-induced activation of ventricular tissue.

Use of translucent indium tin oxide to measure stimulatory effects of a passive conductor during field stimulation of rabbit hearts

Biomathematical models and experiments have indicated that passive extracellular conductors influence field stimulation. Because metallic conductors prevent optical mapping under the conductor, we have evaluated a passive translucent indium tin oxide (ITO) thin-film conductor to allow mapping of transmembrane potential (V(m)) and stimulatory current under the conductor. A 1-cm ITO disk was patterned photolithographically and positioned between 0.3-cm(2) mesh shock electrodes on the ventricular epicardium of isolated perfused rabbit hearts stained with 4-{2-[6-(dibutylamino)-2-naphthylenal]ethenyl}-1-(3-sulfopropyl)-, hydroxide, inner salt (di-4-ANEPPS). For a 1-A, 10-ms shock during the action potential plateau, optical maps from fluorescence collected using emission ratiometry (excitation at 488 nm and emissions at 510-570 and >590 nm) indicated that the disk altered V(m) by as much as the height of an action potential. DeltaV(m) became more positive near the edge of the disk, where the ITO conductance gradient was parallel to applied current, and more negative near the opposite edge, where the gradient was not parallel to current. For diastolic shocks, the disk expedited membrane excitation at the sites of positive DeltaV(m) in the heart and in a cardiac model with realistic ITO disk surface and interfacial conductances. Optical maps of ITO transmittance and the model indicated that the disk introduced anodal and cathodal stimulatory current at opposite edges of the disk. Thus ITO allows study of the stimulatory effects of a passive conductor in an electric field.

Defibrillation Depends on Conductivity Fluctuations and the Degree of Disorganization in Reentry Patterns

Defibrillation depends on conductivity and disorganization.

INTRODUCTION

Cardiac fibrillation is the deterioration of the heart's normally well-organized activity into one or more meandering spiral waves, which subsequently break up into many meandering wave fronts. Delivery of an electric shock (defibrillation) is the only effective way of restoring the normal rhythm. This study focuses on examining whether higher degrees of disorganization requires higher shock strengths to defibrillate and whether microscopic conductivity fluctuations favor shock success.

METHODS AND RESULTS

We developed a three-dimensional computer bidomain model of a block of cardiac tissue with straight fibers immersed in a conductive bath. The membrane behavior was described by the Courtemanche human atrial action potential model incorporating electroporation and an acetylcholine- (ACh) dependent potassium current. Intracellular conductivities were varied stochastically around nominal values with variations of up to 50%. A single rotor reentry was initiated and, by adjusting the spatial ACh variation, the level of organization could be controlled. The single rotor could be stabilized or spiral wave breakup could be provoked leading to fibrillatory-like activity. For each level of organization, multiple shock timings and strengths were applied to compute the probability of shock success as a function of shock strength.

CONCLUSIONS

Our results suggest that the level of the small-scale conductivity fluctuations is a very important factor in defibrillation. A higher variation significantly lowers the required shock strength. Further, we demonstrated that success also heavily depends on the level of organization of the fibrillatory episode. In general, higher levels of disorganization require higher shock strengths to defibrillate.

Approximate solution to the bidomain equations for defibrillation problems

The bidomain model can be used for calculating the electrical potential in the heart during defibrillation. However, this model consists of a coupled system of two partial differential equations that are, in general, difficult and time consuming to solve. In this paper, we present an approximate, iterative method of solving the bidomain equations. After working out the general method, we apply it to four problems: (i) a cylindrical strand in a uniform electric field, (ii) a nonuniform electric field applied to tissue with straight fibers, (iii) a spherical heart in a uniform electric field, and (iv) a two-dimensional sheet of cardiac tissue with curving fibers. Finally, we analyze the general case of three dimensions.

The topology of defibrillation

We describe how Art Winfree's ideas about phase singularities can be used to understand the response of cardiac tissue with a random preexisting pattern of reentrant waves (fibrillation) to a large brief current stimulus. This discussion is organized around spatial dimension, beginning with a discussion of reentry on a periodic ring, followed by reentry in a two-dimensional planar domain (spiral waves), and ending with consideration of three-dimensional reentrant patterns (scroll waves). In all cases, we show how reentrant activity is changed by the application of a shock, describing conditions under which defibrillation is successful or not. Using topological arguments we draw the general conclusion that with a generic placement of stimulating electrodes, large-scale virtual electrodes do not give an adequate explanation for the mechanism of defibrillation.

Optical mapping of transmural activation induced by electrical shocks in isolated left ventricular wall wedge preparations

INTRODUCTION

It is believed that electrical shocks interrupt fibrillation by directly stimulating the bulk of ventricular myocardium in excitable states, but how shocks activate intramural tissue layers is not known. In this study, Vm responses and transmural activation patterns induced by shocks during diastole were measured in isolated coronary perfused preparations of porcine left ventricle.

METHODS AND RESULTS

Rectangular shocks (duration = 10 ms; field strength, E = 1-44 V/cm) were applied across preparations (thickness = 14.9 +/- 2.5 mm, n = 9) via large mesh electrodes during diastole or action potential (AP) plateau. Vm responses at the transmural surface were measured using optical mapping technique (resolution = 1.2 mm). Depending on shock strength, three types of Vm responses were observed. (1) Weak shocks (E approximately 1-4 V/cm) applied in diastole induced APs with simple monophasic upstrokes. The latency and time of transmural activation (TTA) rapidly decreased with increasing shock strength. Earliest activation occurred predominantly at the cathodal side of preparations in the areas that exhibited maximal DeltaVm during AP plateau. (2) Intermediate shocks (E approximately 4-23 V/cm) induced monophasic and biphasic upstrokes that were paralleled with predominantly negative plateau DeltaVm. Activation was initiated at multiple transmural sites and rapidly spread across the myocardial wall (TTA = 0.6 +/- 0.2 ms). (3) Very strong shocks (E approximately 23-44 V/cm) could cause triphasic upstrokes, likely reflecting occurrence of membrane electroporation, and delayed activation (TTA = 6.7 +/- 3.8 ms) at sites of largest negative plateau DeltaVm.

CONCLUSION

Shocks applied during diastole cause direct and rapid (within 1 ms) activation of ventricular bulk over a wide range of shock strengths, supporting the excitatory hypothesis of defibrillation. Very strong shocks can cause multiphasic Vm responses and delayed activation.

Defibrillation threshold computed from normal and supernormal excitable cardiac tissue

The applicability of the 'upper limit of vulnerability' defibrillation theory was evaluated in models of cardiac tissue in which spatial changes within cells are retained. Defibrillation thresholds were computed from two models of cardiac tissue: one with, and one without, a supernormal period, and compared with those predicted by the theory. In the cardiac virtual tissue with a monotonic recovery of excitation - a normal refractory period, the computed defibrillation threshold is consistent with the prediction of the 'upper limit of vulnerability' defibrillation theory. However, in cardiac tissue with non-monotonic recovery of excitation - a supernormal period, the computed defibrillation threshold is significantly less than the theory prediction.

Delayed Success in Termination of Three‐Dimensional Reentry:

INTRODUCTION

Defibrillation shocks slightly stronger than cardioversion threshold may defibrillate not immediately but after a transient period of postshock activity (delayed success). The effect of a defibrillation shock is that it polarizes the tissue, primarily at the surfaces; therefore, surface polarization may play an important role at near-threshold shock intensities.

METHODS AND RESULTS

We numerically investigate the effect of a monophasic transmural electrical shock on a three-dimensional (3D) reentrant wave (scroll wave). For simplicity, we assume uniform polarization of the epicardial and endocardial surfaces. We demonstrate that the effect of surface polarization alone is sufficient to induce delayed termination of self-sustained activity (3-4 beats after the shock). In agreement with experimental observations, both successful and failed shocks cause prolongation of the action potentials on the depolarized side and shortening on the hyperpolarized side, while at the same time inducing a shift from a reentrant to a focal activation pattern. Our simulations suggest that the outcome of the shock is determined by its effect on the shape of the scroll wave's center of rotation (filament). We propose a simple rule to predict the postshock filament shape that allows us to make accurate predictions of success and failure of a termination attempt.

CONCLUSION

Surface polarization due to an electrical shock can terminate a reentrant scroll wave. This mechanism may explain the phenomenon of delayed success in defibrillation.

The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue

Defibrillation of cardiac tissue can be viewed in the context of dynamical systems theory as the attempt to move a dynamical system from the basin of attraction of one attractor (fibrillation) to another (the uniform rest state) by applying a stimulus whose form is physically constrained. Here we give an introduction to the physical mechanism of cardiac defibrillation from this dynamical perspective and examine the role of resistive inhomogeneity on defibrillation efficacy. Using numerical simulations with rotating waves on a one-dimensional periodic ring, we study the role of the spatial scale of resistive inhomogeneity on defibrillation. For a rotating wave on a periodic ring there are three stable attractors, namely the uniform rest state, a wave traveling clockwise and a wave traveling counterclockwise. As a result, the application of a stimulus has the potential for three different outcomes, namely elimination of the wave, phase resetting of the wave, and reversal of the wave. The results presented here show that with resistive inhomogeneities of large spatial scale, all three of these transitions are possible with large amplitude shocks, so that the probability of defibrillation is bounded well below one, independent of stimulus amplitude. On the other hand, resistive inhomogeneities of small spatial scale produce a defibrillation threshold that is qualitatively consistent with that found experimentally, namely the probability of defibrillation success is an increasing function that approaches one for large enough stimulus amplitude. Extending these results to higher dimensions, we describe conditions for successful defibrillation of functional reentry with large scale spatial inhomogeneity, but find that elimination of anatomical reentry is quite difficult. With small spatial scale inhomogeneity, there are no similar restrictions.

Field stimulation of cardiac fibers with random spatial structure

Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (l(c) = 100 +/- 50 microm), diameter (d(c) = 20 +/- 10 microm), thickness of extracellular space (t(e) = 1.18 +/- 0.59 microm), and junctional resistance (R(j) = 2 +/- 1 M(omega)) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (V(m)) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing t(e); R(j), l(c), and d(c) have less influence. The maximum V(m) increases from 3.5 mV in a periodic fiber to 20.5+/-4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold E(th) decreases from 6.9 to 1.59 +/- 0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59 +/- 0.43 versus 1.44 +/- 0.41 V/cm (p value = 0.453). Thus, V(m) arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.

Averaging over depth during optical mapping of unipolar stimulation

Numerical simulations have predicted the distribution of transmembrane potential during electrical stimulation of cardiac tissue. When comparing these predictions to measurements obtained using optical mapping techniques, the optical signal should not be compared to the transmembrane potential calculated at the surface of the tissue, but instead to the transmembrane potential averaged over depth. In this paper, the bidomain model is used to calculate the transmembrane potential in a three-dimensional slab of cardiac tissue, stimulated by a unipolar electrode on the tissue surface. For an optical decay constant of 0.3 mm and an electrode radius of 1 mm, the surface transmembrane potential is more than a factor of three larger than the transmembrane potential averaged over depth. Our results suggest that optical mapping underestimates the surface transmembrane potential during electrical stimulation.

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.

Intramural virtual electrodes during defibrillation shocks in left ventricular wall assessed by optical mapping of membrane potential

BACKGROUND

It is believed that defibrillation is due to shock-induced changes of transmembrane potential (DeltaV(m)) in the bulk of ventricular myocardium (so-called virtual electrodes), but experimental proof of this hypothesis is absent. Here, intramural shock-induced DeltaV(m) were measured for the first time in isolated preparations of left ventricle (LV) by an optical mapping technique.

METHODS AND RESULTS

LV preparations were excised from porcine hearts (n=9) and perfused through a coronary artery. Rectangular shocks (duration 10 ms, field strength E approximately 2 to 50 V/cm) were applied across the wall during the action potential plateau by 2 large electrodes. Shock-induced DeltaV(m) were measured on the transmural wall surface with a 16x16 photodiode array (resolution 1.2 mm/diode). Whereas weak shocks (E approximately 2 V/cm) induced negligible DeltaV(m) in the wall middle, stronger shocks produced intramural DeltaV(m) of 2 types. (1) Shocks with E>4 V/cm produced both positive and negative intramural DeltaV(m) that changed their sign on changing shock polarity, possibly reflecting large-scale nonuniformities in the tissue structure; the DeltaV(m) patterns were asymmetrical, with DeltaV-(m)>DeltaV+(m). (2) Shocks with E>34 V/cm produced predominantly negative DeltaV(m) across the whole transmural surface, independent of the shock polarity. These relatively uniform polarizations could be a result of microscopic discontinuities in tissue structure.

CONCLUSIONS

Strong defibrillation shocks induce DeltaV(m) in the intramural layers of LV. During action potential plateau, intramural DeltaV(m) are typically asymmetrical (DeltaV-(m)>DeltaV+(m)) and become globally negative during very strong shocks.

New currents in electrical stimulation of excitable tissues

Electric fields can stimulate excitable tissue by a number of mechanisms. A uniform long, straight peripheral axon is activated by the gradient of the electric field that is oriented parallel to the fiber axis. Cortical neurons in the brain are excited when the electric field, which is applied along the axon-dendrite axis, reaches a particular threshold value. Cardiac tissue is thought to be depolarized in a uniform electric field by the curved trajectories of its fiber tracts. The bidomain model provides a coherent conceptual framework for analyzing and understanding these apparently disparate phenomena. Concepts such as the activating function and virtual anode and cathode, as well as anode and cathode break and make stimulation, are presented to help explain these excitation events in a unified manner. This modeling approach can also be used to describe the response of excitable tissues to electric fields that arise from charge redistribution (electrical stimulation) and from time-varying magnetic fields (magnetic stimulation) in a self-consistent manner. It has also proved useful to predict the behavior of excitable tissues, to test hypotheses about possible excitation mechanisms, to design novel electrophysiological experiments, and to interpret their findings.

Modelling induction of a rotor in cardiac muscle by perpendicular electric shocks

A strong, properly timed shock applied perpendicularly to a propagating wavefront causes a rotor in the canine myocardium. Experimental data indicate that the induction of this rotor relies on the shock exciting tissue away from the electrodes. The computational study reproduced such direct excitation in a two-dimensional model of a 2.7 x 3 cm sheet of cardiac muscle. The model used experimentally measured extracellular potentials to represent 100 and 150 V shocks delivered through extracellular electrodes. The shock-induced transmembrane potential was computed according to two mechanisms, the activating function and the unit-bundle sawtooth potential. The overall process leading to initiation of a rotor was the same in model and experiment. For the 100 V shock, the directly excited region extended 2.26 cm away from the electrode; the centre of the rotor ('critical point') was 1.28 cm away, where the electric field Ecr was 4.54 Vcm(-1). Increasing the shock strength to 150 V moved the critical point 1.02 cm further and decreased Ecr by 0.39 Vcm(-1). The results are comparable with experimental data. The model suggests that the unit-bundle sawtooth is responsible for the creation of the directly excited region, and the activating function is behind the dependence of Ecr on shock strength.

Nonlinear changes of transmembrane potential during defibrillation shocks: role of Ca(2+) current

Defibrillation shocks induce complex nonlinear changes of transmembrane potential (DeltaV(m)). To elucidate the ionic mechanisms of nonlinear DeltaV(m), we studied the effects of ionic channel blockers on DeltaV(m) in geometrically defined myocyte cultures. Experiments were carried out in cell strands with widths of 0.2 mm (narrow strands) and 0.8 mm (wide strands) produced using a technique of directed cell growth. Uniform-field shocks were applied across strands during the action potential (AP) plateau, and the distribution of shock-induced DeltaV(m) was measured using an optical mapping technique. Nifedipine and 4-aminopyridine were applied to inhibit the L-type calcium current (I:(Ca)) and the transient outward current (I:(to)), respectively. In control conditions, the distribution of DeltaV(m) across cell strands was highly asymmetrical with a large ratio of negative to positive DeltaV(m) (DeltaV(-)(m)/DeltaV(+)(m)) measured at the opposite strand borders. Application of nifedipine caused a large increase of DeltaV(+)(m) and a decrease of DeltaV(-)(m)/DeltaV(+)(m), indicating involvement of I:(Ca) in the asymmetrical DeltaV(m), likely as a result of the outward flow of I:(Ca) when V(m) exceeded the I:(Ca) reversal potential. DeltaV(-)(m) decreased in the narrow strands but remained unchanged in the wide strands, indicating that the changes of DeltaV(-)(m) were caused by electrotonic interaction with an area of depolarization. 4-Aminopyridine did not change DeltaV(-)(m)/DeltaV(+)(m). These results provide evidence that (1) the asymmetry of shock-induced DeltaV(m) during the AP plateau is due to outward flow of I:(Ca) in the depolarized portions of the strands, (2) I:(to) is not involved in the mechanism of DeltaV(m) asymmetry, and (3) the effects of drugs on DeltaV(m) are modulated by the tissue geometry.

Success and failure of the defibrillation shock: insights from a simulation study

INTRODUCTION

This simulation study presents a further inquiry into the mechanisms by which a strong electric shock fails to halt life-threatening cardiac arrhythmias.

METHODS AND RESULTS

The research uses a model of the defibrillation process that represents a sheet of myocardium as a bidomain. The tissue consists of nonuniformly curved fibers in which spiral wave reentry is initiated. Monophasic defibrillation shocks are delivered via two line electrodes that occupy opposite tissue boundaries. In some simulation experiments, the polarity of the shock is reversed. Electrical activity in the sheet is compared for failed and successful shocks under controlled conditions. The maps of transmembrane potential and activation times calculated during and after the shock demonstrate that weak shocks fail to terminate the reentrant activity via two major mechanisms. As compared with strong shocks, weak shocks result in (1) smaller extension of refractoriness in the areas depolarized by the shock, and (2) slower or incomplete activation of the excitable gap created by deexcitation of the negatively polarized areas. In its turn, mechanism 2 is associated with one or more of the following events: (a) lack of some break excitations, (b) latency in the occurrence of the break excitations, and (c) slower propagation through deexcited areas. Reversal of shock polarity results in a change of the extent of the regions of deexcitation, and thus, in a change in defibrillation threshold.

CONCLUSION

The results of this study indicate the paramount importance of shock-induced deexcitation in both defibrillation and postshock arrhythmogenesis.

Mechanism of ventricular defibrillation. The role of tissue geometry in the changes in transmembrane potential in patterned myocyte cultures

BACKGROUND

The geometry of the myocardium may influence changes in transmembrane potential (DeltaVm) during defibrillation. To test this hypothesis, specific nonlinear structures (bifurcations, expansions, and curved strands or "bends") were created in patterned cultures of neonatal rat myocytes.

METHODS AND RESULTS

Extracellular field stimuli (EFS; 7 to 11 V/cm field strength) were applied parallel to the strands. Changes in Vm were measured with microscopic resolution using optical mapping techniques. In bifurcations, EFS produced 2 DeltaVm maxima (so-called secondary sources) at the shoulder of each limb that were separated by a decrease of either hyperpolarization or depolarization at the insertion of the stem strand. In expansions, EFS produced a significant decrease in DeltaVm at the insertion site of the expansion compared with the DeltaVm maxima measured at the lateral borders. In 50% of experiments, tertiary sources of opposite polarity appeared in the strand due to local electrotonic currents. New action potentials were propagated from the sites of DeltaVm maxima located at the lateral borders of the expansions. In bends, the strand oriented in parallel to the field dominated electrotonically and partially cancelled the sources produced by the perpendicular segment.

CONCLUSIONS

In electrically well-coupled nonlinear structures, EFS produced changes in Vm at resistive boundaries that were determined by the electrotonic interaction between sources of different, direction-dependent strength. In addition, the interaction between localized secondary sources at nonlinear boundaries generated local current circuits, which gave rise to further changes in Vm (tertiary sources).

Virtual electrodes and deexcitation: new insights into fibrillation induction and defibrillation

Previous models of fibrillation induction and defibrillation stressed the contribution of depolarization during the response of the heart to a shock. This article reviews recent evidence suggesting that comprehending the role of negative polarization (hyperpolarization) also is crucial for understanding the response to a shock. Negative polarization can "deexcite" cardiac cells, creating regions of excitable tissue through which wavefronts can propagate. These wavefronts can result in new reentrant circuits, inducing fibrillation or causing defibrillation to fail. In addition, deexcitation can lead to rapid propagation through newly excitable regions, resulting in the elimination of excitable gaps soon after the shock and causing defibrillation to succeed.

Nonlinear changes of transmembrane potential caused by defibrillation shocks in strands of cultured myocytes

Organization of cardiac tissue into cell strands and layers has been implicated in changes of transmembrane potential (DeltaV(m)) during defibrillation. To determine the shock-induced DeltaV(m) in such structures, cell strands of variable width [strand width (SW) = 0.15-2 mm] were grown in culture. Uniform-field shocks with variable strength [shock strength (SS) = 2-50 V/cm] were applied across strands during the action potential (AP) plateau, and DeltaV(m) were measured optically. Three different types of DeltaV(m) were observed. Small DeltaV(m) [<40%AP amplitude (APA)] were linearly dependent on SS and SW and were symmetrically distributed about a strand centerline with maximal positive and negative DeltaV(m) on opposite strand sides being equal. Intermediate DeltaV(m) (<200%APA) were strongly asymmetric with negative DeltaV(m) > positive DeltaV(m) because of a negative time-dependent shift of V(m) at the depolarized side of the strands. For large DeltaV(m) (>200%APA), a second time-dependent shift of V(m) to more positive levels was observed in the hyperpolarized portions of strands, causing reduction of the DeltaV(m) asymmetry. We conclude that during application of shocks to cell strands during the AP plateau, passive changes of V(m) were followed by two voltage- and time-dependent shifts of V(m), possibly reflecting changes of ionic currents or membrane electroporation.

Sinusoidal stimulation of myocardial tissue: effects on single cells

INTRODUCTION

Cardiac tissue subjected to sinusoidal stimulus is characterized by action potentials (APs) that have extended plateau phases, sustained for the duration of the stimulus. Extended action potential durations (APDs) are beneficial because they disrupt wandering wavelets in the fibrillating heart. To investigate the mechanisms by which periodic stimulus affects cardiac tissue, particularly the development of sustained depolarization, computer simulations of single cardiac cells exposed to alternating current (AC) are performed.

METHODS AND RESULTS

Two modes of stimulation of the cell are examined: external field stimulation and transmembrane current injection. Several membrane models, including Luo-Rudy I and II, are used in the simulations. External AC field stimuli increase the APD of the single cell. The extended plateau of the cellular AP is characterized by periodic oscillations that are 1:2 phase locked with the applied stimulus. This specific behavior is due to the variations in stimulus magnitude and polarity along the cell border, which elicit opposite electrical responses from the cell sides. These pointwise responses are averaged in the macroscopic cellular response and result in sustained oscillatory depolarization that lasts for the duration of the stimulus. In contrast, the cell undergoing current injection does not develop an extended APD.

CONCLUSION

The simulations demonstrate that variation of membrane potential within a cell is of paramount importance to the formation of an extended AP plateau in response to AC stimulation.

Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects--vortices or spirals--nucleate a transition to a disordered, turbulent state.

Roles of electric field and fiber structure in cardiac electric stimulation

This study investigated roles of the variation of extracellular voltage gradient (VG) over space and cardiac fibers in production of transmembrane voltage changes (DeltaV(m)) during shocks. Eleven isolated rabbit hearts were arterially perfused with solution containing V(m)-sensitive fluorescent dye (di-4-ANEPPS). The epicardium received shocks from symmetrical or asymmetrical electrodes to produce nominally uniform or nonuniform VGs. Extracellular electric field and DeltaV(m) produced by shocks in the absolute refractory period were measured with electrodes and a laser scanner and were simulated with a bidomain computer model that incorporated the anterior left ventricular epicardial fiber field. Measurements and simulations showed that fibers distorted extracellular voltages and influenced the DeltaV(m). For both uniform and nonuniform shocks, DeltaV(m) depended primarily on second spatial derivatives of extracellular voltages, whereas the VGs played a smaller role. Thus, 1) fiber structure influences the extracellular electric field and the distribution of DeltaV(m); 2) the DeltaV(m) depend on second spatial derivatives of extracellular voltage.

Optical transmembrane potential recordings during intracardiac defibrillation-strength shocks

BACKGROUND

The prolongation of the action potential after defibrillation-strength shocks is believed to be a critical component of defibrillation. The response of the transmembrane potential to the shock may affect this prolongation. We studied the effects of an intracardiac shock on the transmembrane potential and action potential duration at multiple sites on the epicardium using a voltage-sensitive dye and optical mapping system.

METHODS AND RESULTS

A laser scanner recorded optical action potentials with voltage-sensitive dye at 63 spots on both the left and right ventricles of six isolated, perfused rabbit hearts. Hearts were paced with epicardial point stimulation followed by the delivery of a 2 A and 20 ms rectangular waveform shock during the relative refractory period. The shock was given between right atrial and right ventricular electrodes. Of 621 total spots analyzed, 241 spots hyperpolarized and 76 spots depolarized with a right ventricular anode, whereas 159 spots hyperpolarized and 145 spots depolarized with a right ventricular cathode (P < 0.05). Both hyperpolarized and depolarized spots exhibited prolonged action potential duration, although prolongation was greater with depolarizing responses (16.7 +/- 9 ms vs. 13.3 +/- 13.4 ms, p<0.001). Hyperpolarized and depolarized spots were not randomly distributed, but clustered into regions. The size of the hyperpolarized regions was larger than the depolarized regions with RV anodal stimulation (27 +/- 20 spots/hyperpolarized region vs. 8.5 +/- 9 spots/depolarized region, p < 0.03) but not with RV cathodal stimulation. With reversal of electrode polarity, spots hyperpolarized near the shocking electrodes frequently did not reverse polarization but remained hyperpolarized.

CONCLUSIONS

Distinct regions of either polarization occur during intracardiac defibrillation-strength shocks. Although hyperpolarizing membrane responses were observed more often than depolarizing responses, depolarizing membrane polarization resulted in greater action potential prolongation. The absence of sign change in polarization in some regions with shocks of opposite polarities suggests that nonlinear intrinsic membrane properties are operative during strong electrical stimulation.

Effects of electroporation on the transmembrane potential distribution in a two-dimensional bidomain model of cardiac tissue

INTRODUCTION

Defibrillation shocks, when delivered through internal electrodes, establish transmembrane potentials (Vm) large enough to electroporate the membrane of cardiac cells. The effects of such shocks on the transmembrane potential distribution are investigated in a two-dimensional rectangular sheet of cardiac muscle modeled as a bidomain with unequal anisotropy ratios.

METHODS AND RESULTS

The membrane is represented by a capacitance Cm, a leakage conductance g(l) and a variable electroporation conductance G, whose rate of growth depends exponentially on the square of Vm. The stimulating current Io, 0.05-20 A/m, is delivered through a pair of electrodes placed 2 cm apart for stimulation along fibers and 1 cm apart for stimulation across fibers. Computer simulations reveal three categories of response to Io: (1) Weak Io, below 0.2 A/m, cause essentially no electroporation, and Vm increases proportionally to Io. (2) Strong Io, between 0.2 and 2.5 A/m, electroporate tissue under the physical electrode. Vm is no longer proportional to Io; in the electroporated region, the growth of Vm is halted and in the region of reversed polarity (virtual electrode), the growth of Vm is accelerated. (3) Very strong Io, above 2.5 A/m, electroporate tissue under the physical and the virtual electrodes. The growth of Vm in all electroporated regions is halted, and a further increase of Io increases both the extent of the electroporated regions and the electroporation conductance G.

CONCLUSION

These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm induced by defibrillation strength shocks.

Patterns of and mechanisms for shock-induced polarization in the heart: a bidomain analysis

This paper examines the combined action of cardiac fiber curvature and transmural fiber rotation in polarizing the myocardium under the conditions of a strong electrical shock. The study utilizes a three-dimensional finite element model and the continuous bidomain representation of cardiac tissue to model steady-state polarization resulting from a defibrillation-strength uniform applied field. Fiber architecture is incorporated in the model via the shape of the heart, an ellipsoid of variable ellipticity index, and via an analytical function, linear or nonlinear, describing the transmural fiber rotation. Analytical estimates and numerical results are provided for the location and shape of the "bulk" polarization (polarization away from the tissue boundaries) as a function of the fiber field, or more specifically, of the conductivity changes in axial and radial direction with respect to the applied electrical field lines. Polarization in the tissue "bulk" is shown to exist only under the condition of unequal anisotropy ratios in the extra- and intracellular spaces. Variations in heart geometry and, thus, fiber curvature, are found to lead to change in location of the zones of significant membrane polarization. The transmural fiber rotation function modulates the transmembrane potential profile in the radial direction. A higher gradient of the transmural transmembrane potential is observed in the presence of fiber rotation as compared to the no rotation case. The analysis presented here is a step forward in understanding the interaction between tissue structure and applied electric field in establishing the pattern of membrane polarization during the initial phase of the defibrillation shock.

Modeling defibrillation: effects of fiber curvature

The goal of this modeling study is to demonstrate extinguishing of a spiral wave reentry in a sheet of myocardium that incorporates curved fibers. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. The spiral wave is initiated via cross-field stimulation of the bidomain sheet. The defibrillation shock is delivered via two line electrodes that occupy opposite tissue boundaries. Simulation results demonstrate that large-scale regions of depolarization are induced under the cathode as well as at locations in the vicinity of the anode. For high shock strengths, the new wavefronts generated from the regions of induced depolarization restrict the spiral wave pathway and render the tissue too refractory to further maintain the reentry. Weak shocks leave large portions of the sheet unaffected allowing the spiral wave to find recovered tissue and thus survive.

Spatiotemporal effects of syncytial heterogeneities on cardiac far-field excitations during monophasic and biphasic shocks

INTRODUCTION

It has recently been postulated that syncytial (anatomic) heterogeneities inherent within cardiac tissue might represent a significant mechanism underlying field-induced polarization of the bulk myocardium. This simulation study examines and characterizes the spatiotemporal excitatory dynamics associated with this newly hypothesized mechanism.

METHODS AND RESULTS

Two-dimensional regions of syncytially heterogeneous cardiac tissue were simulated with active membrane kinetics. Heterogeneities were manifested via random spatial variations of intracellular volume fractions over multiple length scales. Excitation thresholds were determined for uniform rectangular monophasic (M) and symmetric biphasic (B) far-field stimuli, from which strength-duration and strength-interval relationships were constructed. For regions measuring 5.4 x 5.4 mm, baseline diastolic thresholds for longitudinal (L) and transverse (T) shocks of 5-msec total duration averaged (in V/cm, n = 10) M-L = 2.87+/-0.26, M-T = 6.71+/-0.83, B-L = 3.22+/-0.25, and B-T = 7.93+/-0.51. These thresholds decreased by 15% to 25% when the region sizes were increased to 10.8 x 10.8 mm. Strength-duration relationships correlated strongly with the Weiss-Lapicque hyperbolic relationship, with rheobases and chronaxies of 2.33 V/cm and 1.15 msec for M-L stimuli, and 2.28 V/cm and 2.04 msec for B-L stimuli. Strength-interval relationships for M-L and B-L stimuli decreased monotonically with increasing coupling intervals, with similar minimum coupling intervals at absolute refractoriness. However, the B-L thresholds were substantially less sensitive to changes in coupling intervals than their M-L counterparts.

CONCLUSION

This study provides strong additional support for and understanding of the syncytial heterogeneity hypothesis and its manifested properties. Furthermore, these results predict that syncytial heterogeneities of even modest proportions could represent a significant mechanism contributing to the far-field excitation process.

Spatial changes in the transmembrane potential during extracellular electric stimulation

The purpose of this study was to determine the spatial changes in the transmembrane potential caused by extracellular electric field stimulation. The transmembrane potential was recorded in 10 guinea pig papillary muscles in a tissue bath using a double-barrel microelectrode. After 20 S1 stimuli, a 10-ms square wave S2 shock field with a 30-ms S1-S2 coupling interval was given via patch shock electrodes 1 cm on either side of the tissue during the action potential plateau. Two shock strengths (2.1+/-0.2 and 6.5+/-0.6 V/cm) were tested with both shock polarities. The recording site was moved across the tissue along fibers with either 200 micrometer (macroscopic group [n=5], 12 consecutive recording sites over a 2. 2-mm tissue length in each muscle) or 20 micrometer (microscopic group [n=5], 21 consecutive recording sites over a 0.4-mm tissue length in each muscle) between adjacent recording sites. In the macroscopic group, the portion of the tissue toward the anode was hyperpolarized, whereas the portion toward the cathode was depolarized, with 1 zero-potential crossing from hyperpolarization to depolarization present near the center of the tissue. In the microscopic group, only 1 zero-potential crossing was observed in the center region of the tissue, whereas, away from the center, only hyperpolarization was observed toward the anode and depolarization toward the cathode. Although these results are consistent with predictions from field stimulation of continuous representations of myocardial structure, ie, the bidomain and cable equation models, they are not consistent with the prediction of depolarization-hyperpolarization oscillation from representations based on cellular-level resistive discontinuities associated with gap junctions, ie, the sawtooth model.

Syncytial heterogeneity as a mechanism underlying cardiac far-field stimulation during defibrillation-level shocks

INTRODUCTION

The mechanisms by which a defibrillation shock directly stimulates regions of cardiac tissue distal to the stimulus electrodes ("far-field" stimulation) are still not well understood. Existing hypotheses have proposed that intercellular discontinuities and/or fiber curvatures induce the requisite membrane polarizations. This article hypothesizes a third potential mechanism: one based on the existence and influences of syncytial (anatomic) heterogeneities inherent throughout the bulk myocardium itself.

METHODS AND RESULTS

We simulated the effects of such heterogeneities in a model of a two-dimensional region of passive cardiac tissue subjected to uniform 1 V/cm longitudinal or transverse field stimuli. Heterogeneities were manifested via random spatial variations of intracellular volume fractions (fi) over multiple length scales, with mean fi of 80% and standard deviation of fi (sigma[fi]) ranging from 0% to 10%. During field stimulation, many interspersed and variously shaped and sized islands of hyperpolarization and depolarization developed across the tissue, with their locations and extents correlated to the spatial gradients of the underlying heterogeneities. Increases in sigma(fi) correspondingly increased the shock-induced magnitudes of resulting membrane polarizations. The ratio of maximal polarizations for equivalent longitudinal and transverse shocks approximated 2:1 across all sigma(fi) tested. At sigma(fi) = 5%, these maximal induced polarizations were 17.4 +/- 2.4 mV and 8.18 +/- 1.5 mV, respectively. Assuming an excitation threshold of 25 mV, these data suggest corresponding diastolic thresholds of 1.47 +/- 0.20 V/cm and 3.14 +/- 0.50 V/cm, respectively.

CONCLUSION

This study predicts that syncytial heterogeneities inherent within cardiac tissue could represent a significant-and heretofore unappreciated-mechanism underlying field-induced polarizations throughout the bulk myocardium.

Bipolar stimulation of a three-dimensional bidomain incorporating rotational anisotropy

A bidomain model of cardiac tissue was used to examine the effect of transmural fiber rotation during bipolar stimulation in three-dimensional (3-D) myocardium. A 3-D tissue block with unequal anisotropy and two types of fiber rotation (none and moderate) was stimulated along and across fibers via bipolar electrodes on the epicardial surface, and the resulting steady-state interstitial (phi e) and transmembrane (Vm) potentials were computed. Results demonstrate that the presence of rotated fibers does not change the amount of tissue polarized by the point surface stimuli, but does cause changes in the orientation of phi e and Vm in the depth of the tissue, away from the epicardium. Further analysis revealed a relationship between the Laplacian of phi e, regions of virtual electrodes, and fiber orientation that was dependent upon adequacy of spatial sampling and the interstitial anisotropy. These findings help to understand the role of fiber architecture during extracellular stimulation of cardiac muscle.

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.

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.

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.

Activation of cardiac tissue by extracellular electrical shocks: formation of 'secondary sources' at intercellular clefts in monolayers of cultured myocytes

This study investigated the activation of cardiac tissue by "secondary sources," which are localized changes of the transmembrane potential (Vm) during the application of strong extracellular electrical shocks far from the shock electrodes, in cultures of neonatal rat myocytes. Cell monolayers with small intercellular clefts (length, 45 to 270 microm; width, 20 to 70 microm [mean+/-SD, 54+/-13 microm]; n = 46) were produced using a technique of directed cell growth. Changes in Vm relative to the action potential amplitude (deltaVm/APA) were measured using a fluorescent voltage-sensitive dye and a 10 x 10 photodiode array. Shocks with voltage gradients of 4 to 18 V/cm were applied across the clefts during either the action potential (AP) plateau or diastole. During the AP plateau, shocks induced secondary sources in the form of localized hyperpolarizations and depolarizations in the regions immediately adjacent to opposite sides of the clefts. The strength of the secondary sources, defined as the difference of deltaVm/APA across a cleft, increased with increasing cleft length or increasing electrical field gradient. For shocks with a gradient of 8.5 V/cm, the estimated critical cleft length necessary to reach a Vm level corresponding to the diastolic threshold of excitation was 171+/-7 microm. Accordingly, shocks with average strength of 8.2 V/cm applied during diastole produced secondary sources that directly excited cells adjacent to the clefts when the cleft length was 196+/-53 microm (n = 14) and that failed when the cleft length was 84+/-23 microm (n = 9, P<.001). The area of earliest excitation in such cases coincided with the area of maximal depolarization induced during the plateau phase. These data suggest that small inexcitable obstacles may contribute to the Vm changes during the application of strong extracellular electrical shocks in vivo.

Membrane refractoriness and excitation induced in cardiac fibers by monophasic and biphasic shocks

INTRODUCTION

This modeling study examines the effect of low-intensity monophasic and biphasic waveforms on the response of a refractory cardiac fiber to the defibrillation shock.

METHODS AND RESULTS

Two cardiac fiber representations are considered in this study: a continuous fiber and a discrete fiber that incorporates gap junctions. Each fiber is undergoing a propagating action potential. Shocks of various strengths and coupling intervals are delivered extracellularly at fiber ends during the relative refractory period. In a continuous fiber, monophasic shock strengths of three times the diastolic threshold either elicit no response or, for coupling intervals above 380 msec, reinitiate propagation. In contrast, biphasic shocks of same strength are capable of terminating the existing wavefronts by either invoking a nonpropagating response (coupling intervals 370 to 382 msec) that prolongs the refractory period or inducing wavefront collision (coupling intervals above 400 msec). The fiber response is similar for other shock strengths and when cellular discontinuity is accounted for. Thus, for a refractory fiber, biphasic shocks have only a small "vulnerable" window of coupling intervals over which propagation is reinitiated.

CONCLUSION

At short coupling intervals, a significant extension of refractoriness is generated at regions where the biphasic shock induced hyperpolarization followed by depolarization. At large coupling intervals, the enhanced efficacy of biphasic shocks is associated with their ability to induce wavefront collision, thus decreasing the probability of reinitiating fibrillation. Overall, the defibrillation shock affects the tissue through the induced large-scale hyperpolarization and depolarization, and not through the small-scale transmembrane potential oscillations at cell ends.