Virtual cathode effects during stimulation of cardiac muscle. Two-dimensional in vivo experiments

Success and failure of biphasic shocks: results of bidomain simulations

The mechanisms behind the superiority of optimal biphasic defibrillation shocks over monophasic are not fully understood. This simulation study examines how the shock polarity and second-phase magnitude of biphasic shocks influence the virtual electrode polarization (VEP) pattern, and thus the outcome of the shock in a bidomain model representation of ventricular myocardium. A single spiral wave is initiated in a two-dimensional sheet of myocardium that measures 2 x 2 cm(2). The model incorporates non-uniform fiber curvature, membrane kinetics suitable for high strength shocks, and electroporation. Line electrodes deliver a spatially uniform extracellular field. The shocks are biphasic, each phase lasting 10 ms. Two different polarities of biphasic shocks are examined as the first-phase configuration is held constant and the second-phase magnitude is varied between 1 and 10 V/cm. The results show that for each polarity, varying the second-phase magnitude reverses the VEP induced by the first phase in an asymmetric fashion. Further, the size of the post-shock excitable gap is dependent upon the second-phase magnitude and is a factor in determining the success or failure of the shock. The maximum size of a post-shock excitable gap that results in defibrillation success depends on the polarity of the shock, indicating that the refractoriness of the tissue surrounding the gap also contributes to the outcome of the shock.

The mechanisms of the vulnerable window: the role of virtual electrodes and shock polarity

Vulnerability and defibrillation are mechanistically dependent upon shock strength, polarity, and timing. We have recently demonstrated that shock-induced virtual electrode polarization (VEP) may induce reentry. However, it remains unclear how the VEP mechanism may explain the vulnerable window and polarity dependence of vulnerability. We used a potentiometric dye and optical mapping to assess the anterior epicardial electrical activity of Langendorff-perfused rabbit hearts (n = 7) during monophasic shocks (±100 V and ±200 V, duration of 8 ms) applied from a transvenous defibrillation lead at various coupling intervals. Arrhythmias were induced in a coupling interval and shock polarity dependent manner: (i) anodal and cathodal shocks induced arrhythmias in 33.2 ± 30.1% and 53.1 ± 39.3% cases (P < 0.01), respectively, and (ii) the vulnerable window was located near the T-wave. Optical maps revealed that VEP was also modulated by the coupling interval and shock polarity. Recovery of excitability produced by negative polarization, known as de-excitation, and the resulting reentry was more readily achieved during the relative refractory period than the absolute refractory period. Furthermore, anodal shocks produced wavefronts propagating in an inward direction with respect to the electrode, whereas cathodal shocks propagated in an outward direction. Wavefronts produced by anodal shocks were more likely to collide and annihilate each other than those caused by cathodal shocks. The probability of degeneration of the VEP-induced phase singularity into a sustained arrhythmia depends upon the gradient of VEP and the direction of the VEP-induced wavefront. The VEP gradient depends upon the coupling interval, while the direction depends upon shock polarity; these factors explain the vulnerable window and polarity-dependence of vulnerability, respectively.Key words: defibrillation, stimulation, arrhythmia, cardiac vulnerability, optical mapping.

Effects of anodal vs. cathodal pacing on the mechanical performance of the isolated rabbit heart

Previous studies have suggested that anodal pacing enhances electrical conduction in the heart near the pacing site. It was hypothesized that enhanced conduction by anodal pacing would also enhance ventricular pressure in the heart. Left ventricular pressure measurements were made in isolated, Langendorff-perfused rabbit hearts by means of a Millar pressure transducer with the use of a balloon catheter fixed in the left ventricle. The pressure wave was analyzed for maximum pressure (Pmax) generated in the left ventricle and the work done by the left ventricle (Parea). Eight hearts were paced with monophasic square-wave pulses of varying amplitudes (2, 4, 6, and 8 V) with 100 pulses of each waveform delivered to the epicardium. Anodal stimulation pulses showed statistically significant improvement in mechanical response at 2, 4, and 8 V. Relative to unipolar cathodal pacing, unipolar anodal pacing improved Pmax by 4.4 +/- 2.3 (SD), 5.3 +/- 3.1, 3.5 +/- 4.9, and 4.8 +/- 1.9% at 2, 4, 6, and 8 V, respectively. Unipolar anodal stimulation also improved Parea by 9.0 +/- 3.0, 12.0 +/- 6.0, 10.1 +/- 7.7, and 11.9 +/- 6.0% at 2, 4, 6, and 8 V, respectively. Improvements in Pmax and Parea indicate that an anodally paced heart has a stronger mechanical response than does a cathodally paced heart. Anodal pacing might be useful as a novel therapeutic technology to treat mechanically impaired or failed hearts.

Electrophysiological and anatomic heterogeneity in evolving canine myocardial infarction

Although the heterogeneity of electrophysiological properties is increased after myocardial infarction, the degree of this heterogeneity has not been well quantitated and its relationship to the histological changes that occur after infarction has not been carefully examined. The purpose of the present study was to test the hypothesis that alterations in electrophysiological properties in healing canine infarction are related to particular histological changes. Experimental infarction was produced by left anterior descending coronary ligation. Six dogs were used as controls, six were studied 5 days following, and six were studied 8 weeks following infarction. Pacing thresholds, effective refractory periods, and activation-recovery times were determined at 112 sites on the anterior left ventricle using a multiple electrode plaque. Conduction velocity, conduction-heterogeneity index--a measure of conduction disturbance--and histology of the epimyocardium underlying the plaque were assessed. The effective refractory periods and activation-recovery times were greater in both infarction groups, most prominently in the subacute group. In subacute infarction, significant postrepolarization refractoriness was present. In healed infarction, conduction velocity was decreased and the conduction-heterogeneity index was increased compared to controls and subacute infarction. Dispersion of excitability and repolarization was associated with more extensive local scarring. Dispersion of myocardial fiber angles was associated with the conduction-heterogeneity index. Some but not all of the electrophysiological changes noted in the animals with infarction were also seen in sham operated animals. Thus, heterogeneity in repolarization and refractoriness is greatest in the subacute phase of myocardial infarction and is associated with the extent of local cell death. In contrast, disturbances in conduction are greatest in healed infarction and associated with disarray of myocardial fibers.

A simulation study evaluating the performance of high-density electrode arrays on myocardial tissue

Multielectrode arrays used to detect cellular activation have become so dense (electrodes per square millimeter) as to jeopardize the basic assumptions of activation mapping; namely, that electrodes are points adequately separated as to not interfere with the tissue or each other. This paper directly tests these assumptions for high-density electrode arrays. Using a finite element model with modified Fitzhugh-Nagumo kinetics, we represent electrodes as isopotential surfaces of varying widths and spacing ratio (SR) (center-to-center spacing divided by electrode width). We examine the signal strength and ability of a single electrode to detect activation due to a passing wavefront. We find that high-density arrays do not cause significant wavefront curvature or alter activation timing in the underlying tissue. Relationships between signal strength, cross talk, and array design are explained by the interaction of the propagating wavefront and induced sources on the isopotential electrodes. Sensitivity analysis shows that these results may be generalized to a wide range of physiologically relevant designs and applications. We conclude that electrode array designs in which electrode spacing greatly exceeds electrode diameter are overly conservative and that arrays with a SR of less than 2.0 may perform successfully in electrophysiological studies.

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.

Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism

INTRODUCTION

The "critical point hypothesis" for induction of ventricular fibrillation has previously been extended to infer the coexistence of four critical points, and hence four simultaneous spiral reentries or a quatrefoil reentry, resulting from only one premature stimulus delivered to the same location as the pacing stimulus. An optical imaging technique was used to explore its existence and to study the induction mechanism of this peculiar reentry pattern.

METHODS AND RESULTS

In 16 isolated, Langendorff-perfused rabbit hearts, high-speed optical imaging at 133 or 267 frames/sec was performed to observe the induced response with a unipolar point electrode. A novel quatrefoil-shaped reentry pattern consisting of two pairs of opposing rotors was created by delivering long stimuli during the vulnerable phase. Successful induction occurred in a narrow range of coupling intervals. A dogbone pattern of virtual electrodes was established during the premature stimulus. Propagating wavefronts launched from the virtual anodes immediately after the termination of S2. The alternating blocking and conducting effects of the virtual electrodes, as well as the boundary between virtual cathode and virtual anode, provided the necessary pathways for quatrefoil reentry. Propagation directions of the reentrant spiral wavefronts reversed with a reversal in S2 polarity. Quatrefoil reentries were not sustained and lasted 1 to 4 complete cycles.

CONCLUSION

The initiation of quatrefoil reentry followed anodal- or cathodal-break stimulation as a result of local symmetrical enhancement of the dispersion of tissue excitability. The "critical point hypothesis" provides the minimum topology required for this type of reentry; the "graded response hypothesis" can be viewed as providing a more detailed explanation of how this topology is actually realized. Triggering mechanisms due to the "break" mode of stimulation also posits a new mechanism for defibrillation.

Virtual electrode effects in defibrillation

This modeling study demonstrates that a re-entrant activity in a sheet of myocardium can be extinguished by a defibrillation shock delivered via extracellular point-source electrodes which establish spatially non-uniform applied field. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios in the cardiac conductivities. Spiral wave re-entry is initiated in the bidomain sheet following an S1-S2 stimulation protocol. The results indicate that the point-source defibrillation shock establishes large-scale changes in transmembrane potential in the tissue (virtual electrodes) that are 'superimposed' over regions of various degrees of membrane refractoriness in the myocardium. The close proximity of large-scale shock-induced regions of alternating membrane polarity is central to the ability of the shock to terminate the spiral wave. The new wavefronts generated following anode/cathode break phenomena restrict the spiral wave and render the tissue too refractory to further maintain the re-entry. In contrast, shocks delivered via line electrodes establish, in close proximity to the electrode, changes in transmembrane potential that are of same-sign polarity. These shocks are incapable of terminating the re-entrant activation.

Virtual electrode effects in transvenous defibrillation-modulation by structure and interface: evidence from bidomain simulations and optical mapping

INTRODUCTION

Our goal in this combined modeling and experimental study was to gain insight into the transmembrane potential changes in defibrillation conditions, namely, when shocks are delivered by an implantable cardioverter defibrillator (ICD). Two hypotheses concerning the presence and characteristics of virtual electrode effects (VEE) during an ICD shock were tested numerically and experimentally: (H1) anisotropy-dependent VEE are induced over a considerable portion of the "bulk" myocardium; and (H2) surface (epicardial and endocardial) VEE are generated under special tissue bath conditions and are not fully anisotropy determined.

METHODS AND RESULTS

Optical mapping was performed on Langendorff-perfused rabbit hearts (n = 4) stained with di-4-ANEPPS. Monophasic shocks were applied during the plateau phase of an action potential through a 9-mm long distal electrode in the right or left ventricle and a 6-cm proximal electrode positioned 3 cm posteriorly to the heart. We modeled the experiment using an ellipsoidal bidomain heart with transmural fiber rotation, placed in a perfusing bath, and subjected to defibrillation shocks delivered by an electrode configuration as described. Our numerical simulations demonstrated VEE occupying a significant portion of the myocardium in the conditions of unequal anisotropy ratios for the intra- and extracellular domains. Statistically significant differences in epicardial polarization patterns were predicted numerically and confirmed experimentally when the interface conditions varied.

CONCLUSION

The present study concludes that VEE are present in transvenous defibrillation. They are shaped by the combined effect of cardiac tissue characteristics and interface conditions. Because of their size, VEE might contribute significantly to defibrillation outcome.

Optical mapping of cardiac electrical stimulation

Optical mapping has been used to determine changes in transmembrane voltage during electrical stimulation pulses (deltaVm) and whether deltaVm depends on fiber orientation, as predicted from bidomain models. Fiber orientation in an approximately 1 cm2 mm mapped region on the rabbit left or right ventricular epicardium was estimated optically from the fast axis of action potential (AP) propagation. Hearts were paced outside of the region to produce APs. Unipolar stimulation (S2) was then applied early in the AP, when tissue was refractory, so that deltaVm was not obscured by a new AP. Anodal S2 produced negative deltaVm near a point S2 electrode and away from it in the direction perpendicular to the fibers. Anodal S2 produced reversal of the sign of deltaVm about 1 mm from the electrode in the direction parallel to the fibers, such that a positive deltaVm existed about 1-5 mm away from the electrode. Reversal of the sign of deltaVm in the direction parallel to the fibers also occurred with cathodal S2, which produced a negative deltaVm away from the electrode parallel to the fibers. The results indicate a "dogbone" pattern of deltaVm, as predicted from bidomain models that have resistance anisotropy ratios of trabecular muscles (ie, an intracellular ratio that does not equal the extracellular ratio). Thus, optical mapping can indicate fiber orientation and deltaVm, and the deltaVm during unipolar stimulation reverses sign on the axis parallel to the fibers, which differs from one-dimensional model predictions. The deltaVm agrees with multidimensional bidomain model predictions that have unequal resistance anisotropy.

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.

Impact of volume loading and load reduction on ventricular refractoriness and conduction properties in canine congestive heart failure

OBJECTIVES

This investigations was undertaken to examine the alteration of electrophysiologic properties, including refractoriness, strength-interval relations and conduction, with the development of heart failure and to characterize the impact of volume loading on these indexes in the cardiomyopathic setting.

METHODS

Electrophysiologic properties in eight dogs with pacing-induced dilated cardiomyopathy were compared with those in six control dogs before and after rapid infusion of 800 ml of intravenous saline.

RESULTS

The right ventricular (RV) and left ventricular (LV) effective refractory period (ERP) and absolute refractory period (ARP) were significantly longer in dogs with pacing-induced cardiomyopathy than in control dogs: RV ERP 181 +/- 11 ms versus 138 +/- 7 ms (mean +/- SD) (p < 0.0001) and anterior LV ERP 177 +/- 13 ms versus 128 +/- 11 ms (p < 0.0001), respectively; ARP 159 +/- 14 ms versus 114 +/- 7 ms (p < 0.0001) at the RV site and 153 +/- 12 versus 117 +/- 5 ms (p < 0.0001) at the anterior LV site. After volume loading in cardiomyopathic animals, posterior and anterior LV ERPs became prolonged to 178 +/- 5 ms (p = 0.004) and 189 +/- 14 ms (p = 0.065), respectively, shifting the strength-interval relation in the direction of longer S1S2 coupling intervals. Anterior LV monophasic action potential durations at 90% repolarization also became prolonged from 192 +/- 10 ms to 222 +/- 23 ms (p < 0.012) with volume loading. These findings were not altered by subsequent sodium nitroprusside. Local conduction times parallel and perpendicular to fiber orientation were not altered by development of cardiomyopathy or volume alterations.

CONCLUSIONS

The development of dilated cardiomyopathy results in significant prolongation of refractoriness and repolarization that is increased further by volume augmentation but is not reversed by pharmacologic load reduction. Although these abnormalities may contribute to the environment needed for a non-reentrant, triggered or stretch-mediated arrhythmogenic process in cardiomyopathic states, additional studies will be required to demonstrate such a focal mechanism conclusively.

A generalized activating function for predicting virtual electrodes in cardiac tissue

To fully understand the mechanisms of defibrillation, it is critical to know how a given electrical stimulus causes membrane polarizations in cardiac tissue. We have extended the concept of the activating function, originally used to describe neuronal stimulation, to derive a new expression that identifies the sources that drive changes in transmembrane potential. Source terms, or virtual electrodes, consist of either second derivatives of extracellular potential weighted by intracellular conductivity or extracellular potential gradients weighted by derivatives of intracellular conductivity. The full response of passive tissue can be considered, in simple cases, to be a convolution of this "generalized activating function" with the impulse response of the tissue. Computer simulations of a two-dimensional sheet of passive myocardium under steady-state conditions demonstrate that this source term is useful for estimating the effects of applied electrical stimuli. The generalized activating function predicts oppositely polarized regions of tissue when unequally anisotropic tissue is point stimulated and a monopolar response when a point stimulus is applied to isotropic tissue. In the bulk of the myocardium, this new expression is helpful for understanding mechanisms by which virtual electrodes can be produced, such as the hypothetical "sawtooth" pattern of polarization, as well as polarization owing to regions of depressed conductivity, missing cells or clefts, changes in fiber diameter, or fiber curvature. In comparing solutions obtained with an assumed extracellular potential distribution to those with fully coupled intra- and extracellular domains, we find that the former provides a reliable estimate of the total solution. Thus the generalized activating function that we have derived provides a useful way of understanding virtual electrode effects in cardiac tissue.

Transmembrane voltage changes produced by real and virtual electrodes during monophasic defibrillation shock delivered by an implantable electrode

INTRODUCTION

Epicardial point stimulation produces nonuniform changes in the transmembrane voltage of surrounding cells with simultaneous occurrence of areas of transient positive and negative polarization. This is the phenomenon of virtual electrode. We sought to characterize the responses of epicardial ventricular tissue to the application of monophasic electric shocks from an internal transvenous implantable cardioverter defibrillator (ICD) lead.

METHODS AND RESULTS

Langendorff-perfused rabbit hearts (n = 12) were stained with di-4-ANEPPS. A 9-mm-long distal electrode was placed in the right ventricle. A 6-cm proximal electrode was positioned horizontally 3 cm posteriorly and 1 cm superiorly with respect to the heart. Monophasic anodal and cathodal pulses were produced by discharging a 150-microF capacitor. Shocks were applied either during the plateau phase of an action potential (AP) or during ventricular fibrillation. Leading-edge voltage of the pulse was 50 to 150 V, and the pulse duration was 10 msec. Transmembrane voltage was optically recorded during application of the shock, simultaneously from 256 sites on a 11 x 11 mm area of the anterior right ventricular epicardium directly transmural to the distal electrode. The shock effect was evaluated by determining the difference between the AP affected by the shock and the normal AP. During cathodal stimulation an area of depolarization near the electrode was observed, surrounded by areas of hyperpolarization. The amplitude of polarization gradually decreased in areas far from the electrode. Inverting shock polarity reversed this effect.

CONCLUSION

ICD monophasic defibrillation shocks create large dynamically interacting areas of both negative and positive polarization.

Nonsustained reentry following successive stimulation of cardiac tissue through a unipolar electrode

INTRODUCTION

Using numerical simulations, we predict that nonsustained reentry occurs following a strong, premature stimulus through a unipolar electrode.

METHODS AND RESULTS

Our simulations were based on the bidomain model of cardiac tissue, and the active membrane properties were represented by the Beeler-Reuter model. An outwardly propagating wavefront was excited by an initial stimulus (S1). A second stimulus (S2) was then applied through the same electrode. Nonsustained reentry or reentrant-like behavior followed the S2 stimulus for both cathodal and anodal stimulation, and were associated with "break" stimulation but not with "make" stimulation. The direction of spiral-wave rotation was reversed when the polarity of the stimulus was reversed. These complex dynamics occur only for a narrow window of S1-S2 intervals. During anodal S2 stimulation, two different modes of reentry exist. Our simulations also explain the "no response" phenomenon.

CONCLUSION

Our mathematical model predicts that both anodal and cathodal unipolar S2 stimulation results in reentry. This behavior arises from an interaction of virtual anodes and cathodes surrounding the stimulating electrode.

Electrical conductivity values used with the bidomain model of cardiac tissue

Electrical conductivities in the bidomain model of cardiac tissue are expressed as functions of four parameters. These expressions allow simulations to be performed using nominal, equal, and reciprocal anisotropy without introducing undesired effects, such as length constant variations. Relative values of the bidomain conductivities are estimated to be: sigma iL = 1, sigma iT = 0.1, sigma eL = 1, and sigma eT = 0.4.

Effect of varying pacing waveform shapes on propagation and hemodynamics in the rabbit heart

The propagation characteristics of myocardium stimulated with anodal, cathodal, and equiphasic biphasic pacing pulses were examined in Langendorff-perfused rabbit hearts. Conduction velocity measurements were made using an array of bipolar extracellular electrodes, transmembrane potentials recorded using floating intracellular microelectrodes, and hemodynamics measured by fluid-filled catheter transducer systems. Anodal (A) stimulation pulses improved the electrical conduction at all the stimulus amplitudes tested in both longitudinal (e.g., 5 V 2-msec pulse: [A] 54.9 +/- 0.7 cm/sec; cathodal [C] 49.7 +/- 1.5 cm/sec) and transverse (e.g., 5 V 2 msec pulse: [A] 31.3 +/- 1.7 cm/sec; [C] 23.3 +/- 2.9 cm/sec) directions. Microelectrode recordings verified that increased conduction velocities of the anodal pulses were associated with faster upstrokes of the action potentials. The increased threshold associated with anodal pulses may be overcome by using a biphasic (B) waveform, in effect adding a second phase (e.g., 2-msec pulse: [A] 2.03 +/- 1.3 V; [C] 3.85 +/- 1.5 V; [B] 2.15 +/- 0.9 V). The conduction speeds achieved by the biphasic pulses were found to be comparable to the equivalent anodal pulses (e.g., 5 V 2-msec pulse: [B] 55.2 +/- 1.7 cm/sec longitudinal and 32.4 +/- 2.1 cm/sec transverse). It is postulated that the enhanced conduction by anodal and biphasic pulses may be due to preconditioning of the myocardium before stimulation, resulting in more vigorous action potential upstrokes. In preliminary experiments, it was observed that improved conduction elicited by these pulses also resulted in enhanced contractility as measured by shortened electromechanical delays and faster rate of rise of pressure development (dP/dtmax: [A] 25.4 +/- 0.4 mm Hg/sec; [C] 19.4 +/- 0.8 mm Hg/sec; [B] 25.7 +/- 1.2 mm Hg/sec, respectively). Use of novel hybrid pulses involving an anodal component may offer a way for implanted pacemakers to enhance the electro-mechanical response of the heart.

A finite volume model of cardiac propagation

This paper describes a two-dimensional cardiac propagation model based on the finite volume method (FVM). This technique, originally derived and applied within the filed of computational fluid dynamics, is well suited to the investigation of conduction in cardiac electrophysiology. Specifically, the FVM permits the consideration of propagation in a realistic structure, subject to arbitrary fiber orientations and regionally defined properties. In this application of the FVM, an arbitrarily shaped domain is decomposed into a set of constitutive quadrilaterals. Calculations are performed in a computational space, in which the quadrilaterals are all represented simply as squares. Results are related to their physical-space equivalents by means of a transformation matrix. The method is applied to a number of cases. First, large-scale propagation is considered, in which a magnetic resonance-imaged cardiac cross-section serves as the governing geometry. Next, conduction is examined in the presence of an isthmus formed by the microvasculature in a slice of papillary muscle tissue. Under ischemic conditions, the safety factor for propagation is seen to be related to orientation of the fibers within the isthmus. Finally, conduction is studied in the presence of an inexcitable obstacle and a curved fiber field. This example illustrates the dramatic influence of the complex orientation of the fibers on the resulting activation pattern. The FVM provides a means of accurately modeling the cardiac structure and can help bridge the gap between computation and experiment in cardiac electrophysiology.

Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation

Traditional cable analyses cannot explain complex patterns of excitation in cardiac tissue with unipolar, extracellular anodal, or cathodal stimuli. Epifluorescence imaging of the transmembrane potential during and after stimulation of both refractory and excitable tissue shows distinctive regions of simultaneous depolarization and hyperpolarization during stimulation that act as virtual cathodes and anodes. The results confirm bidomain model predictions that the onset (make) of a stimulus induces propagation from the virtual cathode, whereas stimulus termination (break) induces it from the virtual anode. In make stimulation, the virtual anode can delay activation of the underlying tissue, whereas in break stimulation this occurs under the virtual cathode. Thus make and break stimulations in cardiac tissue have a common mechanism that is the result of differences in the electrical anisotropy of the intracellular and extracellular spaces and provides clear proof of the validity of the bidomain model.

A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode

Numerical simulations of electrical stimulation of cardiac tissue using a unipolar extracellular electrode were performed. The bidomain model with unequal anisotropy ratios represented the tissue, and the Beeler-Reuter model represented the active membrane properties. Four types of excitation were considered: cathode make (CM), anode make (AM), cathode break (CB), and anode break (AB). The mechanisms of excitation were: for CM, tissue under the cathode was depolarized to threshold; for AM, tissue at a virtual cathode was depolarized to threshold; for CB, a long cathodal pulse produced a steady-state depolarization under the cathode and hyperpolarization at a virtual anode. At the end (break) of the pulse, the depolarization diffused into the hyperpolarized tissue, resulting in excitation. For AB, a long anodal pulse produced a steady-state hyperpolarization under the anode and depolarization at a virtual cathode. At the end (break) of the pulse, the depolarization diffused into the hyperpolarized tissue, resulting in excitation. For AB stimulation, decay of the hyperpolarization faster than that of the depolarization was necessary. The thresholds for rheobase and diastolic CM, AM, CB, and AB stimulation were 0.038, 0.41, 0.49, and 5.3 mA, respectively, for an electrode length of 1 mm and a surface area of 1.5 mm2. Threshold increased as the size of the electrode increased. The strength-duration curves for CM and AM were similar except when the duration was shorter than 0.2 ms, in which case the AM threshold rose more quickly with decreasing duration than did the CM threshold. CM and AM resulted in similar strength-frequency curves. The model agrees qualitatively, but (in some cases) not quantitatively, with experiments.

Effects of bipolar point and line stimulation in anisotropic rabbit epicardium: assessment of the critical radius of curvature for longitudinal block

Excitation front shape and velocity were studied in anisotropic perfused rabbit epicardium stained with potentiometric fluorescent dye. In the combined results from all experiments, convex excitation fronts produced by stimulation with a single electrode propagated longitudinally 13.3% slower than flat excitation fronts produced by stimulation with a line of electrodes. For transverse propagation, the two stimulation methods produced similar flat excitation fronts and velocities. The critical excitation front radius of curvature for longitudinal block (Rcr), calculated from excitable media theory, was 92 microns in control hearts. In hearts exposed to diacetyl monoxime (20 mmol/L), which decreases inward sodium current, Rcr was 175 microns. The slower longitudinal propagation velocity of convex fronts versus flat fronts and the theoretically predicted critical radius of curvature may be important for propagation and block of ectopic depolarizations in the heart.

Spatial distribution of cardiac transmembrane potentials around an extracellular electrode: dependence on fiber orientation

Recent theoretical models of cardiac electrical stimulation or defibrillation predict a complex spatial pattern of transmembrane potential (Vm) around a stimulating electrode, resulting from the formation of virtual electrodes of reversed polarity. The pattern of membrane polarization has been attributed to the anisotropic structure of the tissue. To verify such model predictions experimentally, an optical technique using a fluorescent voltage-sensitive dye was used to map the spatial distribution of Vm around a 150-microns-radius extracellular unipolar electrode. An S1-S2 stimulation protocol was used, and vm was measured during an S2 pulse having an intensity equal to 10x the cathodal diastolic threshold of excitation. The recordings were obtained on the endocardial surface of bullfrog atrium in directions parallel and perpendicular to the cardiac fibers. In the longitudinal fiber direction, the membrane depolarized for cathodal pulses (and hyperpolarized for anodal pulses) but only in a region within 445 +/- 112 microns (and 616 +/- 78 microns for anodal pulses) from the center of the electrode (n = 9). Outside this region, vm reversed polarity and reached a local maximum at 922 +/- 136 microns (and 988 +/- 117 microns for anodal pulses) (n = 9). Beyond this point vm decayed to zero over a distance of 1.5-2 mm. In the transverse fiber direction, the membrane depolarized for cathodal pulses (and hyperpolarized for anodal pulses) at all distances from the electrode. The amplitude of the response decreased with distance from the electrode with an exponential decay constant of 343 +/- 110 microns for cathodal pulses and 253 +/- 91 microns for anodal pulses (n = 7). The results were qualitatively similar in both fiber directions when the atrium was bathed in a solution containing ionic channel blockers. A two-dimensional computer model was formulated for the case of highly anisotropic cardiac tissue and qualitatively accounts for nearly all the observed spatial and temporal behavior of vm in the two fiber directions. The relationships between vm and both the "activating function" and extracellular potential gradient are discussed.

Threshold reduction with biphasic defibrillator waveforms. Role of charge balance

Mechanism underlying improved defibrillation efficacy of biphasic waveforms at low shock intensities remain poorly understood. Recent studies suggest that biphasic waveforms produce a longer mean postshock response throughout the ventricle. This prolongs the cellular refractory period, blocks fibrillation wave fronts, and causes fibrillation to cease. Previous studies showed that hyperpolarizing monophasic waveforms, delivered during the refractory period, can shorten action potential duration (APD90), which would be deleterious for defibrillation. This study tested the hypothesis that a balanced-charge biphasic waveform produces a longer mean total mean APD than a comparable monophasic waveform by preventing this shortening in hyperpolarized regions as well as by prolonging APD in depolarized regions. To test this hypothesis, the authors examined transmembrane potential changes produced by hyperpolarizing and depolarizing monophasic and balanced-charge symmetrical biphasic waveforms using a computer model of the ventricular action potential. Shock intensities within the low-intensity "window," where biphasic waveforms defibrillate with higher efficacy than monophasic waveforms (1.5-3 times diastolic threshold), were used. Results show that biphasic S2 produced a significantly longer response both under hyperpolarizing and depolarizing conditions. The hyperpolarizing/depolarizing biphasic S2 produced a prolonged response with a well-defined plateau. Following the depolarizing/hyperpolarizing S2, APD90 did not shorten as with the hyperpolarizing monophasic S2. Rather, repolarization continued near the original S1 times course, but with slight prolongation of S1 APD90. These results suggest that biphasic waveforms enhance the prolonged refractory periods required for defibrillation throughout the heart, including regions exposed to both anodal and cathodal stimulation.

Optical recordings of ventricular excitability of frog heart by an extracellular stimulating point electrode

To enhance understanding of the excitability of cardiac muscle during rest, an optical technique using the fluorescent voltage sensitive dye di-4-ANEPPS was used. Unlike conventional electrical recordings, optical recordings are free from electrical artifacts and, therefore, allow the observation of the transmembrane potential not only following the stimulation pulse, but also during the pulse itself. Transmembrane potentials (Vm) were recorded optically from frog ventricular epicardium in calcium containing Ringer's solution directly under an extracellular stimulating point electrode. Anodal and cathodal S1 stimuli were applied at rest. As observed by previous investigators, the post-pulse excitatory responses for cathodal pulses, compared with anodal pulses were greater. Changes in transmembrane potential (delta Vm) during the pulse were as expected for a passive cable only for low intensity pulses (< 4 x the cathodal threshold of excitation in diastole, CTE). However, at the higher intensities necessary to produce an excitatory response (> 6-8 x CTE), an "irregular" response in Vm was observed--a reversal of the hyperpolarization during an anodal stimulus pulse and a reversal of the depolarization during a cathodal stimulus pulse. To elucidate further the biophysical basis for this behavior, delta Vm was mapped around the stimulating electrode. During stimulation, regions could be observed having a response with opposite polarity to that under the electrode (i.e., depolarization for an anodal pulse and hyperpolarization for a cathodal pulse). Removal of the bath solution or the addition of channel blockers did not eliminate the occurrence of these regions. These regions appear to be the basis for the irregular behavior of delta Vm directly under the electrode as well as for anodal excitation.

Bipolar stimulation of cardiac tissue using an anisotropic bidomain model

INTRODUCTION

One of the fundamental electrophysiologic problems that has not yet been completely elucidated is the response of cardiac tissue to externally applied electric currents. A limited number of theoretical and experimental techniques has been used to study the electric behavior of cardiac tissue in the presence of stimulating currents, and to demonstrate that the anisotropy in the passive electrical properties of the tissue plays an important role in the genesis and propagation of the activation wavefront and the resulting potential distributions.

METHODS AND RESULTS

In this work we have applied the finite element method to study the electric and magnetic fields produced by cardiac tissue in response to bipolar current injection, using a linear bidomain model to represent the tissue. We found that the transmembrane potential distribution close to the stimulus electrode has a rather complex geometrical pattern, with adjacent hyperpolarized and depolarized regions.

CONCLUSION

This behavior is consistent with previous theoretical and experimental results and may have implications in the study of electrical stimulation of cardiac tissue that are not apparent using other models.

Electrical stimulation of cardiac tissue: a bidomain model with active membrane properties

Numerical calculations simulated the response of cardiac muscle to stimulation by electrical current. The bidomain model with unequal anisotropy ratios represented the tissue, and parallel leak and active sodium channels represented the membrane conductance. The speed of the wavefront was faster in the direction parallel to the myocardial fibers than in the direction perpendicular to them. However, for cathodal stimulation well above threshold, the wavefront originated farther from the cathode in the direction perpendicular to the myocardial fibers than in the direction parallel to them, consistent with observations of a dog-bone-shaped virtual cathode made by Wikswo et al., Circ. Res. 68:513-530, 1991. The model showed that the virtual cathode size and shape were dependent upon both membrane and tissue conductivities. Increasing the peak sodium conductance or reducing the transverse intracellular conductivity accentuated the dog-bone shape, while the opposite change caused the virtual cathode to become more elliptical, with the major axis of the ellipse transverse to the fiber direction. A cathodal stimulus created regions of hyperpolarization that slowed conduction of the wavefront propagating parallel to the fibers. An anodal stimulus evoked a wavefront with a complex shape; activation originated from two depolarized regions 1 to 2 mm from the stimulus site along the fiber direction. The threshold current strength (0.5 ms duration pulse) for a cathodal stimulus was 0.048 mA, and for an anodal stimulus was 0.67 mA. When the model was modified to simulate the effect of electropermeabilization, which may be present when the transmembrane potential reaches very large values near the stimulating electrode, our qualitative conclusions remained unchanged.(ABSTRACT TRUNCATED AT 250 WORDS)

Virtual electrode effects in myocardial fibers

The changes in transmembrane potential during a stimulation pulse in the heart are not known. We have used transmembrane potential sensitive dye fluorescence to measure changes in transmembrane potential along fibers in an anisotropic arterially perfused rabbit epicardial layer. Cathodal or anodal extracellular point stimulation produced changes in transmembrane potential within 60 microns of the electrode that were positive or negative, respectively. The changes in transmembrane potential did not simply decrease to zero with increasing distance, as would occur with a theoretical fiber space constant, but instead became reversed beyond approximately 1 mm from the electrode consistent with a virtual electrode effect. Even stimulation from a line of terminals perpendicular to the fibers produced negative changes in transmembrane potential for cathodal stimulation with the largest negative changes during a 50-ms pulse at 3-4 mm from the electrode terminals. Negative changes as large as the amplitude of the action potential rising phase occurred during a 50-ms pulse for 20-volt cathodal stimulation. Switching to anodal stimulation reversed the directions of changes in transmembrane potential at most recording spots, however for stimulation during the refractory period negative changes in transmembrane potential were significantly larger than positive changes in transmembrane potential. Anodal stimulation during diastole with 3-ms pulses produced excitation in the region of depolarization that accelerated when the stimulation strength was increased to > 3 times the anodal threshold strength. Thus, virtual electrode effects of unipolar stimulation occur in myocardial fibers, and for sufficiently strong stimuli the virtual electrode effects may influence electrical behavior of the myocardium.

Myocardial electrical propagation in patients with idiopathic dilated cardiomyopathy

Myocardial propagation may contribute to fatal arrhythmias in patients with idiopathic dilated cardiomyopathy (IDC). We examined this property in 15 patients with IDC undergoing cardiac transplantation and in 14 control subjects. An 8 x 8 array with electrodes 2 mm apart was used to determine the electrical activation sequence over a small region of the left ventricular surface. Tissue from the area beneath the electrode array was examined in the patients with IDC. The patients with IDC could be divided into three groups. Group I (n = 7) had activation patterns and estimates of longitudinal (theta L = 0.84 +/- 0.09 m/s) and transverse (theta T = 0.23 +/- 0.05 m/s) conduction velocities that were no different from controls (theta L = 0.80 +/- 0.08 m/s, theta T = 0.23 +/- 0.03 m/s). Group II (n = 4) had fractionated electrograms and disturbed transverse conduction with normal longitudinal activation, features characteristic of nonuniform anisotropic properties. Two of the control patients also had this pattern. Group III (n = 4) had fractionated potentials and severely disturbed transverse and longitudinal propagation. The amount of myocardial fibrosis correlated with the severity of abnormal propagation. We conclude that (a) severe contractile dysfunction is not necessarily accompanied by changes in propagation, and (b) nonuniform anisotropic propagation is present in a large proportion of patients with IDC and could underlie ventricular arrhythmias in this disorder.

A bidomain model with periodic intracellular junctions: a one-dimensional analysis

The classical bidomain model of cardiac tissue views the intracellular and extracellular (interstitial) spaces as two coupled but separate continua. In the present study, the classical bidomain model has been extended by introducing a periodic conductivity in the intracellular space to represent the junctional discontinuity between abutting myocytes. In this model the junctional region of a myocyte is represented in a way that permits variation of junction size and conductivity profile. Employing spectral techniques, a new method was developed for solving the coupled differential equations governing the intracellular and extracellular potentials in a tissue preparation of finite dimensions. Different spectral representations are used for the aperiodic intra- and extracellular potentials (finite Fourier integral transform) and for the periodic intracellular conductivity (Fourier series). As a first application of the method, the response of a 50-cell, single interior fiber to a defibrillating current is examined under steady-state conditions. Transmembrane as well as intra- and extracellular potential distributions along the fiber were calculated.

Reversal of lidocaine effects on sodium currents by isoproterenol in rabbit hearts and heart cells

We demonstrated recently that isoproterenol enhanced the cardiac voltage-dependent sodium currents (INa) in rabbit ventricular myocytes through dual G-protein regulatory pathways. In this study, we tested the hypothesis that isoproterenol reverses the sodium channel blocking effects of class I antiarrhythmic drugs through modulation of INa. The experiments were performed in rabbit ventricular myocytes using whole-cell patch-clamp techniques. Reversal of lidocaine suppression of INa by isoproterenol (1 microM) was significant at various concentrations of lidocaine (20, 65, and 100 microM, P < 0.05). The effects of isoproterenol were voltage dependent, showing reversal of INa suppression by lidocaine at normal and hyperpolarized potentials (negative to -80 mV) but not at depolarized potentials. Isoproterenol enhanced sodium channel availability but did not alter the steady state activation or inactivation of INa nor did it improve sodium channel recovery in the presence of lidocaine. The physiological significance of the single cell INa findings were corroborated by measurements of conduction velocities using an epicardial mapping system in isolated rabbit hearts. Lidocaine (10 microM) significantly suppressed epicardial impulse conduction in both longitudinal (theta L, 0.430 +/- 0.024 vs. 0.585 +/- 0.001 m/s at baseline, n = 7, P < 0.001) and transverse (theta T, 0.206 +/- 0.012 vs. 0.257 +/- 0.014 m/s at baseline, n = 8, P < 0.001) directions. Isoproterenol (0.05 microM) significantly reversed the lidocaine effects with theta L of 0.503 +/- 0.027 m/s and theta T of 0.234 +/- 0.015 m/s (P = 0.014 and 0.004 compared with the respective lidocaine measurements). These results suggest that enhancement of INa is an important mechanism by which isoproterenol reverses the effects of class I antiarrhythmic drugs.

A simulation of cardiac action currents having curl

A digital simulation of a two dimensional cardiac slice has been performed. It is stimulated at the center and an action potential propagates outward. An anisotropic bidomain model is used in which fast sodium physiology connects the intracellular and extracellular domains. For cases in which the inner asymmetry (expressed as longitudinal versus transverse electrical conductivity) is greater than the outer asymmetry, a current flow pattern is observed for which there is nonzero curl. Such a result explains recent observations of nonzero Bz magnetic field detected above a slab of tissue in the x-y plane. The current loop producing this field consists of outer domain current in the longitudinal direction flowing around in space to return at the AP location in the transverse direction in the outer domain and then completing the loop in the longitudinal direction by passing distally through the AP in the inner domain where resistance is extremely low.

Analysis of electric field stimulation of single cardiac muscle cells

Electrical stimulation of cardiac cells by imposed extracellular electric fields results in a transmembrane potential which is highly nonuniform, with one end of the cell depolarized and the other end hyperpolarized along the field direction. To date, the implications of the close proximity of oppositely polarized membranes on excitability have not been explored. In this work we compare the biophysical basis for field stimulation of cells at rest with that for intracellular current injection, using three Luo-Rudy type membrane patches coupled together as a lumped model to represent the cell membrane. Our model shows that cell excitation is a function of the temporal and spatial distribution of ionic currents and transmembrane potential. The extracellular and intracellular forms of stimulation were compared in greater detail for monophasic and symmetric biphasic rectangular pulses, with duration ranging from 0.5 to 10 ms. Strength-duration curves derived for field stimulation show that over a wide range of pulse durations, biphasic waveforms can recruit and activate membrane patches about as effectively as can monophasic waveforms having the same total pulse duration. We find that excitation with biphasic stimulation results from a synergistic, temporal summation of inward currents through the sodium channel in membrane patches at opposite ends of the cell. Furthermore, with both waveform types, a net inward current through the inwardly rectifying potassium channel contributes to initial membrane depolarization. In contrast, models of stimulation by intracellular current injection do not account for the nonuniformity of transmembrane potential and produce substantially different (even contradictory) results for the case of stimulation from rest.

Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers

The influence of interstitial or extracellular potentials on propagation usually has been ignored, often through assuming these potentials to be insignificantly different from zero, presumably because both measurements and calculations become much more complex when interstitial interactions are included. This study arose primarily from an interest in cardiac muscle, where it has been well established that substantial interstitial potentials occur in tightly packed structures, e.g., tens of millivolts within the ventricular wall. We analyzed the electrophysiological interaction between two adjacent unmyelinated fibers within a restricted extracellular space. Numerical evaluations made use of two linked core-conductor models and Hodgkin-Huxley membrane properties. Changes in transmembrane potentials induced in the second fiber ranged from nonexistent with large intervening volumes to large enough to initiate excitation when fibers were coupled by interstitial currents through a small interstitial space. With equal interstitial and intracellular longitudinal conductivities and close coupling, the interaction was large enough (induced Vm approximately 20 mV peak-to-peak) that action potentials from one fiber initiated excitation in the other, for the 40-microns radius evaluated. With close coupling but no change in structure, propagation velocity in the first fiber varied from 1.66 mm/ms (when both fibers were simultaneously stimulated) to 2.84 mm/ms (when the second fiber remained passive). Although normal propagation through interstitial interaction is unlikely, the magnitudes of the electrotonic interactions were large and may have a substantial modulating effect on function.