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

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.

Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators.

Diastolic field stimulation: the role of shock duration in epicardial activation and propagation

Detailed knowledge of tissue response to both systolic and diastolic shock is critical for understanding defibrillation. Diastolic field stimulation has been much less studied than systolic stimulation, particularly regarding transient virtual anodes. Here we investigated high-voltage-induced polarization and activation patterns in response to strong diastolic shocks of various durations and of both polarities, and tested the hypothesis that the activation versus shock duration curve contains a local minimum for moderate shock durations, and it grows for short and long durations. We found that 0.1-0.2-ms shocks produced slow and heterogeneous activation. During 0.8-1 ms shocks, the activation was very fast and homogeneous. Further shock extension to 8 ms delayed activation from 1.55 ± 0.27 ms and 1.63 ± 0.21 ms at 0.8 ms shock to 2.32 ± 0.41 ms and 2.37 ± 0.3 ms (N = 7) for normal and opposite polarities, respectively. The traces from hyperpolarized regions during 3-8 ms shocks exhibited four different phases: beginning negative polarization, fast depolarization, slow depolarization, and after-shock increase in upstroke velocity. Thus, the shocks of >3 ms in duration created strong hyperpolarization associated with significant delay (P < 0.05) in activation compared with moderate shocks of 0.8 and 1 ms. This effect appears as a dip in the activation-versus-shock-duration curve.

Negative curvature boundaries as wave emitting sites for the control of biological excitable media

Understanding the interaction of electric fields with the complex anatomy of biological excitable media is key to optimizing control strategies for spatiotemporal dynamics in those systems. On the basis of a bidomain description, we provide a unified theory for the electric-field-induced depolarization of the substrate near curved boundaries of generalized shapes, resulting in the localized recruitment of control sites. Our findings are confirmed in experiments on cardiomyocyte cell cultures and supported by two-dimensional numerical simulations on a cross section of a rabbit ventricle.

Controlling activation site density by low-energy far-field stimulation in cardiac tissue

Tachycardia and fibrillation are potentially fatal arrhythmias associated with the formation of rotating spiral waves in the heart. Presently, the termination of these types of arrhythmia is achieved by use of antitachycardia pacing or cardioversion. However, these techniques have serious drawbacks, in that they either have limited application or produce undesirable side effects. Low-energy far-field stimulation has recently been proposed as a superior therapy. This proposed therapeutic method would exploit the phenomenon in which the application of low-energy far-field shocks induces a large number of activation sites ("virtual electrodes") in tissue. It has been found that the formation of such sites can lead to the termination of undesired states in the heart and the restoration of normal beating. In this study we investigate a particular aspect of this method. Here we seek to determine how the activation site density depends on the applied electric field through in vitro experiments carried out on neonatal rat cardiac tissue cultures. The results indicate that the activation site density increases exponentially as a function of the intracellular conductivity and the level of cell isotropy. Additionally, we report numerical results obtained from bidomain simulations of the Beeler-Reuter model that are quantitatively consistent with our experimental results. Also, we derive an intuitive analytical framework that describes the activation site density and provides useful information for determining the ratio of longitudinal to transverse conductivity in a cardiac tissue culture. The results obtained here should be useful in the development of an actual therapeutic method based on low-energy far-field pacing. In addition, they provide a deeper understanding of the intrinsic properties of cardiac cells.

ANALYSIS OF THE VIRTUAL ELECTRODE PHENOMENA USING BIDOMAIN MODEL: BASIC CHARACTERISTICS FOR PASSIVE MEMBRANE

The virtual electrode (VE) has been recognized as an important factor for success or failure of cardiac defibrillation. Many researches have been performed to study characteristics of the VE. However, there are some questions which remain unanswered. In this study, we developed a simulator to solve a three-dimensional bidomain model and performed several simulations to elucidate the basic characteristics of VE in a simplified cardiac tissue with passive membrane when a constant unipolar cathodal stimulus was applied. The results showed that for smaller electrodes, VE has a typical dog-bone shaped virtual cathode (VC) and two egg-shaped virtual anodes (VAs). The distributions both in intra- and extracellular potentials have concentric ellipsoidal isosurfaces, but their ellipticities are subtly different, producing VE. For larger electrodes, VC becomes larger and has a flat-dish shape rather than dog-bone, and VA becomes smaller and also flattens and collapses. The peak values of VE are larger for smaller electrodes, but their time courses show similar tendency among the different sized electrodes. The change of stimulus strength and polarity only affects the magnitude of VE in a linear manner and the distribution pattern is unchanged. These results provide us fundamental knowledge about VE.

Liberation of a pinned spiral wave by a single stimulus in excitable media

The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.

Atria are more susceptible to electroporation than ventricles: implications for atrial stunning, shock-induced arrhythmia and defibrillation failure

BACKGROUND

Defibrillation shock is known to induce atrial stunning, which is electrical and mechanical dysfunction.

OBJECTIVE

We hypothesized that atrial stunning is caused by higher atrial susceptibility to electroporation vs ventricles. We also hypothesize that electroporation may be responsible for early recurrence of atrial fibrillation.

METHODS

We investigated electroporation induced by 10-ms epicardial high-intensity shocks applied locally in atria and ventricles of Langendorff-perfused rabbit hearts (n = 12) using optical mapping.

RESULTS

Electroporation was centered at the electrode and was evident from transient diastolic depolarization and reduction of action potential amplitude and maximum upstroke derivative. Electroporation was voltage-dependent and polarity-dependent and was significantly more pronounced in the atria vs ventricles (P <.01), with a summary 50% of Effective Dose (ED50) for main measured parameters of 9.2 +/- 3.6 V/cm and 13.6 +/- 3.2 V/cm in the atria vs 37.4 +/- 1.5 V/cm and 48.4 +/- 2.8 V/cm in the ventricles, for anodal and cathodal stimuli, respectively. In atria (n = 5), shocks of both polarities (27.2 +/- 1.1 V/cm) transiently induced conduction block and reentry around the inexcitable area. Electroporation-induced ectopic activity was a possible trigger for reentry. However, in the thicker ventricles, electroporation and resulting conduction slowing and block were restricted to the surface only, preventing complete block and arrhythmia. The upstroke morphology revealed that the wave front dived below the electroporated region and resurfaced into unaffected epicardial tissue.

CONCLUSION

We showed that the atria are more vulnerable to electroporation and resulting block and arrhythmia than the ventricles.

Evaluating intramural virtual electrodes in the myocardial wedge preparation: simulations of experimental conditions

While defibrillation is the only means for prevention of sudden cardiac death, key aspects of the process, such as the intramural virtual electrodes (VEs), remain controversial. Experimental studies had attempted to assess intramural VEs by using wedge preparations and recording activity from the cut surface; however, applicability of this approach remains unclear. These studies found, surprisingly, that for strong shocks, the entire cut surface was negatively polarized, regardless of boundary conditions. The goal of this study is to examine, by means of bidomain simulations, whether VEs on the cut surface represent a good approximation to VEs in depth of the intact wall. Furthermore, we aim to explore mechanisms that could give rise to negative polarization on the cut surface. A model of wedge preparation was used, in which fiber orientation could be changed, and where the cut surface was subjected to permeable and impermeable boundary conditions. Small-scale mechanisms for polarization were also considered. To determine whether any distortions in the recorded VEs arise from averaging during optical mapping, a model of fluorescent recording was employed. The results indicate that, when an applied field is spatially uniform and impermeable boundary conditions are enforced, regardless of the fiber orientation VEs on the cut surface faithfully represent those intramurally, provided tissue properties are not altered by dissection. Results also demonstrate that VEs are sensitive to the conductive layer thickness above the cut surface. Finally, averaging during fluorescent recordings results in large negative VEs on the cut surface, but these do not arise from small-scale heterogeneities.

Ventricular fibrillation: how do we put the genie back in the bottle?

I am deeply grateful and honored to receive the 2006 Distinguished Scientist Award from the Heart Rhythm Society. Many outstanding individuals have received this award since it was established in 1982, and it is humbling to realize that my small feet are walking in the footsteps of these giants. I would be remiss if I did not thank the numerous colleagues, fellows, and students who performed most of the work leading to the papers of which I am a coauthor.

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.

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.

Mechanisms of superiority of ascending ramp waveforms: new insights into mechanisms of shock-induced vulnerability and defibrillation

Monophasic ascending ramp (AR) and descending ramp (DR) waveforms are known to have significantly different defibrillation thresholds. We hypothesized that this difference arises due to differences in mechanisms of arrhythmia induction for the two waveforms. Rabbit hearts (n = 10) were Langendorff perfused, and AR and DR waveforms (7, 20, and 40 ms) were randomly delivered from two line electrodes placed 10 mm apart on the anterior ventricular epicardium. We optically mapped cellular responses to shocks of various strengths (5, 10, and 20 V/cm) and coupling intervals (CIs; 120, 180, and 300 ms). Optical mapping revealed that maximum virtual electrode polarization (VEP) was reached at significantly different times for AR and DR of the same duration (P < 0.05) for all tested CIs. As a result, VEP for AR were stronger than for DR at the end of the shock. Postshock break excitation resulting from AR generated faster propagation and typically could not form reentry. In contrast, partially dissipated VEP resulting from DR generated slower propagation; the wavefront was able to propagate into deexcited tissue and thus formed a shock-induced reentry circuit. Therefore, for the same delivered energy, AR was less proarrhythmic compared with DR. An active bidomain model was used to confirm the electrophysiological results. The VEP hypothesis explains differences in vulnerability associated with monophasic AR and DR waveforms and, by extension, the superior defibrillation efficacy of the AR waveform compared with the DR waveform.

Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model

Functional reentry in the heart can be caused by a wave front of excitation rotating around its edge. Previous simulations on the basis of monodomain cable equations predicted the existence of self-sustained, vortex-like wave fronts (scroll waves) rotating around a filament in three dimensions. In our simulations, we used the more accurate bidomain model with modified Beeler-Reuter ionic kinetics to study the dynamics of scroll-wave filaments in a 16 x 8 x 1.5-mm slab of ventricular tissue with straight fibers. Wave fronts were identified as the areas with inward current. Their edges represented the filaments. Both transmural and intramural reentries with I- and U-shaped filaments, respectively, were obtained by the S1-S2 point stimulation protocol through the virtual electrode-induced phase singularity mechanism. The filaments meandered along elongated trajectories and tended to attach to the tissue boundaries exposed to air (no current flow) rather than to the bath (zero extracellular potential). They completely detached from electroporated (zero transmembrane potential) boundaries. In our simulations, the presence of the bath led to generation of only U-shaped filaments, which survived for the 1.5-mm-thick slab but not for the slabs of 0.5- or 3-mm thicknesses. Thus boundary conditions may be another determinant of the type and dynamics of reentry.

Synthesis of voltage-sensitive fluorescence signals from three-dimensional myocardial activation patterns

Voltage-sensitive fluorescent dyes are commonly used to measure cardiac electrical activity. Recent studies indicate, however, that optical action potentials (OAPs) recorded from the myocardial surface originate from a widely distributed volume beneath the surface and may contain useful information regarding intramural activation. The first step toward obtaining this information is to predict OAPs from known patterns of three-dimensional (3-D) electrical activity. To achieve this goal, we developed a two-stage model in which the output of a 3-D ionic model of electrical excitation serves as the input to an optical model of light scattering and absorption inside heart tissue. The two-stage model permits unique optical signatures to be obtained for given 3-D patterns of electrical activity for direct comparison with experimental data, thus yielding information about intramural electrical activity. To illustrate applications of the model, we simulated surface fluorescence signals produced by 3-D electrical activity during epicardial and endocardial pacing. We discovered that OAP upstroke morphology was highly sensitive to the transmural component of wave front velocity and could be used to predict wave front orientation with respect to the surface. These findings demonstrate the potential of the model for obtaining useful 3-D information about intramural propagation.

Effects of lidocaine on shock-induced vulnerability

INTRODUCTION

Lidocaine is known to increase the defibrillation threshold (DFT) of monophasic shocks (MS) and have no effect on DFT of biphasic shocks (BS). The aim of this study was to enhance our understanding of the mechanisms of vulnerability and defibrillation through the investigation of this difference.

METHODS AND RESULTS

We studied the effect of 15 microM lidocaine on shock-induced vulnerability using fluorescent imaging of Langendorff-perfused rabbit hearts. Vulnerability was assessed as vulnerable window with shock strengths of 15 to 150 V and vulnerable period (VP) with shock delivery phase of 0% to 100% of action potential duration (% APD). With MS, lidocaine caused a significant increase in both the upper limit of vulnerability (ULV, 71 +/- 17 V vs 120 +/- 1.5 V, P < 0.01) and upper limit of VP (91 +/- 8.0% APD vs 110 +/- 4.2% APD, P < 0.01). With BS, lidocaine had no effect on ULV (40 +/- 3.4 V vs 45 +/- 4.5 V) and did not increase the upper limit of VP (78 +/- 8.9% APD vs 96 +/- 12% APD, P < 0.01). Lidocaine caused reduction of the conduction velocity during pacing (0.58 +/- 0.08 m/s vs 0.44 +/- 0.05 m/s, P < 0.01), shock-induced break excitation (0.82 +/- 0.17 m/s vs 0.30 +/- 0.07 m/s, P < 0.01), and postshock reentry (0.34 +/- 0.07 m/s vs 0.19 +/- 0.08 m/s, P < 0.01). Lidocaine had no effect on shock-induced virtual electrode polarization.

CONCLUSION

Lidocaine increased MS ULV due to slowing of shock-induced break-excitation wavefronts, which resulted in enhanced probability of survival of virtual electrode induced phase singularity. Lidocaine had no effect on BS ULV because no break excitation was induced by BS. Reduction of conduction velocity by lidocaine resulted in increased dispersion of repolarization and led to upper limit of VP increase for both MS and BS.

Upper limit of vulnerability in a defibrillation model of the rabbit ventricles

The goal of this modeling study is to investigate the mechanisms responsible for the upper and lower limits of vulnerability (ULV and LLV) to re-entry induced by electric shocks within the three-dimensional volume of the heart. We use a geometrically accurate rabbit ventricular model with realistic fiber architecture that also includes the blood in the cavities and a perfusing bath. The shocks are delivered over a range of strengths and coupling intervals via two large mesh electrodes located at the vertical boundaries of the perfusing bath. Our results demonstrate that shock-induced virtual electrode polarization (VEP) in the midmyocardium is weaker and more complex than VEP on the surfaces, where only 2 areas, one of positive and one of negative polarization, are induced. Transmural views of the ventricles show that, in all cases, tissue in the LV free wall and in the septum is deexcited by the shock providing an excitable path for wavefront propagation. Conversely, the RV free wall myocardium is depolarized after the end of the shock. The evolution of postshock electrical activity in the RV free wall plays a critical role in determining the outcome of the shock. In all cases, a wavefront starts in the apex at the site of largest transmembrane voltage gradient between oppositely polarized areas. For shocks of strength above the LLV, the postshock refractoriness of the RV free wall produces the unidirectional block necessary for reentry induction. If shock strength is below the ULV, the RV free wall recovers in time to provide the reentrant pathway. In contrast, for shocks of strength above the ULV, the postshock excitable gap in the LV free wall and in the septum is depolarized before the RV free wall recovers. Therefore, both ventricles are refractory and reentry is not induced

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.

Left ventricular geometry immediately following defibrillation: shock-induced relaxation

A previous two-dimensional (2D) ultrasound study suggested that there is relaxation of the myocardium after defibrillation. The 2D study could not measure activity occurring within the first 33 ms after the shock, a period that may be critical for discriminating between shock- and excitation-induced relaxation. The objective of our study was to determine the left ventricular (LV) geometry during the first 33 ms after defibrillation. Biphasic defibrillation shocks were delivered 5-50 s after the induction of ventricular fibrillation in each of the seven dogs. One-dimensional, short-axis ultrasound images of the LV cavity were acquired at a rate of 250 samples/s. The LV cavity diameter was computed from 32 ms before to 32 ms after the shock. Preshock and postshock percent changes in LV diameter were analyzed as a function of time with the use of regression analysis. The normalized mean pre- and postshock slopes (0.2 +/- 2.2 and 3.3 +/- 7.9% per 10 ms) were significantly different (P < 0.01). The postshock slope was positive (P < 0.005). Our results confirm that the bulk of the myocardium is relaxing immediately after defibrillation.

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.

Mechanisms of make and break excitation revisited: paradoxical break excitation during diastolic stimulation

Onset and termination of electric stimulation may result in "make" and "break" excitation of the heart tissue. Wikswo et al. (30) explained both types of stimulations by virtual electrode polarization. Make excitation propagates from depolarized regions (virtual cathodes). Break excitation propagates from hyperpolarized regions (virtual anodes). However, these studies were limited to strong stimulus intensities. We examined excitation during weak near-threshold diastolic stimulation. We optically mapped electrical activity from a 4 x 4-mm area of epicardium of Langendorff-perfused rabbit hearts (n = 12) around the pacing electrode in the presence (n = 12) and absence (n = 2) of 15 mM 2,3-butanedione monoxime. Anodal and cathodal 2-ms stimuli of various intensities were applied. We imaged an excitation wavefront with 528-micros resolution. We found that strong stimuli (x5 threshold) result in make excitation, starting from the virtual cathodes. In contrast, near-threshold stimulation resulted in break excitation, originating from the virtual anodes. Characteristic biphasic upstrokes in the virtual cathode area were observed. Break and make excitation represent two extreme cases of near-threshold and far-above-threshold stimulations, respectively. Both mechanisms are likely to contribute during intermediate clinically relevant strengths.

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.

Intramural multisite recording of transmembrane potential in the heart

Heart surface optical mapping of transmembrane potentials has been widely used in studies of normal and pathological heart rhythms and defibrillation. In these studies, three-dimensional spatio-temporal events can only be inferred from two-dimensional surface potential maps. We present a novel optical system that enables high fidelity transmural recording of transmembrane potentials. A probe constructed from optical fibers is used to deliver excitation light and collect fluorescence from seven positions, each 1 mm apart, through the left ventricle wall of the rabbit heart. Excitation is provided by the 488-nm line of a water-cooled argon-ion laser. The fluorescence of the voltage-sensitive dye di-4-ANEPPS from each tissue site is split at 600 nm and imaged onto separate photodiodes for later signal ratioing. The optics and electronics are easily expandable to accommodate multiple optical probes. The system is used to record the first simultaneous measurements of transmembrane potential at a number of sites through the intact heart wall.

Mechanism of ventricular defibrillation for near-defibrillation threshold shocks: a whole-heart optical mapping study in swine

BACKGROUND

To study the mechanism by which shocks succeed (SDF) or fail (FDF) to defibrillate, global cardiac activation and recovery and their relationship to defibrillation outcome were investigated for shock strengths with approximately equal SDF and FDF outcomes (DFT(50)).

METHODS AND RESULTS

In 6 isolated pig hearts, dual-camera video imaging was used to record optically from approximately 8000 sites on the anterior and posterior ventricular surfaces before and after 10 DFT(50) biphasic shocks. The interval between the shock and the last ventricular fibrillation activation preceding the shock (coupling interval, CI) and the time from shock onset to 90% repolarization of the immediate postshock action potential (RT(90)) were determined at all sites. Of 60 shocks, 31 were SDF. The CI (59+/-7 versus 52+/-6 ms) and RT(90) (108+/-19 versus 88+/-8 ms) were significantly longer for SDF than FDF episodes. Spatial dispersions of CI (36+/-5 versus 34+/-3 ms) and RT(90) (40+/-16 versus 40+/-8 ms) were not significantly different for SDF versus FDF episodes. The first global activation cycle appeared focally on the left ventricular apical epicardium 78+/-32 ms after the shock.

CONCLUSIONS

For near-threshold shocks, defibrillation outcome correlates with the electrical state of the heart at the time of the shock and on RT. Global dispersion of RT was similar in both SDF and FDF episodes, suggesting that it is not crucial in determining defibrillation outcome after DFT(50) shocks.

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.

The role of electroporation in defibrillation

Electric shock is the only effective therapy against ventricular fibrillation. However, shocks are also known to cause electroporation of cell membranes. We sought to determine the impact of electroporation on ventricular conduction and defibrillation. We optically mapped electrical activity in coronary-perfused rabbit hearts during electric shocks (50 to 500 V). Electroporation was evident from transient depolarization, reduction of action potential amplitude, and upstroke dV/dt. Electroporation was voltage dependent and significantly more pronounced at the endocardium versus the epicardium, with thresholds of 229+/-81 versus 318+/-84 V, respectively (P=0.01, n=10), both being above the defibrillation threshold of 181.3+/-45.8 V. Epicardial electroporation was localized to a small area near the electrode, whereas endocardial electroporation was observed at the bundles and trabeculas throughout the entire endocardium. Higher-resolution imaging revealed that papillary muscles (n=10) were most affected. Electroporation and conduction block thresholds in papillary muscles were 281+/-64 V and 380+/-79 V, respectively. We observed no arrhythmia in association with electroporation. Further, preconditioning with high-energy shocks prevented reinduction of fibrillation by 50-V shocks, which were otherwise proarrhythmic. Endocardial bundles are the most susceptible to electroporation and the resulting conduction impairment. Electroporation is not associated with proarrhythmic effects and is associated with a reduction of vulnerability.

Virtual electrode polarization in the far field: implications for external defibrillation

We recently suggested that failure of implantable defibrillation therapy may be explained by the virtual electrode-induced phase singularity mechanism. The goal of this study was to identify possible mechanisms of vulnerability and defibrillation by externally applied shocks in vitro. We used bidomain simulations of realistic rabbit heart fibrous geometry to predict the passive polarization throughout the heart induced by external shocks. We also used optical mapping to assess anterior epicardium electrical activity during shocks in Langendorff-perfused rabbit hearts (n = 7). Monophasic shocks of either polarity (10-260 V, 8 ms, 150 microF) were applied during the T wave from a pair of mesh electrodes. Postshock epicardial virtual electrode polarization was observed after all 162 applied shocks, with positive polarization facing the cathode and negative polarization facing the anode, as predicted by the bidomain simulations. During arrhythmogenesis, a new wave front was induced at the boundary between the two regions near the apex but not at the base. It spread across the negatively polarized area toward the base of the heart and reentered on the other side while simultaneously spreading into the depth of the wall. Thus a scroll wave with a ribbon-shaped filament was formed during external shock-induced arrhythmia. Fluorescent imaging and passive bidomain simulations demonstrated that virtual electrode polarization-induced scroll waves underlie mechanisms of shock-induced vulnerability and failure of external defibrillation.

Reversal of repolarization gradient does not reverse the chirality of shock-induced reentry in the rabbit heart

INTRODUCTION

Two hypotheses have been proposed to explain the mechanisms of vulnerability and related failure of defibrillation therapy: the cross-field-induced critical point hypothesis and the virtual electrode-induced phase singularity hypothesis. These two hypotheses predict the opposite effect of preshock repolarization on the chirality (direction of rotation) of shock-induced reentry. The former suggests its reversal upon reversal of repolarization, whereas the latter suggests its preservation. The aim of this study was to determine, by reversing the repolarization sequence, which of the mechanisms is responsible for internal shock-induced arrhythmia in the Langendorff-perfused rabbit heart.

METHODS AND RESULTS

We used high-resolution optical mapping to assess the chirality of postshock reentry in 11 hearts. Hearts were paced at a coupling interval of 300 msec at various sites around the field of view (13.5 x 13.5 to 16.5 x 16.5 mm). Cathodal monophasic implantable cardioverter defibrillator shocks (-100 V, 8 msec) were applied during the T wave from a 10-mm coil electrode placed into the right ventricular cavity. We used 3.5 +/- 0.8 different pacing sites per heart. Change in direction of repolarization did not result in change of chirality. Chirality was constant in all 11 hearts despite the complete reversal of activation and repolarization patterns. However, the position of resulting vortices depended on transmembrane polarization gradient inverted delta Vm and amplitude of negative polarization Vm (deexcitation). Stronger gradients and deexcitation produced earlier epicardial break excitation (P = 0.04 and P < 0.0001, respectively).

CONCLUSION

Virtual electrode-induced phase singularity mechanism underlies internal shock-induced arrhythmia in this model.

Direct evidence of the role of virtual electrode-induced phase singularity in success and failure of defibrillation

INTRODUCTION

We recently demonstrated that virtual electrode-induced phase singularity is responsible for arrhythmogenesis during T wave shocks and explains the upper and lower limits of vulnerability. Furthermore, we suggested that the same mechanism might be responsible for defibrillation failure. The aim of this study was to experimentally support this hypothesis.

METHODS AND RESULTS

We used the voltage-sensitive dye di-4-ANEPPS and fast imaging to assess electrical activity in Langendorff-perfused rabbit hearts. Ventricular arrhythmias were induced by monophasic shocks applied during T wave. Three types of defibrillation shocks (n = 79) were delivered from an intravenous right ventricular electrode: monophasic (8 msec), optimal biphasic (8/8 msec, 2/1 leading-edge voltage ratio), and nonoptimal biphasic (8/8 msec, 1/1 leading-edge voltage ratio). We found that a monophasic shock extinguished arrhythmic pattern of electrical activity via a virtual electrode polarization effect. However, the virtual electrode polarization was likely to produce phase singularities, leading to another arrhythmia and defibrillation failure. Nonoptimal biphasic shocks produced similar effects. Optimal biphasic shocks were successful because the first phase of the shock erased the arrhythmia via the virtual electrodes effect, whereas the second phase canceled the virtual electrodes, eliminating the substrate for phase singularities and arrhythmia resulting from them.

CONCLUSION

Our data provide the first experimental support of the hypothesis implicating virtual electrode-induced phase singularity in defibrillation failure in the Langendorff-perfused rabbit heart. Optimal biphasic shock has a higher defibrillation efficacy because it does not produce virtual electrode-induced phase singularities.

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.

Regional differences in arrhythmogenic aftereffects of high intensity DC stimulation in the ventricles

Regional differences of the aftereffects of high intensity DC stimulation were investigated in isolated rabbit hearts stained with a voltage-sensitive dye (di-4-ANEPPS). Optical action potential signals were recorded from the epicardial surface of the right and left ventricular free wall (RVep, LVep) and from the right endocardial surface of the interventricular septum (IVS). Ten-millisecond monophasic DC stimulation (S2, 20-120 V) was applied to the signal recording spots during the early plateau phase of the action potential induced by basic stimuli (S1, 2.5 Hz). There was a linear relationship between S2 voltage and the S2 field intensity (FI). S2 caused postshock additional depolarization, giving rise to a prolongation of the shocked action potential. With S2 > or = 40 V (FI > or = approximately 20 V/cm), terminal repolarization of action potential was inhibited, and subsequent postshock S1 action potentials for 1-5 minutes were characterized by a decrease in the maximum diastolic potential and a decrease in the amplitude and a slowing of their upstroke phase. The higher the S2 voltage, the larger the aftereffects. The changes in postshock action potential configuration in RVep were significantly greater than those observed in LVep and IVS when compared at the same levels of S2 intensity. In RVep, 12 of 20 shocks of 120 V resulted in a prolonged refractoriness to S1 (> 1 s), and the arrest was often followed by oscillation of membrane potential. Ventricular tachycardia or fibrillation ensued from the oscillation in five cases. No such long arrest or serious arrhythmias were elicited in LVep and IVS. These results suggest that RVep is more susceptible than LVep and IVS for arrhythmogenic aftereffects of high intensity DC stimulation.

Detection of coronary artery disease using maximum value of ST/HR hysteresis over different number of leads

We have studied the effect of the number and ordering of exercise electrocardiographic (ECG) leads when using the maximum value of the ST segment depression/heart rate (ST/HR) hysteresis over a different number of leads for the detection of coronary artery disease (CAD). The study population consisted of 127 patients with CAD and 220 patients with a low likelihood of the disease referred for an exercise test at Tampere University Hospital, Finland. The lead system used was the Mason-Likar modification of the standard 12-lead system, and exercise tests were performed on a bicycle ergometer. The number of leads was studied using lead sets consisting of first 2 leads, then 3 leads, and so on, up to all 12 leads. The criterion for the order of inclusion of the next lead in the new lead set was based on the maximized area under the receiver operating characteristic (ROC) curve for the new lead set. The importance of the number of leads was evaluated by means of three different approaches: ROC analysis; using a fixed partition criterion of 0.01 mV; and using a fixed specificity value of 80%. According to the results, the most powerful diagnostic capacity of an individual lead was in lead V5, and the most deficient diagnostic capacities were in leads aVL and V1. Using the maximum search procedure, it was possible to improve the diagnostic capacity of the ST/HR hysteresis by anything from 4 up to a maximum of 8 leads. After that it started to decrease rapidly. In conclusion, this study suggests that the diagnostic capacity of the ST/HR hysteresis could be improved by increasing the number of leads. However, the selection of leads is of major importance when using the maximum value of the ST/HR hysteresis over the leads in the detection of CAD.

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.

Virtual electrode-induced reexcitation: A mechanism of defibrillation

Mechanisms of defibrillation remain poorly understood. Defibrillation success depends on the elimination of fibrillation without shock-induced arrhythmogenesis. We optically mapped selected epicardial regions of rabbit hearts (n=20) during shocks applied with the use of implantable defibrillator electrodes during the refractory period. Monophasic shocks resulted in virtual electrode polarization (VEP). Positive values of VEP resulted in a prolongation of the action potential duration, whereas negative polarization shortened the action potential duration, resulting in partial or complete recovery of the excitability. After a shock, new propagated wavefronts emerged at the boundary between the 2 regions and reexcited negatively polarized regions. Conduction velocity and maximum action potential upstroke rate of rise dV/dt (max) of shock-induced activation depended on the transmembrane potential at the end of the shock. Linear regression analysis showed that dV/dt(max) of postshock activation reached 50% of that of normal action potential at a V(m) value of -56.7+/-0.6 mV postshock voltage (n=9257). Less negative potentials resulted in slow conduction and blocks, whereas more negative potentials resulted in faster conduction. Although wavebreaks were produced in either condition, they degenerated into arrhythmias only when conduction was slow. Shock-induced VEP is essential in extinguishing fibrillation but can reinduce arrhythmias by producing excitable gaps. Reexcitation of these gaps through progressive increase in shock strength may provide the basis for the lower and upper limits of vulnerability. The former may correspond to the origination of slow wavefronts of reexcitation and phase singularities. The latter corresponds to fast conduction during which wavebreaks no longer produce sustained arrhythmias.

Shock-induced figure-of-eight reentry in the isolated rabbit heart

The patterns of transmembrane potential on the whole heart during and immediately after fibrillation-inducing shocks are unknown. To study arrhythmia induction, we recorded transmembrane activity from the anterior and posterior epicardial surface of the isolated rabbit heart simultaneously using 2 charge-coupled device cameras (32,512 pixels, 480 frames/second). Isolated hearts were paced from the apex at a cycle length of 250 ms. Two shock coils positioned inside the right ventricle (-) and atop the left atrium (+) delivered shocks at 3 strengths (0.75, 1.5, and 2.25 A) and 6 coupling intervals (130 to 230 ms). The patterns of depolarization and repolarization were similar, as is evident in the uniformity of action potential duration at 75% repolarization (131.4¿8.3 ms). At short coupling intervals (<180 ms), shocks hyperpolarized a large portion of the ventricles and produced a pair of counterrotating waves, one on each side of the heart. The first beat after the shock was reentrant in 90% of short coupling interval episodes. At long coupling intervals (>180 ms), increasingly stronger shocks depolarized an increasingly larger portion of the heart. The first beat after the shock was reentrant in 18% of long coupling interval episodes. Arrhythmias were most often induced at short coupling intervals (98%) than at long coupling intervals (35%). The effect and outcome of the shock were related to the refractory state of the heart at the time of the shock. Hyperpolarization occurred at short coupling intervals, whereas depolarization occurred at long coupling intervals. Consistent with the "critical point" hypothesis, increasing shock strength and coupling interval moved the location where reentry formed (away from the shock electrode and pacing electrode, respectively).

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.

Effect of a bath on the epicardial transmembrane potential during internal defibrillation shocks

Using a three-dimensional model of cardiac tissue, we consider a rectangular slab of tissue. We examine the effect of a defibrillating shock from an intracavitary electrode upon the epicardial transmembrane potential (Vm) for two cases: one in which the epicardium is bounded by air and another in which it is bounded by a conductive bath. We find that the inclusion of the bath changes the polarity of the steady-state Vm in the epicardial region that is closest to the shock electrode. In addition, the magnitude of Vm is increased dramatically if the bath is present; the degree of hyperpolarization increases twenty-fivefold, while the degree of depolarization increases elevenfold. The remaining bulk of the cardiac tissue is relatively unaffected by the inclusion of the bath.