Bipolar stimulation of cardiac tissue using an anisotropic bidomain model

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

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

Modeling bipolar stimulation of cardiac tissue

Unipolar stimulation of cardiac tissue is often used in the design of cardiac pacemakers because of the low current required to depolarize the surrounding tissue at rest. However, the advantages of unipolar over bipolar stimulation are not obvious at shorter coupling intervals when the tissue near the pacing electrode is relatively refractory. Therefore, this paper analyzes bipolar stimulation of cardiac tissue. The strength-interval relationship for bipolar stimulation is calculated using the bidomain model and a recently developed parsimonious ionic current model. The strength-interval curves obtained using different electrode separations and arrangements (electrodes placed parallel to the fibers versus perpendicular to the fibers) indicate that bipolar stimulation results in more complex activation patterns compared to unipolar stimulation. An unusually low threshold stimulus current is observed when the electrodes are close to each other (a separation of 1 mm) because of break excitation. Unlike for unipolar stimulation, anode make excitation is not present during bipolar stimulation, and an abrupt switch from anode break to cathode make excitation can cause dramatic changes in threshold with very small changes in the interval. These results could impact the design of implantable pacemakers and defibrillators.

Imaging of Ventricular Fibrillation and Defibrillation: The Virtual Electrode Hypothesis

Ventricular fibrillation is the major underlying cause of sudden cardiac death. Understanding the complex activation patterns that give rise to ventricular fibrillation requires high resolution mapping of localized activation. The use of multi-electrode mapping unraveled re-entrant activation patterns that underlie ventricular fibrillation. However, optical mapping contributed critically to understanding the mechanism of defibrillation, where multi-electrode recordings could not measure activation patterns during and immediately after a shock. In addition, optical mapping visualizes the virtual electrodes that are generated during stimulation and defibrillation pulses, which contributed to the formulation of the virtual electrode hypothesis. The generation of virtual electrode induced phase singularities during defibrillation is arrhythmogenic and may lead to the induction of fibrillation subsequent to defibrillation. Defibrillating with low energy may circumvent this problem. Therefore, the current challenge is to use the knowledge provided by optical mapping to develop a low energy approach of defibrillation, which may lead to more successful defibrillation.

A model of electrical conduction in cardiac tissue including fibroblasts

Fibroblasts are abundant in cardiac tissue. Experimental studies suggested that fibroblasts are electrically coupled to myocytes and this coupling can impact cardiac electrophysiology. In this work, we present a novel approach for mathematical modeling of electrical conduction in cardiac tissue composed of myocytes, fibroblasts, and the extracellular space. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added a description of fibroblasts, which are electrically coupled with each other and with myocytes. We applied the extended model in exemplary computational simulations of plane waves and conduction in a thin tissue slice assuming an isotropic conductivity of the intra-fibroblast domain. In simulations of plane waves, increased myocyte-fibroblast coupling and fibroblast-myocyte ratio reduced peak voltage and maximal upstroke velocity of myocytes as well as amplitudes and maximal downstroke velocity of extracellular potentials. Simulations with the thin tissue slice showed that inter-fibroblast coupling affected rather transversal than longitudinal conduction velocity. Our results suggest that fibroblast coupling becomes relevant for small intra-myocyte and/or large intra-fibroblast conductivity. In summary, the study demonstrated the feasibility of the extended bidomain model and supports the hypothesis that fibroblasts contribute to cardiac electrophysiology in various manners.

Cathodal stimulation in the recovery phase of a propagating planar wave in the rabbit heart reveals four stimulation mechanisms

The stimulation of cardiac tissue in the recovery phase has significant importance in relation to reentry induction. In the theoretical experiment proposed by Winfree, termed the 'pinwheel' experiment, a point stimulus (S2) is applied in the wake of a freely propagating planar wave (S1). Reentry induced from this S1-S2 pinwheel protocol has been observed experimentally in heart preparations. However, in these experiments, which focused on activation outcomes, only mapping of extracellular voltages has been conducted. The lack of transmembrane potential (Vm) distribution data makes it impossible to analyse the underlying stimulation mechanisms which precede the reentry induction. In this work we sought to elucidate the stimulation mechanisms throughout the heart cycle using the pinwheel protocol. We examined the cardiac tissue responses during and immediately after cathodal stimulation in the refractory wake of a propagating planar wave. The voltage-sensitive dye di-4-ANEPPS was utilized to measure Vm directly from quasi two-dimensional preparations of cryoablated Langendorff-perfused rabbit hearts. Four stimulation mechanisms were observed that depended on the Vm magnitude during S2 cathodal stimulation. Make stimulation always occurred during diastolic stimulation. When stimulation was at the beginning of the relative refractory period (RRP), transitional make-break stimulation was detected. During the RRP the excitation was due to the break mechanism. While approaching the effective refractory period (ERP), the tissue response is characterized by a damped wave mediated response. These four stimulation mechanisms were observed in all hearts whether the S1 planar wave propagation was parallel or perpendicular to the fibre direction. This study is the first examination of Vm and the stimulation mechanisms throughout the cardiac cycle using the pinwheel protocol, and the results have implications in the development and improvement of pacing protocols for artificial cardiostimulators.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

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.

Basic assessment of paced activation sequence mapping: implications for practical use

Some experiences support the use of atrial paced activation sequence mapping, but there is no systematic study assessing its spatial resolution, reproducibility, and influence of pacing parameters. The aim of this study was to evaluate these issues by using a 24-pole catheter positioned at the atrial aspect of the tricuspid and mitral annuli in 15 patients. Bipolar pacing was performed at two sites (right and left atria), 2 cycle lengths (300 and 500 ms) and two outputs (twice and tenfold the late diastolic threshold voltage for 2-ms pulses). The elapsed time between the atrial activation at the two dipoles adjacent to the pacing dipole (activation time [AT]) was measured during each pacing sequence. Changes in cycle length did not modify the AT. The increase in voltage slightly modified the AT (maximum -2 ms at the RA; 95% CI -3 to -1 ms) due to a greater shortening of the conduction time to the dipole located next to the anode. The 95% limits of the intraobserver and interobserver agreements in the AT measurement were -2 to 3 ms and -3 to 3 ms, respectively. The spatial resolution was studied in ten patients by measuring the AT during pacing from each dipole of a 20-pole catheter with a 1-3-1 mm interelectrode distance. The mean AT change was 10 +/- 4 ms per 6 mm of pacing site displacement (95% CI 8-11 ms, range 2.5-20 ms). In conclusion, paced atrial activation sequence analysis is reproducible, accurate, and relatively independent of pacing parameters.

Spatiotemporal dynamics of damped propagation in excitable cardiac tissue

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

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.

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.

Anode/cathode make and break phenomena in a model of defibrillation

The goal of this simulation study is to examine, in a sheet of myocardium, the contribution of anode and cathode break phenomena in terminating a spiral wave reentry by the defibrillation shock. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. Two case studies are presented in this article: tissue that can electroporate at high levels of transmembrane potential, and model tissue that does not support electroporation. In both cases, the spiral wave is initiated via cross-field stimulation of the bidomain sheet. The extracellular defibrillation shock is delivered via two small electrodes located at opposite tissue boundaries. Modifications in the active membrane kinetics enable the delivery of high-strength defibrillation shocks. Numerical solutions are obtained using an efficient semi-implicit predictor-corrector scheme that allows one to execute the simulations within reasonable time. The simulation results demonstrate that anode and/or cathode break excitations contribute significantly to the activity during and after the shock. For a successful defibrillation shock, the virtual electrodes and the break excitations restrict the spiral wave and render the tissue refractory so it cannot further maintain the reentry. The results also indicate that electroporation alters the anode/cathode break phenomena, the major impact being on the timing of the cathode-break excitations. Thus, electroporation results in different patterns of transmembrane potential distribution after the shock. This difference in patterns may or may not result in change of the outcome of the shock.

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

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

Electrical stimulation of cardiac tissue by a bipolar electrode in a conductive bath

A three-dimensional (3-D) computer simulation of the electrical stimulation of passive cardiac tissue from a bipolar electrode placed within a conductive bath is presented. Through the bidomain model, the syncytial and anisotropic properties of cardiac tissue are taken into account; tissues with equal anisotropy and no transverse coupling are also considered. The membrane is represented by a capacitor and passive resistor in parallel. Located within an isotropic bath, the bipolar electrode is oriented either perpendicular or parallel to the tissue surface. For anisotropic tissue with a small cathode-tissue separation, the tissue surface is highly depolarized under the cathode with the depolarization persisting a considerable distance from the electrode in the transverse fiber direction. Adjacent to this region in the longitudinal direction, areas of hyperpolarization exist. At large distances from the cathode, the tissue surface is hyperpolarized in all directions when the electrode axis is perpendicular to the tissue. In the parallel case, surface depolarization creates buried regions of hyperpolarization. For the perpendicular configuration, the ratio of the steady-state maximum depolarization to steady-state maximum hyperpolarization, an estimate of the ratio of anodal to cathodal threshold, decreases rapidly with increasing cathode-tissue separation. In the parallel case, the depth of the conductive bath significantly affected the transmembrane potential distribution in the tissue. The use of a 3-D model more realistically simulates real-life electrical stimulation (such as stimulation with an implantable pacemaker) and provides insight into the effect of the volume conductor adjacent to the tissue.

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.

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.

Mechanism of anode break stimulation in the heart

Anodal stimulation is routinely observed in cardiac tissue, but only recently has a mechanism been proposed. The bidomain cardiac tissue model proposes that virtual cathodes induced at sites distant from the electrode initiate the depolarization. In contrast, none of the existing cardiac action potential models (Luo-Rudy phase I and II, or Oxsoft) predict anodal stimulation at the single-cell level. To determine whether anodal stimulation has a cellular basis, we measured membrane potential and membrane current in mammalian ventricular myocytes by using whole-cell patch clamp. Anode break responses can be readily elicited in single ventricular cells. The basis of this anodal stimulation in single cells is recruitment of the hyperpolarization-activated inward current I(f). The threshold of activation for I(f) is -80 mV in rat cells and -120 mV in guinea pig or canine cells. Persistent I(f) "tail" current upon release of the hyperpolarization drives the transmembrane potential toward the threshold of sodium channels, initiating an action potential. Time-dependent block of the inward rectifier, I(K1), at hyperpolarized potentials decreases membrane conductance and thereby potentiates the ability of I(f) to depolarize the cell on the break of an anodal pulse. Inclusion of I(f), as well as the block and unblock kinetics of I(K1), in the existing Luo-Rudy action potential model faithfully reproduces anode break stimulation. Thus active cellular properties suffice to explain anode break stimulation in cardiac tissue.

Effects of the tissue-bath interface on the induced transmembrane potential: a modeling study in cardiac stimulation

During the initial stages of cardiac stimulation or defibrillation, the distribution of transmembrane potential generated in the myocardium by the external stimulus is determined by the local interactions between fibrous tissue organization and applied electric field. We hypothesize that the pattern of induced transmembrane potential is different, depending on whether the tissue is in insulator, such as air, or in contact with a low-resistance volume conductor, such as blood or perfuseate. The goal of this study is to evaluate the impact of the volume conductor bordering the myocardium on the pattern of stimulus-induced transmembrane potential. Presented here are computer simulations of the steady-state response of model tissue-bath preparations to extracellular current stimuli. Transmembrane potential distributions for various tissue and bath sizes, as well as locations of the stimulation electrodes, are examined. The results indicate that when the external stimuli are located in close proximity to or at the tissue-bath interface, both the magnitude and the distribution of transmembrane potential are significantly altered, compared with the case of an insulated preparation. Thus, the volume conductor seems to be another possible factor contributing to the pattern of membrane hyper- and depolarization in the myocardium. Its influence is, however, modulated by the promixity of the stimuli sites to the tissue-bath interface.

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.

Discrete versus syncytial tissue behavior in a model of cardiac stimulation--I: Mathematical formulation

This paper presents a model describing the steady-state response of a two-dimensional (2-D) slice of myocardium to extracellular current injection. The model incorporates a continuous representation of the multicellular, syncytial cardiac tissue based on the bidomain model. The classical bidomain model is modified by introducing periodic conductivities to better represent the electrical properties of the intracellular space. Thus, junctional discontinuity between abutting myocytes is reflected in the macroscopic representation of cardiac tissue behavior. Since a solution to the resulting coupled differential equations governing the intracellular and extracellular potentials in the tissue preparation is not computationally tractable when traditional numerical approaches, such as finite element or finite difference methods are used, spectral techniques are employed to reduce the problem to the solution of a set of algebraic equations for the transform of the bidomain potentials. Further, the solution to the "periodic" bidomain problem in the Fourier space is decomposed into two separate solutions: One for the classical-bidomain potentials where it is assumed that the intracellular conductivity values along and across cells incorporate the average contribution from cytoplasm and junction, and another for the junctional potential component. The decomposition of the total solution allows to approximately solve for the junctional component thus achieving high overall computational efficiency. The results of simulation are presented in an accompanying paper.

Discrete versus syncytial tissue behavior in a model of cardiac stimulation--II: Results of simulation

The research presented here combines mathematical modeling and computer simulation in developing a new model of the membrane polarization induced in the myocardium by the applied electric field. Employing this new model termed the "period" bidomain model, the steady-state distribution of the transmembrane potential is calculated on a slice of cardiac tissue composed of abutting myocytes and subjected to two point-source extracellular current stimuli. The goal of this study is to examine the relative contribution of cellular discreteness and macroscopic syncytial tissue behavior in the mechanism by which the applied electric field alters the transmembrane potential in cardiac muscle. The results showed the existence of oscillatory changes in the transmembrane potential at cell ends owing to the local resistive inhomogeneities (gap-junctions). This low-magnitude sawtooth component in the transmembrane potential is superimposed over large-scale transmembrane potential excursions associated with the syncytial (collective) fiber behavior. The character of the cardiac response to stimulation is determined primarily by the large-scale syncytial tissue behavior. The sawtooth contributes to the overall tissue response only in regions where the large-scale transmembrane potential component is small.

Impedance to defibrillation countershock: does an optimal impedance exist?

Defibrillation is thought to occur because of changes in the transmembrane potential that are caused by current flow through the heart tissue. Impedance to electric countershock is an important parameter because it is determined by the magnitude and distribution of the current that flows for a specific shock voltage. The impedance is comprised of resistive contributions from: (1) extra-tissue sources, which include the defibrillator, leads, and electrodes; (2) tissue sources, which include intracardiac and extra-cardiac tissue; and (3) the interface between electrode and tissue. Tissue sources dominate the impedance and probably contribute to the wide range of impedance values presented to the defibrillation pulse. Because impedance is not constant within or between subjects, defibrillators must be designed to accommodate these differences without compromising patient safety or therapeutic efficacy. Experimental investigations in animals and humans suggest that impedance changes at several different time scales ranging from milliseconds to years. These alterations are believed to be a result of both electrochemical and physiological mechanisms. It is commonly thought that impedance is optimized when it has been decreased to a minimum, since this allows the most current flow for a given voltage shock. However, if the impedance is lowered by changing the location or size of the electrodes in such a way that current flow is decreased in part of the heart even though current flow is increased elsewhere, then the total voltage, current, and energy needed for defibrillation may increase, not decrease, even though impedance is decreased. A simple boundary element computer model suggests that the most even distribution of current flow through the heart is achieved for those electrode locations in which the impedance across the heart is at or near the maximum cardiac impedance for any location of these particular electrodes. Thus, the optimum shock impedance is achieved when impedance is minimized for extra-tissue and extra-cardiac tissue sources and is at or near a maximum for intracardiac tissue sources.