Digital twins in medicine.

Medical digital twins, which are potentially vital for personalized medicine, have become a recent focus in medical research. Here we present an overview of the state of the art in medical digital twin development, especially in oncology and cardiology, where it is most advanced. We discuss major challenges, such as data integration and privacy, and provide an outlook on future advancements. Emphasizing the importance of this technology in healthcare, we highlight the potential for substantial improvements in patient-specific treatments and diagnostics.

ß-adrenergic stimulation augments transmural dispersion of repolarization via modulation of delayed rectifier currents IKs and IKr in the human ventricle.

Long QT syndrome (LQTS) is an inherited or drug induced condition associated with delayed repolarization and sudden cardiac death. The cardiac potassium channel, IKr, and the adrenergic-sensitive cardiac potassium current, IKs, are two primary contributors to cardiac repolarization. This study aimed to elucidate the role of ß-adrenergic (ß-AR) stimulation in mediating the contributions of IKr and IKs to repolarizing the human left ventricle (n = 18). Optical mapping was used to measure action potential durations (APDs) in the presence of the IKs blocker JNJ-303 and the IKr blocker E-4031. We found that JNJ-303 alone did not increase APD. However, under isoprenaline (ISO), both the application of JNJ-303 and additional E-4031 significantly increased APD. With JNJ-303, ISO decreased APD significantly more in the epicardium as compared to the endocardium, with subsequent application E-4031 increasing mid- and endocardial APD80 more significantly than in the epicardium. We found that ß-AR stimulation significantly augmented the effect of IKs blocker JNJ-303, in contrast to the reduced effect of IKr blocker E-4031. We also observed synergistic augmentation of transmural repolarization gradient by the combination of ISO and E-4031. Our results suggest ß-AR-mediated increase of transmural dispersion of repolarization, which could pose arrhythmogenic risk in LQTS patients.

Mechanisms linking electrical alternans and clinical ventricular arrhythmia in human heart failure.

BACKGROUND: Mechanisms of ventricular tachycardia (VT) and ventricular fibrillation (VF) in patients with heart failure (HF) are undefined. OBJECTIVE: The purpose of this study was to elucidate VT/VF mechanisms in HF by using a computational-clinical approach. METHODS: In 53 patients with HF and 18 control patients, we established the relationship between low-amplitude action potential voltage alternans (APV-ALT) during ventricular pacing at near-resting heart rates and VT/VF on long-term follow-up. Mechanisms underlying the transition of APV-ALT to VT/VF, which cannot be ascertained in patients, were dissected with multiscale human ventricular models based on human electrophysiological and magnetic resonance imaging data (control and HF). RESULTS: For patients with APV-ALT k-score >1.7, complex action potential duration (APD) oscillations (≥2.3% of mean APD), rather than APD alternans, most accurately predicted VT/VF during long-term follow-up (+82%; -90% predictive values). In the failing human ventricular models, abnormal sarcoplasmic reticulum (SR) calcium handling caused APV-ALT (>1 mV) during pacing with a cycle length of 550 ms, which transitioned into large magnitude (>100 ms) discordant repolarization time alternans (RT-ALT) at faster rates. This initiated VT/VF (cycle length <400 ms) by steepening apicobasal repolarization (189 ms/mm) until unidirectional conduction block and reentry. Complex APD oscillations resulted from nonstationary discordant RT-ALT. Restoring SR calcium to control levels was antiarrhythmic by terminating electrical alternans. CONCLUSION: APV-ALT and complex APD oscillations at near-resting heart rates in patients with HF are linked to arrhythmogenic discordant RT-ALT. This may enable novel physiologically tailored, bioengineered indices to improve VT/VF risk stratification, where SR calcium handling and spatial apicobasal repolarization are potential therapeutic targets.

Methodology for image-based reconstruction of ventricular geometry for patient-specific modeling of cardiac electrophysiology.

Patient-specific modeling of ventricular electrophysiology requires an interpolated reconstruction of the 3-dimensional (3D) geometry of the patient ventricles from the low-resolution (Lo-res) clinical images. The goal of this study was to implement a processing pipeline for obtaining the interpolated reconstruction, and thoroughly evaluate the efficacy of this pipeline in comparison with alternative methods. The pipeline implemented here involves contouring the epi- and endocardial boundaries in Lo-res images, interpolating the contours using the variational implicit functions method, and merging the interpolation results to obtain the ventricular reconstruction. Five alternative interpolation methods, namely linear, cubic spline, spherical harmonics, cylindrical harmonics, and shape-based interpolation were implemented for comparison. In the thorough evaluation of the processing pipeline, Hi-res magnetic resonance (MR), computed tomography (CT), and diffusion tensor (DT) MR images from numerous hearts were used. Reconstructions obtained from the Hi-res images were compared with the reconstructions computed by each of the interpolation methods from a sparse sample of the Hi-res contours, which mimicked Lo-res clinical images. Qualitative and quantitative comparison of these ventricular geometry reconstructions showed that the variational implicit functions approach performed better than others. Additionally, the outcomes of electrophysiological simulations (sinus rhythm activation maps and pseudo-ECGs) conducted using models based on the various reconstructions were compared. These electrophysiological simulations demonstrated that our implementation of the variational implicit functions-based method had the best accuracy.

A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models.

Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace-Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.

Minimum Information about a Cardiac Electrophysiology Experiment (MICEE): standardised reporting for model reproducibility, interoperability, and data sharing.

Cardiac experimental electrophysiology is in need of a well-defined Minimum Information Standard for recording, annotating, and reporting experimental data. As a step towards establishing this, we present a draft standard, called Minimum Information about a Cardiac Electrophysiology Experiment (MICEE). The ultimate goal is to develop a useful tool for cardiac electrophysiologists which facilitates and improves dissemination of the minimum information necessary for reproduction of cardiac electrophysiology research, allowing for easier comparison and utilisation of findings by others. It is hoped that this will enhance the integration of individual results into experimental, computational, and conceptual models. In its present form, this draft is intended for assessment and development by the research community. We invite the reader to join this effort, and, if deemed productive, implement the Minimum Information about a Cardiac Electrophysiology Experiment standard in their own work.

Distribution of electromechanical delay in the heart: insights from a three-dimensional electromechanical model.

In the intact heart, the distribution of electromechanical delay (EMD), the time interval between local depolarization and myocyte shortening onset, depends on the loading conditions. The distribution of EMD throughout the heart remains, however, unknown because current experimental techniques are unable to evaluate three-dimensional cardiac electromechanical behavior. The goal of this study was to determine the three-dimensional EMD distributions in the intact ventricles for sinus rhythm (SR) and epicardial pacing (EP) by using a new, to our knowledge, electromechanical model of the rabbit ventricles that incorporates a biophysical representation of myofilament dynamics. Furthermore, we aimed to ascertain the mechanisms that underlie the specific three-dimensional EMD distributions. The results revealed that under both conditions, the three-dimensional EMD distribution is nonuniform. During SR, EMD is longer at the epicardium than at the endocardium, and is greater near the base than at the apex. After EP, the three-dimensional EMD distribution is markedly different; it also changes with the pacing rate. For both SR and EP, late-depolarized regions were characterized with significant myofiber prestretch caused by the contraction of the early-depolarized regions. This prestretch delays myofiber-shortening onset, and results in a longer EMD, giving rise to heterogeneous three-dimensional EMD distributions.

Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms.

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.

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.

Modulation of shock-end virtual electrode polarisation as a direct result of 3D fluorescent photon scattering.

Due to the large transmural variation in transmembrane potential following the application of strong electric shocks, it is thought that fluorescent photon scattering from depth plays a significant role in optical signal modulation at shock-end. For the first time, a model of photon scattering is used to accurately synthesize fluorescent signals over the irregular geometry of the rabbit ventricles following the application of such strong shocks. A bidomain representation of electrical activity is combined with finite element solutions to the photon diffusion equation, simulating both the excitation and emission processes, over an anatomically-based model of rabbit ventricular geometry and fiber orientation. Photon scattering from within a 3D volume beneath the epicardial optical recording site is shown to transduce differences in transmembrane potential within this volume through the myocardial wall. This leads directly to a significantly modulated optical signal response with respect to that predicted by the bidomain simulations, distorting epicardial virtual electrode polarization produced at shock-end. Furthermore, we show that this degree of distortion is very sensitive to the optical properties of the tissue, an important variable to consider during experimental mapping set-ups. These findings provide an essential first-step in aiding the interpretation of experimental optical mapping recordings following strong defibrillation shocks.

Transmural electrophysiological heterogeneities in action potential duration increase the upper limit of vulnerability.

Transmural dispersion in action potential duration (APD) has been shown to contribute to arrhythmia induction in the heart. However, its role in termination of lethal arrhythmias by defibrillation shocks has never been examined. The goal of this study is to investigate how transmural dispersion in APD affects cardiac vulnerability to electric shocks, in an attempt to better understand the mechanisms behind defibrillation failure. This study used a three- dimensional, geometrically accurate finite element bidomain rabbit ventricular model. Transmural heterogeneities in ionic currents were incorporated based on experimental data to generate the transmural APD profile recorded in adult rabbits during pacing. Results show that the incorporation of transmural APD heterogeneities in the model causes an increase in the upper limit of vulnerability from 26.7 V/cm in the homogeneous APD ventricles to 30.5 V/cm in the ventricles with heterogeneous transmural APD profile. Examination of shock-end virtual electrode polarisation and postshock electrical activity reveals that the higher ULV in the heterogeneous model is caused by increased dispersion in postshock repolarisation within the LV wall, which increases the likelihood of the establishment of intramural re-entrant circuits.

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

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

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.

Effect of strength and timing of transmembrane current pulses on isolated ventricular myocytes.

INTRODUCTION: Little is known about how the amplitude and timing of transmembrane current pulses affect transmembrane potential (Vm) and action potential duration (APD) in isolated myocytes. METHODS AND RESULTS: Ten ventricular myocytes were isolated from five rabbit hearts. Each cell was paced at an S1 cycle length of 250 msec, and S2 pulses of 10-msec duration were delivered at various strengths and time intervals. For all S2 strengths (0.2 to 1.5 nA), the magnitude of changes in Vm did not depend on polarity during the plateau, but were larger for depolarizing pulses during phase 3 repolarization. However, the magnitude of changes in APD varied with polarity during the entire action potential for strengths ranging from 0.5 to 1.5 nA. Greater changes in APD occurred for hyperpolarizing pulses during the plateau and depolarizing pulses during phase 3. In addition, we used a cardiac phase variable to quantify the current threshold for regenerative depolarization and repolarization as a function of prestimulus Vm. Regenerative depolarization occurred during phase 3 repolarization, and its current threshold was less than that required for regenerative repolarization that occurred during the plateau. These data were compared to computer simulations in a patch of membrane represented by Luo-Rudy dynamic kinetics, and the results were qualitatively similar, including the higher threshold for regenerative repolarization compared to regenerative depolarization. CONCLUSION: This characterization of the nonlinear response of isolated cells to transmembrane current, including phase resetting, should aid in understanding the mechanisms of defibrillation because shock-induced changes in Vm and APD have been implicated as important factors in determining defibrillation success.

Excitation of a cardiac muscle fiber by extracellularly applied sinusoidal current.

INTRODUCTION: The goal of this study was to examine the effect of AC currents on a cardiac fiber. The study is the second in a series of two articles devoted to the subject. The initial study demonstrated that low-strength sinusoidal currents can cause hemodynamic collapse without inducing ventricular fibrillation. The present modeling study examines possible electrophysiologic mechanisms leading to such hemodynamic collapse. METHODS AND RESULTS: A strand of cardiac myocytes was subjected to an extracellular sinusoidal current stimulus. The stimulus was located 100 microm over one end. Membrane dynamics were described by the Luo-Rudy dynamic model. Examination of the interspike intervals (ISI) revealed that they were dependent on the phase of the stimulus and, as a result, tended to take on discrete values. The frequency dependency of the current threshold to induce an action potential in the cable had a minimum, as has been found experimentally. When a sinus beat was added to the cable, the sinus beat dominated at low-stimulus currents, whereas at high currents the time between action potentials corresponded to the rate observed in a cable without the sinus beat. In between there was a transition region with a wide dispersion of ISIs. CONCLUSION: The following phenomena observed in the initial study were reproduced and explained by the present simulation study: insignificant effect of temporal summation of subthreshold stimuli, frequency dependency of the extrasystole threshold, discrete nature of the ISI, and increase in regularity of the ISI with increasing stimulus strength.

Entrainment by an extracellular AC stimulus in a computational model of cardiac tissue.

INTRODUCTION: Cardiac tissue can be entrained when subjected to sinusoidal stimuli, often responding with action potentials sustained for the duration of the stimulus. To investigate mechanisms responsible for both entrainment and extended action potential duration, computer simulations of a two-dimensional grid of cardiac cells subjected to sinusoidal extracellular stimulation were performed. METHODS AND RESULTS: The tissue is represented as a bidomain with unequal anisotropy ratios. Cardiac membrane dynamics are governed by a modified Beeler-Reuter model. The stimulus, delivered by a bipolar electrode, has a duration of 750 to 1,000 msec, an amplitude range of 800 to 3,200 microA/cm, and a frequency range of 10 to 60 Hz. The applied stimuli create virtual electrode polarization (VEP) throughout the sheet. The simulations demonstrate that periodic extracellular stimulation results in entrainment of the tissue. This phase-locking of the membrane potential to the stimulus is dependent on the location in the sheet and the magnitude of the stimulus. Near the electrodes, the oscillations are 1:1 or 1:2 phase-locked; at the middle of the sheet, the oscillations are 1:2 or 1:4 phase-locked and occur on the extended plateau of an action potential. The 1:2 behavior near the electrodes is due to periodic change in the voltage gradient between VEP of opposite polarity; at the middle of the sheet, it is due to spread of electrotonic current following the collision of a propagating wave with refractory tissue. CONCLUSION: The simulations suggest that formation of VEP in cardiac tissue subjected to periodic extracellular stimulation is of paramount importance to tissue entrainment and formation of an extended oscillatory action potential plateau.

Reentry in a morphologically realistic atrial model.

INTRODUCTION: Atrial fibrillation is the most common cardiac arrhythmia. In ablation procedures, identification of the reentrant pathways is vital. This has proven difficult because of the complex morphology of the atria. The purpose of this study was to ascertain the role of specific anatomic structures on reentry induction and maintenance. METHOD AND RESULTS: A computationally efficient, morphologically realistic, computer model of the atria was developed that incorporates its major structural features, including discrete electrical connections between the right and left atria, physiologic fiber orientation in three dimensions, muscle structures representing the crista terminalis (CT) and pectinate muscles, and openings for the veins and AV valves. Reentries were induced near the venous openings in the left and right atria, the mouth of the coronary sinus, and the free wall of the right atrium. The roles of certain muscular structures were ascertained by selectively removing the structures and observing how the propagation of activity was affected. CONCLUSION: (1) The muscular sheath of the coronary sinus acts as a pathway for a reentrant circuit and stabilizes any circuits that utilize the isthmus near the inferior vena cava. (2) Poor trans-CT coupling serves to stabilize flutter circuits. (3) Wall thickness is an important factor in the propagation of electrical activity, especially in the left atrium. (4) The openings of the inferior and superior venae cavae form natural anatomic anchors that make reentry easier to initiate by allowing for smaller ectopic beats to induce reentry.

Virtual electrode polarization leads to reentry in the far field.

INTRODUCTION: Our previous article examined cardiac vulnerability to reentry in the near field within the framework of the virtual electrode polarization (VEP) concept. The present study extends this examination to the far field and compares its predictions to the critical point hypothesis. METHODS AND RESULTS: We simulate the electrical behavior of a sheet of myocardium using a two-dimensional bidomain model. The fiber field is extrapolated from a set of rabbit heart fiber directions obtained experimentally. An S1 stimulus is applied along the top or left border. An extracellular line electrode on the top delivers a cathodal or anodal S2 stimulus. A VEP pattern matching that seen experimentally is observed and covers the entire sheet, thus constituting a far-field effect. Reentry arises from break excitation, make excitation, or a combination of both, and subsequent propagation through deexcited and recovered areas. Reentry occurs in cross-field, parallel-field, and uniform refractoriness protocols. For long coupling intervals (CIs) above CImake(min) (defined as the shortest CI at which make excitation can take place), rotors move away from the cathodal electrode and the S1 site for increases in S2 strength and CI, respectively. For cathodal S2 stimuli, findings are consistent with the critical point hypothesis. For CIs below CImake(min), reentry is initiated by break excitation only, and the resulting reentrant patterns are no longer consistent with those predicted by the critical point hypothesis. CONCLUSION: Shock-induced VEP can explain vulnerability in the far field. The VEP theory of vulnerability encompasses the critical point hypothesis for cathodal S2 shocks at long CIs.

Wave front-obstacle interactions in cardiac tissue: a computational study.

An understanding of wave front-obstacle interactions will greatly enhance our knowledge of the mechanisms involved in cardiac arrhythmias and their therapy. The goal of this computational study is to examine the interactions between wave fronts and various obstacles in a two-dimensional sheet of myocardium. The myocardium is modeled as an isotropic sheet with Luo-Rudy I membrane kinetics. An examination is conducted of wave front interactions with nonconductive and passive-tissue obstacles. Simulations were performed either in environments of reduced myocardial excitability, or with rapid stimulation via a line electrode. The shape of the obstacles and their ability to withdraw current from the active tissue greatly influence wave front-obstacle interactions in each of these environments. The likelihood of wave front detachment from an obstacle corner increases as the curvature of the obstacle corner is increased. A passive-tissue obstacle promotes wave front-obstacle separation in regions of depressed excitability. Under rapid pacing, the presence of the passive obstacle results in wave fragmentation, while the insulator obstacle promotes wave front detachment. The results of this study reveal the importance of obstacle composition and geometry in wave front interactions with cardiac obstacles.

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.