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

Nonlocal based FISTA network for noninvasive cardiac transmembrane potential imaging

Objective. The primary aim of our study is to advance our understanding and diagnosis of cardiac diseases. We focus on the reconstruction of myocardial transmembrane potential (TMP) from body surface potential mapping.Approach. We introduce a novel methodology for the reconstruction of the dynamic distribution of TMP. This is achieved through the integration of convolutional neural networks with conventional optimization algorithms. Specifically, we utilize the subject-specific transfer matrix to describe the dynamic changes in TMP distribution and ECG observations at the body surface. To estimate the TMP distribution, we employ LNFISTA-Net, a learnable non-local regularized iterative shrinkage-thresholding network. The coupled estimation processes are iteratively repeated until convergence.Main results. Our experiments demonstrate the capabilities and benefits of this strategy. The results highlight the effectiveness of our approach in accurately estimating the TMP distribution, thereby providing a reliable method for the diagnosis of cardiac diseases.Significance. Our approach demonstrates promising results, highlighting its potential utility for a range of applications in the medical field. By providing a more accurate and dynamic reconstruction of TMP, our methodology could significantly improve the diagnosis and treatment of cardiac diseases, thereby contributing to advancements in healthcare.

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.

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.

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.

The effect of the cut surface during electrical stimulation of a cardiac wedge preparation

Optical mapping from the cut surface of a "wedge preparation" allows observation inside the heart wall, below the epicardium or endocardium. We use numerical simulations based on the bidomain model to illustrate how the transmembrane potential is influenced by the cut surface. The distribution of transmembrane potential around a unipolar cathode depends on the fiber angle. For intermediate angles, hyperpolarization appears on only one side of the electrode, and is large and widespread.

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.

Virtual electrode theory explains pacing threshold increase caused by cardiac tissue damage

The virtual electrode polarization (VEP) effect is believed to play a key role in electrical stimulation of heart muscle. However, under certain conditions, including clinically, its existence and importance remain unknown. We investigated the influence of acute tissue damage produced by continuous pacing with strong current (40-mA, 4-ms biphasic pulses with 4-Hz frequency for 5 min) on stimulus-generated VEPs and pacing thresholds. A fluorescent optical mapping technique was used to obtain stimulus-induced transmembrane potential distribution around a pacing electrode applied to the ventricular surface of a Langendorff-perfused rabbit heart ( n = 5). Maps and pacing thresholds were recorded before and after tissue damage. Spatial extents of electroporation and cell uncoupling were assessed by propidium iodide ( n = 2) and connexin43 ( n = 3) antibody staining, respectively. On the basis of these data, passive and active three-dimensional bidomain models were built to determine VEP patterns and thresholds for different-sized areas of the damaged region. Electrophysiological results showed that acute tissue damage led to disappearance of the VEP with an associated significant increase in pacing thresholds. Damage was expressed in electroporation and cell uncoupling within a ∼1.0-mm-diameter area around the tip of the electrode. According to computer simulations, cell uncoupling, rather than electroporation, might be the direct cause of VEP elimination and threshold increase, which was nonlinearly dependent on the size of the damaged region. Fiber rotation with depth did not substantially affect the numerical results. The study explains failure to stimulate damaged tissue within the concepts of the VEP theory.

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.

Vortex cordis as a mechanism of postshock activation: arrhythmia induction study using a bidomain model

INTRODUCTION

The ventricular apex has a helical arrangement of myocardial fibers called the "vortex cordis." Experimental studies have demonstrated that the first postshock activation originates from the ventricular apex, regardless of the electrical shock outcome; however, the related underlying mechanism is unclear. We hypothesized that the vortex cordis contributes to the initiation of postshock activation. To clarify this issue, we numerically studied the transmembrane potential distribution produced by various electrical shocks.

METHODS AND RESULTS

Using an active membrane model, we simulated a two-dimensional bidomain myocardial tissue incorporating a typical fiber orientation of the vortex cordis. Monophasic or biphasic shock was delivered via two line electrodes located at opposite tissue borders. Transmembrane potential distribution during the monophasic shock at the center of the vortex cordis showed a gradient high enough to initiate postshock activation. The postshock activation from the center of the vortex cordis was not suppressed, regardless of the initiation of spiral wave reentry. Spiral wave reentry was induced by the monophasic shock when the center area of the vortex cordis was partially excited by the nonuniform virtual electrode polarization. Postshock activation following the biphasic shock also originated from the center of the vortex cordis, but it tended to be suppressed due to the narrower excitable gap around the center of the vortex cordis. The electroporation effect, which was maximal at the center of the vortex cordis, is another possible mechanism of postshock activation.

CONCLUSION

Our simulations suggest that the vortex cordis may cause postshock activation.

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.

Effects of electrode-myocardial separation on cardiac stimulation in conductive solution

INTRODUCTION

Effects of a conductive bath and electrode-myocardial separation on cardiac stimulation have not been elucidated. These factors may play a role in endocardial catheter stimulation or defibrillation.

METHODS AND RESULTS

We studied effects of a bath and separation on transmembrane voltage changes during stimulation (deltaVm) and excitation thresholds in rabbit hearts, cultured rat cardiac cell monolayers, and cardiac bidomain computer models. Similar to previous epicardial measurements with no bath, a dogbone pattern of deltaVm during stimulation was found in bathed epicardium and right ventricular septal endocardium and in models of bathed anisotropic myocardium. Electrode-myocardial separation altered spatial distributions of deltaVm, moved reversals of the sign of deltaVm farther from the stimulation epicenter, and decreased aspect ratio of deltaVm (i.e., length/width of dogbone contours of deltaVm). The separation increased thresholds and reduced maximal deltaVm, while deltaVm at sites away from maxima increased or decreased. Anodal thresholds in models initially were larger than those in experiments and decreased when models were altered to include nonuniform cellular coupling. Existence of nonuniformity in monolayers was indicated by irregular excitation patterns.

CONCLUSION

Electrode-myocardial separation alters spatial distributions of deltaVm, which may impact on arrhythmia induction by altering distributions of states of deltaVm-sensitive ion channels. The results also indicate that excitation thresholds may depend on tissue nonuniformities.

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.