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.

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.

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.

Limitations of approximate solutions for computing the extracellular potential of single fibers and bundle equivalents.

The mathematical description of the extracellular field generated by activity in an excitable fiber in an unbounded volume conductor will depend on assumptions made about the sources and the source-field relationship. This paper examines and compares the rigorous and conventional approximate solutions of Laplace's equation used to evaluate the extracellular potential of a single, cylindrical fiber. The single fiber is considered as both a prototypical element (such as a nerve or muscle fiber) and an elementary model of an entire multicellular preparation (e.g., nerve bundle or Purkinje strand). The effects of the fiber radius, the intracellular and extracellular conductivities, and the shape and extent of the source function (either the transmembrane potential or the intracellular potential) on the solutions are discussed. The results show that, in general, the approximate solutions are unsatisfactory for computing the surface extracellular potential when the single fiber is used to represent a large bundle (greater than 300 microns).

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.

The response of a spherical heart to a uniform electric field: a bidomain analysis of cardiac stimulation.

A mathematical model describing electrical stimulation of the heart is developed, in which a uniform electric field is applied to a spherical shell of cardiac tissue. The electrical properties of the tissue are characterized using the bidomain model. Analytical expressions for the induced transmembrane potential are derived for the cases of equal anisotropy ratios in the intracellular and interstitial (extracellular) spaces, and no transverse coupling between fibers. Numerical calculations of the transmembrane potential are also performed using realistic electrical conductivities. The model illustrates several mechanisms for polarization of the cell membrane, which can be divided into two categories, depending on if they polarize fibers at the heart surface only or if they polarize fibers both at the surface and within the bulk of the tissue. The latter mechanisms can be classified further according to whether they originate from continuous or discrete properties of cardiac tissue. If cardiac tissue had equal anisotropy ratios, a large membrane polarization would be induced at the heart surface that would become negligible a few length constants into the tissue. If cardiac tissue were continuous and had no transverse coupling between fibers, a membrane polarization would be induced throughout the bulk that would arise from an "activating function" similar to the one used to describe neural stimulation. Polarization would occur if the fibers were curving, if the cross-sectional area of the tissue were changing (fiber branching), or both. The numerically calculated transmembrane potential is intermediate between those predicted using the assumptions of equal anisotropy ratios and no transverse coupling between fibers. Although discrete properties of cardiac tissue are not incorporated into this model, an estimate of their effect indicates that the amplitude of the polarization caused by the resistance of the cellular junctions is similar to that caused by fiber curvature and branching. The spatial distribution of the polarization, however, is quite different.

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.

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.

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.

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.

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.

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.

Extracellular potentials of single active muscle fibres: effects of finite fibre length.

The extracellular action potentials (ECAPs) of single active muscle fibres immersed an isotropic volume conductor were investigated. The origination of excitation in the motor end-plate and its reaching the fibre end were taken into consideration. It was explained why at short radial distances the ECAPs over the fibre at points close to the end were similar in shape to the first time derivative and at points close to the motor end-plate - to the first time derivative of the intracellular action potential (ICAP) taken with minus sign. The fibre end changed the ECAP which would be recorded if the fibre was infinite and this change called pure termination potential (PTP) was a biphase positive-negative potential, proportional to the first time derivative of the ICAP at points close to the membrane and over the very end. With increasing the radial and axial distances PTP decreases in amplitude. Taking into account the PTP, the genesis of the terminal positive phase of the ECAPs (Gydikov and Kosarov 1972a, b) can be explained. The onset of the fibre or the motor end-plate also changed the potential which would be recorded if the fibre was infinite. This change was given the term of pure onset potential (POP) - a biphase negative-positive potential, proportional to the first time derivative of the ICAP taken with minus sign at a point close to the membrane and over the motor end-plate. With increasing the radial and the axial distance POP decreased in amplitude. Close to the membrane PTP and POP were commensurable with the potential of an infinite fibre only at points close to the ends or to the motor end-plate. At long radial distances they were commensurable with the potential of an infinite fibre for all axial distances.

Role of virtual electrodes in arrhythmogenesis: pinwheel experiment revisited.

INTRODUCTION: Recent experimental evidence demonstrates that a point stimulus generates a nonuniform distribution of transmembrane potential (virtual electrode pattern) consisting of large adjacent areas of depolarization and hyperpolarization. This simulation study focuses on the role of virtual electrodes in reentry induction. METHODS AND RESULTS: We simulated the electrical behavior of a sheet of myocardium using a two-dimensional bidomain model with straight fibers. Membrane kinetics were represented by the Beeler-Reuter Drouhard-Roberge model. Simulations were conducted for equal and unequal anisotropy ratios. S1 wavefront was planar and propagated parallel or perpendicular to the fibers. S2 unipolar stimulus was cathodal or anodal. With regard to unequal anisotropy, for both cathodal and anodal stimuli, the S2 stimulus negatively polarizes some portion of membrane, deexciting it and opening an excitable pathway in a region of otherwise unexcitable tissue. Reentry is generated by break excitation of this tissue and subsequent propagation through deexcited and recovered areas of myocardium. Figure-of-eight and quatrefoil reentry are observed, with figure-of-eight most common. Figure-of-eight rotation is seen in the direction predicted by the critical point hypothesis. With regard to equal anisotropy, reentry was observed for cathodal stimuli only at strengths > -95 A/m. CONCLUSION: The key to reentry induction is the close proximity of S2-induced excited and deexcited areas, with adjacent nonexcited areas available for propagation.

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.

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.