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Sinusoidal Stimulation of Cardiac Sheet.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 μA/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.

Presented here is an efficient algorithm for solving the bidomain equations describing myocardial tissue with active membrane kinetics. An analysis of the accuracy shows advantages of this numerical technique over other simple and therefore popular approaches. The modular structure of the algorithm provides the critical flexibility needed in simulation studies: fiber orientation and membrane kinetics can be easily modified. The computational tool described here is designed specifically to simulate cardiac defibrillation, i. e., to allow modeling of strong electric shocks applied to the myocardium extracellularly. Accordingly, the algorithm presented also incorporates modifications of the membrane model to handle the high transmembrane voltages created in the immediate vicinity of the defibrillation electrodes.

Sinusoidal Stimulation of Cardiac Cells. Introduction: Cardiac tissue subjected to sinasoidal stimulus Is characterized by action potentials (APs) that have extended plateau phases, sustained for the duration of the stimulus. Extended action potential durations (APDs) are beneficial because they disrupt wandering wavelets in the fibrillating heart. To investigate the mechanisms by which periodic stimulus affects cardiac tissue, particularly the development of sustained depolarization, computer simulations of single cardiac cells exposed to alternating current (AC) are performed. Methods and Results: Two modes of stimulation of the cell are examined: external field stimulation and transmembrane current injection. Several membrane models, including Luo-Rudy I and II, are used in the simulations. External AC field stimuli increase the APD of the single cell. The extended plateau of the cellular AP is characterized by periodic oscillations that are 1:2 phase locked with the applied stimulus. This specific behavior is due to the variations in stimulus magnitude and polarity along the cell border, which elicit opposite electrical responses from the cell sides. These pointwise responses are averaged in the macroscopic cellular response and result in sustained oscillatory depolarization that lasts for the duration of the stimulus. In contrast, the cell undergoing current injection does not develop an extended APD. Conclusion: The simulations demonstrate that variation of membrane potential within a cell is of paramount importance to the formation of an extended AP plateau in response to AC stimulation.

This study investigated roles of the variation of extracellular voltage gradient (VG) over space and cardiac fibers in production of transmembrane voltage changes (DeltaV(m)) during shocks. Eleven isolated rabbit hearts were arterially perfused with solution containing V(m)-sensitive fluorescent dye (di-4-ANEPPS). The epicardium received shocks from symmetrical or asymmetrical electrodes to produce nominally uniform or nonuniform VGs. Extracellular electric field and DeltaV(m) produced by shocks in the absolute refractory period were measured with electrodes and a laser scanner and were simulated with a bidomain computer model that incorporated the anterior left ventricular epicardial fiber field. Measurements and simulations showed that fibers distorted extracellular voltages and influenced the DeltaV(m). For both uniform and nonuniform shocks, DeltaV(m) depended primarily on second spatial derivatives of extracellular voltages, whereas the VGs played a smaller role. Thus, 1) fiber structure influences the extracellular electric field and the distribution of DeltaV(m); 2) the DeltaV(m) depend on second spatial derivatives of extracellular voltage.

This simulation study presents an inquiry into the mechanisms by which a strong electric shock halts life-threatening cardiac arrhythmias. It examines the "extension of refractoriness" hypothesis for defibrillation which postulates that the shock induces an extension of the refractory period of cardiac cells thus blocking propagating waves of arrhythmia and fibrillation. The present study uses a model of the defibrillation process that represents a sheet of myocardium as a biodomain with unequal anisotropy ratios. The tissue consists of curved fibers in which spiral wave reentry is initiated. The defibrillation shock is delivered via two line electrodes that occupy opposite tissue boundaries. Simulation results demonstrate that a large-scale region of depolarization is induced throughout most of the tissue. This depolarization extends the refractoriness of the cells in the region. In addition, new wavefronts are generated from the regions of induced hyperpolarization that further restrict the spiral wave pathway and cause its termination.

Electroporation in a Two-Dimensional Myocardium. Introduction: Defibrillation shocks, when delivered through internal electrodes, establish transmembrane potentials (Vm) large enough to electroporate the membrane of cardiac cells. The effects of such shocks on the transmembrane potential distribution are investigated in a two-dimensional rectangular sheet of cardiac muscle modeled as a bidomain with unequal anisotropy ratios. Methods and Results: The membrane is represented by a capacitance Cnv, a leakage conductance gv and a variable electroporation conductance G, whose rate of growth depends exponentially on the square of Vm. The stimulating current Io, 0.05–20 A/m, is delivered through a pair of electrodes placed 2 cm apart for stimulation along fibers and 1 cm apart for stimulation across fibers. Computer simulations reveal three categories of response to Io: (1) Weak Io. below 0.2 A/m, cause essentially no electroporation, and Vm: increases proportionally to Io. (2) Strong Io, between 0.2 and 2.5 A/m, electroporate tissue under the physical electrode. Vm is no longer proportional to Io; in the electroporated region, the growth of Vm is halted and in the region of reversed polarity (virtual electrode), the growth of Vm is accelerated. (3) Very strong Io, above 2.5 A/m, electroporate tissue under the physical and the virtual electrodes. The growth of Vm in ail electroporated regions is halted, and a further increase of Vo: increases both the extent of the electroporated regions and the electroporation conductance G. Conclusion: These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm: induced by defibrillation strength shocks.

Optimizing lead placement in transvenous defibrillation remains central to the clinical aspects of the defibrillation procedure. Studies involving superior vena cava (SVC) return electrodes have found that left ventricular (LV) leads or septal positioning of the right ventricular (RV) lead minimizes the voltage defibrillation threshold (VDFT) in endocardial lead-->SVC defibrillation systems. However, similar studies have not been conducted for active-can configurations. The goal of this study was to determine the optimal lead position to minimize the VDFT for systems incorporating an active can. This study used a high resolution finite element model of a human torso that includes the fiber architecture of the ventricular myocardium to find the role of lead positioning in a transvenous LEAD-->can defibrillation electrode system. It was found that, among single lead systems, posterior positioning of leads in the right ventricle lowers VDFTs appreciably. Furthermore, a septal location of leads resulted in lower VDFTs than free-wall positioning. Increasing the number of leads, and thus the effective lead surface area in the right ventricle also resulted in lower VDFTs. However, the lead configuration that resulted in the lowest VDFTs is a combination of mid-cavity right ventricle lead and a mid-cavity left ventricle lead. The addition of a left ventricular lead resulted in a reduction in the size of the low gradient regions and a change of its location from the left ventricular free wall to the septal wall.

See related article, pages 1256–1264 The mechanisms behind the complex activation sequences during ventricular fibrillation (VF) have been the topic of intense research over many years. Experimental studies in animal models of VF, as well as clinical studies of human VF,1–8 have provided a wealth of data on the nature of electric activity in the fibrillating heart. Supplemented by computer simulations and a theoretical framework of wave propagation in excitable media,9,10 our community has amassed significant insights into the mechanisms that lead to the degradation of electric activity into VF and of VF maintenance. However, the majority of these studies have been devoted to VF mechanisms in the short time period after VF onset (short-duration VF, lasting less than 1 minute). In an episode of cardiac arrest outside of the hospital, the median time to delivery of the first defibrillation shock is 4.4 minutes,11 with VF episodes often lasting as long as 10 minutes (long-duration VF); over this period, the heart becomes ischemic while being subjected to excessively high excitation rates. Changes in the electrophysiological properties of the myocardium take place over these long-duration VF episodes. This is reflected in the altered outcome of a defibrillation shock, with survival rates decreasing rapidly with the increase in minutes spent in VF.12 Similarly, the guidelines for optimal resuscitation therapy differ depending on VF duration: immediate defibrillation is prescribed if time from VF onset is less than 4 or …

While cardiac vulnerability to electric shocks and failure of defibrillation has been attributed to the formation of new reentries via critical points1 or virtual electrode-induced phase singularities,2 an exhaustive study of all mechanisms responsible for shock failure is far from complete, impeding progress in the quest to significantly lower the defibrillation threshold (DFT) and to ultimately achieve low-voltage defibrillation. One of the most sought-after insights is the mechanism by which the first postshock activation originates in failed defibrillation episodes.

For pt. I see ibid., vol. 43, no. 12, p. 1129-40 (1996). 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 "periodic" 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.

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 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 (see ibid., vol. 43, no. 12, p. 1141-50, 1996).

A three-dimensional (3D) finite element electromechanical model of the heart is employed in simulations of seismocardiograms (SCGs). To simulate SCGs, a previously developed 3D model of ventricular contraction is extended by adding the mechanical interaction of the heart with the chest and internal organs. The proposed model reproduces the major peaks of seismocardiographic signals during the phases of the cardiac cycle. Results indicate that SCGs record the pressure of the heart acting on the ribs. In addition, the model reveals that the rotation of the rib with respect to the heart has a minor effect on seismocardiographic signal morphology during the respiratory cycle. SCGs are obtained from 24 human volunteers and their morphology is analyzed. Experimental results demonstrate that the peak of the maximum acceleration of blood in the aorta occurs at the same time as the global minimum of the SCG. It is confirmed that the first SCG peak after the electrocardiogram R-wave corresponds to aortic valve opening, as determined from the impedance cardiogram (p = 0.92). The simulation results reveal that the SCG peaks corresponding to aortic valve opening and the maximum acceleration of blood in the aorta result from ventricular contraction in the longitudinal direction of the ventricles and a decrease in the dimensions of the ventricles due to the ejection of blood, respectively.

An approximate, computationally tractable solution is proposed for the potentials in the bidomain model with periodic intracellular junctions (the periodic bidomain model). This new approach is based on the one-dimensional rigorous spectral method described previously by Trayanova and Pilkington ( IEEE Trans. Biomed. Eng. , May 1993). The total solution to the one-dimensional periodic bidomain problem is decomposed in the spectral domain into solutions to (1) the single-fiber classical bidomain problem in which the intracellular conductivity value incorporates the average contribution from cytoplasm and junction and (2) the “junctional” potential problem due to the presence of junctions at discrete locations alone. Solving for the junctional term rigorously requires most of the numerical effort in the solution for the periodic bidomain potentials. Here the junctional potential is found approximately with little numerical effort. A comparison between the rigorous and the approximate solutions serves as a justification for the proposed approximate solution procedure. The procedure outlined in this paper is applicable to higher spatial dimensions where both tissue anisotropy and junctional inhomogeneities play a role in establishing the transmembrane potential distribution.

Background: Alternans of calcium cycling and action potential voltage is associated with ventricular arrhythmia. Mechanical alternans (MA) has been observed in heart failure (HF) patients. However, predictive value of MA in comparison with T wave alternans (TWA) has not been studied in prospective cohort study. Methods: We prospectively studied 74 patients (mean age 59.6 15.7; 53 male [72%], ejection fraction 28.7 18.7%) admitted to the intensive cardiac care unit due to congestive HF exacerbation (54 patients, 73%) or acute myocardial infarction (20 patients, 27%). Patients with pericardial effusion or valvular heart disease were excluded. About half of patients population (N 34, 46%) had an ICD or CRT-D implanted. Digital surface ECG was recorded simultaneously with arterial pressure via peripheral arterial line for at least 12 hours. Recordings with frequent premature ventricular complexes and atrial fibrillation were excluded. MA and TWA were measured by correlation method and enhanced modified moving average method from a nonoverlapping sliding window of successive 10 pairs. Sustained MA was defined as arterial pressure alternans that lasted 20 beats with alternating pressure 4 mmHg. Sustained TWA was defined as TWA 20 V that lasted 20 beats. Patients were folowed prospectively; all-cause mortality served as end-point. esults: Both sustained MA and TWA were detected in 35 patients (47.3%). WA without MA was detected in 1 patient (1.4%), whereas sustained MA ithout TWA was found in 3 patients (4.1%). Overall 7725 sustained alternans vents were analyzed. Clusters of sustained MA and TWA events occurred at he same time. Sustained MA immediately preceded TWA in 1593 (20.6%) vents, occurred simultaneously with TWA in 4587 (59.4%) events, was receded by TWA in 641 (8.3%) events, and was isolated in 904 (11.7%). uring 111 132 days of follow-up 18 patients (24.3%) died. In patients with YHA class I-III HF the Kaplan-Meier analysis showed that both MA and WA were associated with increased risk of all-cause death (log rank test P 05). In patients with NYHA class IV neither MA nor TWA predicted outome. onclusions: Sustained MA strongly correlates with TWA and predicts eath in mild and moderate, but not end-stage HF patients.

Brugada syndrome is a genetic disorder that results in decreased expression of cardiac Na+ channels, leading to abnormal electrical activity with onset in the right ventricle (RV). Given that INa is reduced globally, it remains unclear why the RV is more susceptible to arrhythmogenesis. This study tests the hypothesis that differences in geometry between left ventricle (LV) and RV promote altered conduction patterns under reduced INa. Using a 3D rabbit ventricular model that incorporates realistic geometry, simulations were performed where INa maximal conductance was varied from 60 to 100% of the normal level. Reentry was induced via diastolic stimulation of the LV or RV epicardium. Sustained reentry developed only at the 60% INa level for RV stimulation, while no reentry was induced for the LV regardless of INa levels. Activation map (figure) for the 60% INa model shows conduction block at the RV insertion region, where the safety factor (the ratio of total intracellular current vs. current needed to excite the cell) was zero. Propagation from the thin RV has insufficient current to excite tissue in the septum/LV, resulting in source-sink mismatch and block, thus predisposing the RV to arrhythmogenesis under reduced INa.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Simulation results in the paper are not affected by this error since the correct expressions were used in generating the results. In Sect. 2.6, first paragraph, the sentence “In this semiimplicit scheme, xk+1 (the value of x at the next integration step) was used for extrapolation of dx dt and for integration of the first equation in (7) ...” should read as follows: “In this semi-implicit scheme, xk+1 (the value of x at the next integration step) was used for extrapolation of dx dt and for integration of the first equation in (8) ...”.

Background: We have recently demonstrated in computer simulations that electrotonic interactions between atrial myocytes and heterogeneously-distributed fibroblasts result in the genesis of complex fractionated atrial electrograms (CFAEs) during chronic atrial fibrillation (AF). However, previous research has not provided sufficient evidence that ablation targeting such fibroblast-derived CFAEs can terminate AF. Methods: To clarify this issue, we repeated simulations of CFAE-targeted ablation in the model of human chronic AF under heart failure, and we analyzed details of the excitation propagation until the AF was terminated by the application of CFAE-targeted ablation. Results: (1) Sustained spiral wave reentry, as a model of chronic AF, was found to terminate earlier as the number of ablation sites increased. (2) CFAE-targeted ablation site transiently pinned the spiral wave, preventing wave breakup by blocking the shortcut of the reentry. (3) The spiral wave drifted between ablation sites, and after a short time the spiral wave was pushed out of the CFAE area, resulting in AF termination. (4) For more effective CFAE-targeted ablation, avoiding collagen accumulation area and keeping an appropriate distance between ablation sites were required. Conclusion: Our findings might contribute to better understanding of the mechanisms of CFAE-targeted AF ablation.

The classical bidomain model of cardiac tissue views the intracellular and extracellular (interstitial) spaces as two coupled but separate continua. In the present study, the classical bidomain model has been extended by introducing a periodic conductivity in the intracellular space to represent the junctional discontinuity between abutting myocytes. In this model the junctional region of a myocyte is represented in a way that permits variation of junction size and conductivity profile. Employing spectral techniques, a new method was developed for solving the coupled differential equations governing the intracellular and extracellular potentials in a tissue preparation of finite dimensions. Different spectral representations are used for the aperiodic intra- and extracellular potentials (finite Fourier integral transform) and for the periodic intracellular conductivity (Fourier series). As a first application of the method, the response of a 50-cell, single interior fiber to a defibrillating current is examined under steady-state conditions. Transmembrane as well as intra- and extracellular potential distributions along the fiber were calculated.

One reason the bidomain model has not seen more widespread use in propagation studies is the computational cost required to calculate the interstitial potentials. To augment this limitation, we examined a number of iterative solution schemes to determine interstitial potentials. A number of these methods had computational costs which were less than the computational cost to determine the transmembrane potentials.

The classical bidomain model of cardiac tissue is extended by introducing a periodic intracellular conductivity to represent the junctional resistances between abutting myocytes. The response of a finite two-dimensional "periodic"-bidomain sheet of cells to a current stimulus is examined under steady-state condidtions.

The purpose of this study was to quantify the changes in motor-unit action potentials (MUAP) and force during a standard motor-unit fatigue test. MUAP waveforms were characterized by the measurement of amplitude, duration, area, and shape (as reflected in a coefficient of proportionality). Fatigue-resistant motor units exhibited small, but statistically significant, changes in MUAP amplitude and area during the fatigue test, whereas fatigable motor units displayed variable changes in MUAP amplitude, duration, and area. For all motor-unit types, the coefficient of proportionality did not change, and hence the change in MUAP area was proportional to the combined changes in amplitude and duration. The between- and within-train changes in MUAP were also distinct for the fatigue-resistant and fatigable motor units. Although several mechanisms could be responsible for the changes in the MUAP as the fatigue test proceeded, the dissociation of the time courses for MUAP and force indicated that these MUAP changes were not the principal reason for the decline in force under these conditions.

Based on mathematical expressions governing the electric field, the extracellular potentials generated by a single active fiber in a restricted circular cylindrical volume conductor are evaluated. This paper examines the effect of the extent of the volume conductor, with radius b, on the extracellular potentials at different field points. For values of b less than 1.5 times the fiber radius, the extracellular potentials in the volume conductor are always the core conductor potentials, independent of the shape and amplitude of the transmembrane potential. For b greater than a critical radius (a value that depends on the transmembrane potential waveform), the extracellular potentials at and near the membrane are the same as if the volume conductor were unbounded. Near the boundary with the insulator, the amplitude of the extracellular potentials is equal to the core conductor amplitude, although the potentials are much broader than the core conductor potential.

SPIRAL WAVE CONTROL BY REGIONAL COOLING IN A BIDOMAIN MODEL Takashi Ashihara, MD, PhD, Natalia A. Trayanova, PhD, Kazuo Nakazawa, PhD, Masatoshi Yamazaki, MD, Haruo Honjo, MD, PhD, Ichiro Sakuma, PhD, Kaichiro Kamiya, MD, PhD and Itsuo Kodama, MD, PhD. Kyoto University Graduate School of Medicine, Kyoto, Japan, Tulane University, New Orleans, LA, National Cardiovascular Center Research Institute, Suita, Japan, Nagoya University, Nagoya, Japan and University of Tokyo, Tokyo, Japan.