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N A Trayanova

Publications and source records attributed to N A Trayanova.

At least 19 recordsLinked to original sources
PubMed2001

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.

Animals↗
PubMed2001

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.

Animals↗
PubMed2001

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.

Action Potentials↗
PubMed2001

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.

Action Potentials↗
PubMed2001

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.

Action Potentials↗
PubMed2001

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.

Animals↗
PubMed2000

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.

Anisotropy↗
PubMed1999

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.

Anisotropy↗
PubMed1999

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.

Action Potentials↗
PubMed1999

Impact of transvenous lead position on active-can ICD defibrillation: a computer simulation study.

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.

Catheterization, Central Venous↗
PubMed1999

Sinusoidal stimulation of myocardial tissue: effects on single cells.

INTRODUCTION: Cardiac tissue subjected to sinusoidal 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.

Action Potentials↗
PubMed1999

Effects of electroporation on the transmembrane potential distribution in a two-dimensional bidomain model of cardiac tissue.

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 Cm, a leakage conductance g(l) 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 all electroporated regions is halted, and a further increase of Io 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.

Anisotropy↗
PubMed1999

Extension of refractoriness in a model of cardiac defibrillation.

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.

Anisotropy↗
PubMed1993

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.

Electric Conductivity↗
PubMed1990

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).

Fourier Analysis↗
PubMed1986

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.

Action Potentials↗
PubMedDate not supplied

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.

Animals↗