Kirill Skouibine

The role of cardiac tissue structure in defibrillation

The purpose of this paper is to investigate the relationship between cardiac tissue structure, applied electric field, and the transmembrane potential induced in the process of defibrillation. It outlines a general understanding of the structural mechanisms that contribute to the outcome of a defibrillation shock. Electric shocks defibrillate by changing the transmembrane potential throughout the myocardium. In this process first and foremost the shock current must access the bulk of myocardial mass. The exogenous current traverses the myocardium along convoluted intracellular and extracellular pathways channeled by the tissue structure. Since individual fibers follow curved pathways in the heart, and the fiber direction rotates across the ventricular wall, the applied current perpetually engages in redistribution between the intra- and extracellular domains. This redistribution results in changes in transmembrane potential (membrane polarization): regions of membrane hyper- and depolarization of extent larger than a single cell are induced in the myocardium by the defibrillation shock. Tissue inhomogeneities also contribute to local membrane polarization in the myocardium which is superimposed over the large-scale polarization associated with the fibrous organization of the myocardium. The paper presents simulation results that illustrate various mechanisms by which cardiac tissue structure assists the changes in transmembrane potential throughout the myocardium. (c) 1998 American Institute of Physics.

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.

A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium

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.

Success and failure of the defibrillation shock: insights from a simulation study.

Mechanisms for Shock Failure. Introduction: This simulation study presents a further inquiry into the mechanisms by which a strong electric shock fails to halt life‐threatening; cardiac arrhythmins.

Modeling defibrillation: Effects of fiber curvature

The goal of this modeling study is to demonstrate extinguishing of a spiral wave reentry in a sheet of myocardium that incorporates curved fibers. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. The spiral wave is initiated via cross-field stimulation of the bidomain sheet. The defibrillation shock is delivered via two line electrodes that occupy opposite tissue boundaries. Simulation results demonstrate that large-scale regions of depolarization are induced under the cathode as well as at locations in the vicinity of the anode. For high shock strengths, the new wavefronts generated from the regions of induced depolarization restrict the spiral wave pathway and render the tissue too refractory to further maintain the reentry. Weak shocks leave large portions of the sheet unaffected allowing the spiral wave to find recovered tissue and thus survive.

Increasing the computational efficiency of a bidomain model of defibrillation using a time-dependent activating function.

AbstractRealistic simulations of the effects of strong shocks on cardiac muscle require solving the bidomain model, a continuum representation of cardiac tissue by a system of two reaction–diffusion equations. For two- and three-dimensional problems, the computations tend to take a prohibitively long time. This study develops a computationally efficient and accurate approximation of the bidomain model: a “reduced bidomain” model. The approximation is based on the fact that during a strong shock, the extracellular field in the muscle changes only slightly and, therefore, can be approximated by an activating function, following the concept introduced by Rattay (Rattay, F. Analysis of models for external stimulation of axons. IEEE Trans. Biomed. Eng. 33:974–977, 1986). The activating function used here is time-dependent and is computed using an iterative algorithm. The results show that in two spatial dimensions, the “reduced bidomain” model, as implemented in this study, cuts the computational cost by two orders of magnitude while preserving most properties of the “full bidomain” model. It faithfully represents the spatial pattern and the temporal development of the muscle polarization. Consequently, relative errors in the “defibrillation” threshold, the strength of the weakest shock that terminates all electrical activity within 100 ms, are below 10%.

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

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

Success and failure of the defibrillation shock: does it depend on the fiber field?

This modeling study demonstrates that shocks of the same strength and duration are more successful in extinguishing spiral wave activity in cases when the preparation incorporates fiber curvature. The tissue is represented as a two-dimensional bidomain of unequal anisotropy ratios. Stable reentry is induced via cross-field stimulation of the myocardial sheet. The defibrillation shock is delivered by extracellular line electrodes located at opposite tissue borders. The simulation results demonstrate that the defibrillation shock induces virtual electrodes in the curved fiber preparation. These virtual electrodes are responsible for depolarizing the tissue away from the physical cathode and for giving rise to new activation fronts after the defibrillation shock. Thus, shocks of the same strength and duration are successful in preparations with fiber curvature, while in straight-fiber preparations they only minimally disturb the spiral wave.

Reorganization and termination of a spiral wave reentry following a defibrillation shock

This modeling study examines the behavior of a spiral wave reentry during and after a defibrillation shock in tissue slices of various dimensions. The tissue is represented as a two-dimensional anisotropic bidomain with modified Beeler-Reuter kinetics. Stable reentry is induced by means of cross-stimulation. The defibrillation shock is delivered via extracellular line or point electrodes located at the opposite tissue borders. Shocks delivered through line electrodes were less successful in extinguishing the rotor. The advantage of the shocks administered via the point electrodes in terminating the reentrant circuit is attributed to their ability to generate interelectrode regions of depolarization.

Reduced bidomain model of defibrillation

A bidomain model of the myocardium has been successfully used in predicting the tissue response to a strong shock. The studies of active tissue behavior have been limited due the computational expense of solving bidomain equations. The goal of the present research is to develop a reasonable approximation to the bidomain that would require a fraction of computer time necessary for full bidomain simulation. This reduced bidomain model preserves such important characteristics of the full bidomain as the shape of virtual electrodes, the rate at which they develop, and the effect they have on existing fibrillation wavefronts.