Electroporation and shock-induced transmembrane potential in a cardiac fiber during defibrillation strength shocks

Phase-field model of bilipid membrane electroporation

This paper proposes a new model of membrane electropermeabilisation that combines the water content of the membrane and the transmembrane voltage. Interestingly, thanks to a well defined free-energy of the membrane, we somehow generalise the seminal approach of Chizmadzhev, Weaver and Krassowska, getting rid of the geometrical cylindrical assumption upon which most of the current electroporation models are based. Our approach is physically relevant and we recover a surface diffusion equation of the lipid phase proposed by Leguèbe et al. in a previous phenomenological model. We also perform a fine analysis of the involved nonlocal operators in two simple configurations (a spherical membrane and a flat periodic membrane) that enables us to compare the time constants of the phenomenon in spherical and flat membranes. An accurate splitting scheme combined with Fast Fourier Transforms is developed for efficient computations of the model. Our numerical results enable us to make a link between the molecular dynamics simulations of membrane permeabilisation and the experimental observations on vesicles and cells.

Enhanced Drug Uptake on Application of Electroporation in a Single-Cell Model

Electroporation method is a useful tool for delivering drugs into various diseased tissues in the human body. As a result of an applied electric field, drug particles enter the intracellular compartment through the temporarily permeabilized cell membrane. Consequently, electroporation method allows better penetration of the drug into the diseased tissue and improves treatment clinically. In this study, a more generalized model of drug transport in a single cell is proposed. The model is able to capture non-homogeneous drug transport in the cell due to non-uniform cell membrane permeabilization. Several numerical experiments are conducted to understand the effects of electric field and drug permeability on drug uptake into the cell. Through investigation, the appropriate electric field and drug permeability are identified, which lead to sufficient drug uptake into the cell. This model can be used by experimentalists to get information prior to conduct any experiment, and it may help reduce the number of actual experiments that might be conducted otherwise.

Gene Electrotransfer into Mammalian Cells Using Commercial Cell Culture Inserts with Porous Substrate

Gene electrotransfer is one of the main non-viral methods for intracellular delivery of plasmid DNA, wherein pulsed electric fields are used to transiently permeabilize the cell membrane, allowing enhanced transmembrane transport. By localizing the electric field over small portions of the cell membrane using nanostructured substrates, it is possible to increase considerably the gene electrotransfer efficiency while preserving cell viability. In this study, we expand the frontier of localized electroporation by designing an electrotransfer approach based on commercially available cell culture inserts with polyethylene-terephthalate (PET) porous substrate. We first use multiscale numerical modeling to determine the pulse parameters, substrate pore size, and other factors that are expected to result in successful gene electrotransfer. Based on the numerical results, we design a simple device combining an insert with substrate containing pores with 0.4 µm or 1.0 µm diameter, a multiwell plate, and a pair of wire electrodes. We test the device in three mammalian cell lines and obtain transfection efficiencies similar to those achieved with conventional bulk electroporation, but at better cell viability and with low-voltage pulses that do not require the use of expensive electroporators. Our combined theoretical and experimental analysis calls for further systematic studies that will investigate the influence of substrate pore size and porosity on gene electrotransfer efficiency and cell viability.

Response characteristics and optimization of electroporation: simulation based on finite element method

Electroporation has been widely used in biology, medicine, and the food industry as a means to transport various molecules through the cell membrane. The phenomenon of electroporation is the result of cell membrane damage caused by the application of an electric field. In order to understand more precisely how cells function, we established a dielectric model of a spherical cell and analyzed its characteristics by the finite element method. The effects of altering different electrical parameters were determined. The results showed that the electric field strength was positively related to the transmembrane voltage (TMV) and pore density. There was a minimum electric field strength necessary to induce a critical TMV for the formation of pores. Pulse width also had to be long enough to charge the cell membrane, compared with the normal membrane charging time constant of about 1 μs. When the pulse width was shorter than the charging time constant, it was necessary to increase pulse frequency to create a high enough TMV. The rise-time of the electric pulse also affected electroporation: a fast rise-time pulse not only allowed penetration of the plasma membrane but also the organelle membrane. With slow rise-time pulse, the organelle was shielded from electroporation. This study defines the response characteristics of electrical parameters on the electric load cell and establishes the specificity of parameters for different purposes.

Dynamic Electroporation Model Evaluation on Rabbit Tissues

Biological electroporation is a process of opening pores in the cell membrane when exposed to intense electric fields. This work provides results for validation of a dynamic model of electroporation on biological tissues. Computational simulations were carried out and results for the electrical current through the tissue and increase of the tissue temperature were compared to experimental results. Two calculation methods were used: Equivalent Circuit Method and Finite Element Method. With Equivalent Circuit Method the dielectric dispersion present in biological tissues was included. Liver, kidney and heart of rabbit were used in the experiments. Voltage pulse protocols and voltage ramps were applied using stainless steel needles electrodes. There is good agreement between the simulated and experimental results with mean errors below 15%, with the simulated results within the experimental standard deviation. Only for the protocol with fundamental frequency of 50 kHz, the simulation performed by the Finite Element Method using a commercial software did not correctly represent the current, with errors reaching 50%. The justification for the error found is due to the dielectric dispersion that was not included in this simulator.

Proof-of-Concept of Electrical Activation of Liposome Nanocarriers: From Dry to Wet Experiments

The increasing interest toward biocompatible nanotechnologies in medicine, combined with electric fields stimulation, is leading to the development of electro-sensitive smart systems for drug delivery applications. To this regard, recently the use of pulsed electric fields to trigger release across phospholipid membranes of liposomes has been numerically studied, for a deeper understanding of the phenomena at the molecular scale. Aim of this work is to give an experimental validation of the feasibility to control the release from liposome vesicles, using nanosecond pulsed electric fields characterized by a 10 ns duration and intensity in the order of MV/m. The results are supported by multiphysics simulations which consider the coupling of three physics (electromagnetics, thermal and pore kinetics) in order to explain the occurring physical interactions at the microscopic level and provide useful information on the characteristics of the train of pulses needed to obtain quantitative results in terms of liposome electropermeabilization. Finally, a complete characterization of the exposure system is also provided to support the reliability and validity of the study.

Irreversible Electroporation: Background, Theory, and Review of Recent Developments in Clinical Oncology

Irreversible electroporation (IRE) has established a clinical niche as an alternative to thermal ablation for the eradication of unresectable tumors, particularly those near critical vascular structures. IRE has been used in over 50 independent clinical trials and has shown clinical success when used as a standalone treatment and as a single component within combinatorial treatment paradigms. Recently, many studies evaluating IRE in larger patient cohorts and alongside other novel therapies have been reported. Here, we present the basic principles of reversible electroporation and IRE followed by a review of preclinical and clinical data with a focus on tumors in three organ systems in which IRE has shown great promise: the prostate, pancreas, and liver. Finally, we discuss alternative and future developments, which will likely further advance the use of IRE in the clinic.

Numerical study of the effect of soft layer properties on bacterial electroporation

We present a numerical model of electroporation in a gram-positive bacterium, which accounts for the presence of a negatively charged soft polyelectrolyte layer (which may include a periplasmic space, peptidoglycan layer, cilia, flagella, and other surface appendages) surrounding its plasma membrane. We model the ion transport within and outside the soft layer using the soft layer electrokinetics-based Poisson-Nernst-Planck formalism. Additionally, we model the electroporation dynamics on the plasma membrane using the pore nucleation-based electroporation formalism developed by Krassowska and Filev. We find that ion transport within the soft layer (surface conduction), which depends on the relative importance of the soft layer charged group concentration compared to the buffer concentration, significantly alters the transmembrane voltage across the plasma membrane and hence the pore characteristics. Our numerical simulations suggest that surface conduction significantly lowers the pore number in the plasma membrane. This observation is consistent with experimental studies that show that gram-positive bacteria, in general, have lower transformation efficiencies compared to gram-negative bacteria. Our studies highlight a strong dependence of bacterial electroporation on cell envelope properties and buffer conditions, which need to be taken into consideration when designing electroporation protocols.

Bidomain Predictions of Virtual Electrode-Induced Make and Break Excitations around Blood Vessels

Introduction and background

Virtual electrodes formed by field stimulation during defibrillation of cardiac tissue play an important role in eliciting activations. It has been suggested that the coronary vasculature is an important source of virtual electrodes, especially during low-energy defibrillation. This work aims to further the understanding of how virtual electrodes from the coronary vasculature influence defibrillation outcomes.

Methods

Using the bidomain model, we investigated how field stimulation elicited activations from virtual electrodes around idealized intramural blood vessels. Strength–interval curves, which quantify the stimulus strength required to elicit wavefront propagation from the vessels at different states of tissue refractoriness, were computed for each idealized geometry.

Results

Make excitations occurred at late diastolic intervals, originating from regions of depolarization around the vessel. Break excitations occurred at early diastolic intervals, whereby the vessels were able to excite surrounding refractory tissue due to the local restoration of excitability by virtual electrode-induced hyperpolarizations. Overall, strength–interval curves had similar morphologies and underlying excitation mechanisms compared with previous experimental and numerical unipolar stimulation studies of cardiac tissue. Including the presence of the vessel wall increased the field strength required for make excitations but decreased the field strength required for break excitations, and the field strength at which break excitations occurred was generally greater than 5 V/cm. Finally, in a more realistic ventricular slice geometry, the proximity of virtual electrodes around subepicardial vessels was seen to cause break excitations in the form of propagating unstable wavelets to the subepicardial layer.

Conclusion

Representing the blood vessel wall microstructure in computational bidomain models of defibrillation is recommended as it significantly alters the electrophysiological response of the vessel to field stimulation. Although vessels may facilitate excitation of relatively refractory tissue via break excitations, the field strength required for this is generally greater than those used in the literature on low-energy defibrillation. However, the high-intensity shocks used in standard defibrillation may elicit break excitation propagation from the coronary vasculature.

Comparison between direct and reverse electroporation of cells in situ: a simulation study

The discovery of the human genome has unveiled new fields of genomics, transcriptomics, and proteomics, which has produced paradigm shifts on how to study disease mechanisms, wherein a current central focus is the understanding of how gene signatures and gene networks interact within cells. These gene function studies require manipulating genes either through activation or inhibition, which can be achieved by temporarily permeabilizing the cell membrane through transfection to deliver cDNA or RNAi. An efficient transfection technique is electroporation, which applies an optimized electric pulse to permeabilize the cells of interest. When the molecules are applied on top of seeded cells, it is called “direct” transfection and when the nucleic acids are printed on the substrate and the cells are seeded on top of them, it is termed “reverse” transfection. Direct transfection has been successfully applied in previous studies, whereas reverse transfection has recently gained more attention in the context of high‐throughput experiments. Despite the emerging importance, studies comparing the efficiency of the two methods are lacking. In this study, a model for electroporation of cells in situ is developed to address this deficiency. The results indicate that reverse transfection is less efficient than direct transfection. However, the model also predicts that by increasing the concentration of deliverable molecules by a factor of 2 or increasing the applied voltage by 20%, reverse transfection can be approximately as efficient as direct transfection.

PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry

A computational study of an optimal control approach for cardiac defibrillation in a 3D geometry is presented. The cardiac bioelectric activity at the tissue and bath volumes is modeled by the bidomain model equations. The model includes intramural fiber rotation, axially symmetric around the fiber direction, and anisotropic conductivity coefficients, which are extracted from a histological image. The dynamics of the ionic currents are based on the regularized Mitchell-Schaeffer model. The controls enter in the form of electrodes, which are placed at the boundary of the bath volume with the goal of dampening undesired arrhythmias. The numerical optimization is based on Newton techniques. We demonstrated the parallel architecture environment for the computation of potentials on multidomains and for the higher order optimization techniques.

Advantage of four-electrode over two-electrode defibrillators

Defibrillation is the standard clinical treatment used to stop ventricular fibrillation. An electrical device delivers a controlled amount of electrical energy via a pair of electrodes in order to reestablish a normal heart rate. We propose a technique that is a combination of biphasic shocks applied with a four-electrode system rather than the standard two-electrode system. We use a numerical model of a one-dimensional ring of cardiac tissue in order to test and evaluate the benefit of this technique. We compare three different shock protocols, namely a monophasic and two types of biphasic shocks. The results obtained by using a four-electrode system are compared quantitatively with those obtained with the standard two-electrode system. We find that a huge reduction in defibrillation threshold is achieved with the four-electrode system. For the most efficient protocol (asymmetric biphasic), we obtain a reduction in excess of 80% in the energy required for a defibrillation success rate of 90%. The mechanisms of successful defibrillation are also analyzed. This reveals that the advantage of asymmetric biphasic shocks with four electrodes lies in the duration of the cathodal and anodal phase of the shock.

An engineered membrane to measure electroporation: effect of tethers and bioelectronic interface

This article reports on the construction and predictive models for a platform comprised of an engineered tethered membrane. The platform provides a controllable and physiologically relevant environment for the study of the electroporation process. The mixed self-assembled membrane is formed via a rapid solvent exchange technique. The membrane is tethered to the gold electrode and includes an ionic reservoir separating the membrane and gold surface. Above the membrane, there is an electrolyte solution, and a gold counterelectrode. A voltage is applied between the gold electrodes and the current measured. The current is dependent on the energy required to form aqueous pores and the conductance of each pore. A two-level predictive model, consisting of a macroscopic and a continuum model, is developed to relate the pore dynamics to the measured current. The macroscopic model consists of an equivalent circuit model of the tethered membrane, and asymptotic approximations to the Smoluchowski-Einstein equation of electroporation that is dependent on the pore conductance and the energy required to form aqueous pores. The continuum model is a generalized Poisson-Nernst-Planck (GPNP) system where an activity coefficient to account for steric effects of ions is added to the standard PNP system. The GPNP is used to evaluate the conductance of aqueous pores, and the electrical energy required to form the pores. As an outcome of the setup of the device and the two-level model, biologically important variables can be estimated from experimental measurements. To validate the accuracy of the two-level model, the predicted current is compared with experimentally measured current for different tethering densities.

Effects of premature anodal stimulations on cardiac transmembrane potential and intracellular calcium distributions computed by anisotropic Bidomain models

AIMS

Cardiac unipolar electrode stimulations induce a particular structure of the transmembrane potential distribution (Vm), called virtual electrode polarization (VEP), which plays an important role in the mechanisms of cardiac excitation, reentry induction, and ventricular defibrillation. Recent experimental studies, based on the optical mapping techniques, have shown that premature stimulations also induce significant changes in the intracellular calcium (Cai) spatial distribution. The aim of this work is to investigate and compare by means of numerical simulations the morphology of the Vm and Cai patterns, generated by applying an S1-S2 stimulation protocol with a premature S2 anodal pulse.

METHODS AND RESULTS

We perform parallel finite element simulations of a three-dimensional orthotropic Bidomain model on a block of ventricular tissue by using four membrane models of two species (guinea pig and rabbit), that incorporate the phenomenological or more detailed mechanistic descriptions of the calcium dynamics. During the S2 anodal stimulus, the Cai spatial distribution, computed with all the considered models, presents a configuration similar to the typical VEP pattern of Vm, with a minimum inside the virtual anode and two maxima in the virtual cathodes. After the S2 stimulus turns off, the anode break excitation mechanism yields a Vm pattern exhibiting a clearly propagating wavefront. Differently, the Cai patterns do not show a clear separation between the resting and the activated regions, with the exception of one of the phenomenological models considered, but they show warped dog-bone shaped equi-level lines around an elevation in the virtual anode region.

CONCLUSION

The VEP pattern of the Cai spatial distribution during the S2 stimulus is in agreement with the previous experimental studies. Moreover, the Cai minimum in the virtual anode can be mainly attributable to the outflow of calcium ions produced by the sodium-calcium (NCX) exchanger, without a significant contribution of the ICaL current.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

Modeling defibrillation of the heart: approaches and insights

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices (ICDs), constitutes the most important means of combating sudden cardiac death. While ICD therapy has proved to be efficient and reliable, defibrillation is a traumatic experience. Thus, research on defibrillation mechanisms, particularly aimed at lowering defibrillation voltage, remains an important topic. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart is the most promising approach to achieve this goal. The aim of this paper is to assess the current state-of-the-art in ventricular defibrillation modeling, focusing on both numerical modeling approaches and major insights that have been obtained using defibrillation models, primarily those of realistic ventricular geometry. The paper showcases the contributions that modeling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modeling of the heart (i.e., cardiac defibrillation) that has advanced the understanding of cardiac electrophysiological interaction at the organ level and has the potential to contribute to the betterment of the clinical practice of defibrillation.

Electroporation induced by internal defibrillation shock with and without recovery in intact rabbit hearts

Defibrillation shocks from implantable cardioverter defibrillators can be lifesaving but can also damage cardiac tissues via electroporation. This study characterizes the spatial distribution and extent of defibrillation shock-induced electroporation with and without a 45-min postshock period for cell membranes to recover. Langendorff-perfused rabbit hearts (n = 31) with and without a chronic left ventricular (LV) myocardial infarction (MI) were studied. Mean defibrillation threshold (DFT) was determined to be 161.4 ± 17.1 V and 1.65 ± 0.44 J in MI hearts for internally delivered 8-ms monophasic truncated exponential (MTE) shocks during sustained ventricular fibrillation (>20 s, SVF). A single 300-V MTE shock (twice determined DFT voltage) was used to terminate SVF. Shock-induced electroporation was assessed by propidium iodide (PI) uptake. Ventricular PI staining was quantified by fluorescent imaging. Histological analysis was performed using Masson's Trichrome staining. Results showed PI staining concentrated near the shock electrode in all hearts. Without recovery, PI staining was similar between normal and MI groups around the shock electrode and over the whole ventricles. However, MI hearts had greater total PI uptake in anterior (P < 0.01) and posterior (P < 0.01) LV epicardial regions. Postrecovery, PI staining was reduced substantially, but residual staining remained significant with similar spacial distributions. PI staining under SVF was similar to previously studied paced hearts. In conclusion, electroporation was spatially correlated with the active region of the shock electrode. Additional electroporation occurred in the LV epicardium of MI hearts, in the infarct border zone. Recovery of membrane integrity postelectroporation is likely a prolonged process. Short periods of SVF did not affect electroporation injury.

Optimal control approach to termination of re-entry waves in cardiac electrophysiology

This work proposes an optimal control approach for the termination of re-entry waves in cardiac electrophysiology. The control enters as an extracellular current density into the bidomain equations which are well established model equations in the literature to describe the electrical behavior of the cardiac tissue. The optimal control formulation is inspired, in part, by the dynamical systems behavior of the underlying system of differential equations. Existence of optimal controls is established and the optimality system is derived formally. The numerical realization is described in detail and numerical experiments, which demonstrate the capability of influencing and terminating reentry phenomena, are presented.

Effects of nanosecond pulsed electric fields on the activity of a Hodgkin and Huxley neuron model

The cell membrane poration is one of the main assessed biological effects of nanosecond pulsed electric fields (nsPEF). This structural change of the cell membrane appears soon after the pulse delivery and lasts for a time period long enough to modify the electrical activity of excitable membranes in neurons. Inserting such a phenomenon in a Hodgkin and Huxley neuron model by means of an enhanced time varying conductance resulted in the temporary inhibition of the action potential generation. The inhibition time is a function of the level of poration, the pore resealing time and the background stimulation level of the neuron. Such results suggest that the neuronal activity may be efficiently modulated by the delivery of repeated pulses. This opens the way to the use of nsPEFs as a stimulation technique alternative to the conventional direct electric stimulation for medical applications such as chronic pain treatment.

Improved numerical approach for electrical modeling of biological cell clusters

This article presents an efficient numerical approach to simulate the process of polarization and ion conduction in membranes of biological cells subjected to intense electric fields. The proposed method uses Coulomb's law to calculate the electric field on the surface of the cell membrane and the continuity equation for calculating the difference in electric potential between the faces of the membrane. The behavior of the membrane conductance is described by a model of electroporation proposed in literature. This method provides results that agree well with the analytical model of polarization of an isolated cell suspended in electrolytic solution and also provides results for the conductance of the membrane during electroporation of cells in concentrated suspensions that agree with experimental results already published.

Solving the coupled system improves computational efficiency of the bidomain equations

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

Spatial distribution and extent of electroporation by strong internal shock in intact structurally normal and chronically infarcted rabbit hearts

INTRODUCTION

Although life-saving, a strong internal defibrillation shock may temporarily or permanently damage the heart via disruption of cell membranes (electroporation). Spatial extent of electroporation in intact, normal, or infarcted hearts has not been investigated. In this study, shock-induced electroporation in intact rabbit hearts with and without chronic (>4 weeks) left ventricular myocardial infarction (MI) was characterized.

METHODS AND RESULTS

A coil shock electrode was inserted in the right ventricle of Langendorff-perfused hearts. One truncated exponential monophasic shock (+300 V, 8 ms) was delivered by a 150 microF capacitor clinical defibrillator while the heart was perfused with membrane-impermeant dye propidium iodide (PI). The heart was sectioned transversely, and uptake of PI into ventricular myocardium through electropores was quantified. Histological evaluation was performed via Masson's trichrome staining. PI accumulation was minimal in the control (n = 3) and MI (n = 3) hearts without shock. Following shock delivery, (1) in control (n = 5) and MI (n = 5) hearts, electroporation mostly occurred near the shock electrode and was longitudinally distributed along the active region of the shock electrode; (2) in MI group, electroporation was significantly increased (P < 0.05) in the surviving anterior epicardial layers of the infarcted region; and (3) between the control and MI groups, the overall extent of electroporation was similar.

CONCLUSION

Shock-induced electroporation was spatially dependent on the location and dimension of the active region of the shock electrode. The overall extent of electroporation in the MI heart was comparable with the control heart, but the surviving anterior epicardial layers in the infarcted region were more susceptible to electroporation.

The role of mechanoelectric feedback in vulnerability to electric shock

Experimental and clinical studies have shown that ventricular dilatation is associated with increased arrhythmogenesis and elevated defibrillation threshold; however, the underlying mechanisms remain poorly understood. The goal of the present study was to test the hypothesis that (1) stretch-activated channel (SAC) recruitment and (2) geometrical deformations in organ shape and fiber architecture lead to increased arrhythmogenesis by electric shocks following acute ventricular dilatation. To elucidate the contribution of these two factors, the study employed, for the first time, a combined electro-mechanical simulation approach. Acute dilatation was simulated in a model of rabbit ventricular mechanics by raising the LV end-diastolic pressure from 0.6 (control) to 4.2 kPa (dilated). The output of the mechanics model was used in the electrophysiological model. Vulnerability to shocks was examined in the control, the dilated ventricles, and in the dilated ventricles that also incorporated currents through SAC as a function of local strain, by constructing vulnerability grids. Results showed that dilatation-induced deformation alone decreased upper limit of vulnerability (ULV) slightly and did not result in increased vulnerability. With SAC recruitment in the dilated ventricles, the number of shock-induced arrhythmia episodes increased by 37% (from 41 to 56) and the lower limit of vulnerability (LLV) decreased from 9 to 7 V/cm, while ULV did not change. The heterogeneous activation of SAC caused by the heterogeneous fiber strain in the ventricular walls was the main reason for increased vulnerability to electric shocks since it caused dispersion of electrophysiological properties in the tissue, resulting in postshock unidirectional block and establishment of reentry.

Effect of electroporation on cardiac electrophysiology

Defibrillation shocks are commonly used to terminate life-threatening arrhythmias. According to the excitation theory of defibrillation, such shocks are aimed at depolarizing the membranes of most cardiac cells, resulting in resynchronization of electrical activity in the heart. If shock-induced transmembrane potentials are large enough, they can cause transient tissue damage due to electroporation. In this review, evidence is presented that electroporation of the heart tissue can occur during clinically relevant intensities of the external electrical field and that electroporation can affect the outcome of defibrillation therapy, being both pro- and antiarrhythmic.Here, we present experimental evidence for electroporation in cardiac tissue, which occurs above a threshold of 25 V/cm as evident from propidium iodide uptake, transient diastolic depolarization, and reductions of action potential amplitude and its derivative. These electrophysiological changes can induce tachyarrhythmia, due to conduction block and possibly triggered activity; however, our findings provide the foundation for future design of effective methods to deliver genes and drugs to cardiac tissues, while avoiding possible side effects such as arrhythmia and mechanical stunning.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.

Algebraic multigrid preconditioner for the cardiac bidomain model

The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7.

Cardiac defibrillation and the role of mechanoelectric feedback in postshock arrhythmogenesis

Ventricular dilatation increases the defibrillation threshold (DFT). In order to elucidate the mechanisms responsible for this increase, the present article investigates changes in the postshock behavior of the myocardium upon stretch. A two-dimensional electro-mechanical model of cardiac tissue incorporating heterogeneous fiber orientation was used to explore the effect of sustained stretch on postshock behavior via (a) recruitment of mechanosensitive channels (MSC) and (b) tissue deformation and concomitant changes in tissue conductivities. Recruitment of MSC had no influence on vulnerability to electric shocks as compared to control, but increased the complexity of postshock VF patterns. Stretch-induced deformation and changes in tissue conductivities resulted in a decrease in vulnerability to electric shocks.

Hybrid finite element method for describing the electrical response of biological cells to applied fields

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

Electrical behavior and pore accumulation in a multicellular model for conventional and supra-electroporation

Extremely large but very short (20 kV/cm, 300 ns) electric field pulses were reported recently to non-thermally destroy melanoma tumors. The stated mechanism for field penetration into cells is pulse characteristic times faster than charge redistribution (displacement currents). Here we use a multicellular model with irregularly shaped, closely spaced cells to show that instead overwhelming pore creation (supra-electroporation) is dominant, with field penetration due to pores (ionic conduction currents) during most of the pulse. Moreover, the model's maximum membrane potential (about 1.2 V) is consistent with recent experimental observations on isolated cells. We also use the model to show that conventional electroporation resulting from 100 microsecond, 1 kV/cm pulses yields a spatially heterogeneous electroporation distribution. In contrast, the melanoma-destroying pulses cause nearly homogeneous electroporation of cells and their nuclear membranes. Electropores can persist for times much longer than the pulses, and are likely to be an important mechanism contributing to cell death.

Modeling electroporation in a single cell

Electroporation uses electric pulses to promote delivery of DNA and drugs into cells. This study presents a model of electroporation in a spherical cell exposed to an electric field. The model determines transmembrane potential, number of pores, and distribution of pore radii as functions of time and position on the cell surface. For a 1-ms, 40 kV/m pulse, electroporation consists of three stages: charging of the cell membrane (0-0.51 micros), creation of pores (0.51-1.43 micros), and evolution of pore radii (1.43 micros to 1 ms). This pulse creates approximately 341,000 pores, of which 97.8% are small ( approximately 1 nm radius) and 2.2% are large. The average radius of large pores is 22.8 +/- 18.7 nm, although some pores grow to 419 nm. The highest pore density occurs on the depolarized and hyperpolarized poles but the largest pores are on the border of the electroporated regions of the cell. Despite their much smaller number, large pores comprise 95.3% of the total pore area and contribute 66% to the increased cell conductance. For stronger pulses, pore area and cell conductance increase, but these increases are due to the creation of small pores; the number and size of large pores do not increase.

Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation

The recent applications of nanosecond, megavolt-per-meter electric field pulses to biological systems show striking cellular and subcellular electric field induced effects and revive the interest in the biophysical mechanism of electroporation. We first show that the absolute rate theory, with experimentally based parameter input, is consistent with membrane pore creation on a nanosecond time scale. Secondly we use a Smoluchowski equation-based model to formulate a self-consistent theoretical approach. The analysis is carried out for a planar cell membrane patch exposed to a 10 ns trapezoidal pulse with 1.5 ns rise and fall times. Results demonstrate reversible supraelectroporation behavior in terms of transmembrane voltage, pore density, membrane conductance, fractional aqueous area, pore distribution, and average pore radius. We further motivate and justify the use of Krassowska's asymptotic electroporation model for analyzing nanosecond pulses, showing that pore creation dominates the electrical response and that pore expansion is a negligible effect on this time scale.

A High-Voltage Pulse Generation Instrument for Electrochemotherapy Method

Electrochemotherapy (ECT) is a new method that uses anticancer drugs delivery with intensive electrical pulses. Recently, ECT as the treatment method can be applied for basal cell and spin cell carcinoma and for melanoma metastases. In this paper, a new design of a high voltage pulse generator with variable output pulse magnitude, repetition frequency, and pulse duration is presented. Furthermore, it has presented the basic theory of ECT, the importance/advantages against other cancer treatment methods, the theoretical model of electroporated cell membrane, and the application ways of ECT method. The proposed instrument is suitable for effective drug delivery of ECT in anti-tumor treatment. Also, this instrument can be applied to gene transfer/therapy methods.

Nanopore Formation and Phosphatidylserine Externalization in a Phospholipid Bilayer at High Transmembrane Potential

Atomic-resolution molecular dynamics simulations of lipid bilayers containing 7% phosphatidylserine (PS) on one leaflet are consistent with experimental observations of membrane poration and PS externalization in living cells exposed to nanosecond, megavolt-per-meter electric pulses. Nanometer-diameter aqueous pores develop within nanoseconds after application of an electric field of 450 mV/nm, and electrophoretic transport of the anionic PS headgroup along the newly constructed hydrophilic pore surface commences even while pore formation is still in progress.

Microdosimetry for conventional and supra-electroporation in cells with organelles

Conventional electroporation (EP) by 0.1 to 1 kV/cm pulses longer than 100 micros, and supra-electroporation by 10 to 300 kV/cm pulses shorter than 1 micros cause different cellular effects. Conventional EP delivers DNA, proteins, small drugs, and fluorescent indicators across the plasma membrane (PM) and causes moderate levels of phosphatidylserine (PS) translocation at the PM. We hypothesize that supra-EP is central to intracellular effects such as apoptosis induction and higher levels of PS translocation. Our cell system model has 20,000 interconnected local models for small areas of the PM and organelle membranes, small regions of aqueous media, appropriate resting potentials, and the asymptotic EP model. Conventional EP primarily affects the PM, but with a hint of endoplasmic reticulum involvement. Supra-EP can involve all of a cell's membrane at the largest fields. Conventional EP fields tend to go around cells, but supra-EP fields go through cells, extensively penetrating organelles.

Post-shock myocardial stunning: A prospective randomised double-blind comparison of monophasic and biphasic waveforms

INTRODUCTION

Compared with monophasic defibrillation, biphasic defibrillation is associated with less myocardial stunning and earlier activation of sodium channels. We therefore hypothesised that earlier sodium channel activation would result in earlier restoration of the first sinus beat following elective DC cardioversion.

METHODS

Adults undergoing elective DC cardioversion were randomised to receive either monophasic or biphasic escalating transthoracic shocks. The ECG was recorded electronically during defibrillation and the time from delivery of the shock to restoration of the first sinus beat, measured from the beginning of the 'P' wave, was calculated.

RESULTS

Seventy four patients were studied. Data were unavailable from 18 patients. There was no demographic difference between groups. Median time to the first sinus beat following monophasic defibrillation (n=25) was 3.66 s (95% CI 2.55-4.61 s) and following biphasic defibrillation (n=33) was 2.21s (95% CI 1.76-2.56 s; P<or=0.0001). Linear regression confirmed that the waveform was an independent predictor of time to restoration of sinus rhythm; P<0.0001. The final defibrillation energy level used to achieve cardioversion was not an independent predictor of time to restoration of sinus rhythm; P=0.49.

CONCLUSION

Biphasic defibrillation for elective DC cardioversion achieved more rapid restoration of the first sinus beat compared with a monophasic waveform. Waveform, but not energy level that achieved defibrillation, was an independent predictor of time to restoration of the first sinus beat. The mechanism for this may be related to the earlier reactivation of sodium channels associated with the biphasic waveform.

Cell and tissue responses to electric shocks

AIM

Existing models of myocardial membrane kinetics have not been able to reproduce the experimentally-observed negative bias in the asymmetry of transmembrane potential changes (DeltaV(m)) induced by strong electric shocks. The goals of this study are (1) to demonstrate that this negative bias could be reproduced by the addition, to the membrane model, of electroporation and an outward current, I(a), part of the K(+) flow through the L-type Ca(2+)-channel, and (2) to determine how such modifications in the membrane model affect shock-induced break excitation in a 2D preparation.

METHODS AND RESULTS

We conducted simulations of shocks in bidomain fibres and sheets with membrane dynamics represented by the Luo-Rudy dynamic model (LRd'2000), to which electroporation (LRd + EP model) and the outward current, I(a), activated upon strong shock-induced depolarization (aLRd model) was added. Assuming I(a) is a part of K(+) flow through the L-type Ca(2+)-channel enabled us to reproduce both the experimentally observed rectangularly-shaped positive DeltaV(m) and the value of near 2 of the negative-to-positive DeltaV(m) ratio. In the sheet, I(a) not only contributed to the negative bias in DeltaV(m) asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaV(m). Electroporation, in its turn, was responsible for the decrease in cathode-break excitation threshold in the aLRd sheet, compared with the other two cases, as well as for the occurrence of the excitation after the shock-end rather than during the shock.

CONCLUSIONS

The incorporation of electroporation and I(a) in a membrane model ensures match between simulation results and experimental data. The use of the aLRd model results in a lower threshold for shock-induced break excitation.

Electroporation of the heart

Defibrillation shocks are commonly used to terminate life-threatening arrhythmias. According to the excitation theory of defibrillation, such shocks are aimed at depolarizing the membranes of most cardiac cells resulting in resynchronization of electrical activity in the heart. If shock-induced changes in transmembrane potential are large enough, they can cause transient tissue damage due to electroporation. In this review evidence is presented that (a) electroporation of the heart tissue can occur during clinically relevant intensities of the external electrical field, and (b) electroporation can affect the outcome of defibrillation therapy; being both pro- and anti-arrhythmic.

Asymmetry in membrane responses to electric shocks: insights from bidomain simulations

Models of myocardial membrane dynamics have not been able to reproduce the experimentally observed negative bias in the asymmetry of transmembrane potential changes (DeltaVm) induced by strong electric shocks delivered during the action potential plateau. The goal of this study is to determine what membrane model modifications can bridge this gap between simulation and experiment. We conducted simulations of shocks in bidomain fibers and sheets with membrane dynamics represented by the LRd'2000 model. We found that in the fiber, the negative bias in DeltaVm asymmetry could not be reproduced by addition of electroporation only, but by further addition of hypothetical outward current, Ia, activated upon strong shock-induced depolarization. Furthermore, the experimentally observed rectangularly shaped positive DeltaVm, negative-to-positive DeltaVm ratio (asymmetry ratio) = approximately 2, electroporation occurring at the anode only, and the increase in positive DeltaVm caused by L-type Ca2+-channel blockade were reproduced in the strand only if Ia was assumed to be a part of K+ flow through the L-type Ca2+-channel. In the sheet, Ia not only contributed to the negative bias in DeltaVm asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaVm. Inclusion of Ia and electroporation is thus the bridge between experiment and simulation.

Defibrillation Depends on Conductivity Fluctuations and the Degree of Disorganization in Reentry Patterns

Defibrillation depends on conductivity and disorganization.

INTRODUCTION

Cardiac fibrillation is the deterioration of the heart's normally well-organized activity into one or more meandering spiral waves, which subsequently break up into many meandering wave fronts. Delivery of an electric shock (defibrillation) is the only effective way of restoring the normal rhythm. This study focuses on examining whether higher degrees of disorganization requires higher shock strengths to defibrillate and whether microscopic conductivity fluctuations favor shock success.

METHODS AND RESULTS

We developed a three-dimensional computer bidomain model of a block of cardiac tissue with straight fibers immersed in a conductive bath. The membrane behavior was described by the Courtemanche human atrial action potential model incorporating electroporation and an acetylcholine- (ACh) dependent potassium current. Intracellular conductivities were varied stochastically around nominal values with variations of up to 50%. A single rotor reentry was initiated and, by adjusting the spatial ACh variation, the level of organization could be controlled. The single rotor could be stabilized or spiral wave breakup could be provoked leading to fibrillatory-like activity. For each level of organization, multiple shock timings and strengths were applied to compute the probability of shock success as a function of shock strength.

CONCLUSIONS

Our results suggest that the level of the small-scale conductivity fluctuations is a very important factor in defibrillation. A higher variation significantly lowers the required shock strength. Further, we demonstrated that success also heavily depends on the level of organization of the fibrillatory episode. In general, higher levels of disorganization require higher shock strengths to defibrillate.

Paradoxical loss of excitation with high intensity pulses during electric field stimulation of single cardiac cells

Transmembrane potential responses of single cardiac cells stimulated at rest were studied with uniform rectangular field pulses having durations of 0.5-10 ms. Cells were enzymatically isolated from guinea pig ventricles, stained with voltage sensitive dye di-8-ANEPPS, and stimulated along their long axes. Fluorescence signals were recorded with spatial resolution of 17 microm for up to 11 sites along the cell. With 5 and 10 ms pulses, all cells (n = 10) fired an action potential over a broad range of field amplitudes (approximately 3-65 V/cm). With 0.5 and 1 ms pulses, all cells (n = 7) fired an action potential for field amplitudes ranging from the threshold value (approximately 4-8 V/cm) to 50-60 V/cm. However, when the field amplitude was further increased, five of seven cells failed to fire an action potential. We postulated that this paradoxical loss of excitation for higher amplitude field pulses is the result of nonuniform polarization of the cell membrane under conditions of electric field stimulation, and a counterbalancing interplay between sodium current and inwardly rectifying potassium current with increasing field strength. This hypothesis was verified using computer simulations of a field-stimulated guinea pig ventricular cell. In conclusion, we show that for stimulation with short-duration pulses, cells can be excited for fields ranging between a low amplitude excitation threshold and a high amplitude threshold above which the excitation is suppressed. These results can have implications for the mechanistic understanding of defibrillation outcome, especially in the setting of diseased myocardium.

Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model

Functional reentry in the heart can be caused by a wave front of excitation rotating around its edge. Previous simulations on the basis of monodomain cable equations predicted the existence of self-sustained, vortex-like wave fronts (scroll waves) rotating around a filament in three dimensions. In our simulations, we used the more accurate bidomain model with modified Beeler-Reuter ionic kinetics to study the dynamics of scroll-wave filaments in a 16 x 8 x 1.5-mm slab of ventricular tissue with straight fibers. Wave fronts were identified as the areas with inward current. Their edges represented the filaments. Both transmural and intramural reentries with I- and U-shaped filaments, respectively, were obtained by the S1-S2 point stimulation protocol through the virtual electrode-induced phase singularity mechanism. The filaments meandered along elongated trajectories and tended to attach to the tissue boundaries exposed to air (no current flow) rather than to the bath (zero extracellular potential). They completely detached from electroporated (zero transmembrane potential) boundaries. In our simulations, the presence of the bath led to generation of only U-shaped filaments, which survived for the 1.5-mm-thick slab but not for the slabs of 0.5- or 3-mm thicknesses. Thus boundary conditions may be another determinant of the type and dynamics of reentry.

Model of creation and evolution of stable electropores for DNA delivery

Electroporation, in which electric pulses create transient pores in the cell membrane, is becoming an important technique for gene therapy. To enable entry of supercoiled DNA into cells, the pores should have sufficiently large radii (>10 nm), remain open long enough for the DNA chain to enter the cell (milliseconds), and should not cause membrane rupture. This study presents a model that can predict such macropores. The distinctive features of this model are the coupling of individual pores through membrane tension and the electrical force on the pores, which is applicable to pores of any size. The model is used to explore the process of pore creation and evolution and to determine the number and size of pores as a function of the pulse magnitude and duration. Next, our electroporation model is combined with a heuristic model of DNA uptake and used to predict the dependence of DNA uptake on pulsing parameters. Finally, the model is used to examine the mechanism of a two-pulse protocol, which was proposed specifically for gene delivery. The comparison between experimental results and the model suggests that this model is well-suited for the investigation of electroporation-mediated DNA delivery.