Roles of electric field and fiber structure in cardiac electric stimulation

Prediction of experimental cardiac magnetostimulation thresholds using pig-specific body models

PURPOSE

Modern high-amplitude gradient systems can be limited by the International Electrotechnical Commission 60601-2-33 cardiac stimulation (CS) limit, which was set in a conservative manner based on electrode experiments and E-field simulations in uniform ellipsoidal body models. Here, we show that coupled electromagnetic-electrophysiological modeling in detailed body and heart models can predict CS thresholds, suggesting that such modeling might lead to more detailed threshold estimates in humans. Specifically, we compare measured and predicted CS thresholds in eight pigs.

METHODS

We created individualized porcine body models using MRI (Dixon for the whole body, CINE for the heart) that replicate the anatomy and posture of the animals used in our previous experimental CS study. We model the electric fields induced along cardiac Purkinje and ventricular muscle fibers and predict the electrophysiological response of these fibers, yielding CS threshold predictions in absolute units for each animal. Additionally, we assess the total modeling uncertainty through a variability analysis of the 25 main model parameters.

RESULTS

Predicted and experimental CS thresholds agree within 19% on average (normalized RMS error), which is smaller than the 27% modeling uncertainty. No significant difference was found between the modeling predictions and experiments (p < 0.05, paired t-test).

CONCLUSION

Predicted thresholds matched the experimental data within the modeling uncertainty, supporting the model validity. We believe that our modeling approach can be applied to study CS thresholds in humans for various gradient coils, body shapes/postures, and waveforms, which is difficult to do experimentally.

Measurement of magnetostimulation thresholds in the porcine heart

PURPOSE

Powerful MRI gradient systems can surpass the International Electrotechnical Commission (IEC) 60601-2-33 limit for cardiac stimulation (CS), which was determined by simple electromagnetic simulations and electrode stimulation experiments. Only a few canine studies measured magnetically induced CS thresholds in vivo and extrapolating them to human safety limits can be challenging.

METHODS

We measured cardiac magnetostimulation thresholds in 10 healthy, anesthetized pigs using capacitors discharged into a flat spiral coil to produce damped sinusoidal waveforms with effective stimulus duration ts,eff  = 0.45 ms. Electrocardiography (ECG), blood pressure, and peripheral oximetry signals were recorded to determine threshold coil currents yielding cardiac capture. Dixon and CINE MR volumes from each animal were segmented to generate porcine-specific electromagnetic models to calculate dB/dt and E-field values in the porcine heart at threshold. For comparison, we also simulated maximum dB/dt and E-field values created by three MRI gradient systems in the heart of a human body model.

RESULTS

The average dB/dt threshold estimated in the porcine heart was 1.66 ± 0.23 kT/s, which is 11-fold greater than the IEC dB/dt limit at ts,eff  = 0.45 ms, and 31-fold greater than the maximum value created by the investigated MRI gradients in the human heart. The average E-field threshold estimated in the porcine heart was 92.9 ± 13.5 V/m, which is 6-fold greater than the IEC E-field limit at ts,eff  = 0.45 ms and 37-fold greater than the maximum gradient-induced E-field in the human heart.

CONCLUSION

This first measurement of cardiac magnetostimulation thresholds in pigs indicates that the IEC cardiac safety limit is conservative for the investigated stimulus duration (ts,eff  = 0.45 ms).

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Ultrafast four-dimensional imaging of cardiac mechanical wave propagation with sparse optoacoustic sensing

Propagation of electromechanical waves in excitable heart muscles follows complex spatiotemporal patterns holding the key to understanding life-threatening arrhythmias and other cardiac conditions. Accurate volumetric mapping of cardiac wave propagation is currently hampered by fast heart motion, particularly in small model organisms. Here we demonstrate that ultrafast four-dimensional imaging of cardiac mechanical wave propagation in entire beating murine heart can be accomplished by sparse optoacoustic sensing with high contrast, ∼115-µm spatial and submillisecond temporal resolution. We extract accurate dispersion and phase velocity maps of the cardiac waves and reveal vortex-like patterns associated with mechanical phase singularities that occur during arrhythmic events induced via burst ventricular electric stimulation. The newly introduced cardiac mapping approach is a bold step toward deciphering the complex mechanisms underlying cardiac arrhythmias and enabling precise therapeutic interventions.

Investigating cardiac stimulation limits of MRI gradient coils using electromagnetic and electrophysiological simulations in human and canine body models

Purpose:

Cardiac stimulation (CS) limits to gradient coil switching speed are difficult to measure in humans; instead, current regulatory guidelines (IEC 60601–2-33) are based on animal experiments and electric field–to-dB/dt conversion factors computed for a simple, homogeneous body model. We propose improvement to this methodology by using more detailed CS modeling based on realistic body models and electrophysiological models of excitable cardiac fibers.

Methods:

We compute electric fields induced by a solenoid, coplanar loops, and a commercial gradient coil in two human body models and a canine model. The canine simulations mimic previously published experiments. We generate realistic fiber topologies for the cardiac Purkinje and ventricular muscle fiber networks using rule-based algorithms, and evaluate CS thresholds using validated electrodynamic models of these fibers.

Results:

We were able to reproduce the average measured canine CS thresholds within 5%. In all simulations, the Purkinje fibers were stimulated before the ventricular fibers, and therefore set the effective CS threshold. For the investigated gradient coil, simulated CS thresholds for the x-, y-, and z-axis were at least one order of magnitude greater than the International Electrotechnical Commission limit.

Conclusion:

We demonstrate an approach to simulate gradient-induced CS using a combination of electromagnetic and electrophysiological modeling. Pending additional validation, these simulations could guide the assessment of CS limits to MRI gradient coil switching speed. Such an approach may lead to less conservative, but still safe, operation limits, enabling the use of the maximum gradient amplitude versus slew rate parameter space of recent, powerful gradient systems.

Cardiac optogenetics: a novel approach to cardiovascular disease therapy

Optogenetics is a cell-type specific and high spatial-temporal resolution method that combines genetic encoding of light-sensitive proteins and optical manipulation techniques. Optogenetics technology provides a novel approach for research on cardiac arrhythmia treatment, including pacing, recovering the conduction system, and achieving cardiac resynchronization with precise and low-energy optical control. Photosensitive proteins, which usually act as ion channels, pumps, or receptors, are delivered to target cells, where they respond to light pulses of specific wavelengths, evoke transient flows of transmembrane ion currents, and induce signal transmission. With the development of gene technology, the in vivo efficiency of optogenetics in cardiology has been trialed, and in vitro experiments have been performed to test its potential in cardiac electrophysiology. Challenges for applying optogenetics in large animals and humans include the effectiveness, safety, and long-term expression of photosensitive proteins, unscattered and unattenuated exogenous light stimulation, and the need for implantable miniature light stimulators. Photosensitive proteins, genetic engineering technology, and light equipment are essential for experiments in cardiac optogenetics. Optogenetics may provide an alternative method for evaluating the mechanism of cardiac arrhythmias, testing hypotheses, and treating cardiovascular diseases.

Will cardiac optogenetics find the way through the obscure angles of heart physiology?

Optogenetics is a technique exploded in the last 10 years, which revolutionized several areas of biological research. The brightest side of this technology is the use of light to modulate non-invasively, with high spatial resolution and millisecond time scale, excitable cells genetically modified to express light-sensitive microbial ion channels (opsins). Neuroscience has first benefited from such fascinating strategy, in intact organisms. By shining light to specific neuronal subpopulations, optogenetics allowed unearth the mechanisms involved in cell-to-cell communication within the context of intact organs, such as the brain, formed by complex neuronal circuits. More recently, scientists looked at optogenetics as a tool to answer some of the questions, remained in the dark, of cardiovascular physiology. In this review, we focus on the application of optogenetics in the study of the heart, a complex multicellular organ, homing different populations of excitable cells, spatially and functionally interconnected. Moving from the first proof-of-principle works, published in 2010, to the present time, we discuss the in vitro and in vivo applications of optogenetics for the study of electrophysiology of the different cardiac cell types, and for the dissection of cellular mechanisms underlying arrhythmias. We also present how molecular biology and technology foster the evolution of cardiac optogenetics, with the aim to further our understanding of fundamental questions in cardiac physiology and pathology. Finally, we confer about the therapeutic potential of such biotechnological strategy for the treatment of heart rhythm disturbances (e.g. cardiac pacing, cardioversion).

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

Optogenetic pacing in Drosophila melanogaster

Electrical stimulation is currently the gold standard for cardiac pacing. However, it is invasive and nonspecific for cardiac tissues. We recently developed a noninvasive cardiac pacing technique using optogenetic tools, which are widely used in neuroscience. Optogenetic pacing of the heart provides high spatial and temporal precisions, is specific for cardiac tissues, avoids artifacts associated with electrical stimulation, and therefore promises to be a powerful tool in basic cardiac research. We demonstrated optogenetic control of heart rhythm in a well-established model organism, Drosophila melanogaster. We developed transgenic flies expressing a light-gated cation channel, channelrhodopsin-2 (ChR2), specifically in their hearts and demonstrated successful optogenetic pacing of ChR2-expressing Drosophila at different developmental stages, including the larva, pupa, and adult stages. A high-speed and ultrahigh-resolution optical coherence microscopy imaging system that is capable of providing images at a rate of 130 frames/s with axial and transverse resolutions of 1.5 and 3.9 μm, respectively, was used to noninvasively monitor Drosophila cardiac function and its response to pacing stimulation. The development of a noninvasive integrated optical pacing and imaging system provides a novel platform for performing research studies in developmental cardiology.

Neuron matters: electric activation of neuronal tissue is dependent on the interaction between the neuron and the electric field

In laboratory research and clinical practice, externally-applied electric fields have been widely used to control neuronal activity. It is generally accepted that neuronal excitability is controlled by electric current that depolarizes or hyperpolarizes the excitable cell membrane. What determines the amount of polarization? Research on the mechanisms of electric stimulation focus on the optimal control of the field properties (frequency, amplitude, and direction of the electric currents) to improve stimulation outcomes. Emerging evidence from modeling and experimental studies support the existence of interactions between the targeted neurons and the externally-applied electric fields. With cell-field interaction, we suggest a two-way process. When a neuron is positioned inside an electric field, the electric field will induce a change in the resting membrane potential by superimposing an electrically-induced transmembrane potential (ITP). At the same time, the electric field can be perturbed and re-distributed by the cell. This cell-field interaction may play a significant role in the overall effects of stimulation. The redistributed field can cause secondary effects to neighboring cells by altering their geometrical pattern and amount of membrane polarization. Neurons excited by the externally-applied electric field can also affect neighboring cells by ephaptic interaction. Both aspects of the cell-field interaction depend on the biophysical properties of the neuronal tissue, including geometric (i.e., size, shape, orientation to the field) and electric (i.e., conductivity and dielectricity) attributes of the cells. The biophysical basis of the cell-field interaction can be explained by the electromagnetism theory. Further experimental and simulation studies on electric stimulation of neuronal tissue should consider the prospect of a cell-field interaction, and a better understanding of tissue inhomogeneity and anisotropy is needed to fully appreciate the neural basis of cell-field interaction as well as the biological effects of electric stimulation.

New insights into defibrillation of the heart from realistic simulation studies

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices, constitutes the most important means of combating sudden cardiac death. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart, particularly under diseased conditions, is a promising approach to achieve an optimal therapy. The aim of this article is to assess the current state-of-the-art in whole-heart defibrillation modelling, focusing on major insights that have been obtained using defibrillation models, primarily those of realistic heart geometry and disease remodelling. The article showcases the contributions that modelling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modelling 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.

Transmembrane current imaging in the heart during pacing and fibrillation

Recently, we described a method to quantify the time course of total transmembrane current (Im) and the relative role of its two components, a capacitive current (Ic) and a resistive current (Iion), corresponding to the cardiac action potential during stable propagation. That approach involved recording high-fidelity (200 kHz) transmembrane potential (Vm) signals with glass microelectrodes at one site using a spatiotemporal coordinate transformation via measured conduction velocity. Here we extend our method to compute these transmembrane currents during stable and unstable propagation from fluorescence signals of Vm at thousands of sites (3 kHz), thereby introducing transmembrane current imaging. In contrast to commonly used linear Laplacians of extracellular potential (Ve) to compute Im, we utilized nonlinear image processing to compute the required second spatial derivatives of Vm. We quantified the dynamic spatial patterns of current density of Im and Iion for both depolarization and repolarization during pacing (including nonplanar patterns) by calibrating data with the microelectrode signals. Compared to planar propagation, we found that the magnitude of Iion was significantly reduced at sites of wave collision during depolarization but not repolarization. Finally, we present uncalibrated dynamic patterns of Im during ventricular fibrillation and show that Im at singularity sites was monophasic and positive with a significant nonzero charge (Im integrated over 10 ms) in contrast with nonsingularity sites. Our approach should greatly enhance the understanding of the relative roles of functional (e.g., rate-dependent membrane dynamics and propagation patterns) and static spatial heterogeneities (e.g., spatial differences in tissue resistance) via recordings during normal and compromised propagation, including arrhythmias.

Placement of implantable cardioverter-defibrillators in paediatric and congenital heart defect patients: a pipeline for model generation and simulation prediction of optimal configurations

There is currently no reliable way of predicting the optimal implantable cardioverter-defibrillator (ICD) placement in paediatric and congenital heart defect (CHD) patients. This study aimed to: (1) develop a new image processing pipeline for constructing patient-specific heart-torso models from clinical magnetic resonance images (MRIs); (2) use the pipeline to determine the optimal ICD configuration in a paediatric tricuspid valve atresia patient; (3) establish whether the widely used criterion of shock-induced extracellular potential (Φe) gradients ≥5 V cm(-1) in ≥95% of ventricular volume predicts defibrillation success. A biophysically detailed heart-torso model was generated from patient MRIs. Because transvenous access was impossible, three subcutaneous and three epicardial lead placement sites were identified along with five ICD scan locations. Ventricular fibrillation was induced, and defibrillation shocks were applied from 11 ICD configurations to determine defibrillation thresholds (DFTs). Two configurations with epicardial leads resulted in the lowest DFTs overall and were thus considered optimal. Three configurations shared the lowest DFT among subcutaneous lead ICDs. The Φe gradient criterion was an inadequate predictor of defibrillation success, as defibrillation failed in numerous instances even when 100% of the myocardium experienced such gradients. In conclusion, we have developed a new image processing pipeline and applied it to a CHD patient to construct the first active heart-torso model from clinical MRIs.

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.

Transmembrane potential generated by a magnetically induced transverse electric field in a cylindrical axonal model

During the electrical stimulation of a uniform, long, and straight nerve axon, the electric field oriented parallel to the axon has been widely accepted as the major field component that activates the axon. Recent experimental evidence has shown that the electric field oriented transverse to the axon is also sufficient to activate the axon, by inducing a transmembrane potential within the axon. The transverse field can be generated by a time-varying magnetic field via electromagnetic induction. The aim of this study was to investigate the factors that influence the transmembrane potential induced by a transverse field during magnetic stimulation. Using an unmyelinated axon model, we have provided an analytic expression for the transmembrane potential under spatially uniform, time-varying magnetic stimulation. Polarization of the axon was dependent on the properties of the magnetic field (i.e., orientation to the axon, magnitude, and frequency). Polarization of the axon was also dependent on its own geometrical (i.e., radius of the axon and thickness of the membrane) and electrical properties (i.e., conductivities and dielectric permittivities). Therefore, this article provides evidence that aside from optimal coil design, tissue properties may also play an important role in determining the efficacy of axonal activation under magnetic stimulation. The mathematical basis of this conclusion was discussed. The analytic solution can potentially be used to modify the activation function in current cable equations describing magnetic stimulation.

Optogenetic control of heart muscle in vitro and in vivo

Electrical stimulation is the standard technique for exploring electrical behavior of heart muscle, but this approach has considerable technical limitations. Here we report expression of the light-activated cation channel channelrhodopsin-2 for light-induced stimulation of heart muscle in vitro and in mice. This method enabled precise localized stimulation and constant prolonged depolarization of cardiomyocytes and cardiac tissue resulting in alterations of pacemaking, Ca(2+) homeostasis, electrical coupling and arrhythmogenic spontaneous extrabeats.

High defibrillation threshold: the science, signs and solutions

Defibrillation threshold (DFT) testing has traditionally been an integral part of implantable cardioverter defibrillator (ICD) implantation. With the increasing number of patients receiving ICDs, physicians are encountering high DFT more often than before. Tackling the problem of high DFT, warrants an in-depth understanding of the science of defibrillation including the key electrophysiological concepts and the underlying molecular mechanisms. Numerous factors have been implicated in the causation of high DFT. Due consideration to the past medical history, pharmacotherapy, laboratory data and cardiac imaging, help in assessing the pre-procedural risk for occurrence of high DFT. Drugs, procedural changes, type and location of ICD lead system are some of the key players in predicting DFT during implantation. In the event of encountering an unacceptably high DFT, we recommend to follow a step-wise algorithm. Ruling out procedural complications like pneumothorax and tamponade is imperative before embarking on a search for potentially reversible clinical or metabolic derangements. Finally, if these attempts fail, the electrophysiologist must choose from a wide range of options for device adjustment and system modification. Although this review article is meant to be a treatise on the science, signs and solutions for high DFT, it is bound by limitations of space and scope of the article.

Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.

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.

Tunnel propagation of postshock activations as a hypothesis for fibrillation induction and isoelectric window

Comprehensive understanding of the ventricular response to shocks is the approach most likely to succeed in reducing defibrillation threshold. We propose a new theory of shock-induced arrhythmogenesis that unifies all known aspects of the response of the heart to monophasic (MS) and biphasic (BS) shocks. The central hypothesis is that submerged "tunnel" propagation of postshock activations through shock-induced intramural excitable areas underlies fibrillation induction and the existence of isoelectric window. We conducted simulations of fibrillation induction using a realistic bidomain model of rabbit ventricles. Following pacing, MS and BS of various strengths/timings were delivered. The results demonstrated that, during the isoelectric window, an activation originated deep within the ventricular wall, arising from virtual electrodes; it then propagated fully intramurally through an excitable tunnel induced by the shock, until it emerged onto the epicardium, becoming the earliest-propagated postshock activation. Differences in shock outcomes for MS and BS were found to stem from the narrower BS intramural postshock excitable area, often resulting in conduction block, and the difference in the mechanisms of origin of the postshock activations, namely intramural virtual electrode-induced phase singularity for MS and virtual electrode-induced propagated graded response for BS. This study provides a novel analysis of the 3D mechanisms underlying the origin of postshock activations in the process of fibrillation induction by MS and BS and the existence of isoelectric window. The tunnel propagation hypothesis could open a new avenue for interventions exploration to achieve significantly lower defibrillation threshold.

Evaluating intramural virtual electrodes in the myocardial wedge preparation: simulations of experimental conditions

While defibrillation is the only means for prevention of sudden cardiac death, key aspects of the process, such as the intramural virtual electrodes (VEs), remain controversial. Experimental studies had attempted to assess intramural VEs by using wedge preparations and recording activity from the cut surface; however, applicability of this approach remains unclear. These studies found, surprisingly, that for strong shocks, the entire cut surface was negatively polarized, regardless of boundary conditions. The goal of this study is to examine, by means of bidomain simulations, whether VEs on the cut surface represent a good approximation to VEs in depth of the intact wall. Furthermore, we aim to explore mechanisms that could give rise to negative polarization on the cut surface. A model of wedge preparation was used, in which fiber orientation could be changed, and where the cut surface was subjected to permeable and impermeable boundary conditions. Small-scale mechanisms for polarization were also considered. To determine whether any distortions in the recorded VEs arise from averaging during optical mapping, a model of fluorescent recording was employed. The results indicate that, when an applied field is spatially uniform and impermeable boundary conditions are enforced, regardless of the fiber orientation VEs on the cut surface faithfully represent those intramurally, provided tissue properties are not altered by dissection. Results also demonstrate that VEs are sensitive to the conductive layer thickness above the cut surface. Finally, averaging during fluorescent recordings results in large negative VEs on the cut surface, but these do not arise from small-scale heterogeneities.

Role of intramural virtual electrodes in shock-induced activation of left ventricle: Optical measurements from the intact epicardial surface

BACKGROUND

According to one hypothesized mechanism of defibrillation, shocks directly excite the bulk of ventricular myocardium in the excitable state due to intramural virtual electrodes; however, this hypothesis has not been examined in intact myocardium.

OBJECTIVES

The purpose of this study was examine the role of intramural virtual electrodes in shock-induced activation of intact left ventricular (LV) tissue.

METHODS

Twelve isolated porcine LV preparations were stained with a transmembrane potential (V(m))-sensitive dye by two methods: (1) surface staining and (2) global staining via coronary perfusion. Shocks (E approximately 0.8-48 V/cm, duration = 10 ms) were applied across the wall from epicardium to endocardium during diastole via transparent electrodes. Shock-induced V(m) responses were measured optically from the intact epicardial surface after surface staining and global staining.

RESULTS

Surface-staining recordings demonstrated different V(m) responses to cathodal and anodal shocks. Whereas cathodal shocks caused depolarization and rapid activation of the epicardial surface, anodal shocks induced hyperpolarization and delayed surface activation. In contrast, global-staining V(m) responses to cathodal and anodal shocks were qualitatively similar. Both responses were characterized by activation with small latency and rapid propagation. Weak shocks of both polarities induced monotonic action potential upstrokes; stronger shocks induced nonmonotonic upstrokes with two rising phases at shock onset and end. Such features of global-staining V(m) responses as make activation of the epicardium by anodal shocks and the nonmonotonic action potential upstrokes can be explained by the presence of subepicardial intramural virtual electrodes.

CONCLUSION

These data suggest that shocks induce intramural virtual electrodes that directly excite LV tissue and account for the shape of optical V(m) responses recorded from the epicardial surface.

Defibrillation of the heart: insights into mechanisms from modelling studies

Despite its critical role in restoring cardiac rhythm and thus in saving human life, cardiac defibrillation remains poorly understood. Further mechanistic inquiry is hampered by the inability of presently available experimental techniques to resolve, with sufficient accuracy, electrical behaviour confined to the depth of the ventricles. The objective of this review article is to demonstrate that realistic 3-D simulations of the ventricular defibrillation process in close conjunction with experimental observations are capable of bringing a new level of understanding of the electrical events that ensue from the interaction between fibrillating myocardium and applied shock. The article does this by reviewing the results of two studies, one on vulnerability to electric shocks and another on defibrillation. An overview of the modelling tools used in these studies is also provided.

Imaging of cardiac movement using ratiometric and nonratiometric optical mapping: effects of ischemia and 2, 3-butaneodione monoxime

Transmembrane voltage-sensitive fluorescent dyes are used to study electrical activity in hearts. Green and red fluorescence emissions from di-4-ANEPPS excited with 488 nm light indicate both transmembrane voltage changes and heart movement. We have previously shown that the ratio, green fluorescence divided by red fluorescence, indicates the transmembrane voltage without effects of movement. Here we examine the feasibility of measuring the movement, which is useful for the study of cardiac function, by subtracting this ratiometric signal from the red or green fluorescence signal. The results of this subtraction show tissue movement and its relative changes during cardiac ischemia and perfusion with an electromechanical uncoupling agent. By incorporating the spatial variations in fluorescence intensity from the heart, tissue movement can be qualitatively mapped to examine relative changes, however, with limited ability to quantify absolute displacement. Since these maps are obtained simultaneously with corresponding transmembrane potentials, the method allows study of spatiotemporal cardiac movement patterns and their relationship to the action potential.

Cardiac microimpedance measurement in two-dimensional models using multisite interstitial stimulation

We analyzed central interstitial potential differences during multisite stimulation to assess the feasibility of using those recordings to measure cardiac microimpedances in multidimensional preparations. Because interstitial current injected and removed using electrodes with different proximities allows modulation of the portion of current crossing the membrane, we hypothesized that multisite interstitial stimulation would give rise to central interstitial potential differences that depend on intracellular and interstitial microimpedances, allowing measurement of those microimpedances. Simulations of multisite stimulation with fine and wide spacing in two-dimensional models that included dynamic membrane equations for guinea pig ventricular myocytes were performed to generate test data ( partial differentialphio). Isotropic interstitial and intracellular microimpedances were prescribed for one set of simulations, and anisotropic microimpedances with unequal ratios (intracellular to interstitial) along and across fibers were prescribed for another set of simulations. Microimpedance measurements were then obtained by making statistical comparisons between partial differentialphio values and interstitial potential differences from passive bidomain simulations (Deltaphio) in which a wide range of possible microimpedances were considered. Possible microimpedances were selected at 25% increments. After demonstrating the effectiveness of the overall method with microimpedance measurements using one-dimensional test data, we showed microimpedance measurements within 25% of prescribed values in isotropic and anisotropic models. Our findings suggest that development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.

Effect of plunge electrodes in active cardiac tissue with curving fibers

OBJECTIVES

Our goal is to determine if plunge electrodes change how the heart responds to electrical stimulation.

BACKGROUND

Several experiments designed to study the induction of a rotor in cardiac tissue have used plunge electrodes to measure the transmural potential. It is our hypothesis that these electrodes may have affected the electrical response of the tissue to a shock.

METHODS

We previously have shown that a single plunge electrode in two-dimensional, passive cardiac tissue induces a significant transmembrane potential when stimulated by a large shock. In this study, we expand our simulation to include an array of nine electrodes in active tissue with curving fibers. We compare the thresholds for rotor induction in tissue with and without electrodes by initiating a planar S1 wavefront and then stimulating the tissue at different intervals with a uniform S2 electric field perpendicular to S1. In tissue without plunge electrodes, virtual electrode polarization due to the curving fibers is generally widespread over the entire tissue, whereas polarization tends to be localized around the electrodes in tissue including them.

RESULTS

Our results show that at some S1-S2 intervals, the presence of plunge electrodes can result in reentry when it otherwise would not be possible. For other S1-S2 intervals, such as during the vulnerable period when the reentry threshold is at a minimum, the induction of reentry is unaffected by the presence of plunge electrodes.

CONCLUSIONS

Plunge electrodes can play an important role during the stimulation of cardiac tissue, but this is highly dependent on the chosen S1-S2 interval.

Differences between left and right ventricular chamber geometry affect cardiac vulnerability to electric shocks

Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have been extensively documented, the contribution of ventricular anatomy to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been quantified; this is caused by lack of experimental methodology capable of mapping 3-D electrical activity. The goal of this study was to use optical imaging experiments and 3-D bidomain simulations to investigate the role of structural differences between left and right ventricles in vulnerability to electric shocks in rabbit hearts. The ventricles were paced apically, and uniform-field, truncated-exponential, monophasic shocks of reversed polarity were applied over a range of coupling intervals (CIs) in experiment and model. Experiments and simulations revealed that reversing the direction of externally-applied field (RV- or LV- shocks) alters the shape of the vulnerability area (VA), the 2-D grid encompassing episodes of arrhythmia induction. For RV- shocks, VA was nearly rectangular indicating little dependence of postshock arrhythmogenesis on CI. For LV- shocks, the probability of arrhythmia induction was higher for longer than for shorter CIs. The 3-D simulations demonstrated that these effects stem from the fact that reversal of field direction results in relocation of the main postshock excitable area from LV wall (RV- shocks) to septum (LV- shocks). Furthermore, the effect of septal (but not LV) excitable area in postshock propagation was found to strongly depend on preshock state. Knowledge regarding the location of the main postshock excitable area within the 3-D ventricular volume could be important for improving defibrillation efficacy.

Use of translucent indium tin oxide to measure stimulatory effects of a passive conductor during field stimulation of rabbit hearts

Biomathematical models and experiments have indicated that passive extracellular conductors influence field stimulation. Because metallic conductors prevent optical mapping under the conductor, we have evaluated a passive translucent indium tin oxide (ITO) thin-film conductor to allow mapping of transmembrane potential (V(m)) and stimulatory current under the conductor. A 1-cm ITO disk was patterned photolithographically and positioned between 0.3-cm(2) mesh shock electrodes on the ventricular epicardium of isolated perfused rabbit hearts stained with 4-{2-[6-(dibutylamino)-2-naphthylenal]ethenyl}-1-(3-sulfopropyl)-, hydroxide, inner salt (di-4-ANEPPS). For a 1-A, 10-ms shock during the action potential plateau, optical maps from fluorescence collected using emission ratiometry (excitation at 488 nm and emissions at 510-570 and >590 nm) indicated that the disk altered V(m) by as much as the height of an action potential. DeltaV(m) became more positive near the edge of the disk, where the ITO conductance gradient was parallel to applied current, and more negative near the opposite edge, where the gradient was not parallel to current. For diastolic shocks, the disk expedited membrane excitation at the sites of positive DeltaV(m) in the heart and in a cardiac model with realistic ITO disk surface and interfacial conductances. Optical maps of ITO transmittance and the model indicated that the disk introduced anodal and cathodal stimulatory current at opposite edges of the disk. Thus ITO allows study of the stimulatory effects of a passive conductor in an electric field.

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.

The sensitivity of the heart to static magnetic fields

Static magnetic fields induce flow potentials in arterial flows in and around the heart, that have been detected as distortions in the ECG. The resultant currents flowing through the myocardium could alter the rate or rhythm of the heart. No such changes have been seen in animal experiments, or with humans, in static fields up to 8 T. The possible effects of such currents induced by fields larger than 8 T on cardiac pacemaker rate, and arrhythmogenesis are reviewed, using virtual cardiac tissues-computational models of cardiac electrophysiology. Arrhythmogenesis can be by the initiation of ectopic beats, or by re-entry, whose probability of occurrence is increased by any increase in the electrical heterogeneity, in particular, the action potential duration heterogeneity of the ventricle. Focal ectopic activity would be readily detectable, but since re-entrant arrhythmias are very rare events, even a large increase in their probability of occurrence still leaves them unlikely to be observed. Both of these two arrhythmogenic mechanisms would show a steep sigmoidal, or threshold dependence on induced current intensity, with the threshold for increasing the vulnerability to re-entry less than the threshold for initiating activity. Failure to observe them at fields less than 8 T provides only a lower bound for any threshold for arrhythmogenesis.

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.

Epicardial fiber organization in swine right ventricle and its impact on propagation

Fiber organization is important for myocardial excitation and contraction. It can be a major factor in arrhythmogenesis and current distribution during defibrillation shocks. In this study, we report the discovery of a previously undetected thin epicardial layer in swine right ventricle (RV) with distinctly different fiber orientation, which significantly affects epicardial propagation. Experiments were conducted in isolated coronary-perfused right ventricular free wall preparations (n=8) stained with the voltage-sensitive dye di-4-ANEPPS. Optical signals were recorded from the epicardium with a CCD video camera at 800 fps. Preparations were sectioned parallel to the epicardial surface with a resolution of 50 mum or better. To link the histological data with the observed activation patterns, resulting fiber angles were introduced into a 3D computer model to simulate the electrical activation and voltage-dependent optical signals. In all preparations, we detected a thin epicardial layer with almost no depth-dependent fiber rotation. The thickness of this layer (z(0)) varied from 110 to 930 microm. At the boundary of this layer, we observed an abrupt change in fiber angle by 64+/-13 degrees followed by a gradual fiber rotation in the underlying layers. In preparations with z(0) <700 microm, optical mapping during epicardial stimulation revealed unusual diamond- and rectangular-shaped activation fronts with two axes of fast conduction. Computer simulations accurately predicted the features of the experimentally recorded activation fronts. The free wall of swine RV has a thin epicardial layer with distinctly different fiber orientation, which can significantly affect propagation and give rise to unusually shaped activation fronts. This is important for understanding electrical propagation in the heart, and further refines the existing knowledge of myocardial fiber architecture.

Effect of Rapid Biphasic Shock Subpulse Switching on Ventricular Defibrillation Thresholds

INTRODUCTION

The aim of this study was to demonstrate that significant reductions in defibrillation threshold (DFT) can be achieved by rapidly switching defibrillation pulses within an overall biphasic envelope between multiple endovascular electrode sets.

METHODS AND RESULTS

Defibrillation electrodes were implanted in four locations in nine anesthetized swine (41.7 +/- 8.7 kg). Electrodes were implanted into the right ventricular apex (RV), the superior vena cava (SVC), over the left pectoral region as a "hot can" (Can), and within the middle cardiac vein on the posterior left ventricular (LV) surface. The 50% DFT (level for which 50% of delivered shocks successfully defibrillated) for control shocks (7-ms first phase, 0.5-ms interpulse period, 4-ms second phase, RV- --> SVC+ + Can+) were determined to have energy of 20.5 +/- 5.5 J (mean +/- SD). Mean 50% DFTs were also determined for waveforms that split each phase of the same overall biphasic waveform between various electrode sets. Each phase was divided into 2, 3, 4, or 6 subpulses, the defibrillation shock was sequentially delivered to multiple electrode sets, and DFTs were determined (11.9 +/- 4.8 J, 11.7 +/- 2.9 J, 17.9 +/- 8.7 J, 16.7 +/- 6.1 J, respectively). DFT energy was statistically lower than the control (Wilcoxon sign rank test; P < 0.05) when each phase was divided into 2 or 3 subpulses.

CONCLUSION

Rapid shock switching within an overall biphasic waveform between electrode sets including an electrode in the middle cardiac vein potentially can lower DFT energy by 40% or more.

Optical mapping of transmural activation induced by electrical shocks in isolated left ventricular wall wedge preparations

INTRODUCTION

It is believed that electrical shocks interrupt fibrillation by directly stimulating the bulk of ventricular myocardium in excitable states, but how shocks activate intramural tissue layers is not known. In this study, Vm responses and transmural activation patterns induced by shocks during diastole were measured in isolated coronary perfused preparations of porcine left ventricle.

METHODS AND RESULTS

Rectangular shocks (duration = 10 ms; field strength, E = 1-44 V/cm) were applied across preparations (thickness = 14.9 +/- 2.5 mm, n = 9) via large mesh electrodes during diastole or action potential (AP) plateau. Vm responses at the transmural surface were measured using optical mapping technique (resolution = 1.2 mm). Depending on shock strength, three types of Vm responses were observed. (1) Weak shocks (E approximately 1-4 V/cm) applied in diastole induced APs with simple monophasic upstrokes. The latency and time of transmural activation (TTA) rapidly decreased with increasing shock strength. Earliest activation occurred predominantly at the cathodal side of preparations in the areas that exhibited maximal DeltaVm during AP plateau. (2) Intermediate shocks (E approximately 4-23 V/cm) induced monophasic and biphasic upstrokes that were paralleled with predominantly negative plateau DeltaVm. Activation was initiated at multiple transmural sites and rapidly spread across the myocardial wall (TTA = 0.6 +/- 0.2 ms). (3) Very strong shocks (E approximately 23-44 V/cm) could cause triphasic upstrokes, likely reflecting occurrence of membrane electroporation, and delayed activation (TTA = 6.7 +/- 3.8 ms) at sites of largest negative plateau DeltaVm.

CONCLUSION

Shocks applied during diastole cause direct and rapid (within 1 ms) activation of ventricular bulk over a wide range of shock strengths, supporting the excitatory hypothesis of defibrillation. Very strong shocks can cause multiphasic Vm responses and delayed activation.

Field Stimulation of 2-D Sheets of Excitable Tissue

This paper develops equations for the transmembrane potentials (Vm) that occur in two-dimensional (2-D) sheets of tissue in response to field stimulation from an electrode near but not on the surface of the tissue. Comparison of results with those for one dimension shows that an additional term is present in the 2-D equations that influences the evolution of Vm in the interval between the end of the stimulus and the active propagation that may follow. The results provide an analytical framework for understanding Vm in response to field stimulation in two dimensions, both during the tissue's critical linear phase and thereafter.

Defibrillation threshold computed from normal and supernormal excitable cardiac tissue

The applicability of the 'upper limit of vulnerability' defibrillation theory was evaluated in models of cardiac tissue in which spatial changes within cells are retained. Defibrillation thresholds were computed from two models of cardiac tissue: one with, and one without, a supernormal period, and compared with those predicted by the theory. In the cardiac virtual tissue with a monotonic recovery of excitation - a normal refractory period, the computed defibrillation threshold is consistent with the prediction of the 'upper limit of vulnerability' defibrillation theory. However, in cardiac tissue with non-monotonic recovery of excitation - a supernormal period, the computed defibrillation threshold is significantly less than the theory prediction.

Postshock arrhythmogenesis in a slice of the canine heart

INTRODUCTION

Recent evidence has demonstrated that defibrillation shocks terminate or reset reentrant activity in the myocardium through the generation of virtual electrode polarization (VEP). Previous research has revealed that the shock establishes phase singularities (PSs) in the tissue via the VEP mechanism. The aim of this study was to examine, as a function of shock strength and electrode configuration, the relationship between end-shock PSs and the reentrant circuits established after failed defibrillation attempts.

METHODS AND RESULTS

The study uses a complex three-dimensional finite-element bidomain model of a slice of the canine heart characterized by realistic geometry and fiber architecture and undergoing a single scroll wave. Defibrillation shocks of increasing strength are delivered through three different electrode configurations. The results demonstrated that >98% of all PSs have a lifetime of half a reentrant cycle or less. Stronger shocks result in a faster rate of annihilation of postshock PSs. For failed shocks, the surviving PSs underlie the activity of one or more scroll waves, which remain stationary in the slice. For all electrode configurations tested, the increase in shock strength leads to a rapid initial increase in the number of postshock reentries followed by a slower decrease; similar behavior is observed with regard to end-shock PSs.

CONCLUSION

These results present new evidence regarding the mechanisms underlying failure of defibrillation shocks.

Vortex cordis as a mechanism of postshock activation: arrhythmia induction study using a bidomain model

INTRODUCTION

The ventricular apex has a helical arrangement of myocardial fibers called the "vortex cordis." Experimental studies have demonstrated that the first postshock activation originates from the ventricular apex, regardless of the electrical shock outcome; however, the related underlying mechanism is unclear. We hypothesized that the vortex cordis contributes to the initiation of postshock activation. To clarify this issue, we numerically studied the transmembrane potential distribution produced by various electrical shocks.

METHODS AND RESULTS

Using an active membrane model, we simulated a two-dimensional bidomain myocardial tissue incorporating a typical fiber orientation of the vortex cordis. Monophasic or biphasic shock was delivered via two line electrodes located at opposite tissue borders. Transmembrane potential distribution during the monophasic shock at the center of the vortex cordis showed a gradient high enough to initiate postshock activation. The postshock activation from the center of the vortex cordis was not suppressed, regardless of the initiation of spiral wave reentry. Spiral wave reentry was induced by the monophasic shock when the center area of the vortex cordis was partially excited by the nonuniform virtual electrode polarization. Postshock activation following the biphasic shock also originated from the center of the vortex cordis, but it tended to be suppressed due to the narrower excitable gap around the center of the vortex cordis. The electroporation effect, which was maximal at the center of the vortex cordis, is another possible mechanism of postshock activation.

CONCLUSION

Our simulations suggest that the vortex cordis may cause postshock activation.

The effects of electrode position on the excitability of rat atria during postnatal development

Cardiac excitability is determined by the direction of the electric field, which is defined by the positioning of electrodes. However, important morphological and physiological modifications that happen during the postnatal development of the heart may affect the cardiac threshold. In this work we have evaluated the effect of electrode positioning on the excitability threshold of isolated Wistar rat atria (left auricles) during postnatal development. This was performed by determining the parameters of strength-duration curves for stimuli (rheobase, chronaxie and normalized minimum pulse energy) of atria from rats at ages (days) 5, 15, 30, 60, 90 and 120. These parameters were determined using electric field stimulation in four different orientations (apex-base, base-apex, left-right and right-left). Atrial rheobase decreased by 1.5- to 4-fold with animal age and was altered by electric field orientation in a diversified way, whereas atrial chronaxie increased only with animal age. The minimum pulse energy decreased two- to nine-fold with ageing. This was mainly due to rheobase dependence with electric field direction. We showed that the appropriate cardiac stimulation depends on the effects of three combined factors (pulse parameters, electrode position and animal age) on the atrial tissue excitability.

Artifacts, assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart

Insidious experimental artifacts and invalid theoretical assumptions complicate the comparison of numerical predictions and observed data. Such difficulties are particularly troublesome when studying electrical stimulation of the heart. During unipolar stimulation of cardiac tissue, the artifacts include nonlinearity of membrane dyes, optical signals blocked by the stimulating electrode, averaging of optical signals with depth, lateral averaging of optical signals, limitations of the current source, and the use of excitation-contraction uncouplers. The assumptions involve electroporation, membrane models, electrode size, the perfusing bath, incorrect model parameters, the applicability of a continuum model, and tissue damage. Comparisons of theory and experiment during far-field stimulation are limited by many of these same factors, plus artifacts from plunge and epicardial recording electrodes and assumptions about the fiber angle at an insulating boundary. These pitfalls must be overcome in order to understand quantitatively how the heart responds to an electrical stimulus. (c) 2002 American Institute of Physics.

Shock-induced arrhythmogenesis in the myocardium

The focus of this article is the investigation of the electrical behavior of the normal myocardium following the delivery of high-strength defibrillation shocks. To achieve its goal, the study employs a complex three-dimensional defibrillation model of a slice of the canine heart characterized with realistic geometry and fiber architecture. Defibrillation shocks of various strengths and electrode configurations are delivered to the model preparation in which a sustained ventricular tachycardia is induced. Instead of analyzing the post-shock electrical events as progressions of transmembrane potential maps, the study examines the evolution of the postshock phase singularities (PSs) which represent the organizing centers of reentry. The simulation results demonstrate that the shock induces numerous PSs the majority of which vanish before the reentrant wavefronts associated with them complete half of a single rotation. Failed shocks are characterized with one or more PSs that survive the initial period of PS annihilation to establish a new postshock arrhythmia. The increase in shock strength results in an overall decrease of the number of PSs that survive over 200 ms after the end of the shock; however, the exact behavior of the PSs is strongly dependent on the shock electrode configuration. (c) 2002 American Institute of Physics.

Cardiac microstructure: implications for electrical propagation and defibrillation in the heart

Our understanding of the electrophysiological properties of the heart is incomplete. We have investigated two issues that are fundamental to advancing that understanding. First, there has been widespread debate over the mechanisms by which an externally applied shock can influence a sufficient volume of heart tissue to terminate cardiac fibrillation. Second, it has been uncertain whether cardiac tissue should be viewed as an electrically orthotropic structure, or whether its electrical properties are, in fact, isotropic in the plane orthogonal to myofiber direction. In the present study, a computer model that incorporates a detailed three-dimensional representation of cardiac muscular architecture is used to investigate these issues. We describe a bidomain model of electrical propagation solved in a discontinuous domain that accurately represents the microstructure of a transmural block of rat left ventricle. From analysis of the model results, we conclude that (1) the laminar organization of myocytes determines unique electrical properties in three microstructurally defined directions at any point in the ventricular wall of the heart, and (2) interlaminar clefts between layers of cardiomyocytes provide a substrate for bulk activation of the ventricles during defibrillation.

Spatial heterogeneity of transmembrane potential responses of single guinea-pig cardiac cells during electric field stimulation

Changes in transmembrane voltage (V(m)) of cardiac cells during electric field stimulation have a complex spatial- and time-dependent behaviour that differs significantly from electrical stimulation of space-clamped membranes by current pulses. A multisite optical mapping system was used to obtain 17 or 25 microm resolution maps of V(m) along the long axis of guinea-pig ventricular cells (n = 57) stained with voltage-sensitive dye (di-8-ANEPPS) and stimulated longitudinally with uniform electric field (2, 5 or 10 ms, 3-62 V cm(-1)) pulses (n = 201). The initial polarizations of V(m) responses (V(mr)) varied linearly along the cell length and reversed symmetrically upon field reversal. The remainder of the V(m) responses had parallel time courses among the recording sites, revealing a common time-varying signal component (V(ms)). V(ms) was depolarizing for pulses during rest and hyperpolarizing for pulses during the early plateau phase. V(ms) varied in amplitude and time course with increasing pulse amplitude. Four types of plateau response were observed, with transition points between the different responses occurring when the maximum polarization at the ends of the cell reached values estimated as 60, 110 and 220 mV. Among the cells that had a polarization change of > 200 mV at their ends (for fields > 45 V cm(-1)), some (n = 17/25) had non-parallel time courses among V(m) recordings of the various sites. This implied development of an intracellular field (E(i)) that was found to increase exponentially with time (tau = 7.2 +/- 3.2 ms). Theoretical considerations suggest that V(ms) represents the intracellular potential (phi(i)) as well as the average polarization of the cell, and that V(mr) is the manifestation of the extracellular potential gradient resulting from the field stimulus. For cells undergoing field stimulation, phi(i) acts as the cellular physiological state variable and substitutes for V(m), which is the customary variable for space-clamped membranes.

Optical mapping of arrhythmias induced by strong electrical shocks in myocyte cultures

Strong electrical shocks can induce arrhythmias, which might explain why shocks fail to defibrillate. In this work, the localization of arrhythmia source and the relationship with local changes of transmembrane potential (V(m)) were determined in geometrically defined cell cultures using optical mapping technique. Uniform-field shocks with strength (E) of 10 to 50 V/cm were applied across cell strands with width of 0.2 and 0.8 mm. The threshold for arrhythmia induction was dependent on the strand width: in the 0.8- and 0.2-mm strands, arrhythmias were induced at E>/=20.6+/-1.8 V/cm (n=8) and E>/=30.3+/-1.8 V/cm (n=8), respectively. At the same shock strength, the arrhythmia rate and duration were larger in the wider strands. During shocks that induced arrhythmias, the V(m) waveforms on the anodal side revealed a positive V(m) shift that followed the initial large hyperpolarization and postshock elevation of the diastolic V(m). These V(m) changes were absent during failed shocks. To determine the localization of the arrhythmia source, arrhythmias were induced in narrow cell strands containing regions of local expansion. Optical mapping of the first extrabeat with a coupling interval of 315+/-60 ms revealed that in the majority of cases (9 out of 13) the source of arrhythmias was localized in the areas of shock-induced hyperpolarization. Thus, (1) induction of postshock arrhythmias, their rate, and their duration strongly depend on the tissue structure; (2) arrhythmia induction coincides with the appearance of a positive V(m) shift in the areas of hyperpolarization; and (3) the source of postshock arrhythmias is located in the areas of shock-induced hyperpolarization.