Electrical stimulation of cardiac tissue: a bidomain model with active membrane properties

A multi-scale simulation of retinal physiology

We present a detailed physiological model of the (human) retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system of partial differential equations based on the mathematical framework of the bi-domain equations, which we have generalized to account for multiple cell-types. We discretize in space with non-uniform finite differences and step through time with a custom adaptive time-stepper that employs a backward differentiation formula and an inexact Newton method. A refinement study confirms the accuracy and efficiency of our numerical method. Numerical simulations using the model compare favorably with experimental findings, such as desensitization to light stimuli and calcium buffering in photoreceptors. Other numerical simulations suggest an interplay between photoreceptor gap junctions and inner segment, but not outer segment, calcium concentration. Applications of this model and simulation include analysis of retinal calcium imaging experiments, the design of electroretinograms, the design of visual prosthetics, and studies of ephaptic coupling within the retina.

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.

Conceptual Intra-Cardiac Electrode Configurations That Facilitate Directional Cardiac Stimulation for Optimal Electrotherapy

OBJECTIVE

Electrotherapy remains the most effective direct therapy against lethal cardiac arrhythmias. When an arrhythmic event is sensed, either strong electric shocks or controlled rapid pacing is automatically applied directly to the heart via an implanted cardioverter defibrillator (ICDs). Despite their success, ICDs remain a highly non-optimal therapy: the strong shocks required for defibrillation cause significant extra-cardiac stimulation, resulting in pain and long-term tissue damage, and can also limit battery life. When used in anti-tachycardia pacing mode, ICDs are also often ineffective, as the pacing electrode can be far away from the centre of the arrhythmia, making it hard for the paced wave to interrupt and terminate it.

METHODS

In this paper, we present two conceptual intra-cardiac directional electrode configurations in silico based on novel arrangements of pairs of positive-negative electrodes. Both configurations have the potential to cause preferential excitation on specific regions of the heart.

RESULTS

We demonstrate how the properties of the induced field varies spatially around the electrodes and how it depends upon the specific arrangements of dipole electrode pairs. The results show that when tested within anatomically-realistic rabbit ventricular models, both electrode configurations produce strong virtual electrodes on the targeted endocardial surfaces, with weaker virtual electrodes produced elsewhere.

CONCLUSIONS

The proposed electrode configurations may facilitate targeted far-field anti-tachycardia pacing and/or defibrillation, which may be useful in cases where conventional anti-tachycardia pacing fails. In addition, the conceptual electrode designs intrinsically confine the electric field to the immediate vicinity of the electrodes, and may, thus, minimize pain due to unnecessary extra-cardiac stimulation.

Non-selective His bundle pacing with a biphasic waveform: enhancing septal resynchronization

Aims

His bundle pacing has shown to prevent detrimental effects from right ventricular apical pacing (RVA) and proved to resynchronize many conduction disturbances cases. However, the extent of His bundle pacing resynchronization is limited. An optimized stimulation waveform could expand this limit when implemented in His bundle pacing sets. In this work, we temporarily implemented RVA and Non-selective His bundle pacing with a biphasic anodal-first waveform (AF-nHB) and compared their effects against sinus rhythm (SR).

Methods and results

Fifteen patients referred for electrophysiologic study with conduction disturbances, cardiomyopathy and ejection fraction below 35% were enrolled for the study. The following acute parameters were measured: QRS duration, left ventricular activation (RLVT), time of isovolumic contraction (IVCT), ejection fraction (EF), and dP/dtmax. QRS duration and RLVT decreased markedly under AF-nHB (SR: 169 ± 34 ms vs. nHB: 116 ± 31 ms, P < 0.0005) while RVA significantly increased QRS duration (SR: 169 ms vs. RVA: 198 ms, P < 0.05) and did not change RLVT (P = NS). Consistently, IVCT moderately decreased under AF-nHB (SR: 238 ms vs. RVA: 184 ms, P < 0.05 vs. SR) and dP/dtmax showed a 93.35 [mmHg] average increase under AF-nHB against SR. Also, T-wave inversions were observed during AF-nHB immediately after SR and RVA pacing suggesting the occurrence of cardiac memory.

Conclusions

AF-nHB corrected bundle branch blocks in patients with severe conduction disturbances, even in those with dilated cardiomiopathy, outstanding from RVA. Also, the occurrence of cardiac memory during AF-nHB turned up as an observational finding of this study.

Effects of biphasic and monophasic electrical stimulation on mitochondrial dynamics, cell apoptosis, and cell proliferation

Currently, electrical stimulation (ES) is used to induce changes in various tissues and cellular processes, but its effects on mitochondrial dynamics and mechanisms are unknown. The aim of this study was to compare the effects of monophasic and biphasic, anodal, and cathodal ES on apoptosis, proliferation, and mitochondrial dynamics in neuroblastoma SH-SY5Y cells. Cells were cultured and treated with ES. Alamar blue assay was performed to measure cell proliferation. The proteins expression of apoptotic-related proteins Bcl-2 associated X (Bax), B cell lymphoma 2 (Bcl-2), optic-atrophy-1 (OPA1), mitofusin2 (Mfn2), phosphorylated dynamin-related protein 1 at serine 616 (p-DRP1), and total dynamin-related protein 1 (Total-DRP1) were also determined. The results showed that monophasic anodal and biphasic anodal/cathodal (Bi Anod) ES for 1 hr at 125 pulses per minute (2.0 Hz) produced the most significant increase in cell proliferation. In addition, monophasic anodal and Bi Anod ES treated cells displayed a significant increase in the levels of anti-apoptotic protein Bcl-2, whereas the Bax levels were not changed. Moreover, the levels of Mfn2 were increased in the cells treated by Bi Anod, and OPA1 was increased by monophasic anodal and Bi Anod ES, indicating increased mitochondrial fusion in these ES-treated cells. However, the levels of mitochondrial fission indicated by DRP1 remained unchanged compared with non-stimulated cells. These findings were confirmed through visualization of mitochondria using Mitotracker Deep Red, demonstrating that monophasic anodal and Bi Anod ES could induce pro-survival effects in SH-SY5Y cells through increasing cell proliferation and mitochondrial fusion. Future research is needed to validate these findings for the clinical application of monophasic anodal and Bi Anod ES.

Toward a More Efficient Implementation of Antifibrillation Pacing

We devise a methodology to determine an optimal pattern of inputs to synchronize firing patterns of cardiac cells which only requires the ability to measure action potential durations in individual cells. In numerical bidomain simulations, the resulting synchronizing inputs are shown to terminate spiral waves with a higher probability than comparable inputs that do not synchronize the cells as strongly. These results suggest that designing stimuli which promote synchronization in cardiac tissue could improve the success rate of defibrillation, and point towards novel strategies for optimizing antifibrillation pacing.

A patient-specific model of virtual ablation for atrial fibrillation

The purpose of this study was to propose a patient-specific model of atrial fibrillation (AF) and apply it to virtual radiofrequency ablation (RFA). We obtained patient-specific geometries of the left atrium (LA) from CT data and constructed three-dimensional (3D) simulation models. A bidomain Courtemanche model was used to simulate the 3D electric waves on the LA surface, and an S1-S2 protocol was applied to induce AF in the model. To identify scar areas in the models, we converted clinically measured voltage data on the LA surface to the scar maps of the simulation model. Then, after initiation of AF, we applied the virtual ablation scheme to the model and investigated whether the AF was terminated by the scheme. The computed results of AF and ablation were similar to those of clinical observation, providing a clinically important simulation method for preclinical virtual trials of AF treatment.

A spatially distributed computational model of brain cellular metabolism

This paper develops a three-dimensional spatially distributed model of brain cellular metabolism and investigates how the locus of the synaptic activity in reference to the capillaries and diffusion affects the behavior of the model, a type of analysis which is impossible to carry out in spatially lumped models, which are shown to be consistent spatially averaged approximations of the distributed model. To avoid a geometrically detailed modeling of the complex structure of the tissue consisting of different cell types and the extracellular space, the distributed model is based on a novel multi-domain formulation of reaction-diffusion equations, accounting also for separate mitochondria. The model reduction relating the spatially distributed model and lower dimensional reduced models, including the well-mixed spatially lumped compartment model, is carefully explained. We illustrate the effects of losing the spatial resolution with a computed example which is based on a reduced one-dimensional distributed radial model, and look into how the model behaves when the locus of the synaptic activity in reference to the capillaries is changed. By averaging the fluxes and concentrations in the distributed radial model to correspond to quantities in a lumped model, and further by estimating the parameters in the lumped, we conclude that varying the locus of the synaptic activity in reference to the capillaries alters significantly the lumped model parameters. This observation seems to be consequential for parameter estimation procedures from data when the spatial resolution is insufficient to determine the locus of the activity, indicating that the model uncertainty is an inherent feature of lumped models.

Modelling extracellular electrical stimulation: part 4. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

OBJECTIVE

The objective of this paper is to present a concrete application of the cellular composite model for calculating the membrane potential, described in an accompanying paper.

APPROACH

A composite model that is used to determine the membrane potential for both longitudinal and transverse modes of stimulation is demonstrated.

MAIN RESULTS

Two extreme limits of the model, near-field and far-field for an electrode close to or distant from a neuron, respectively, are derived in this paper. Results for typical neural tissue are compared using the composite, near-field and far-field models as well as the standard isotropic volume conductor model. The self-consistency of the composite model, its spatial profile response and the extracellular potential time behaviour are presented. The magnitudes of the longitudinal and transverse components for different values of electrode-neurite separations are compared.

SIGNIFICANCE

The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

Intracellular calcium and the mechanism of the dip in the anodal strength-interval curve in cardiac tissue

BACKGROUND

The strength-interval (SI) curve is an important measure of refractoriness in cardiac tissue. The anodal SI curve contains a "dip" in which the S2 threshold increases with interval. Two explanations exist for this dip: (1) electrotonic interaction between regions of depolarization and hyperpolarization; and (2) the sodium-calcium exchange (NCX) current. The goal of this study is to use mathematical modeling to determine which explanation is correct.

METHODS AND RESULTS

The bidomain model represents cardiac tissue and the Luo-Rudy model describes the active membrane. The SI curve is determined by applying a threshold stimulus at different time intervals after a previous action potential. During space-clamped and equal-anisotropy-ratios simulations, anodal excitation does not occur. During unequal-anisotropy-ratios simulations, electrotonic currents, not membrane currents, are present during the few milliseconds before excitation. The dip disappears with no NCX current, but is present with 50% or 75% reduction of it. The calcium-induced-calcium-release (CICR) current has little effect on the dip.

CONCLUSIONS

These results indicate that neither the NCX nor the CICR current is responsible for the dip in the anodal SI curve. It is caused by the electrotonic interaction between regions of depolarization and hyperpolarization following the S2 stimulus.

Current approaches to model extracellular electrical neural microstimulation

Nowadays, high-density microelectrode arrays provide unprecedented possibilities to precisely activate spatially well-controlled central nervous system (CNS) areas. However, this requires optimizing stimulating devices, which in turn requires a good understanding of the effects of microstimulation on cells and tissues. In this context, modeling approaches provide flexible ways to predict the outcome of electrical stimulation in terms of CNS activation. In this paper, we present state-of-the-art modeling methods with sufficient details to allow the reader to rapidly build numerical models of neuronal extracellular microstimulation. These include (1) the computation of the electrical potential field created by the stimulation in the tissue, and (2) the response of a target neuron to this field. Two main approaches are described: First we describe the classical hybrid approach that combines the finite element modeling of the potential field with the calculation of the neuron's response in a cable equation framework (compartmentalized neuron models). Then, we present a “whole finite element” approach allowing the simultaneous calculation of the extracellular and intracellular potentials, by representing the neuronal membrane with a thin-film approximation. This approach was previously introduced in the frame of neural recording, but has never been implemented to determine the effect of extracellular stimulation on the neural response at a sub-compartment level. Here, we show on an example that the latter modeling scheme can reveal important sub-compartment behavior of the neural membrane that cannot be resolved using the hybrid approach. The goal of this paper is also to describe in detail the practical implementation of these methods to allow the reader to easily build new models using standard software packages. These modeling paradigms, depending on the situation, should help build more efficient high-density neural prostheses for CNS rehabilitation.

The strength-interval curve in cardiac tissue

The bidomain model describes the electrical properties of cardiac tissue and is often used to simulate the response of the heart to an electric shock. The strength-interval curve summarizes how refractory tissue is excited. This paper analyzes calculations of the strength-interval curve when a stimulus is applied through a unipolar electrode. In particular, the bidomain model is used to clarify why the cathodal and anodal strength-interval curves are different, and what the mechanism of the “dip” in the anodal strength-interval curve is.

Stimulus intensity in left ventricular leads and response to cardiac resynchronization therapy

Background

Increased left ventricular (LV) stimulus intensity has been shown to improve conduction velocity and cardiac output. However, high-output pacing would shorten device battery life. Our prospective trial analyzed the clinical effects of high- versus low-output LV pacing.

Methods and Results

Thirty-nine patients undergoing initial cardiac resynchronization therapy device implantation with bipolar LV leads were assigned to 3 months of either high-output LV pacing (Hi) or low-output LV pacing (Lo) in a randomized, blinded crossover fashion. Hi and Lo settings were determined with a rigorous intraoperative protocol specific to each patient. Clinical and echocardiographic data were obtained at randomization, at 3 months, and a subsequent 3 months after crossover. Mean age was 66.4±9.8 years, and mean QRS duration was 159.3±23.1 ms. Compared to baseline, both arms had significant improvements in Minnesota Living With Heart Failure score (given as mean [95% confidence interval]) (baseline versus Lo: 43.3 [35.5 to 51.1] versus 21.3 [14.6 to 28.0], P<0.01; baseline versus Hi: 43.3 [35.5 to 51.1] versus 23.6 [16.1 to 31.1], P<0.01) and 6-minute walk distance (baseline versus Lo: 692 ft [581 to 804] versus 995 ft [876 to 1114], P<0.01; baseline versus Hi: 699 ft [585 to 813] versus 982 ft [857 to 1106], P<0.01). Although both Hi and Lo arms had some echocardiographic parameters that significantly improved compared to baseline (baseline end-diastolic diameter 5.7 cm [5.5 to 6.0] versus Lo 5.5 cm [5.1 to 5.8], P<0.01; baseline end-systolic diameter 4.9 cm [4.6 to 5.3] versus Hi 4.7 cm [4.3 to 5.0], P<0.05), there were no significant differences observed when comparing the Hi- versus Lo-output arms.

Conclusions

Low-output LV pacing with a relatively narrow safety margin above capture threshold affords significant improvement from baseline and is clinically equivalent to high-output LV pacing. These data support a strategy of minimizing the programmed LV safety margin to increase battery life in cardiac resynchronization therapy devices.

Clinical Trial Registration Information

URL: http://www.clinicaltrials.gov. Unique identifier: NCT01060449

Current steering for high resolution retinal implants

To significantly increase the resolution achievable by a retinal prosthesis without requiring additional electrodes, a current steering technique could be utilized. In this study, a finite element model was constructed to analyze the local concentrations of charge carrying ions within a saline bath due to concurrent stimulation from two electrodes surrounded by a hexagonal arrangement of return electrodes. By altering the return pathways, tissue activation and identification of unique stimulation patterns is possible. Ag/Ag-Cl electrodes and a voltage controlled current source were developed to validate the finite element model, with the model accurately predicting saline bath measurements. The average error in the returned currents between the finite element model and experimental results was 2% relative to the stimulus current.

Simulating a dual-array electrode configuration to investigate the influence of skeletal muscle fatigue following functional electrical stimulation

A novel, anatomically-accurate model of a tibialis anterior muscle is used to investigate the electro-physiological properties of denervated muscles following functional electrical stimulation. The model includes a state-of-the-art description of cell electro-physiology. The main objective of this work is to develop a computational framework capable of predicting the effects of different stimulation trains and electrode configurations on the excitability and fatigue of skeletal muscle tissue. Utilizing a reduced but computationally amenable model, the effects of different electrode sizes and inter-electrode distances on the number of activated muscle fibers are investigated and qualitatively compared to existing literature. To analyze muscle fatigue, the sodium current, specifically the K+ ion concentrations within the t-tubule and the calcium release from the sarcoplasmic reticulum, is used to quantify membrane and metabolic fatigue. The simulations demonstrate that lower stimulation frequencies and biphasic pulse waveforms cause less fatigue than higher stimulation frequencies and monophasic pulses. A comparison between single and dual electrode configurations (with the same overall stimulation surface) is presented to locally investigate the differences in muscle fatigue. The dual electrode configuration causes the muscle tissue to fatigue quicker.

Probing field-induced tissue polarization using transillumination fluorescent imaging

Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart, recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock electrodes. There is little consensus as to whether these differences result from deficiencies of experimental techniques, artifacts of tissue damage, or deficiencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensitive dyes and transillumination optical imaging to perform, for the first time that we know of, noninvasive probing of field effects deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold diastolic field stimulation produces activation of deep myocardial layers 2-6 mm away from the cathodal surface, contrary to theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous bidomain model.

Modeling of microcavity electrodes for medical implants

A common, limiting factor in neuroprosthesis design is the safe charge-carrying capacity of the metallic electrodes that deliver electrical stimuli to biological tissue. If exceeded, adverse effects can occur, including electrode dissolution and cell necrosis. A straightforward method of addressing charge-carrying capacity limitations is to increase the surface area of the stimulating electrodes. However, for planar electrode arrays, this approach typically requires a corresponding increase in the distance between electrodes which can be detrimental to the efficacy of the device, particularly in sensory applications such as visual or auditory prostheses where densely-packed electrodes may offer advantage. An alternative approach involves fabricating electrodes such that they have a three-dimensional structure and, thus allow electrode spacing to be maintained while increasing the surface area. Here we describe a mathematical model that assists in the exploration of cup-shaped, micro-cavity electrodes within an insulating substrate. This model simulates the electrical fields generated by these electrodes and is used to explore the relationship between the micro-cavity electrode depth and the electrical field generated within the electrolyte. For electrode diameters of 350 µ, spaced at a pitch of 600 εm, the model predicts that the most efficacious microcavity depth is 400 εm.

Models of cardiac tissue electrophysiology: progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Purkinje-mediated effects in the response of quiescent ventricles to defibrillation shocks

In normal cardiac function, orderly activation of the heart is facilitated by the Purkinje system (PS), a specialized network of fast-conducting fibers that lines the ventricles. Its role during ventricular defibrillation remains unelucidated. Physical characteristics of the PS make it a poor candidate for direct electrical observation using contemporary experimental techniques. This study uses a computer modeling approach to assess contributions by the PS to the response to electrical stimulation. Normal sinus rhythm was simulated and epicardial breakthrough sites were distributed in a manner consistent with experimental results. Defibrillation shocks of several strengths and orientations were applied to quiescent ventricles, with and without PS, and electrical activation was analyzed. All shocks induced local polarizations in PS branches parallel to the field, which led to the rapid spread of excitation through the network. This produced early activations at myocardial sites where tissue was unexcited by the shock and coupled to the PS. Shocks along the apico-basal axis of the heart resulted in a significant abbreviation of activation time when the PS was present; these shocks are of particular interest because the fields generated by internal cardioverter defibrillators tend to have a strong component in the same direction. The extent of PS-induced changes, both temporal and spatial, was constrained by the amount of shock-activated myocardium. Increasing field strength decreased the transmission delay between PS and ventricular tissue at Purkinje-myocardial junctions (PMJs), but this did not have a major effect on the organ-level response. Weaker shocks directly affect a smaller volume of myocardial tissue but easily excite the PS, which makes the PS contribution to far field excitation more substantial than for stronger shocks.

Activating function of needle electrodes in anisotropic tissue

We present an analytical solution for the electrical potential and activating function (AF) established by cylindrical needle electrodes in anisotropic tissue. We compare this activating function to (1) AF computed assuming line-source electrodes and (2) AF computed using a finite element program. The results show that when the fiber is two needle diameters away from the electrodes, the maximum of the AF for needle electrodes is 1.43-times larger than for line-source electrodes, which results in lower thresholds for stimulation and electroporation. Therefore, for fibers that are close to the stimulating electrodes, one would benefit from using the formula that accounts for the electrodes' geometry.

Charge recovery during concurrent stimulation for a vision prosthesis

Parallel or concurrent stimulation in an epiretinal neuroprosthesis is likely necessary in order to deliver sufficient phosphenes for effective vision. Important issues with concurrent stimulation are the effect of current distribution which introduces current leakage or 'cross talk' between adjacent electrodes and charge recovery which determines balanced charge being delivered/recovered at each electrode from the previous phase. In this paper, we present the effect of concurrent stimulation of two hexagonally arranged platinum electrode arrays on charge recovery. Balanced and imbalanced (unequal) currents were delivered to the hexagonal arrays when they were immersed in physiological saline. Both simulation and experimental results revealed that charge was not recovered at individual electrodes, particularly when imbalanced currents were delivered. However, total charge injected to both hexagonal arrays was recovered.

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.

Reverse Polarity Pacing:The Hemodynamic Benefit of Anodal Currents at Lead Tips forCardiac Resynchronization Therapy

BACKGROUND

Myocardial depolarization can be achieved with currents of either anodal or cathodal polarity. In contrast to conventional cathodal pacing, anodal pacing initially hyperpolarizes tissue and improves myocardial contractility in animal models.

METHODS AND RESULTS

In 13 patients undergoing cardiac resynchronization therapy (CRT) device implantation, we compared the mean left ventricular outflow velocity-time integral (LV-VTI) for anodal and cathodal polarities in three different pacing configurations. Intraoperative continuous-wave Doppler measurements were taken at a fixed interrogation angle, while polarities were switched during unipolar left ventricular, unipolar biventricular, and shared-coil biventricular pacing. Comparisons used identical pacing rates, intervals, and stimulus strengths. Patients had a mean ejection fraction of 0.18 +/- 0.08 and a mean QRS duration of 140 +/- 34 ms. All capture thresholds were less than 4.5 volts at a pulse width of 0.4 ms. Data were suitable for analysis in 37 of the 39 pairs of Doppler measurements. Anodal polarity significantly increased average LV-VTI in 36 of these 37 comparisons. The mean increase in LV-VTI for each configuration with anodal versus cathodal polarity was 2.8 +/- 2.6 cm (P < 0.001). The combined mean LV-VTI for all configurations was similarly higher for anodal polarity (24.4 +/- 11.7 cm) versus cathodal polarity (21.7 +/- 10.9 cm; P < 0.001).

CONCLUSION

Anodal pacing polarity significantly improves a measure of LV function compared to traditional cathodal currents. Anodal pacing, which can be achieved by a simple reversal of pacing circuit polarity, may represent an important therapeutic addition to future resynchronization devices.

Current distribution during parallel stimulation: implications for an epiretinal neuroprosthesis

A simplified mathematical model has been developed in order to better understand local current spread when multiple simultaneous current sources are used in an epiretinal neuroprosthesis. To test the model, pairs of platinum electrodes of 430 &#956;m diameter and an intra-pair spacing of 1 mm between centers, were arranged either in-line or in parallel, in a bath of physiological saline. Each pair was separated by distances from 1 mm to 6 mm. The currents in each electrode in the bath were measured and compared with the computational model of the same arrangement. This approach allowed us to quantify return current interaction between parallel sources. As predicted, with parallel electrodes and matching currents in each electrode pair, there is no current cross-talk. However with imbalanced current sources, significant cross-talk is evident. The cross-talk decreases as a function of electrode pair separation. The implication of this work in the design of an epiretinal neuroprosthesis is discussed.

Optical Action Potential Upstroke Morphology Reveals Near-Surface Transmural Propagation Direction

The analysis of surface-activation patterns and measurements of conduction velocity in ventricular myocardium is complicated by the fact that the electrical wavefront has a complex 3D shape and can approach the heart surface at various angles. Recent theoretical studies suggest that the optical upstroke is sensitive to the subsurface orientation of the wavefront. Our goal here was to (1) establish the quantitative relationship between optical upstroke morphology and subsurface wavefront orientation using computer modeling and (2) test theoretical predictions experimentally in isolated coronary-perfused swine right ventricular preparations. We show in numerical simulations that by suitable placement of linear epicardial stimulating electrodes, the angle φ of wavefronts with respect to the heart surface can be controlled. Using this method, we developed theoretical predictions of the optical upstroke shape dependence on φ. We determined that the level V F * at which the rate of rise of the optical upstroke reaches the maximum linearly depends on φ. A similar relationship was found in simulations with epicardial point stimulation. The optical mapping data were in good agreement with theory. Plane waves propagating parallel to myocardial fibers produced upstrokes with V F *<0.5, consistent with theoretical predictions for φ>0. Similarly, we obtained good agreement with theory for plane waves propagating in a direction perpendicular to fibers ( V F *>0.5 when φ<0). Finally, during epicardial point stimulation, we discovered characteristic saddle-shaped V F * maps that were in excellent agreement with theoretically predicted changes in φ during wavefront expansion. Our findings should allow for improved interpretation of the results of optical mapping of intact heart preparations.

A bidomain model of epiretinal stimulation

A computational bidomain model of epiretinal stimulation is presented, consisting of a continuum description of active retinal tissue in contact with bulk vitreous fluid. Results from two-electrode and four-electrode bipolar stimulation suggest that a biphasic cathodic-anodic stimulus sequence is effective in providing targeted focal activation of retinal tissue. Undesired secondary activations beneath each electrode return may be eliminated by using multiple returns for each stimulus electrode.

Simulated prosthetic visual fixation, saccade, and smooth pursuit

A visual tracking task was administered to 20 subjects afforded simulated prosthetic vision (a phosphene array); a total of 3h data was taken from each subject over the course of 10 visits. The experiment assessed prosthetic visual fixation, saccade and smooth pursuit and the effect of practice. Further, we demonstrated an image analysis technique that assisted fixation and pursuit (but not saccade) accuracy, and required less vigorous movement of the phosphene array in pursuing the target. As measured by mean deviation from the target, fixation and pursuit accuracies were improved by 8.3 and 3.3 min of visual arc, respectively (35.8% and 6.8%), for inter-phosphene spacing of 1.9 degrees . The analysis technique, involving overlapping Gaussian kernels, was an heuristic design; this is the first step of an iterative, experimental approach to devising effective image analysis to be contained in an electronic vision prosthesis. The approach should ultimately afford implanted patients improved prosthetic visual function.

Computer simulations of successful defibrillation in decoupled and non-uniform cardiac tissue

Aim

The aim of the present study is to investigate the origin and effect of virtual electrode polarization in uniform, decoupled and non-uniform cardiac tissue during field stimulation.

Methods

A discrete bidomain model with active membrane behaviour was used to simulate normal cardiac tissue as well as cardiac tissue that is decoupled due to fibrosis and gap junction remodelling. Various uniform and non-uniform electric fields were applied to the external domain of uniform, decoupled and non-uniform resting cardiac tissue as well as cardiac tissue in which spiral waves were induced.

Results

Field stimulation applied on non-uniform tissue results in more virtual electrodes compared with uniform tissue. The spiral waves were terminated in decoupled tissue, but not in uniform, homogeneous tissue. By gradually increasing local differences in intracellular conductivities, the amount and spread of virtual electrodes increased and the spiral waves were terminated.

Conclusion

Fast depolarization of the tissue after field stimulation may be explained by intracellular decoupling and spatial heterogeneity present in normal and pathological cardiac tissue. We demonstrated that termination of spiral waves by means of field stimulation can be achieved when the tissue is modelled as a non-uniform, anisotropic bidomain with active membrane behaviour.

Does cardiac pacing reproduce the mechanism of focal impulse initiation?

Stimulation of myocardium by either a native pacemaker or an artificial stimulus requires the initiation of a self-propagating wave of depolarization originating from the site of initial activation. In the present study we perform artificial stimulation at a site of focal discharge with the aim to compare the two mechanisms of impulse formation. High resolution epicardial mapping in senescent rat hearts provided examples of focal discharge during sinus rhythm at a single epicardial breakthrough (BKT) point emerging from an isolated Purkinje-ventricular muscle junction (PMJ) site. Stimulation was also performed at the same BKT point and potential distributions recorded during spontaneous and artificial stimulation were compared. During excitation latency, the negative potential pattern was elongated perpendicularly to fiber direction at both pacing and BKT point, in agreement with virtual cathode membrane polarization predicted by the bidomain model during point stimulation. During impulse initiation, activation wave fronts were initially circular around pacing site or BKT point and then elongated along local fiber direction. The similarity between impulse initiation during focal discharge and point stimulation in cardiac muscle suggests that high resolution pace mapping studies can help to elucidate the mechanism of abnormal impulse formation.

High resolution magnetic images of planar wave fronts reveal bidomain properties of cardiac tissue

We magnetically imaged the magnetic action field and optically imaged the transmembrane potentials generated by planar wavefronts on the surface of the left ventricular wall of Langendorff-perfused isolated rabbit hearts. The magnetic action field images were used to produce a time series of two-dimensional action current maps. Overlaying epifluorescent images allowed us to identify a net current along the wavefront and perpendicular to gradients in the transmembrane potential. This is in contrast to a traditional uniform double-layer model where the net current flows along the gradient in the transmembrane potential. Our findings are supported by numerical simulations that treat cardiac tissue as a bidomain with unequal anisotropies in the intra- and extracellular spaces. Our measurements reveal the anisotropic bidomain nature of cardiac tissue during plane wave propagation. These bidomain effects play an important role in the generation of the whole-heart magnetocardiogram and cannot be ignored.

Basic assessment of paced activation sequence mapping: implications for practical use

Some experiences support the use of atrial paced activation sequence mapping, but there is no systematic study assessing its spatial resolution, reproducibility, and influence of pacing parameters. The aim of this study was to evaluate these issues by using a 24-pole catheter positioned at the atrial aspect of the tricuspid and mitral annuli in 15 patients. Bipolar pacing was performed at two sites (right and left atria), 2 cycle lengths (300 and 500 ms) and two outputs (twice and tenfold the late diastolic threshold voltage for 2-ms pulses). The elapsed time between the atrial activation at the two dipoles adjacent to the pacing dipole (activation time [AT]) was measured during each pacing sequence. Changes in cycle length did not modify the AT. The increase in voltage slightly modified the AT (maximum -2 ms at the RA; 95% CI -3 to -1 ms) due to a greater shortening of the conduction time to the dipole located next to the anode. The 95% limits of the intraobserver and interobserver agreements in the AT measurement were -2 to 3 ms and -3 to 3 ms, respectively. The spatial resolution was studied in ten patients by measuring the AT during pacing from each dipole of a 20-pole catheter with a 1-3-1 mm interelectrode distance. The mean AT change was 10 +/- 4 ms per 6 mm of pacing site displacement (95% CI 8-11 ms, range 2.5-20 ms). In conclusion, paced atrial activation sequence analysis is reproducible, accurate, and relatively independent of pacing parameters.

Simulation of a plane wavefront propagating in cardiac tissue using a cellular automata model

We present a detailed description of a cellular automata model for the propagation of action potential in a planar cardiac tissue, which is very fast and easy to use. The model incorporates anisotropy in the electrical conductivity and a spatial variation of the refractory time. The transmembrane potential distribution is directly derived from the cell states, and the intracellular and extracellular potential distributions are calculated for the particular case of a plane wavefront. Once the potential distributions are known, the associated current densities are calculated by Ohm's law, and the magnetic field is determined at a plane parallel to the cardiac tissue by applying the law of Biot and Savart. The results obtained for propagation speed and for magnetic field amplitude with the cellular automata model are compared with values predicted by the bidomain formulation, for various angles between wavefront propagation and fibre direction, characterizing excellent agreement between the models.

Electrode systems for measuring cardiac impedances using optical transmembrane potential sensors and interstitial electrodes--theoretical design

The cardiac electrical substrate is a challenge to direct measurement of its properties. Optical technology together with the capability to fabricate small electrodes at close spacings opens new possibilities. Here, those possibilities are explored from a theoretical viewpoint. It appears that with careful measurements from a well-designed set of electrodes one can obtain structural conductivities, separating intracellular from interstitial values, and longitudinal from transverse. Resting membrane resistance also can be obtained.

Field stimulation of cardiac fibers with random spatial structure

Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (l(c) = 100 +/- 50 microm), diameter (d(c) = 20 +/- 10 microm), thickness of extracellular space (t(e) = 1.18 +/- 0.59 microm), and junctional resistance (R(j) = 2 +/- 1 M(omega)) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (V(m)) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing t(e); R(j), l(c), and d(c) have less influence. The maximum V(m) increases from 3.5 mV in a periodic fiber to 20.5+/-4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold E(th) decreases from 6.9 to 1.59 +/- 0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59 +/- 0.43 versus 1.44 +/- 0.41 V/cm (p value = 0.453). Thus, V(m) arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.

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.

Success and failure of biphasic shocks: results of bidomain simulations

The mechanisms behind the superiority of optimal biphasic defibrillation shocks over monophasic are not fully understood. This simulation study examines how the shock polarity and second-phase magnitude of biphasic shocks influence the virtual electrode polarization (VEP) pattern, and thus the outcome of the shock in a bidomain model representation of ventricular myocardium. A single spiral wave is initiated in a two-dimensional sheet of myocardium that measures 2 x 2 cm(2). The model incorporates non-uniform fiber curvature, membrane kinetics suitable for high strength shocks, and electroporation. Line electrodes deliver a spatially uniform extracellular field. The shocks are biphasic, each phase lasting 10 ms. Two different polarities of biphasic shocks are examined as the first-phase configuration is held constant and the second-phase magnitude is varied between 1 and 10 V/cm. The results show that for each polarity, varying the second-phase magnitude reverses the VEP induced by the first phase in an asymmetric fashion. Further, the size of the post-shock excitable gap is dependent upon the second-phase magnitude and is a factor in determining the success or failure of the shock. The maximum size of a post-shock excitable gap that results in defibrillation success depends on the polarity of the shock, indicating that the refractoriness of the tissue surrounding the gap also contributes to the outcome of the shock.

Entrainment by an extracellular AC stimulus in a computational model of cardiac tissue

INTRODUCTION

Cardiac tissue can be entrained when subjected to sinusoidal stimuli, often responding with action potentials sustained for the duration of the stimulus. To investigate mechanisms responsible for both entrainment and extended action potential duration, computer simulations of a two-dimensional grid of cardiac cells subjected to sinusoidal extracellular stimulation were performed.

METHODS AND RESULTS

The tissue is represented as a bidomain with unequal anisotropy ratios. Cardiac membrane dynamics are governed by a modified Beeler-Reuter model. The stimulus, delivered by a bipolar electrode, has a duration of 750 to 1,000 msec, an amplitude range of 800 to 3,200 microA/cm, and a frequency range of 10 to 60 Hz. The applied stimuli create virtual electrode polarization (VEP) throughout the sheet. The simulations demonstrate that periodic extracellular stimulation results in entrainment of the tissue. This phase-locking of the membrane potential to the stimulus is dependent on the location in the sheet and the magnitude of the stimulus. Near the electrodes, the oscillations are 1:1 or 1:2 phase-locked; at the middle of the sheet, the oscillations are 1:2 or 1:4 phase-locked and occur on the extended plateau of an action potential. The 1:2 behavior near the electrodes is due to periodic change in the voltage gradient between VEP of opposite polarity; at the middle of the sheet, it is due to spread of electrotonic current following the collision of a propagating wave with refractory tissue.

CONCLUSION

The simulations suggest that formation of VEP in cardiac tissue subjected to periodic extracellular stimulation is of paramount importance to tissue entrainment and formation of an extended oscillatory action potential plateau.

Virtual electrode polarization in the far field: implications for external defibrillation

We recently suggested that failure of implantable defibrillation therapy may be explained by the virtual electrode-induced phase singularity mechanism. The goal of this study was to identify possible mechanisms of vulnerability and defibrillation by externally applied shocks in vitro. We used bidomain simulations of realistic rabbit heart fibrous geometry to predict the passive polarization throughout the heart induced by external shocks. We also used optical mapping to assess anterior epicardium electrical activity during shocks in Langendorff-perfused rabbit hearts (n = 7). Monophasic shocks of either polarity (10-260 V, 8 ms, 150 microF) were applied during the T wave from a pair of mesh electrodes. Postshock epicardial virtual electrode polarization was observed after all 162 applied shocks, with positive polarization facing the cathode and negative polarization facing the anode, as predicted by the bidomain simulations. During arrhythmogenesis, a new wave front was induced at the boundary between the two regions near the apex but not at the base. It spread across the negatively polarized area toward the base of the heart and reentered on the other side while simultaneously spreading into the depth of the wall. Thus a scroll wave with a ribbon-shaped filament was formed during external shock-induced arrhythmia. Fluorescent imaging and passive bidomain simulations demonstrated that virtual electrode polarization-induced scroll waves underlie mechanisms of shock-induced vulnerability and failure of external defibrillation.

Effects of cardiac microstructure on propagating electrical waveforms

Electrical waveforms measured during propagation at microscopic level are considerably affected by normal variations in cardiac microstructure as well as by the superfusing fluid. On the basis of evidence we present in this article, we argue that the anisotropic waveform variations discussed here are explained primarily by the associated variations in different microstructural components of myocardial architecture rather than by the effects of the perfusing bath. The results suggest that different components of myocardial architecture have preferential effects on f1.gif" BORDER="0">(max) and on the shape of the foot of the transmembrane action potential (V(m) foot). Resistive discontinuities primarily affect f1.gif" BORDER="0">(max), and an additional capacitive component in the local circuit due to the capillaries in interstitial space primarily affects V(m) foot. Resistive discontinuities also have an important influence on cardiac conduction. These discontinuities include spatial variations in the size of interstitial space (interstitial resistive discontinuities) and the role of cellular scaling (effects of cell size) when changes occur in the cellular and multicellular distribution of gap junctions during remodeling of normal mature myocardium to proarrhythmic structural substrates. The full text of this article is available at http://www.circresaha.org.

Roles of electric field and fiber structure in cardiac electric stimulation

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

Optical transmembrane potential recordings during intracardiac defibrillation-strength shocks

BACKGROUND

The prolongation of the action potential after defibrillation-strength shocks is believed to be a critical component of defibrillation. The response of the transmembrane potential to the shock may affect this prolongation. We studied the effects of an intracardiac shock on the transmembrane potential and action potential duration at multiple sites on the epicardium using a voltage-sensitive dye and optical mapping system.

METHODS AND RESULTS

A laser scanner recorded optical action potentials with voltage-sensitive dye at 63 spots on both the left and right ventricles of six isolated, perfused rabbit hearts. Hearts were paced with epicardial point stimulation followed by the delivery of a 2 A and 20 ms rectangular waveform shock during the relative refractory period. The shock was given between right atrial and right ventricular electrodes. Of 621 total spots analyzed, 241 spots hyperpolarized and 76 spots depolarized with a right ventricular anode, whereas 159 spots hyperpolarized and 145 spots depolarized with a right ventricular cathode (P < 0.05). Both hyperpolarized and depolarized spots exhibited prolonged action potential duration, although prolongation was greater with depolarizing responses (16.7 +/- 9 ms vs. 13.3 +/- 13.4 ms, p<0.001). Hyperpolarized and depolarized spots were not randomly distributed, but clustered into regions. The size of the hyperpolarized regions was larger than the depolarized regions with RV anodal stimulation (27 +/- 20 spots/hyperpolarized region vs. 8.5 +/- 9 spots/depolarized region, p < 0.03) but not with RV cathodal stimulation. With reversal of electrode polarity, spots hyperpolarized near the shocking electrodes frequently did not reverse polarization but remained hyperpolarized.

CONCLUSIONS

Distinct regions of either polarization occur during intracardiac defibrillation-strength shocks. Although hyperpolarizing membrane responses were observed more often than depolarizing responses, depolarizing membrane polarization resulted in greater action potential prolongation. The absence of sign change in polarization in some regions with shocks of opposite polarities suggests that nonlinear intrinsic membrane properties are operative during strong electrical stimulation.

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

INTRODUCTION

Defibrillation shocks, when delivered through internal electrodes, establish transmembrane potentials (Vm) large enough to electroporate the membrane of cardiac cells. The effects of such shocks on the transmembrane potential distribution are investigated in a two-dimensional rectangular sheet of cardiac muscle modeled as a bidomain with unequal anisotropy ratios.

METHODS AND RESULTS

The membrane is represented by a capacitance Cm, a leakage conductance g(l) and a variable electroporation conductance G, whose rate of growth depends exponentially on the square of Vm. The stimulating current Io, 0.05-20 A/m, is delivered through a pair of electrodes placed 2 cm apart for stimulation along fibers and 1 cm apart for stimulation across fibers. Computer simulations reveal three categories of response to Io: (1) Weak Io, below 0.2 A/m, cause essentially no electroporation, and Vm increases proportionally to Io. (2) Strong Io, between 0.2 and 2.5 A/m, electroporate tissue under the physical electrode. Vm is no longer proportional to Io; in the electroporated region, the growth of Vm is halted and in the region of reversed polarity (virtual electrode), the growth of Vm is accelerated. (3) Very strong Io, above 2.5 A/m, electroporate tissue under the physical and the virtual electrodes. The growth of Vm in all electroporated regions is halted, and a further increase of Io increases both the extent of the electroporated regions and the electroporation conductance G.

CONCLUSION

These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm induced by defibrillation strength shocks.

A novel mechanism of anode-break stimulation predicted by bidomain modeling

-Anodal stimulation by external pacemakers has been explained on the basis of bidomain models of cardiac tissue. Bidomain models predict that anodal stimuli will hyperpolarize the underlying tissue while adjacent regions become depolarized (virtual cathodes), initiating excitation. We investigated the contribution of active cellular properties to anode-break stimulation. A bidomain model was implemented in which each cell contained realistic ionic currents, including those recruited by hyperpolarization. Simulations reveal that anode-break excitation can originate at the site of stimulation itself and not only from adjacent regions of induced depolarization. The threshold for initiating excitation at the site of stimulation is lower than that for stimulation initiating from adjacent depolarized regions. Thus, incorporation of active cellular properties into a bidomain model predicts a novel mechanism for anode-break stimulation of the heart. The results will improve our understanding of anodal pacing and its risks and benefits in patients.

Propagation in cardiac tissue adjacent to connective tissue: two-dimensional modeling studies

The conditions for activation transmission across a region of extracellular space was demonstrated in two-dimensional preparations with results consistent with those previously seen in the one-dimensional fiber studies. In addition, one sees changes in action potential morphology which occur in the tissue nearest the connective-tissue border as well as changes in conduction velocity along the border. These results hinge on an adequate representation of the connective-tissue region achieved by careful implementation of the boundary conditions in the intracellular and interstitial spaces and the expansion of the connective-tissue discretization to a "double-tier network" description. Through a series of simulations, a clear dependence on fiber orientation is illustrated in the efficacy to transmit activation. The collision of a front with an embedded connective-tissue region was also examined. The results revealed that fibers aligned normal to a planar stimulus would more greatly disrupt the advancement of a planar front. Such pronounced disruptions have been shown to be proarrhythmic in the literature. The increasing evidence of the ability of connective tissue to transmit activation has implications in understanding spread of activation through infarcted tissues and through the healthy ventricular wall in the presence of connective-tissue sheets.