The effect of plunge electrodes during electrical stimulation of cardiac tissue

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.

Ventricular Endocardial Tissue Geometry Affects Stimulus Threshold and Effective Refractory Period

BACKGROUND

Understanding the biophysical processes by which electrical stimuli applied to cardiac tissue may result in local activation is important in both the experimental and clinical electrophysiology laboratory environments, as well as for gaining a more in-depth knowledge of the mechanisms of focal-trigger-induced arrhythmias. Previous computational models have predicted that local myocardial tissue architecture alone may significantly modulate tissue excitability, affecting both the local stimulus current required to excite the tissue and the local effective refractory period (ERP). In this work, we present experimental validation of this structural modulation of local tissue excitability on the endocardial tissue surface, use computational models to provide mechanistic understanding of this phenomena in relation to localized changes in electrotonic loading, and demonstrate its implications for the capture of afterdepolarizations.

METHODS AND RESULTS

Experiments on rabbit ventricular wedge preparations showed that endocardial ridges (surfaces of negative mean curvature) had a stimulus capture threshold that was 0.21 ± 0.03 V less than endocardial grooves (surfaces of positive mean curvature) for pairwise comparison (24% reduction, corresponding to 56.2 ± 6.4% of the energy). When stimulated at the minimal stimulus strength for capture, ridge locations showed a shorter ERP than grooves (n = 6, mean pairwise difference 7.4 ± 4.2 ms). When each site was stimulated with identical-strength stimuli, the difference in ERP was further increased (mean pairwise difference 15.8 ± 5.3 ms). Computational bidomain models of highly idealized cylindrical endocardial structures qualitatively agreed with these findings, showing that such changes in excitability are driven by structural modulation in electrotonic loading, quantifying this relationship as a function of surface curvature. Simulations further showed that capture of delayed afterdepolarizations was more likely in trabecular ridges than grooves, driven by this difference in loading.

CONCLUSIONS

We have demonstrated experimentally and explained mechanistically in computer simulations that the ability to capture tissue on the endocardial surface depends upon the local tissue architecture. These findings have important implications for deepening our understanding of excitability differences related to anatomical structure during stimulus application that may have important applications in the translation of novel experimental optogenetics pacing strategies. The uncovered preferential vulnerability to capture of afterdepolarizations of endocardial ridges, compared to grooves, provides important insight for understanding the mechanisms of focal-trigger-induced arrhythmias.

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.

ANALYSIS OF THE VIRTUAL ELECTRODE PHENOMENA USING BIDOMAIN MODEL: BASIC CHARACTERISTICS FOR PASSIVE MEMBRANE

The virtual electrode (VE) has been recognized as an important factor for success or failure of cardiac defibrillation. Many researches have been performed to study characteristics of the VE. However, there are some questions which remain unanswered. In this study, we developed a simulator to solve a three-dimensional bidomain model and performed several simulations to elucidate the basic characteristics of VE in a simplified cardiac tissue with passive membrane when a constant unipolar cathodal stimulus was applied. The results showed that for smaller electrodes, VE has a typical dog-bone shaped virtual cathode (VC) and two egg-shaped virtual anodes (VAs). The distributions both in intra- and extracellular potentials have concentric ellipsoidal isosurfaces, but their ellipticities are subtly different, producing VE. For larger electrodes, VC becomes larger and has a flat-dish shape rather than dog-bone, and VA becomes smaller and also flattens and collapses. The peak values of VE are larger for smaller electrodes, but their time courses show similar tendency among the different sized electrodes. The change of stimulus strength and polarity only affects the magnitude of VE in a linear manner and the distribution pattern is unchanged. These results provide us fundamental knowledge about VE.

A new optrode design for intramural optical recordings

Intramural measurements of V(m) and Ca(i)(2+) are important in the studies of cardiac arrhythmias and defibrillation. We developed a new design of an "optrode" (bundle of optical fibers) for use in intramural cardiac mapping. The optrodes are made from seven optical fibers with the fiber ends polished at 45° angle and coated with mirror surfaces. The optrodes are enclosed in smooth epoxy resin cast, which protects mirror surfaces from damage and ensures constant optrode diameter along its length. The optrodes are strong enough to be easily inserted into heart muscle, can be reused multiple times, and they may reduce artifacts in the measurements of the effects of defibrillation shocks on V(m).

The potential of dual camera systems for multimodal imaging of cardiac electrophysiology and metabolism

Fluorescence imaging has become a common modality in cardiac electrodynamics. A single fluorescent parameter is typically measured. Given the growing emphasis on simultaneous imaging of more than one cardiac variable, we present an analysis of the potential of dual camera imaging, using as an example our straightforward dual camera system that allows simultaneous measurement of two dynamic quantities from the same region of the heart. The advantages of our system over others include an optional software camera calibration routine that eliminates the need for precise camera alignment. The system allows for rapid setup, dichroic image separation, dual-rate imaging, and high spatial resolution, and it is generally applicable to any two-camera measurement. This type of imaging system offers the potential for recording simultaneously not only transmembrane potential and intracellular calcium, two frequently measured quantities, but also other signals more directly related to myocardial metabolism, such as [K(+)](e), NADH, and reactive oxygen species, leading to the possibility of correlative multimodal cardiac imaging. We provide a compilation of dye and camera information critical to the design of dual camera systems and experiments.

Optical measurements of intramural action potentials in isolated porcine hearts using optrodes

BACKGROUND

Measurements of intramural membrane potential (Vm) would greatly increase knowledge of cardiac arrhythmias and defibrillation. Optrodes offer the possibility for three-dimensional Vm mapping, but their signal quality has been inadequate.

OBJECTIVE

The purpose of this work was to improve optrode signal quality and use optrodes to measure intramural distribution of action potentials and shock-induced Vm changes in porcine hearts.

METHODS

Optrodes were made from seven optical fibers 225 or 325 microm in diameter. Fiber ends were polished at a 45 degrees angle, which improved light collection and allowed their insertion without a needle. Fluorescent measurements were performed in isolated porcine hearts perfused with Tyrode's solution or blood using Vm-sensitive dye RH-237 and a 200-W Hg/Xe lamp.

RESULTS

The signal-to-noise ratio for 325-microm fibers was 44 +/- 23 in blood-perfused hearts (n = 5) and 106 +/- 45 in Tyrode's-perfused hearts (n = 3), which represents an approximately four-fold improvement over previously reported data. There was close correspondence between optical and electrical measurements of activation times and action potential duration (APD). No significant intramural APD gradients were observed at cycle lengths up to 4 s and in the presence of dofetilide or d-sotalol. Application of shocks (5-50 V/cm) produced large intramural Vm changes (up to approximately 200% action potential amplitude), possibly reflecting a combined effect of tissue discontinuities and optrode geometry.

CONCLUSIONS

A substantial improvement of optrode signal quality was achieved. Optical measurements of APD and activation times matched electrical measurements. Optrode measurements revealed no significant intramural APD gradients. Application of shocks caused large intramural Vm changes that could be influenced by the optrode geometry.

Transmural and endocardial Purkinje activation in pigs before local myocardial activation after defibrillation shocks

BACKGROUND

Earliest recorded postshock myocardial activations in pigs originate in the subepicardium of the apex and lateral free wall of the left ventricle (LV) 30-90 ms after the shock.

OBJECTIVE

The purpose of this study was to determine whether the Purkinje system is a candidate for the source of postshock activations by performing endocardial and transmural postshock activation mapping.

METHODS

In five pigs, 32 plunge needles with 12 electrodes (1-mm spacing) were inserted into the LV apex and lateral free wall. Up to 70 plunge needles with six electrodes (2-mm spacing) were spread throughout the remainder of the LV, while 9-12 plunge needles with four electrodes (2-mm spacing) were inserted into the right ventricle. A basket catheter with 32 bipolar recording sites was inserted into the LV. Defibrillation-threshold (DFT)-level shocks were delivered during 10 episodes of electrically induced ventricular fibrillation. Electrograms of postshock activation cycles were analyzed for Purkinje and myocardial activations.

RESULTS

Purkinje activations were recorded before local myocardial activation in 9% of basket electrograms and in 15% of plunge needles during the first postshock activation cycle. Purkinje activations were identified during the first and subsequent several postshock activation cycles in at least one basket and one needle electrogram in 96% and 98% of defibrillation episodes, respectively.

CONCLUSIONS

The Purkinje system is active during the early postshock activation cycles after DFT-level shocks. Further studies are required to determine whether activation initiates in the Purkinje system or whether it is activated by the myocardium or by Purkinje-myocardial junctional cells.

Solving the cardiac bidomain equations for discontinuous conductivities

Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.

How to explain why "unequal anisotropy ratios" is important using pictures but no mathematics

"Unequal anisotropy ratios" is an important property of cardiac tissue. Many of the fundamental mechanisms governing how the heart responds to an electrical shock require unequal anisotropy ratios. In this paper, I explain the role of unequal anisotropy ratios using pictures rather than mathematics. My goal is to develop physical insight, so has to understand qualitatively why the condition of unequal anisotropy ratios is so important.

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.

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.

Unpinning and removal of a rotating wave in cardiac muscle

Rotating waves in cardiac muscle may be pinned to a heterogeneity, as it happens in superconductors or in superfluids. We show that the physics of electric field distribution between cardiac cells permits one to deliver an electric pulse exactly to the core of a pinned wave, without knowing its position, and even to locations where a direct access is not possible. Thus, unpinning or removal of rotating waves can be achieved. The energy needed is 2 orders of magnitude less than defibrillation energy. This opens a way to new manipulations with pinned vortices both in experiments and in cardiac clinics.

Virtual electrode theory explains pacing threshold increase caused by cardiac tissue damage

The virtual electrode polarization (VEP) effect is believed to play a key role in electrical stimulation of heart muscle. However, under certain conditions, including clinically, its existence and importance remain unknown. We investigated the influence of acute tissue damage produced by continuous pacing with strong current (40-mA, 4-ms biphasic pulses with 4-Hz frequency for 5 min) on stimulus-generated VEPs and pacing thresholds. A fluorescent optical mapping technique was used to obtain stimulus-induced transmembrane potential distribution around a pacing electrode applied to the ventricular surface of a Langendorff-perfused rabbit heart ( n = 5). Maps and pacing thresholds were recorded before and after tissue damage. Spatial extents of electroporation and cell uncoupling were assessed by propidium iodide ( n = 2) and connexin43 ( n = 3) antibody staining, respectively. On the basis of these data, passive and active three-dimensional bidomain models were built to determine VEP patterns and thresholds for different-sized areas of the damaged region. Electrophysiological results showed that acute tissue damage led to disappearance of the VEP with an associated significant increase in pacing thresholds. Damage was expressed in electroporation and cell uncoupling within a ∼1.0-mm-diameter area around the tip of the electrode. According to computer simulations, cell uncoupling, rather than electroporation, might be the direct cause of VEP elimination and threshold increase, which was nonlinearly dependent on the size of the damaged region. Fiber rotation with depth did not substantially affect the numerical results. The study explains failure to stimulate damaged tissue within the concepts of the VEP theory.

Three-dimensional mapping of earliest activation after near-threshold ventricular defibrillation shocks

INTRODUCTION

Following shocks with a 50% defibrillation success (DFT50) delivered from electrodes at the right ventricular (RV) apex and superior vena cava (SVC), the earliest epicardial postshock activation always appears focally in the left ventricular (LV) apex for both successful and failed shocks. Because the heart is a three-dimensional (3D) structure, questions remain whether this activation truly arises from a focus or the focal pattern represents epicardial breakthrough resulting from intramural reentry. To answer these questions, 3D electrical mapping was performed.

METHODS AND RESULTS

In six pigs, 60 to 84 epoxy fiberglass needles (0.7-mm-diameter), each containing six electrodes 2 mm apart, were inserted into the LV with 3- to 5-mm spacing around the apex and 5- to 10-mm spacing near the base. Ten DFT50 shocks (RV-->SVC, biphasic, 6/4 msec) were delivered after 10 seconds of fibrillation in each animal. The first five activations after each shock were mapped. Of 60 DFT50 shocks, 31 were successful, of which the first postshock cycle was a sinus beat in 13. In the other 18 successful shock episodes, the first postshock activation was detected 63 +/- 16 msec after the shock, which was not significantly different from the 58 +/- 23 msec postshock interval for the 29 failed shock episodes. In these 47 successful and failed shock episodes, the earliest postshock activation always arose focally from the LV apex. Its origin was in the subepicardium in 76% +/- 17%, midmyocardium in 16% +/- 12%, and subendocardium in 8% +/- 6% of cases.

CONCLUSION

Following near-DFT50 shocks, the first postshock cycles did not arise by macroreentry. Instead, they originated from a true focus or microreentry, most commonly near the epicardium.

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.