Effects of bath resistance on action potentials in the squid giant axon: myocardial implications

Thermal block of action potentials is primarily due to voltage-dependent potassium currents: a modeling study

OBJECTIVE

Thermal block of action potential conduction using infrared lasers is a new modality for manipulating neural activity. It could be used for analysis of the nervous system and for therapeutic applications. We sought to understand the mechanisms of thermal block.

APPROACH

To analyze the mechanisms of thermal block, we studied both the original Hodgkin/Huxley model, and a version modified to more accurately match experimental data on thermal responses in the squid giant axon.

MAIN RESULTS

Both the original and modified models suggested that thermal block, especially at higher temperatures, is primarily due to a depolarization-activated hyperpolarization as increased temperature leads to faster activation of voltage-gated potassium ion channels. The minimum length needed to block an axon scaled with the square root of the axon's diameter.

SIGNIFICANCE

The results suggest that voltage-dependent potassium ion channels play a major role in thermal block, and that relatively short lengths of axon could be thermally manipulated to selectively block fine, unmyelinated axons, such as C fibers, that carry pain and other sensory information.

Standing excitation waves in the heart induced by strong alternating electric fields

We studied the effect of sinusoidal electric fields on cardiac tissue both experimentally and numerically. We found that periodic forcing at 5-20 Hz using voltage applied in the bathing solution could stop the propagation of excitation waves by producing standing waves of membrane depolarization. These patterns were independent of the driving frequency in contrast to classical standing waves. The stimulus strength required for pattern formation was large compared to the excitation threshold. A novel tridomain representation of cardiac tissue was required to reproduce this behavior numerically.

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.

Influence of a perfusing bath on the foot of the cardiac action potential

Recently, Spach et al (Circ Res. 1998;83:1144-1164) measured the transmembrane action potential 150 to 200 microm below the tissue surface during longitudinal and transverse propagation. They found that "during longitudinal propagation there was initial slowing of V(m) [action potential] foot that resulted in deviations from a simple exponential. " (p 1144). They attributed this behavior to the effects of capillaries on propagation. The purpose of this commentary is to show that the perfusing bath plays an important role in determining the time course of the action potential foot, even when the transmembrane potential is measured 150 microm below the tissue surface. Using numerical simulations based on the bidomain model, we find that the action potential foot for transverse propagation is nearly exponential (tau(foot)=314 micros). For longitudinal propagation, the action potential foot is not exponential because of an initial slowing (best-fit tau(foot)=483 micros). We conclude that the perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction, even if the transmembrane potential is measured 150 microm below the tissue surface.

Effects of spatial segmentation in the continuous model of excitation propagation in cardiac muscle

INTRODUCTION

Spatial segmentation is essential for the numerical simulation of excitation propagation in cardiac muscle.

METHODS AND RESULTS

This study evaluated the effects of spatial segmentation on action potential and on the velocity of propagation in a continuous one-dimensional model of cardiac muscle [intracellular and extracellular resistivities along (L) and transverse (T) to the muscle fibers: 402 omega(cm) (R(e), L), 3,620 omega(cm) (R(e), T), 48 omega(cm) (R(e), L), and 126 omega(cm) (R(e), T), J of Physiol 255:335-346, 1976) and either Luo-Rudy (L-R, Circ Res 68:1501-1526, 1991) or Beeler-Reuter (B-R, J Physiol 268:177-210, 1977) ionic currents. Related cable equations for active membrane are derived. Spatial segmentations of < 31.2 microm (L, L-R), < 11.5 microm (T, L-R), < 44.7 microm (L, B-R), and < 16.5 microm (T, B-R) were required for < 1% errors in the characteristic parameters of action potential. Similarly, spatial segmentations of < 54.5 microm (L, L-R), < 20.1 microm (T, L-R), < 84.3 microm (L, B-R), and < 31.2 microm (T, B-R) were required for < 1 % errors in the velocity of conduction.

CONCLUSION

In general, spatial segmentations of < 26.9% and < 50.8% of the space constant of a fully activated membrane gave < 1.0% errors in the characteristic parameters of action potential and in the velocity of propagation, respectively, for both membranes. The action potential duration was relatively insensitive to the spatial segmentation. Our analysis suggests that lambda(full is a better criterion for the selection of spatial segmentation in numerical simulation than the space constant of the resting membrane.

Virtual electrode effects in transvenous defibrillation-modulation by structure and interface: evidence from bidomain simulations and optical mapping

INTRODUCTION

Our goal in this combined modeling and experimental study was to gain insight into the transmembrane potential changes in defibrillation conditions, namely, when shocks are delivered by an implantable cardioverter defibrillator (ICD). Two hypotheses concerning the presence and characteristics of virtual electrode effects (VEE) during an ICD shock were tested numerically and experimentally: (H1) anisotropy-dependent VEE are induced over a considerable portion of the "bulk" myocardium; and (H2) surface (epicardial and endocardial) VEE are generated under special tissue bath conditions and are not fully anisotropy determined.

METHODS AND RESULTS

Optical mapping was performed on Langendorff-perfused rabbit hearts (n = 4) stained with di-4-ANEPPS. Monophasic shocks were applied during the plateau phase of an action potential through a 9-mm long distal electrode in the right or left ventricle and a 6-cm proximal electrode positioned 3 cm posteriorly to the heart. We modeled the experiment using an ellipsoidal bidomain heart with transmural fiber rotation, placed in a perfusing bath, and subjected to defibrillation shocks delivered by an electrode configuration as described. Our numerical simulations demonstrated VEE occupying a significant portion of the myocardium in the conditions of unequal anisotropy ratios for the intra- and extracellular domains. Statistically significant differences in epicardial polarization patterns were predicted numerically and confirmed experimentally when the interface conditions varied.

CONCLUSION

The present study concludes that VEE are present in transvenous defibrillation. They are shaped by the combined effect of cardiac tissue characteristics and interface conditions. Because of their size, VEE might contribute significantly to defibrillation outcome.