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

Modeling bipolar stimulation of cardiac tissue

Unipolar stimulation of cardiac tissue is often used in the design of cardiac pacemakers because of the low current required to depolarize the surrounding tissue at rest. However, the advantages of unipolar over bipolar stimulation are not obvious at shorter coupling intervals when the tissue near the pacing electrode is relatively refractory. Therefore, this paper analyzes bipolar stimulation of cardiac tissue. The strength-interval relationship for bipolar stimulation is calculated using the bidomain model and a recently developed parsimonious ionic current model. The strength-interval curves obtained using different electrode separations and arrangements (electrodes placed parallel to the fibers versus perpendicular to the fibers) indicate that bipolar stimulation results in more complex activation patterns compared to unipolar stimulation. An unusually low threshold stimulus current is observed when the electrodes are close to each other (a separation of 1 mm) because of break excitation. Unlike for unipolar stimulation, anode make excitation is not present during bipolar stimulation, and an abrupt switch from anode break to cathode make excitation can cause dramatic changes in threshold with very small changes in the interval. These results could impact the design of implantable pacemakers and defibrillators.

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

Introduction and background

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

Methods

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

Results

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

Conclusion

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

Cardiac strength-interval curves calculated using a bidomain tissue with a parsimonious ionic current

The strength-interval curve plays a major role in understanding how cardiac tissue responds to an electrical stimulus. This complex behavior has been studied previously using the bidomain formulation incorporating the Beeler-Reuter and Luo-Rudy dynamic ionic current models. The complexity of these models renders the interpretation and extrapolation of simulation results problematic. Here we utilize a recently developed parsimonious ionic current model with only two currents—a sodium current that activates rapidly upon depolarization I_Na and a time-independent inwardly rectifying repolarization current I_K—which reproduces many experimentally measured action potential waveforms. Bidomain tissue simulations with this ionic current model reproduce the distinctive dip in the anodal (but not cathodal) strength-interval curve. Studying model variants elucidates the necessary and sufficient physiological conditions to predict the polarity dependent dip: a voltage and time dependent I_Na, a nonlinear rectifying repolarization current, and bidomain tissue with unequal anisotropy ratios.

The Mechanism of Reflection Type Reentry: A Simulation Study

INTRODUCTION

Reflection is a special type of reentry in which an electrical wave front travels in a forward direction through tissue that is then re-excited by a wave front that propagates backward. This type of reentry has been studied computationally in 1-dimensional fibers and verified experimentally. Different hypotheses explaining reflected reentry have been proposed based on the structure and heterogeneity of the tissue properties, but the mechanism remains uncertain.

METHODS AND RESULTS

We used the bidomain model to represent cardiac tissue and the Luo-Rudy model to describe the active membrane properties. We consider an ischemic region in a volume of ventricular myocardium. Our results show that a slow depolarization in the ischemic border zone caused by electrotonic coupling to depolarized tissue in the normal region creates a delay between proximal and distal regions that produces enough electrotonic current in the distal region to re-excite the proximal region.

CONCLUSION

Our simulation shows that an early afterdepolarization (EAD) is not the source of the reflection. It depends on the pacing interval and stimulus strength necessary to maintain enough time delay between proximal and distal regions.

ELECTRICAL INSTABILITY DUE TO REGIONAL INCREASE IN EXTRACELLULAR POTASSIUM ION CONCENTRATION

INTRODUCTION

Ventricular tachycardia and ventricular fibrillation are the two most dangerous arrhythmias. Both are related to reentrant electrical activity in the ventricles. Many studies of arrhythmias consider a homogeneous sheet of cardiac tissue. Since normal ventricular myocardium is inhomogeneous and inhomogeneities play an important role in the induction of reentry, we investigate the effect of a localized inhomogeniety developed at the border between normal and ischemic region.

METHODS

We used the bidomain model to represent the electrical properties of cardiac tissue and a modified version of the dynamic Luo-Rudy (LRd) model to represent the active properties of the membrane. To investigate the effect of a localized inhomogeneity, the extracellular potassium [K]e concentration is raised to 10 mM from normal [K]e (4 mM) on the right half of the tissue.

RESULTS AND DISCUSSION

A train of cathodal stimuli are applied from the lower left corner of the tissue with different basic cycle lengths (BCL). At certain BCL, the spatial heterogeneity created with regional elevation of [K]e can lead to action potential instability (alternans) in the normal and border regions, and 2:1 conduction block in the ischemic region. We observed the reentry when local heterogeneity in [K]e is changed from 10 to 12 mM on the right half of the virtual ventricular myocardium sheet.

CONCLUSION

Electrical alternans occur during high heart rates and are observed in patients suffering from ventricular tachycardia. It is an early indication of left ventricular systolic impairment. This study will help to evaluate alternans as a predictor and guide for antiarrhythmic therapy.