Asymptotics of The Spectrum of a Two-Dimensional Hartree-Type Operator with a Coulomb Self-Action Potential Near the Lower Boundaries of Spectral Clusters

Atrial fibrillation (AF) is believed to be perpetuated by recirculating spiral waves. Atrial structures are often characterized with action potentials of varying morphologies; however, the role of the structure-dependent atrial electrophysiological heterogeneity in spiral wave behaviour is not well understood. The purpose of this study is to determine the effect of action potential morphology heterogeneity associated with the major atrial structures in spiral wave maintenance. The present study also focuses on how this effect is further modulated by the presence of the inherent periodicity in atrial structure. The goals of the study are achieved through the simulation of electrical behaviour in a two-dimensional atrial tissue model that incorporates the representation of action potentials in various structurally distinct regions in the right atrium. Periodic boundary conditions are then imposed to form a cylinder (quasi three-dimensional), thus allowing exploration of the additional effect of structure periodicity on spiral wave behaviour. Transmembrane potential maps and phase singularity traces are analysed to determine effects on spiral wave behaviour. Results demonstrate that the prolonged refractoriness of the crista terminalis (CT) affects the pattern of spiral wave reentry, while the variation in action potential morphology of the other structures does not. The CT anchors the spiral waves, preventing them from drifting away. Spiral wave dynamics is altered when the ends of the sheet are spliced together to form a cylinder. The main effect of the continuous surface is the generation of secondary spiral waves which influences the primary rotors. The interaction of the primary and secondary spiral waves decreased as cylinder diameter increased.

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Cardiac alternans induced by fibroblast-myocyte coupling: mechanistic insights from computational models

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00341.2009 ◽

2009 ◽

Vol 297 (2) ◽

pp. H775-H784 ◽

Cited By ~ 66

Author(s):

Yuanfang Xie ◽

Alan Garfinkel ◽

James N. Weiss ◽

Zhilin Qu

Keyword(s):

Action Potential ◽

Computational Models ◽

Cardiac Tissue ◽

Experimental Studies ◽

Outward Current ◽

Transient Outward Current ◽

Two Dimensional ◽

Background Current ◽

Cardiac Alternans ◽

Main Components

Recent experimental studies have shown that fibroblasts can electrotonically couple to myocytes via gap junctions. In this study, we investigated how this coupling affects action potential and intracellular calcium (Cai) cycling dynamics in simulated fibroblast-myocyte pairs and in two-dimensional tissue with random fibroblast insertions. We show that a fibroblast coupled with a myocyte generates a gap junction current flowing to the myocyte with two main components: an early pulse of transient outward current, similar to the fast transient outward current, and a later background current during the repolarizing phase. Depending on the relative prominence of the two components, fibroblast-myoycte coupling can 1) prolong or shorten action potential duration (APD), 2) promote or suppress APD alternans due to steep APD restitution (voltage driven) and also result in a novel mechanism of APD alternans at slow heart rates, 3) promote Cai-driven alternans and electromechanically discordant alternans, and 4) promote spatially discordant alternans by two mechanisms: by altering conduction velocity restitution and by heterogeneous fibroblast distribution causing electromechanically concordant and discordant alternans in different regions of the tissue. Thus, through their coupling with myocytes, fibroblasts alter repolarization and Cai cycling alternans at both the cellular and tissue scales, which may play important roles in arrhythmogenesis in diseased cardiac tissue with fibrosis.

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Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1999.276.1.h269 ◽

1999 ◽

Vol 276 (1) ◽

pp. H269-H283 ◽

Cited By ~ 111

Author(s):

Zhilin Qu ◽

James N. Weiss ◽

Alan Garfinkel

Keyword(s):

Action Potential ◽

Antiarrhythmic Drugs ◽

Cardiac Tissue ◽

Potential Model ◽

Spiral Wave ◽

Spiral Waves ◽

Two Dimensional ◽

Recovery From Inactivation ◽

Main Determinants ◽

The Stability

Spiral wave breakup is a proposed mechanism underlying the transition from ventricular tachycardia to fibrillation. We examined the importance of the restitution of action potential duration (APD) and of conduction velocity (CV) to the stability of spiral wave reentry in a two-dimensional sheet of simulated cardiac tissue. The Luo-Rudy ventricular action potential model was modified to eliminate its restitution properties, which are caused by deactivation or recovery from inactivation of K+, Ca2+, and Na+ currents ( I K, I Ca, and I Na, respectively). In this model, we find that 1) restitution of I Ca and I Na are the main determinants of the steepness of APD restitution; 2) for promoting spiral breakup, the range of diastolic intervals over which the APD restitution slope is steep is more important than the maximum steepness; 3) CV restitution promotes spiral wave breakup independently of APD restitution; and 4) “defibrillation” of multiple spiral wave reentry is most effectively achieved by combining an antifibrillatory intervention based on altering restitution with an antitachycardia intervention. These findings suggest a novel paradigm for developing effective antiarrhythmic drugs.

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THE FORMATION OF A RE-ENTRANT ACTION POTENTIAL WAVE FRONT IN TISSUE WITH UNEQUAL ANISOTROPY RATIOS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127491000671 ◽

1991 ◽

Vol 01 (04) ◽

pp. 927-928 ◽

Cited By ~ 11

Author(s):

BRADLEY J. ROTH ◽

JOSHUA M. SAYPOL

Keyword(s):

Action Potential ◽

Wave Front ◽

Two Dimensional ◽

Potential Wave ◽

Phase Singularities

In a syncytial tissue, the intracellular and extracellular spaces may have different degrees of anisotropy. This property allows generation of a re-entrant wave front in a two-dimensional sheet of tissue after two successive stimuli are applied through the same electrode, if the second stimulus is delivered during the vulnerable phase of the first action potential. The re-entrant wave front contains four phase singularities placed symmetrically about the position of the electrode.

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