Initiation of Ventricular Fibrillation by a Single Ectopic Beat in Three Dimensional Numerical Models of Ischemic Heart Disease: Abrupt Transition to Chaos

Charles F Babbs

doi:10.4172/2155-9880.1000346

Abstract

Background: To explore the conditions most dangerous for the emergence of sustained Ventricular Tachycardia or Ventricular Fibrillation (VT/VF) a new computational model of ventricular myocardium including 2592 finite elements in three dimensions was created. Methods: The fully three dimensional model of right and left ventricular muscle was used to simulate the spread of electrical activation and the resulting electrocardiogram. Localized zones of ischemic muscle tissue were characterized by reduced conduction velocity and reduced refractory period, and VT/VF was initiated by single ectopic beats. The simulated body surface Electrocardiogram (ECG) was also computed. Results: In this system clinically realistic VT/VF is readily produced by single stimuli. Reduced conduction velocity and reduced effective refractory period in localized abnormal muscle predispose to VT/VF. Transition to chaos was abrupt. No one specific pattern of re-entry, spiral waves, or vortices could be identified that later decomposed into VT/VF. Instead, there was a wide variety of activation patterns leading to chaos, depending sensitively on initial conditions. Nonetheless, a clear border between stable vs. chaotic behavior was defined by a critical threshold impulse wavelength, the product of conduction velocity and refractory period, γ*, in local ischemic tissue. This threshold, separating stable and chaotic regimes, can be specified precisely as γ*=FV1/3 , where V is the local volume of diseased tissue and 0 γ F γ 1 is a shape factor, near 1 for compact volumes and progressively smaller for flattened volumes. When the impulse wavelength is ≤γ*, VT/VF happens. Typical values for γ* range from 1 to 3 cm. Such behavior is characteristic of classical chaotic systems. Conclusions: The patterns of muscle activation leading to self-sustaining VT/VF observed in three dimensional diseased hearts are much more complex and variable than traditional re-entry in two dimensions. Instead a model of abrupt transition to chaos emerges from the application of first-principles cardiac electrophysiology, realistic ventricular anatomy, and the pathophysiology of ischemic cardiac muscle. This phenomenon may represent a higher order form of mathematical chaos than has been previously studied.

Highlights

In ventricular tachycardia or ventricular fibrillation (VT/VF, or VF for short) wavelets of electrical activation propagate, seemingly randomly, across the myocardium, leading to profound reduction or complete loss of pumping action
To study the genesis of Ventricular Tachycardia or Ventricular Fibrillation (VT/VF) a computer-based mathematical model of the cardiac ventricles was created to describe the spread of electrical activation throughout the myocardium and the resulting electrocardiogram
As well, have previously demonstrated the importance of wall thickness in a number of model systems [9,10,11,13]. These findings suggest that phenomena in the third, radial dimension are not necessary for the genesis of VT/VF, but do substantially increase the likelihood of VT/VF

Summary

Introduction

In ventricular tachycardia or ventricular fibrillation (VT/VF , or VF for short) wavelets of electrical activation propagate, seemingly randomly, across the myocardium, leading to profound reduction or complete loss of pumping action. In computer modeling one can create a realistically shaped three dimensional syncytium of ventricular tissue to study in detail the differences between self-limited ectopic beats and self-sustaining VT/VF. Such studies can capture the essence of underlying pathophysiology and shine light on some risk factors that make VF more likely by sharpening understanding of its proximal causes. Perhaps a better way forward from a modeling perspective is to envision the simplest possible model that incorporates key features relevant to human pathophysiology These include three dimensional muscle mass shaped like human sized cardiac ventricles, at least one localized area of viable but ischemic muscle tissue, and the initiation of VT/VF by premature beats rather than by continuous electrical stimulation or rapid pacing. To explore the conditions most dangerous for the emergence of sustained Ventricular Tachycardia or Ventricular Fibrillation (VT/VF) a new computational model of ventricular myocardium including 2592 finite elements in three dimensions was created

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Discussion

Conclusion