Clinical & Experimental Cardiology
Open Access

Abstract

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

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.