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

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, λ*, in local ischemic tissue. This threshold, separating stable and chaotic regimes, can be specified precisely as λ*=FV 1/3 , where V is the local volume of diseased tissue and 0 < F < 1 is a shape factor, near 1 for compact volumes and progressively smaller for flattened volumes. When the impulse wavelength is <=λ*, VT/VF happens. Typical values for λ* 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.

The effect of the localisation of an underlying ST-elevation myocardial infarction on the VF-waveform: A multi-centre cardiac arrest study

“…18 Given the chaotic and complex nature of VF-signals, which is also impacted by myocardial geometry, future studies with additional VFcharacteristics and advanced signal analysis techniques may provide valuable insights. 5,37 Secondly, VF-characteristics are studied to guide defibrillation during OHCA. Several previous studies showed an association between high AMSA and shock success, and an increase in AMSA following chest compressions.…”

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

“…Real-world chaotic and fractal systems span the spectrum from leaky faucets [3], to ferns [4], to heart rates [5][6][7], to cryptography [8,9]. Many scholars have studied the implications of nonlinearity, chaos and fractals for the social sciences, including sociology [10,11], urban studies [12][13][14][15][16], economics [17][18][19][20][21], architecture [22,23] and city planning [24][25][26][27].…”

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

“…Real-world chaotic and fractal systems span the spectrum from leaky faucets [3], to ferns [4], to heart rates [5][6][7], to cryptography [8,9]. Many scholars have studied the implications of nonlinearity, chaos and fractals for the social sciences, including sociology [10,11], urban studies [12][13][14][15][16], economics [17][18][19][20][21], architecture [22,23] and city planning [24][25][26][27].…”