A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death.

BACKGROUND: Ventricular fibrillation (VF) is characterized by multiple wavelets and rotors. No equation to predict the number of rotors and wavelets observed during fibrillation has been validated in human VF. OBJECTIVE: The purpose of this study was to test the hypothesis that a single equation derived from a Markov M/M/∞ birth-death process could predict the number of rotors and wavelets occurring in human clinical VF. METHODS: Epicardial induced VF (256-electrode) recordings obtained from patients undergoing cardiac surgery were studied (12 patients; 62 epochs). Rate constants for phase singularity (PS) (which occur at the pivot points of rotors) and wavefront (WF) formation and destruction were derived by fitting distributions to PS and WF interformation and lifetimes. These rate constants were combined in an M/M/∞ governing equation to predict the number of PS and WF in VF episodes. Observed distributions were compared to those predicted by the M/M/∞ equation. RESULTS: The M/M/∞ equation accurately predicted average PS and WF number and population distribution, demonstrated in all epochs. Self-terminating episodes of VF were distinguished from VF episodes requiring termination by a trend toward slower PS destruction, slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second largest eigenvalue modulus of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter interactivation time intervals compared to shorter-lasting PS lasting <150 ms (∼1 PS rotation in human VF). CONCLUSION: The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics.

Atrial fibrosis and substrate based characterization in atrial fibrillation: Time to move forwards.

Atrial fibrillation (AF) is the most commonly encountered cardiac arrhythmia in clinical practice. However, current therapeutic interventions for atrial fibrillation have limited clinical efficacy as a consequence of major knowledge gaps in the mechanisms sustaining atrial fibrillation. From a mechanistic perspective, there is increasing evidence that atrial fibrosis plays a central role in the maintenance and perpetuation of atrial fibrillation. Electrophysiologically, atrial fibrosis results in alterations in conduction velocity, cellular refractoriness, and produces conduction block promoting meandering, unstable wavelets and micro-reentrant circuits. Clinically, atrial fibrosis has also linked to poor clinical outcomes including AF-related thromboembolic complications and arrhythmia recurrences post catheter ablation. In this article, we review the pathophysiology behind the formation of fibrosis as AF progresses, the role of fibrosis in arrhythmogenesis, surrogate markers for detection of fibrosis using cardiac magnetic resonance imaging, echocardiography and electroanatomic mapping, along with their respective limitations. We then proceed to review the current evidence behind therapeutic interventions targeting atrial fibrosis, including drugs and substrate-based catheter ablation therapies followed by the potential future use of electro phenotyping for AF characterization to overcome the limitations of contemporary substrate-based methodologies.

M/M/Infinity Birth-Death Processes - A Quantitative Representational Framework to Summarize and Explain Phase Singularity and Wavelet Dynamics in Atrial Fibrillation.

RATIONALE: A quantitative framework to summarize and explain the quasi-stationary population dynamics of unstable phase singularities (PS) and wavelets in human atrial fibrillation (AF) is at present lacking. Building on recent evidence showing that the formation and destruction of PS and wavelets in AF can be represented as renewal processes, we sought to establish such a quantitative framework, which could also potentially provide insight into the mechanisms of spontaneous AF termination. OBJECTIVES: Here, we hypothesized that the observed number of PS or wavelets in AF could be governed by a common set of renewal rate constants λ f (for PS or wavelet formation) and λ d (PS or wavelet destruction), with steady-state population dynamics modeled as an M/M/∞ birth-death process. We further hypothesized that changes to the M/M/∞ birth-death matrix would explain spontaneous AF termination. METHODS AND RESULTS: AF was studied in in a multimodality, multispecies study in humans, animal experimental models (rats and sheep) and Ramirez-Nattel-Courtemanche model computer simulations. We demonstrated: (i) that λ f and λ d can be combined in a Markov M/M/∞ process to accurately model the observed average number and population distribution of PS and wavelets in all systems at different scales of mapping; and (ii) that slowing of the rate constants λ f and λ d is associated with slower mixing rates of the M/M/∞ birth-death matrix, providing an explanation for spontaneous AF termination. CONCLUSION: M/M/∞ birth-death processes provide an accurate quantitative representational architecture to characterize PS and wavelet population dynamics in AF, by providing governing equations to understand the regeneration of PS and wavelets during sustained AF, as well as providing insight into the mechanism of spontaneous AF termination.