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 lambda(f) (for PS or wavelet formation) and lambda(d) (PS or wavelet destruction), with steady-state population dynamics modeled as an M/M/infinity birth-death process. We further hypothesized that changes to the M/M/infinity 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 lambda(f) and lambda(d) can be combined in a Markov M/M/infinity 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 lambda(f) and lambda(d) is associated with slower mixing rates of the M/M/infinity birth-death matrix, providing an explanation for spontaneous AF termination.Conclusion: M/M/infinity 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.