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

TY - JOUR

T1 - M/M/Infinity Birth-Death Processes - A Quantitative Representational Framework to Summarize and Explain Phase Singularity and Wavelet Dynamics in Atrial Fibrillation

AU - Dharmaprani, Dhani

AU - Jenkins, Evan

AU - Aguilar, Martin

AU - Quah, Jing X

AU - Lahiri, Anandaroop

AU - Tiver, Kathryn

AU - Mitchell, Lewis

AU - Kuklik, Pawel

AU - Meyer, Christian

AU - Willems, Stephan

AU - Clayton, Richard

AU - Nash, Martyn

AU - Nattel, Stanley

AU - McGavigan, Andrew D

AU - Ganesan, Anand N

N1 - Copyright © 2021 Dharmaprani, Jenkins, Aguilar, Quah, Lahiri, Tiver, Mitchell, Kuklik, Meyer, Willems, Clayton, Nash, Nattel, McGavigan and Ganesan.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

U2 - 10.3389/fphys.2020.616866

DO - 10.3389/fphys.2020.616866

M3 - SCORING: Journal article

C2 - 33519522

VL - 11

JO - FRONT PHYSIOL

JF - FRONT PHYSIOL

SN - 1664-042X

M1 - 616866

ER -