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https://hdl.handle.net/2440/130129
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Type: | Journal article |
Title: | M/M/infinity birth-death processes - a quantitative representational framework to summarize and explain phase singularity and wavelet dynamics in atrial fibrillation |
Author: | Dharmaprani, D. Jenkins, E. Aguilar, M. Quah, J.X. Lahiri, A. Tiver, K. Mitchell, L. Kuklik, P. Meyer, C. Willems, S. Clayton, R. Nash, M. Nattel, S. McGavigan, A.D. Ganesan, A.N. |
Citation: | Frontiers in Physiology, 2020; 11:616866-1-616866-17 |
Publisher: | Frontiers Media |
Issue Date: | 2020 |
ISSN: | 1664-042X 1664-042X |
Statement of Responsibility: | Dhani Dharmaprani, Evan Jenkins, Martin Aguilar, Jing X. Quah, Anandaroop Lahiri ... Lewis Mitchell ... et al. |
Abstract: | 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 λf (for PS or wavelet formation) and λd (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 λf and λd 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 λf and λd 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. |
Keywords: | Markov model atrial fibrillation birth–death process phase singularity wavelet |
Rights: | © 2021 Dharmaprani, Jenkins, Aguilar, Quah, Lahiri, Tiver, Mitchell, Kuklik, Meyer,Willems, Clayton, Nash, Nattel, McGavigan and Ganesan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. |
DOI: | 10.3389/fphys.2020.616866 |
Grant ID: | http://purl.org/au-research/grants/nhmrc/1063754 |
Published version: | http://dx.doi.org/10.3389/fphys.2020.616866 |
Appears in Collections: | Aurora harvest 4 Medicine publications |
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hdl_130129.pdf | Published version | 6.3 MB | Adobe PDF | View/Open |
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