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|Title:||Understanding the origins of the basic equations of statistical fibrillatory dynamics|
|Citation:||Chaos: an interdisciplinary journal of nonlinear science, 2022; 32(3):032101-1-032101-12|
|Evan V. Jenkins, Dhani Dharmaprani, Madeline Schopp, Jing Xian Quah, Kathryn Tiver, Lewis Mitchell, Kenneth Pope, and Anand N. Ganesan|
|Abstract:||The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with con- servative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker’s transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pat- tern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.|
|Rights:||© 2022 Author(s). Published under an exclusive license by AIP Publishing.|
|Appears in Collections:||Mathematical Sciences publications|
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