Understanding the origins of the basic equations of statistical fibrillatory dynamics

Simple item page
dc.contributor.authorJenkins, E.V.
dc.contributor.authorDharmaprani, D.
dc.contributor.authorSchopp, M.
dc.contributor.authorQuah, J.X.
dc.contributor.authorTiver, K.
dc.contributor.authorMitchell, L.
dc.contributor.authorPope, K.
dc.contributor.authorGanesan, A.N.
dc.date.issued2022
dc.description.abstractThe 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.
dc.description.statementofresponsibilityEvan V. Jenkins, Dhani Dharmaprani, Madeline Schopp, Jing Xian Quah, Kathryn Tiver, Lewis Mitchell, Kenneth Pope, and Anand N. Ganesan
dc.identifier.citationChaos, 2022; 32(3):032101-1-032101-12
dc.identifier.doi10.1063/5.0062095
dc.identifier.issn1054-1500
dc.identifier.issn1089-7682
dc.identifier.orcidDharmaprani, D. [0000-0003-4660-0119]
dc.identifier.orcidMitchell, L. [0000-0001-8191-1997]
dc.identifier.urihttps://hdl.handle.net/2440/134921
dc.language.isoen
dc.publisherAIP Publishing
dc.relation.granthttp://purl.org/au-research/grants/nhmrc/2010522
dc.rights© 2022 Author(s). Published under an exclusive license by AIP Publishing.
dc.source.urihttps://doi.org/10.1063/5.0062095
dc.subjectHumans
dc.subjectAtrial Fibrillation
dc.subjectVentricular Fibrillation
dc.subjectComputer Simulation
dc.subject.meshHumans
dc.subject.meshAtrial Fibrillation
dc.subject.meshVentricular Fibrillation
dc.subject.meshComputer Simulation
dc.titleUnderstanding the origins of the basic equations of statistical fibrillatory dynamics
dc.typeJournal article
pubs.publication-statusPublished

Files

Collections

Mathematical Sciences publications