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Tyree TJ, Murphy P, Rappel WJ. Annihilation dynamics during spiral defect chaos revealed by particle models. CHAOS (WOODBURY, N.Y.) 2024; 34:053131. [PMID: 38787314 PMCID: PMC11141445 DOI: 10.1063/5.0203319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Accepted: 04/30/2024] [Indexed: 05/25/2024]
Abstract
Pair-annihilation events are ubiquitous in a variety of spatially extended systems and are often studied using computationally expensive simulations. Here, we develop an approach in which we simulate the pair-annihilation of spiral wave tips in cardiac models using a computationally efficient particle model. Spiral wave tips are represented as particles with dynamics governed by diffusive behavior and short-ranged attraction. The parameters for diffusion and attraction are obtained by comparing particle motion to the trajectories of spiral wave tips in cardiac models during spiral defect chaos. The particle model reproduces the annihilation rates of the cardiac models and can determine the statistics of spiral wave dynamics, including its mean termination time. We show that increasing the attraction coefficient sharply decreases the mean termination time, making it a possible target for pharmaceutical intervention.
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Affiliation(s)
- Timothy J. Tyree
- Department of Physics, University of California San Diego, San Diego, California 92093, USA
| | - Patrick Murphy
- Department of Mathematics and Statistics, San Jose State University, San Jose, California 95192, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California San Diego, San Diego, California 92093, USA
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Arno L, Quan J, Nguyen NT, Vanmarcke M, Tolkacheva EG, Dierckx H. A Phase Defect Framework for the Analysis of Cardiac Arrhythmia Patterns. Front Physiol 2021; 12:690453. [PMID: 34630135 PMCID: PMC8494009 DOI: 10.3389/fphys.2021.690453] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 08/19/2021] [Indexed: 11/24/2022] Open
Abstract
During cardiac arrhythmias, dynamical patterns of electrical activation form and evolve, which are of interest to understand and cure heart rhythm disorders. The analysis of these patterns is commonly performed by calculating the local activation phase and searching for phase singularities (PSs), i.e., points around which all phases are present. Here we propose an alternative framework, which focuses on phase defect lines (PDLs) and surfaces (PDSs) as more general mechanisms, which include PSs as a specific case. The proposed framework enables two conceptual unifications: between the local activation time and phase description, and between conduction block lines and the central regions of linear-core rotors. A simple PDL detection method is proposed and applied to data from simulations and optical mapping experiments. Our analysis of ventricular tachycardia in rabbit hearts (n = 6) shows that nearly all detected PSs were found on PDLs, but the PDLs had a significantly longer lifespan than the detected PSs. Since the proposed framework revisits basic building blocks of cardiac activation patterns, it can become a useful tool for further theory development and experimental analysis.
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Affiliation(s)
- Louise Arno
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
| | - Jan Quan
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
| | - Nhan T Nguyen
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
| | | | - Elena G Tolkacheva
- Biomedical Engineering Department, University of Minnesota, Minneapolis, MN, United States
| | - Hans Dierckx
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
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Brugada-Terradellas C, Hellemans A, Brugada P, Smets P. Sudden cardiac death: A comparative review of humans, dogs and cats. Vet J 2021; 274:105696. [PMID: 34148018 DOI: 10.1016/j.tvjl.2021.105696] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Revised: 05/22/2021] [Accepted: 05/24/2021] [Indexed: 01/14/2023]
Abstract
Sudden death is one of the most common causes of death in humans in Western countries. Approximately 85% of these cases are of cardiac origin. In dogs and cats, sudden cardiac death (SCD) also commonly occurs, but fewer pathophysiological and prevalence data are available. Both structural, primarily 'electrical' and ischemic heart diseases are known to cause SCD, many of which share similar underlying arrhythmogenic mechanisms between humans and companion animals. As for underlying genetics, numerous mutations on multiple loci have been related to SCD in humans, but only a few mutations associated with dilated cardiomyopathy and SCD have been identified in dogs, e.g. in the phospholamban and titin genes. Information published from human medicine can therefore inform future veterinary studies, but also dogs and cats could act as spontaneous models of SCD in humans. Further research in both fields is therefore warranted to better understand the pathophysiology, genetics, and prevention of SCD.
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Affiliation(s)
- Celine Brugada-Terradellas
- Small Animal Department, Faculty of Veterinary Medicine, Ghent University, Salisburylaan 133, 9820 Merelbeke, Belgium.
| | - Arnaut Hellemans
- Small Animal Department, Faculty of Veterinary Medicine, Ghent University, Salisburylaan 133, 9820 Merelbeke, Belgium
| | - Pedro Brugada
- Pedro Brugada, Cardiovascular Division, UZ Brussel - VUB, Avenue du Laerbeek 101, 1090 Brussels, Belgium
| | - Pascale Smets
- Small Animal Department, Faculty of Veterinary Medicine, Ghent University, Salisburylaan 133, 9820 Merelbeke, Belgium
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Rajagopal K, Parastesh F, Azarnoush H, Hatef B, Jafari S, Berec V. Spiral waves in externally excited neuronal network: Solvable model with a monotonically differentiable magnetic flux. CHAOS (WOODBURY, N.Y.) 2019; 29:043109. [PMID: 31042930 DOI: 10.1063/1.5088654] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2019] [Accepted: 03/21/2019] [Indexed: 06/09/2023]
Abstract
Spiral waves are particular spatiotemporal patterns connected to specific phase singularities representing topological wave dislocations or nodes of zero amplitude, witnessed in a wide range of complex systems such as neuronal networks. The appearance of these waves is linked to the network structure as well as the diffusion dynamics of its blocks. We report a novel form of the Hindmarsh-Rose neuron model utilized as a square neuronal network, showing the remarkable multistructure of dynamical patterns ranging from characteristic spiral wave domains of spatiotemporal phase coherence to regions of hyperchaos. The proposed model comprises a hyperbolic memductance function as the monotone differentiable magnetic flux. Hindmarsh-Rose neurons with an external electromagnetic excitation are considered in three different cases: no excitation, periodic excitation, and quasiperiodic excitation. We performed an extensive study of the neuronal dynamics including calculation of equilibrium points, bifurcation analysis, and Lyapunov spectrum. We have found the property of antimonotonicity in bifurcation scenarios with no excitation or periodic excitation and identified wide regions of hyperchaos in the case of quasiperiodic excitation. Furthermore, the formation and elimination of the spiral waves in each case of external excitation with respect to stimuli parameters are investigated. We have identified novel forms of Hindmarsh-Rose bursting dynamics. Our findings reveal multipartite spiral wave formations and symmetry breaking spatiotemporal dynamics of the neuronal model that may find broad practical applications.
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Affiliation(s)
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15875-4413, Iran
| | - Hamed Azarnoush
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15875-4413, Iran
| | - Boshra Hatef
- Neuroscience Research Center, Baqiyatallah University of Medical Sciences, Tehran 14359-16471, Iran
| | - Sajad Jafari
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
| | - Vesna Berec
- Institute of Nuclear Sciences, Vinca, PO Box 522, 11001 Belgrade, Serbia
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Dierckx H, Panfilov AV, Verschelde H, Biktashev VN, Biktasheva IV. Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves. Phys Rev E 2019; 99:022217. [PMID: 30934367 DOI: 10.1103/physreve.99.022217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/09/2023]
Abstract
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.
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Affiliation(s)
- Hans Dierckx
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - A V Panfilov
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620075, Russia
| | - H Verschelde
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - I V Biktasheva
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
- Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom
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Dierckx H, Biktasheva IV, Verschelde H, Panfilov AV, Biktashev VN. Filament Tension and Phase Locking of Meandering Scroll Waves. PHYSICAL REVIEW LETTERS 2017; 119:258101. [PMID: 29303350 DOI: 10.1103/physrevlett.119.258101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2017] [Indexed: 06/07/2023]
Abstract
Meandering spiral waves are often observed in excitable media such as the Belousov-Zhabotinsky reaction and cardiac tissue. We derive a theory for drift dynamics of meandering rotors in general reaction-diffusion systems and apply it to two types of external disturbances: an external field and curvature-induced drift in three dimensions. We find two distinct regimes: with small filament curvature, meandering scroll waves exhibit filament tension, whose sign determines the stability and drift direction. In the regimes of strong external fields or meandering motion close to resonance, however, phase locking of the meander pattern is predicted and observed.
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Affiliation(s)
- Hans Dierckx
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - I V Biktasheva
- Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - H Verschelde
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - A V Panfilov
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
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