1
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Li TC, Li QH, Song Z, Pan DB, Zhong W, Luo J. Drift of sparse and dense spiral waves under joint external forces. Phys Rev E 2023; 107:024213. [PMID: 36932583 DOI: 10.1103/physreve.107.024213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2022] [Accepted: 02/07/2023] [Indexed: 06/18/2023]
Abstract
Many methods have been employed to investigate the drift behaviors of spiral waves in an effort to understand and control their dynamics. Drift behaviors of sparse and dense spirals induced by external forces have been investigated, yet they remain incompletely understood. Here we employ joint external forces to study and control the drift dynamics. First, sparse and dense spiral waves are synchronized by the suitable external current. Then, under another weak current or heterogeneity, the synchronized spirals undergo a directional drift, and the dependence of their drift velocity on the strength and frequency of the joint external force is studied.
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Affiliation(s)
- Teng-Chao Li
- School of Physics, Hangzhou Normal University, Hangzhou 311121, China
| | - Qi-Hao Li
- Peng Cheng Laboratory, Shenzhen, Guangdong 518066, China
| | - Zhen Song
- Peng Cheng Laboratory, Shenzhen, Guangdong 518066, China
| | - De-Bei Pan
- Department of Physics, Guangxi Medical University, Nanning 530021, China
| | - Wei Zhong
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Jinming Luo
- School of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
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2
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He YJ, Xia YX, Mei JT, Zhou K, Jiang C, Pan JT, Zheng D, Zheng B, Zhang H. Topological charge-density-vector method of identifying filaments of scroll waves. Phys Rev E 2023; 107:014217. [PMID: 36797968 DOI: 10.1103/physreve.107.014217] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Scroll waves have been found in a variety of three-dimensional excitable media, including physical, chemical, and biological origins. Scroll waves in cardiac tissue are of particular significance as they underlie ventricular fibrillation that can cause sudden death. The behavior of a scroll wave is characterized by a line of phase singularity at its organizing center, known as a filament. A thorough investigation into the filament dynamics is the key to further exploration of the general theory of scroll waves in excitable media and the mechanisms of ventricular fibrillation. In this paper, we propose a method to identify filaments of scroll waves in excitable media. From the definition of the topological charge of filaments, we obtain the discrete expression of the topological charge-density vector, which is useful in calculating the topological charge vectors at each grid in the space directly. The set of starting points of these topological charge vectors represents a set of phase singularities, thereby forming a line of phase singularity, that is, a filament of a scroll wave.
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Affiliation(s)
- Yin-Jie He
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Yuan-Xun Xia
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Jin-Tao Mei
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Kuangshi Zhou
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Chenyang Jiang
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Dafang Zheng
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Bo Zheng
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
- School of Physics and Astronomy, Yunnan University, Kunming 650091, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
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3
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Pravdin SF, Patrakeev MA, Panfilov AV. Meander pattern of spiral wave and the spatial distribution of its cycle length. Phys Rev E 2023; 107:014215. [PMID: 36797919 DOI: 10.1103/physreve.107.014215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 01/06/2023] [Indexed: 01/27/2023]
Abstract
One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside T^{out} and inside T^{in} the meandering trajectory with a ratio of T^{in}/T^{out}=(n+1)/n for the inward and (n-1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.
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Affiliation(s)
- Sergei F Pravdin
- Krasovskii Institute of Mathematics and Mechanics, 620108 Ekaterinburg, Russia and Ural Federal University, High-Performance Computing Department, 620002 Ekaterinburg, Russia
| | - Mikhail A Patrakeev
- Krasovskii Institute of Mathematics and Mechanics, 620108 Ekaterinburg, Russia and Ural Federal University, Mathematical Analysis Department, 620002 Ekaterinburg, Russia
| | - Alexander V Panfilov
- Ural Federal University, Research Laboratory "Mathematical Modeling in Physiology and Medicine Based on Supercomputers", 620002 Ekaterinburg, Russia and World-Class Research Center "Digital biodesign and personalized healthcare", Sechenov University, 119146 Moscow, Russia
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4
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Li QH, Xia YX, Xu SX, Song Z, Pan JT, Panfilov AV, Zhang H. Control of spiral waves in optogenetically modified cardiac tissue by periodic optical stimulation. Phys Rev E 2022; 105:044210. [PMID: 35590553 DOI: 10.1103/physreve.105.044210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 03/30/2022] [Indexed: 06/15/2023]
Abstract
Resonant drift of nonlinear spiral waves occurs in various types of excitable media under periodic stimulation. Recently a novel methodology of optogenetics has emerged, which allows to affect excitability of cardiac cells and tissues by optical stimuli. In this paper we study if resonant drift of spiral waves in the heart can be induced by a homogeneous weak periodic optical stimulation of cardiac tissue. We use a two-variable and a detailed model of cardiac tissue and add description of depolarizing and hyperpolarizing optogenetic ionic currents. We show that weak periodic optical stimulation at a frequency equal to the natural rotation frequency of the spiral wave induces resonant drift for both depolarizing and hyperpolarizing optogenetic currents. We quantify these effects and study how the speed of the drift and its direction depend on the initial conditions. We also derive analytical formulas based on the response function theory which correctly predict the drift velocity and its trajectory. We conclude that optogenetic methodology can be used for control of spiral waves in cardiac tissue and discuss its possible applications.
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Affiliation(s)
- Qi-Hao Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
- Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518066, China
| | - Yuan-Xun Xia
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Shu-Xiao Xu
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhen Song
- Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518066, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620002, Russia
- World-Class Research Center "Digital biodesign and personalized healthcare," Sechenov University, Moscow 119146, Russia
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
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Galappaththige SK, Pathmanathan P, Bishop MJ, Gray RA. Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study. Front Physiol 2019; 10:564. [PMID: 31164829 PMCID: PMC6536150 DOI: 10.3389/fphys.2019.00564] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Accepted: 04/24/2019] [Indexed: 01/07/2023] Open
Abstract
Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.
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Affiliation(s)
- Suran K Galappaththige
- Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
| | - Pras Pathmanathan
- Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
| | - Martin J Bishop
- Division of Imaging Sciences, Department of Biomedical Engineering, King's College London, London, United Kingdom
| | - Richard A Gray
- Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
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Hornung D, Biktashev VN, Otani NF, Shajahan TK, Baig T, Berg S, Han S, Krinsky VI, Luther S. Mechanisms of vortices termination in the cardiac muscle. ROYAL SOCIETY OPEN SCIENCE 2017; 4:170024. [PMID: 28405398 PMCID: PMC5383855 DOI: 10.1098/rsos.170024] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2017] [Accepted: 02/14/2017] [Indexed: 06/07/2023]
Abstract
We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.
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Affiliation(s)
- D. Hornung
- Max Planck Institute DS, BMPG, Gottingen, Germany
| | | | - N. F. Otani
- Rochester Institute of Technology, Rochester, NY, USA
| | - T. K. Shajahan
- National Institute of Technology Karnataka, Bangalore, India
| | - T. Baig
- Max Planck Institute DS, BMPG, Gottingen, Germany
- Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen
| | - S. Berg
- Max Planck Institute DS, BMPG, Gottingen, Germany
- Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen
| | - S. Han
- Rochester Institute of Technology, Rochester, NY, USA
| | - V. I. Krinsky
- Max Planck Institute DS, BMPG, Gottingen, Germany
- INLN, CNRS, Valbonne, France
| | - S. Luther
- Max Planck Institute DS, BMPG, Gottingen, Germany
- Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen
- Department of Pharmacology, University Medical Centre Göttingen, Robert-Koch-Str. 40, 37075 Göttingen, Germany
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7
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Alonso S, Bär M, Echebarria B. Nonlinear physics of electrical wave propagation in the heart: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:096601. [PMID: 27517161 DOI: 10.1088/0034-4885/79/9/096601] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.
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Affiliation(s)
- Sergio Alonso
- Physikalisch-Technische Bundesanstalt, Abbestr. 2-12 10587, Berlin, Germany. Department of Physics, Universitat Politècnica de Catalunya, Av. Dr. Marañón 44, E-08028 Barcelona, Spain
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8
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Li TC, Gao X, Zheng FF, Cai MC, Li BW, Zhang H, Dierckx H. Phase-locked scroll waves defy turbulence induced by negative filament tension. Phys Rev E 2016; 93:012216. [PMID: 26871082 DOI: 10.1103/physreve.93.012216] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2015] [Indexed: 11/07/2022]
Abstract
Scroll waves in a three-dimensional media may develop into turbulence due to negative tension of the filament. Such negative tension-induced instability of scroll waves has been observed in the Belousov-Zhabotinsky reaction systems. Here we propose a method to restabilize scroll wave turbulence caused by negative tension in three-dimensional chemical excitable media using a circularly polarized (rotating) external field. The stabilization mechanism is analyzed in terms of phase-locking caused by the external field, which makes the effective filament tension positive. The phase-locked scroll waves that have positive tension and higher frequency defy the turbulence and finally restore order. A linear theory for the change of filament tension caused by a generic rotating external field is presented and its predictions closely agree with numerical simulations.
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Affiliation(s)
- Teng-Chao Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Xiang Gao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Fei-Fei Zheng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Mei-Chun Cai
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China
| | - Bing-Wei Li
- Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Hans Dierckx
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
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9
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Filament Dynamics during Simulated Ventricular Fibrillation in a High-Resolution Rabbit Heart. BIOMED RESEARCH INTERNATIONAL 2015; 2015:720575. [PMID: 26587544 PMCID: PMC4637469 DOI: 10.1155/2015/720575] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2014] [Accepted: 02/06/2015] [Indexed: 11/30/2022]
Abstract
The mechanisms underlying ventricular fibrillation (VF) are not well understood. The electrical activity on the heart surface during VF has been recorded extensively in the experimental setting and in some cases clinically; however, corresponding transmural activation patterns are prohibitively difficult to measure. In this paper, we use a high-resolution biventricular heart model to study three-dimensional electrical activity during fibrillation, focusing on the driving sources of VF: “filaments,” the organising centres of unstable reentrant scroll waves. We show, for the first time, specific 3D filament dynamics during simulated VF in a whole heart geometry that includes fine-scale anatomical structures. Our results suggest that transmural activity is much more complex than what would be expected from surface observations alone. We present examples of complex intramural activity, including filament breakup and reattachment, anchoring to the thin right ventricular apex; rapid transitions among various filament shapes; and filament lengths much greater than wall thickness. We also present evidence for anatomy playing a major role in VF development and coronary vessels and trabeculae influencing filament dynamics. Overall, our results indicate that intramural activity during simulated VF is extraordinarily complex and suggest that further investigation of 3D filaments is necessary to fully comprehend recorded surface patterns.
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Abstract
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
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Affiliation(s)
- Zhilin Qu
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Correspondence to: Zhilin Qu, PhD, Department of Medicine, Division of Cardiology, David Geffen School of Medicine at UCLA, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095, Tel: 310-794-6050, Fax: 310-206-9133,
| | - Gang Hu
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Alan Garfinkel
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Integrative Biology and Physiology, University of California, Los Angeles, California 90095, USA
| | - James N. Weiss
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
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Trayanova NA, Boyle PM. Advances in modeling ventricular arrhythmias: from mechanisms to the clinic. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2013; 6:209-24. [PMID: 24375958 DOI: 10.1002/wsbm.1256] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2013] [Revised: 10/16/2013] [Accepted: 11/12/2013] [Indexed: 11/12/2022]
Abstract
Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.
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Affiliation(s)
- Natalia A Trayanova
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, USA
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12
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Hörning M. Termination of pinned vortices by high-frequency wave trains in heartlike excitable media with anisotropic fiber orientation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031912. [PMID: 23030949 DOI: 10.1103/physreve.86.031912] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2012] [Revised: 07/22/2012] [Indexed: 06/01/2023]
Abstract
A variety of chemical and biological nonlinear excitable media, including heart tissue, exhibit vortices (spiral waves) that can anchor to nonexcitable obstacles. Such anchored vortices can be terminated by the application of high-frequency wave trains, as shown previously in isotropic excitable media. In this study, we examined the basic dependencies of the conduction velocities of planar waves and waves around curved obstacles as a function of anisotropy through numerical simulations of excitable media that mimic the fiber orientation in a real heart. We also investigated the unpinning of anchored spiral waves by high-frequency wave trains in an anisotropic excitable medium. Unlike the findings regarding the termination of spiral waves in isotropic excitable systems, we found a nonmonotonic relationship between the maximum unpinning period and the obstacle radius depending on the fiber orientation, where the formation of unwanted secondary pinned vortices or chaotic waves is seen over a wide range of parameters.
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Affiliation(s)
- Marcel Hörning
- Department of Physics, Graduate School of Science, Kyoto University, Japan.
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13
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Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics. Bull Math Biol 2012; 75:1351-76. [DOI: 10.1007/s11538-012-9748-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2011] [Accepted: 06/28/2012] [Indexed: 10/28/2022]
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14
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Alonso S, Bär M, Panfilov AV. Effects of reduced discrete coupling on filament tension in excitable media. CHAOS (WOODBURY, N.Y.) 2011; 21:013118. [PMID: 21456832 DOI: 10.1063/1.3551500] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.
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Affiliation(s)
- Sergio Alonso
- Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany.
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15
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Sridhar S, Sinha S, Panfilov AV. Anomalous drift of spiral waves in heterogeneous excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051908. [PMID: 21230501 DOI: 10.1103/physreve.82.051908] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2009] [Revised: 04/15/2010] [Indexed: 05/30/2023]
Abstract
We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in the distribution of ion-channel expression or cellular coupling. We report the anomalous drift of spiral waves toward regions having shorter period or stronger coupling, in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatiotemporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.
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Affiliation(s)
- S Sridhar
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
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16
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Foulkes AJ, Biktashev VN. Riding a spiral wave: numerical simulation of spiral waves in a comoving frame of reference. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046702. [PMID: 20481855 DOI: 10.1103/physreve.81.046702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2010] [Indexed: 05/29/2023]
Abstract
We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.
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Affiliation(s)
- A J Foulkes
- Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, United Kingdom
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