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Abstract
The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.
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Affiliation(s)
- Wouter-Jan Rappel
- Department of Physics, University of California San Diego, La Jolla, CA 92037
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2
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Feng X, Yin X, Wen J, Wu H, Gao X. Removal of spiral turbulence by virtual electrodes through the use of a circularly polarized electric field. CHAOS (WOODBURY, N.Y.) 2022; 32:093145. [PMID: 36182381 DOI: 10.1063/5.0102031] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
Heart disease is the leading cause of death and is often accompanied by cardiac fibrillation. Defibrillation using the virtual electrode effects is a promising alternative compared to using the high-voltage electric shock in the clinic. Our earlier works [S. L. Murphy, K. D. Kochanek, J. Xu, and E. Arias, NCHS Data Brief 427 (2021); R. A. Gray, A. M. Pertsov, and J. Jalife, Nature 392, 75-78 (1998); F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, Nature 392, 78-82 (1998); M. Santini, C. Pandozi, G. Altamura, G. Gentilucci, M. Villani, M. C. Scianaro, A. Castro, F. Ammirati, and B. Magris, J. Interv. Card. Electrophysiol. 3, 45-51 (1999).] prove that, compared with other external electric fields, a low voltage circularly polarized electric field is more efficient in turning non-excitable defects in cardiac tissue into virtual electrodes. It, therefore, needs lower voltage to stimulate the excitation waves and causes less harm to reset the spiral turbulence of cardiac excitation for defibrillation. In this paper, we investigate the virtual electrode effect of multiple defects by the circularly polarized electric field for the removal of spiral turbulence. Considering different shapes, sizes, and distributions of multiple defects, we reveal the phase locking of stimulated excitations around multiple virtual electrodes. Furthermore, the circularly polarized electric field parameters are optimized to remove the spiral turbulence.
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Affiliation(s)
- Xia Feng
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - XunLi Yin
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - JunQing Wen
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - Hua Wu
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - Xiang Gao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
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3
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Das TS, Wilson D. Optimal entrainment for removal of pinned spiral waves. Phys Rev E 2022; 105:064213. [PMID: 35854563 DOI: 10.1103/physreve.105.064213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
Cardiac fibrillation is caused by self-sustaining spiral waves that occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. A small electrical stimulation is often sufficient to unpin these spirals but only if it is applied during the vulnerable unpinning window. Even if these unpinning windows can be inferred from data, when multiple pinned spirals exist, their unpinning windows will not generally overlap. Using phase-based reduction techniques, we formulate and solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a collection of heterogeneous obstacles. Upon synchronization, the unpinning windows overlap so that they can be simultaneously unpinned by applying an external voltage gradient pulse at an appropriate moment. Numerical validation is presented in bidomain model simulations. Results represent a proof-of-concept illustration of the proposed unpinning strategy which explicitly incorporates heterogeneity in the problem formulation and requires no real-time feedback about the system state.
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Affiliation(s)
- Tuhin Subhra Das
- Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Dan Wilson
- Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA
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4
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Rappel WJ. Intermittent trapping of spiral waves in a cardiac model. Phys Rev E 2022; 105:014404. [PMID: 35193211 PMCID: PMC9020409 DOI: 10.1103/physreve.105.014404] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 12/21/2021] [Indexed: 01/21/2023]
Abstract
Spiral waves are found in many excitable systems and are thought to play a role in the incoherent electrical activation that underlies cardiac arrhythmias. It is well-known that spiral waves can be permanently trapped by local heterogeneities. In this paper, we demonstrate that spiral waves can also be intermittently trapped by such heterogeneities. Using simulations of a cardiac model in two dimensions, we show that a tissue heterogeneity of sufficient strength or size can result in a spiral wave that is trapped for a few rotations, after which it dislodges and meanders away from the heterogeneity. We also show that these results can be captured by a particle model in which the particle represents the spiral wave tip. For both models, we construct a phase diagram which quantifies which parameter combinations of heterogeneity size and strength result in permanent, intermittent, or no trapping. Our results are consistent with clinical observations in patients with atrial fibrillation that showed that spiral wave reentry can be intermittent.
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Roth BJ. Bidomain modeling of electrical and mechanical properties of cardiac tissue. BIOPHYSICS REVIEWS 2021; 2:041301. [PMID: 38504719 PMCID: PMC10903405 DOI: 10.1063/5.0059358] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 10/15/2021] [Indexed: 03/21/2024]
Abstract
Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.
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Affiliation(s)
- Bradley J. Roth
- Department of Physics, Oakland University, Rochester, Michigan 48309, USA
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6
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Loppini A, Barone A, Gizzi A, Cherubini C, Fenton FH, Filippi S. Thermal effects on cardiac alternans onset and development: A spatiotemporal correlation analysis. Phys Rev E 2021; 103:L040201. [PMID: 34005953 PMCID: PMC8202768 DOI: 10.1103/physreve.103.l040201] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 03/09/2021] [Indexed: 01/08/2023]
Abstract
Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)PREHBM2470-004510.1103/PhysRevE.100.020201] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.
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Affiliation(s)
- Alessandro Loppini
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Alessandro Barone
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Christian Cherubini
- Department of Science and Technology for Humans and the Environment and ICRA, Campus Bio-Medico University of Rome, 00128 Rome, Italy and International Center for Relativistic Astrophysics Network-ICRANet, 65122 Pescara, Italy
| | - Flavio H. Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia, USA
| | - Simonetta Filippi
- Department of Engineering and ICRA, Campus Bio-Medico University of Rome, 00128 Rome, Italy and International Center for Relativistic Astrophysics Network-ICRANet, 65122 Pescara, Italy
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7
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Overdrive pacing of spiral waves in a model of human ventricular tissue. Sci Rep 2020; 10:20632. [PMID: 33244010 PMCID: PMC7691998 DOI: 10.1038/s41598-020-77314-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2019] [Accepted: 10/30/2020] [Indexed: 01/03/2023] Open
Abstract
High-voltage electrical defibrillation remains the only reliable method of quickly controlling life-threatening cardiac arrhythmias. This paper is devoted to studying an alternative approach, low-voltage cardioversion (LVC), which is based on ideas from non-linear dynamics and aims to remove sources of cardiac arrhythmias by applying high-frequency stimulation to cardiac tissue. We perform a detailed in-silico study of the elimination of arrhythmias caused by rotating spiral waves in a TP06 model of human cardiac tissue. We consider three parameter sets with slopes of the APD restitution curve of 0.7, 1.1 and 1.4, and we study LVC at the baseline and under the blocking of INa and ICaL and under the application of the drugs verapamil and amiodarone. We show that pacing can remove spiral waves; however, its efficiency can be substantially reduced by dynamic instabilities. We classify these instabilities and show that the blocking of INa and the application of amiodarone increase the efficiency of the method, while the blocking of ICaL and the application of verapamil decrease the efficiency. We discuss the mechanisms and the possible clinical applications resulting from our study.
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8
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Punacha S, A NK, Shajahan TK. Theory of unpinning of spiral waves using circularly polarized electric fields in mathematical models of excitable media. Phys Rev E 2020; 102:032411. [PMID: 33076004 DOI: 10.1103/physreve.102.032411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Accepted: 08/31/2020] [Indexed: 06/11/2023]
Abstract
Spiral waves of excitation are common in many physical, chemical, and biological systems. In physiological systems like the heart, such waves can lead to cardiac arrhythmias and need to be eliminated. Spiral waves anchor to heterogeneities in the excitable medium, and to eliminate them they need to be unpinned first. Several groups focused on developing strategies to unpin such pinned waves using electric shocks, pulsed electric fields, and recently, circularly polarized electric fields (CPEF). It was shown that in many situations, CPEF is more efficient at unpinning the wave compared to other existing methods. Here, we study how the circularly polarized field acts on the pinned spiral waves and unpins it. We show that the termination always happens within the first rotation of the electric field. For a given obstacle size, there exists a threshold time period of the CPEF below which the spiral can always be terminated. Our analytical formulation accurately predicts this threshold and explains the absence of the traditional unpinning window with the CPEF. We hope our theoretical work will stimulate further experimental studies about CPEF and low energy methods to eliminate spiral waves.
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Affiliation(s)
- Shreyas Punacha
- Department of Physics, National Institute of Technology Karnataka Surathkal, Mangalore, Karnataka, 575025, India
| | - Naveena Kumara A
- Department of Physics, National Institute of Technology Karnataka Surathkal, Mangalore, Karnataka, 575025, India
| | - T K Shajahan
- Department of Physics, National Institute of Technology Karnataka Surathkal, Mangalore, Karnataka, 575025, India
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9
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Punacha S, Berg S, Sebastian A, Krinski VI, Luther S, Shajahan TK. Spiral wave unpinning facilitated by wave emitting sites in cardiac monolayers. Proc Math Phys Eng Sci 2019; 475:20190420. [PMID: 31736652 DOI: 10.1098/rspa.2019.0420] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Accepted: 09/23/2019] [Indexed: 11/12/2022] Open
Abstract
Rotating spiral waves of electrical activity in the heart can anchor to unexcitable tissue (an obstacle) and become stable pinned waves. A pinned rotating wave can be unpinned either by a local electrical stimulus applied close to the spiral core, or by an electric field pulse that excites the core of a pinned wave independently of its localization. The wave will be unpinned only when the pulse is delivered inside a narrow time interval called the unpinning window (UW) of the spiral. In experiments with cardiac monolayers, we found that other obstacles situated near the pinning centre of the spiral can facilitate unpinning. In numerical simulations, we found increasing or decreasing of the UW depending on the location, orientation and distance between the pinning centre and an obstacle. Our study indicates that multiple obstacles could contribute to unpinning in experiments with intact hearts.
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Affiliation(s)
- Shreyas Punacha
- National Institute of Technology Karnataka, Surathkal, Mangalore 575025, India
| | - Sebastian Berg
- Max Planck Institute of Dynamics and Self Organization, Göttingen 37017, Germany
| | - Anupama Sebastian
- National Institute of Technology Karnataka, Surathkal, Mangalore 575025, India
| | - Valentin I Krinski
- Max Planck Institute of Dynamics and Self Organization, Göttingen 37017, Germany
| | - Stefan Luther
- Max Planck Institute of Dynamics and Self Organization, Göttingen 37017, Germany
| | - T K Shajahan
- National Institute of Technology Karnataka, Surathkal, Mangalore 575025, India.,Max Planck Institute of Dynamics and Self Organization, Göttingen 37017, Germany
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10
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Diaz-Maue L, Schwaerzle M, Ruther P, Luther S, Richter C. Follow the Light - From Low-Energy Defibrillation to Multi-Site Photostimulation. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2019; 2018:4832-4835. [PMID: 30441427 DOI: 10.1109/embc.2018.8513124] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
One major cause of death in the industrialized world is sudden cardiac death, which so far can be reliably treated only by applying strong electrical shocks. Developing improved methods, aiming at lowering shock intensity and associated side effects potentially has significant clinical implications. Thus, optogenetic stimulation using structured illumination has been introduced as a promising experimental tool to investigate mechanisms underlying multi-site pacing and to optimize potential low-energy approaches. Furthermore, an objective of this work is to strengthen the application of optogenetic tools for cardiac arrhythmia research, which in turn is expected to improve applicable technologies towards tissue-protective defibrillation.
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11
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Loppini A, Gizzi A, Cherubini C, Cherry EM, Fenton FH, Filippi S. Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue. Phys Rev E 2019; 100:020201. [PMID: 31574686 DOI: 10.1103/physreve.100.020201] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Indexed: 06/10/2023]
Abstract
Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20 cm during one-to-one responses and it decreases to a specific value of about 3 cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1 cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.
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Affiliation(s)
- Alessandro Loppini
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
| | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
| | - Christian Cherubini
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
- ICRANet, Piazza delle Repubblica 10, I-65122 Pescara, Italy
| | - Elizabeth M Cherry
- School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332, USA
| | - Simonetta Filippi
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
- ICRANet, Piazza delle Repubblica 10, I-65122 Pescara, Italy
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12
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Quiñonez Uribe RA, Luther S, Diaz-Maue L, Richter C. Energy-Reduced Arrhythmia Termination Using Global Photostimulation in Optogenetic Murine Hearts. Front Physiol 2018; 9:1651. [PMID: 30542292 PMCID: PMC6277892 DOI: 10.3389/fphys.2018.01651] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Accepted: 11/02/2018] [Indexed: 02/01/2023] Open
Abstract
Complex spatiotemporal non-linearity as observed during cardiac arrhythmia strongly correlates with vortex-like excitation wavelengths and tissue characteristics. Therefore, the control of arrhythmic patterns requires fundamental understanding of dependencies between onset and perpetuation of arrhythmia and substrate instabilities. Available treatments, such as drug application or high-energy electrical shocks, are discussed for potential side effects resulting in prognosis worsening due to the lack of specificity and spatiotemporal precision. In contrast, cardiac optogenetics relies on light sensitive ion channels stimulated to trigger excitation of cardiomyocytes solely making use of the inner cell mechanisms. This enables low-energy, non-damaging optical control of cardiac excitation with high resolution. Recently, the capability of optogenetic cardioversion was shown in Channelrhodopsin-2 (ChR2) transgenic mice. But these studies used mainly structured and local illumination for cardiac stimulation. In addition, since optogenetic and electrical stimulus work on different principles to control the electrical activity of cardiac tissue, a better understanding of the phenomena behind optogenetic cardioversion is still needed. The present study aims to investigate global illumination with regard to parameter characterization and its potential for cardioversion. Our results show that by tuning the light intensity without exceeding 1.10 mW mm-2, a single pulse in the range of 10–1,000 ms is sufficient to reliably reset the heart into sinus rhythm. The combination of our panoramic low-intensity photostimulation with optical mapping techniques visualized wave collision resulting in annihilation as well as propagation perturbations as mechanisms leading to optogenetic cardioversion, which seem to base on other processes than electrical defibrillation. This study contributes to the understanding of the roles played by epicardial illumination, pulse duration and light intensity in optogenetic cardioversion, which are the main variables influencing cardiac optogenetic control, highlighting the advantages and insights of global stimulation. Therefore, the presented results can be modules in the design of novel illumination technologies with specific energy requirements on the way toward tissue-protective defibrillation techniques.
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Affiliation(s)
- Raúl A Quiñonez Uribe
- RG Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Stefan Luther
- RG Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.,Institute for Nonlinear Dynamics, Georg-August University, Göttingen, Germany.,Department of Pharmacology and Toxicology, University Medical Center, Göttingen, Germany.,German Center for Cardiovascular Research (DZHK e.V.), Partner Site Göttingen, Göttingen, Germany
| | - Laura Diaz-Maue
- RG Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Claudia Richter
- RG Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.,German Center for Cardiovascular Research (DZHK e.V.), Partner Site Göttingen, Göttingen, Germany.,Department of Cardiology and Pneumology, University Medical Center, Göttingen, Germany
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13
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Kitahata H, Tanaka M. Mathematical approach to unpinning of spiral waves anchored to an obstacle with high-frequency pacing. Biophys Physicobiol 2018; 15:196-203. [PMID: 30349804 PMCID: PMC6194964 DOI: 10.2142/biophysico.15.0_196] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Accepted: 08/27/2018] [Indexed: 12/04/2022] Open
Abstract
Spiral waves are observed in wide variety of reaction-diffusion systems. Those observed in cardiac tissues are important since they are related to serious disease that threatens human lives, such as atrial or ventricular fibrillation. We consider the unpinning of spiral waves anchored to a circular obstacle on excitable media using high-frequency pacing. Here, we consider two types of the obstacle; i.e., that without any diffusive interaction with the environment, and that with diffusive interaction. We found that the threshold frequency for success in unpinning is lower for the obstacle with diffusive interaction than for the one without it. We discuss the threshold frequency based on the angular velocity of a chemical wave anchoring the obstacle.
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Affiliation(s)
- Hiroyuki Kitahata
- Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan
| | - Masanobu Tanaka
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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14
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Katsumata H, Konishi K, Hara N. System identification of propagating wave segments in excitable media and its application to advanced control. Phys Rev E 2018; 97:042210. [PMID: 29758666 DOI: 10.1103/physreve.97.042210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Indexed: 06/08/2023]
Abstract
The present paper proposes a scheme for controlling wave segments in excitable media. This scheme consists of two phases: in the first phase, a simple mathematical model for wave segments is derived using only the time series data of input and output signals for the media; in the second phase, the model derived in the first phase is used in an advanced control technique. We demonstrate with numerical simulations of the Oregonator model that this scheme performs better than a conventional control scheme.
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Affiliation(s)
- Hisatoshi Katsumata
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
| | - Keiji Konishi
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
| | - Naoyuki Hara
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
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15
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Lim H, Cun W, Wang Y, Gray RA, Glimm J. The role of conductivity discontinuities in design of cardiac defibrillation. CHAOS (WOODBURY, N.Y.) 2018; 28:013106. [PMID: 29390616 DOI: 10.1063/1.5019367] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Fibrillation is an erratic electrical state of the heart, of rapid twitching rather than organized contractions. Ventricular fibrillation is fatal if not treated promptly. The standard treatment, defibrillation, is a strong electrical shock to reinitialize the electrical dynamics and allow a normal heart beat. Both the normal and the fibrillatory electrical dynamics of the heart are organized into moving wave fronts of changing electrical signals, especially in the transmembrane voltage, which is the potential difference between the cardiac cellular interior and the intracellular region of the heart. In a normal heart beat, the wave front motion is from bottom to top and is accompanied by the release of Ca ions to induce contractions and pump the blood. In a fibrillatory state, these wave fronts are organized into rotating scroll waves, with a centerline known as a filament. Treatment requires altering the electrical state of the heart through an externally applied electrical shock, in a manner that precludes the existence of the filaments and scroll waves. Detailed mechanisms for the success of this treatment are partially understood, and involve local shock-induced changes in the transmembrane potential, known as virtual electrode alterations. These transmembrane alterations are located at boundaries of the cardiac tissue, including blood vessels and the heart chamber wall, where discontinuities in electrical conductivity occur. The primary focus of this paper is the defibrillation shock and the subsequent electrical phenomena it induces. Six partially overlapping causal factors for defibrillation success are identified from the literature. We present evidence in favor of five of these and against one of them. A major conclusion is that a dynamically growing wave front starting at the heart surface appears to play a primary role during defibrillation by critically reducing the volume available to sustain the dynamic motion of scroll waves; in contrast, virtual electrodes occurring at the boundaries of small, isolated blood vessels only cause minor effects. As a consequence, we suggest that the size of the heart (specifically, the surface to volume ratio) is an important defibrillation variable.
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Affiliation(s)
- Hyunkyung Lim
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
| | - Wenjing Cun
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
| | - Yue Wang
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
| | - Richard A Gray
- Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland 20993-0002, USA
| | - James Glimm
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
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16
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Buran P, Bär M, Alonso S, Niedermayer T. Control of electrical turbulence by periodic excitation of cardiac tissue. CHAOS (WOODBURY, N.Y.) 2017; 27:113110. [PMID: 29195336 DOI: 10.1063/1.5010787] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Electrical turbulence in cardiac tissue is associated with arrhythmias such as life-threatening ventricular fibrillation. Recent experimental studies have shown that a sequence of low-energy electrical far-field pulses is able to terminate fibrillation more gently than a single high-energy pulse which causes severe side effects. During this low-energy antifibrillation pacing (LEAP), only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to optimize LEAP, we performed extensive simulations of cardiac tissue perforated by blood vessels, employing two alternative cellular models that exhibit electrical turbulence at a similar length scale. Moreover, the scale of blood vessels in our two-dimensional simulations was chosen such that the threshold for single pulse defibrillation matches experimental values. For each of the 100 initial conditions, we tested different electrical field strengths, pulse shapes, numbers of pulses, and periods between the pulses. LEAP is successful for both models, albeit with substantial differences. One model exhibits a spectrum of chaotic activity featuring a narrow peak around a dominant frequency. In this case, the optimal period between low-energy pulses matches this frequency and LEAP greatly reduces the required energy for successful defibrillation. For pulses with larger energies, the system is perturbed such that underdrive pacing becomes advantageous. The spectrum of the second model features a broader peak, resulting in a less pronounced optimal pacing period and a decreased energy reduction. In both cases, pacing with five or six pulses which are separated by the dominant period maximizes the energy reduction.
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Affiliation(s)
- Pavel Buran
- Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany
| | - Markus Bär
- Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Av. Dr. Marañón 44, 08028 Barcelona, Spain
| | - Thomas Niedermayer
- Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany
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17
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Bittihn P, Berg S, Parlitz U, Luther S. Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium. CHAOS (WOODBURY, N.Y.) 2017; 27:093931. [PMID: 28964139 DOI: 10.1063/1.4999604] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.
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Affiliation(s)
- Philip Bittihn
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Sebastian Berg
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
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18
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Gizzi A, Loppini A, Ruiz-Baier R, Ippolito A, Camassa A, La Camera A, Emmi E, Di Perna L, Garofalo V, Cherubini C, Filippi S. Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential. CHAOS (WOODBURY, N.Y.) 2017; 27:093919. [PMID: 28964112 DOI: 10.1063/1.4999610] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
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Affiliation(s)
- A Gizzi
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - A Loppini
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - R Ruiz-Baier
- Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG Oxford, United Kingdom
| | - A Ippolito
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - A Camassa
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - A La Camera
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - E Emmi
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - L Di Perna
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - V Garofalo
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - C Cherubini
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - S Filippi
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
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19
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Katsumata H, Konishi K, Hara N. Proportional-integral control of propagating wave segments in excitable media. Phys Rev E 2017; 95:042216. [PMID: 28505760 DOI: 10.1103/physreve.95.042216] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Indexed: 11/07/2022]
Abstract
Numerical simulations are performed to demonstrate that proportional-integral control, one of the most commonly used feedback schemes in control engineering, can stabilize propagating wave segments in excitable media to a desired size. The proportional-integral controller measures the size of a wave segment and applies a spatially uniform signal to the medium. This controller has the following features: difficult trial-and-error adjustment is not necessary, wave segments can be stabilized to different sizes without readjusting the controller, and the wave segment size can be maintained even in media having position-dependent parameters.
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Affiliation(s)
- Hisatoshi Katsumata
- Department of Electrical and Information Systems, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
| | - Keiji Konishi
- Department of Electrical and Information Systems, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
| | - Naoyuki Hara
- Department of Electrical and Information Systems, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
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20
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Connolly AJ, Vigmond E, Bishop MJ. Bidomain Predictions of Virtual Electrode-Induced Make and Break Excitations around Blood Vessels. Front Bioeng Biotechnol 2017; 5:18. [PMID: 28396856 PMCID: PMC5366349 DOI: 10.3389/fbioe.2017.00018] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Accepted: 03/02/2017] [Indexed: 11/16/2022] Open
Abstract
Introduction and background Virtual electrodes formed by field stimulation during defibrillation of cardiac tissue play an important role in eliciting activations. It has been suggested that the coronary vasculature is an important source of virtual electrodes, especially during low-energy defibrillation. This work aims to further the understanding of how virtual electrodes from the coronary vasculature influence defibrillation outcomes. Methods Using the bidomain model, we investigated how field stimulation elicited activations from virtual electrodes around idealized intramural blood vessels. Strength–interval curves, which quantify the stimulus strength required to elicit wavefront propagation from the vessels at different states of tissue refractoriness, were computed for each idealized geometry. Results Make excitations occurred at late diastolic intervals, originating from regions of depolarization around the vessel. Break excitations occurred at early diastolic intervals, whereby the vessels were able to excite surrounding refractory tissue due to the local restoration of excitability by virtual electrode-induced hyperpolarizations. Overall, strength–interval curves had similar morphologies and underlying excitation mechanisms compared with previous experimental and numerical unipolar stimulation studies of cardiac tissue. Including the presence of the vessel wall increased the field strength required for make excitations but decreased the field strength required for break excitations, and the field strength at which break excitations occurred was generally greater than 5 V/cm. Finally, in a more realistic ventricular slice geometry, the proximity of virtual electrodes around subepicardial vessels was seen to cause break excitations in the form of propagating unstable wavelets to the subepicardial layer. Conclusion Representing the blood vessel wall microstructure in computational bidomain models of defibrillation is recommended as it significantly alters the electrophysiological response of the vessel to field stimulation. Although vessels may facilitate excitation of relatively refractory tissue via break excitations, the field strength required for this is generally greater than those used in the literature on low-energy defibrillation. However, the high-intensity shocks used in standard defibrillation may elicit break excitation propagation from the coronary vasculature.
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Affiliation(s)
- Adam J Connolly
- Department of Biomedical Engineering and Imaging Sciences, King's College London , London , UK
| | - Edward Vigmond
- IHU Liryc, Electrophysiology and Heart Modeling Instituté, Fondation Bordeaux Université, Bordeaux, France; IMB, UMR 5251, Univ. Bordeaux, Talence, France
| | - Martin J Bishop
- Department of Biomedical Engineering and Imaging Sciences, King's College London , London , UK
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21
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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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22
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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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23
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Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media. Sci Rep 2016; 6:21876. [PMID: 26905367 PMCID: PMC4764807 DOI: 10.1038/srep21876] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2015] [Accepted: 02/02/2016] [Indexed: 11/09/2022] Open
Abstract
Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.
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24
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Nakouzi E, Totz JF, Zhang Z, Steinbock O, Engel H. Hysteresis and drift of spiral waves near heterogeneities: From chemical experiments to cardiac simulations. Phys Rev E 2016; 93:022203. [PMID: 26986327 DOI: 10.1103/physreve.93.022203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2015] [Indexed: 06/05/2023]
Abstract
Dissipative patterns in excitable reaction-diffusion systems can be strongly affected by spatial heterogeneities. Using the photosensitive Belousov-Zhabotinsky reaction, we show a hysteresis effect in the transition between free and pinned spiral rotation. The latter state involves the rotation around a disk-shaped obstacle with an impermeable and inert boundary. The transition is controlled by changes in light intensity. For permeable heterogeneities of higher excitability, we observe spiral drift along both linear and circular boundaries. Our results confirm recent theoretical predictions and, in the case of spiral drift, are further reproduced by numerical simulations with a modified Oregonator model. Additional simulations with a cardiac model show that orbital motion can also exist in anisotropic and three-dimensional systems.
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Affiliation(s)
- Elias Nakouzi
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
| | - Jan Frederik Totz
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Zhihui Zhang
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
| | - Oliver Steinbock
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
| | - Harald Engel
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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25
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Feng X, Gao X, Tang JM, Pan JT, Zhang H. Wave trains induced by circularly polarized electric fields in cardiac tissues. Sci Rep 2015; 5:13349. [PMID: 26302781 PMCID: PMC4548189 DOI: 10.1038/srep13349] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Accepted: 07/22/2015] [Indexed: 11/28/2022] Open
Abstract
Clinically, cardiac fibrillation caused by spiral and turbulent waves can be terminated by globally resetting electric activity in cardiac tissues with a single high-voltage electric shock, but it is usually associated with severe side effects. Presently, a promising alternative uses wave emission from heterogeneities induced by a sequence of low-voltage uniform electric field pulses. Nevertheless, this method can only emit waves locally near obstacles in turbulent waves and thereby requires multiple obstacles to globally synchronize myocardium and thus to terminate fibrillation. Here we propose a new approach using wave emission from heterogeneities induced by a low-voltage circularly polarized electric field (i.e., a rotating uniform electric field). We find that, this approach can generate circular wave trains near obstacles and they propagate outwardly. We study the characteristics of such circular wave trains and further find that, the higher-frequency circular wave trains can effectively suppress spiral turbulence.
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Affiliation(s)
- Xia Feng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Xiang Gao
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China.,School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Juan-Mei Tang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jun-Ting Pan
- Institute of Physical Oceanography and Ocean College, Zhejiang University, Hangzhou 310058, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
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26
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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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27
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Defauw A, Vandersickel N, Dawyndt P, Panfilov AV. Small size ionic heterogeneities in the human heart can attract rotors. Am J Physiol Heart Circ Physiol 2014; 307:H1456-68. [PMID: 25217650 DOI: 10.1152/ajpheart.00410.2014] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Rotors occurring in the heart underlie the mechanisms of cardiac arrhythmias. Answering the question whether or not the location of rotors is related to local properties of cardiac tissue has important practical applications. This is because ablation of rotors has been shown to be an effective way to fight cardiac arrhythmias. In this study, we investigate, in silico, the dynamics of rotors in two-dimensional and in an anatomical model of human ventricles using a Ten Tusscher-Noble-Noble-Panfilov (TNNP) model for ventricular cells. We study the effect of small size ionic heterogeneities, similar to those measured experimentally. It is shown that such heterogeneities cannot only anchor, but can also attract, rotors rotating at a substantial distance from the heterogeneity. This attraction distance depends on the extent of the heterogeneities and can be as large as 5-6 cm in realistic conditions. We conclude that small size ionic heterogeneities can be preferred localization points for rotors and discuss their possible mechanism and value for applications.
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Affiliation(s)
- Arne Defauw
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
| | - Nele Vandersickel
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
| | - Peter Dawyndt
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium; and
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium; Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region, Russia
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28
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Chen JX, Peng L, Zheng Q, Zhao YH, Ying HP. Influences of periodic mechanical deformation on pinned spiral waves. CHAOS (WOODBURY, N.Y.) 2014; 24:033103. [PMID: 25273183 DOI: 10.1063/1.4886356] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In a generic model of excitable media, we study the behavior of spiral waves interacting with obstacles and their dynamics under the influences of simple periodic mechanical deformation (PMD). Depending on the characteristics of the obstacles, i.e., size and excitability, the rotation of a pinned spiral wave shows different scenarios, e.g., embedding into or anchoring on an obstacle. Three different drift phenomena induced by PMD are observed: scattering on small partial-excitable obstacles, meander-induced unpinning on big partial-excitable obstacles, and drifting around small unexcitable obstacles. Their underlying mechanisms are discussed. The dependence of the threshold amplitude of PMD on the characteristics of the obstacles to successfully remove pinned spiral waves on big partial-excitable obstacles is studied.
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Affiliation(s)
- Jiang-Xing Chen
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Liang Peng
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Qiang Zheng
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Ye-Hua Zhao
- Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - He-Ping Ying
- Department of Physics, Zhejiang University, Hangzhou 310027, China
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29
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Unpinning of rotating spiral waves in cardiac tissues by circularly polarized electric fields. Sci Rep 2014; 4:4831. [PMID: 24777360 PMCID: PMC4003477 DOI: 10.1038/srep04831] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Accepted: 04/10/2014] [Indexed: 12/05/2022] Open
Abstract
Spiral waves anchored to obstacles in cardiac tissues may cause lethal arrhythmia. To unpin these anchored spirals, comparing to high-voltage side-effect traditional therapies, wave emission from heterogeneities (WEH) induced by the uniform electric field (UEF) has provided a low-voltage alternative. Here we provide a new approach using WEH induced by the circularly polarized electric field (CPEF), which has higher success rate and larger application scope than UEF, even with a lower voltage. And we also study the distribution of the membrane potential near an obstacle induced by CPEF to analyze its mechanism of unpinning. We hope this promising approach may provide a better alternative to terminate arrhythmia.
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30
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Li TC, Li BW. Reversal of spiral waves in an oscillatory system caused by an inhomogeneity. CHAOS (WOODBURY, N.Y.) 2013; 23:033130. [PMID: 24089966 DOI: 10.1063/1.4819900] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Spatial heterogeneities are commonly found in realistic systems and play significant roles in dynamics of spiral waves. We here demonstrate a novel phenomenon that a localized inhomogeneity put around the spiral core could lead to the reversal of spiral waves in an oscillatory system, e.g., the complex Ginzburg-Landau equation. With the amplitude-phase representation, we analyze underling mechanism and conditions of the wave reversal in detail, which is found to agree with the numerical evidence.
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Affiliation(s)
- Teng-Chao Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
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31
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Zhao YH, Lou Q, Chen JX, Sun WG, Ma J, Ying HP. Emitting waves from heterogeneity by a rotating electric field. CHAOS (WOODBURY, N.Y.) 2013; 23:033141. [PMID: 24089977 DOI: 10.1063/1.4822417] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
In a generic model of excitable media, we simulate wave emission from a heterogeneity (WEH) induced by an electric field. Based on the WEH effect, a rotating electric field is proposed to terminate existed spatiotemporal turbulence. Compared with the effects resulted by a periodic pulsed electric field, the rotating electric field displays several improvements, such as lower required intensity, emitting waves on smaller obstacles, and shorter suppression time. Furthermore, due to rotation of the electric field, it can automatically source waves from the boundary of an obstacle with small curvature.
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Affiliation(s)
- Ye-Hua Zhao
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
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32
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Majumder R, Nayak AR, Pandit R. Nonequilibrium arrhythmic states and transitions in a mathematical model for diffuse fibrosis in human cardiac tissue. PLoS One 2012; 7:e45040. [PMID: 23071505 PMCID: PMC3466321 DOI: 10.1371/journal.pone.0045040] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2012] [Accepted: 08/11/2012] [Indexed: 11/29/2022] Open
Abstract
We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to fibroblasts via a gap-junctional conductance , reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.
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Affiliation(s)
- Rupamanjari Majumder
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
| | - Alok Ranjan Nayak
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
- * E-mail:
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Bittihn P, Hörning M, Luther S. Negative curvature boundaries as wave emitting sites for the control of biological excitable media. PHYSICAL REVIEW LETTERS 2012; 109:118106. [PMID: 23005683 DOI: 10.1103/physrevlett.109.118106] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2012] [Indexed: 06/01/2023]
Abstract
Understanding the interaction of electric fields with the complex anatomy of biological excitable media is key to optimizing control strategies for spatiotemporal dynamics in those systems. On the basis of a bidomain description, we provide a unified theory for the electric-field-induced depolarization of the substrate near curved boundaries of generalized shapes, resulting in the localized recruitment of control sites. Our findings are confirmed in experiments on cardiomyocyte cell cultures and supported by two-dimensional numerical simulations on a cross section of a rabbit ventricle.
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Affiliation(s)
- Philip Bittihn
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.
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34
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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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35
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Zemlin CW, Pertsov AM. Anchoring of drifting spiral and scroll waves to impermeable inclusions in excitable media. PHYSICAL REVIEW LETTERS 2012; 109:038303. [PMID: 22861905 DOI: 10.1103/physrevlett.109.038303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2011] [Revised: 04/10/2012] [Indexed: 05/22/2023]
Abstract
Anchoring of spiral and scroll waves in excitable media has attracted considerable interest in the context of cardiac arrhythmias. Here, by bombarding inclusions with drifting spiral and scroll waves, we explore the forces exerted by inclusions onto an approaching spiral and derive the equations of motion governing spiral dynamics in the vicinity of inclusion. We demonstrate that these forces nonmonotonically depend on distance and can lead to complex behavior: (a) anchoring to small but circumnavigating larger inclusions; (b) chirality-dependent anchoring.
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Affiliation(s)
- Christian W Zemlin
- Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23528, USA
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36
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Hörning M, Takagi S, Yoshikawa K. Controlling activation site density by low-energy far-field stimulation in cardiac tissue. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061906. [PMID: 23005126 DOI: 10.1103/physreve.85.061906] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2011] [Revised: 03/19/2012] [Indexed: 06/01/2023]
Abstract
Tachycardia and fibrillation are potentially fatal arrhythmias associated with the formation of rotating spiral waves in the heart. Presently, the termination of these types of arrhythmia is achieved by use of antitachycardia pacing or cardioversion. However, these techniques have serious drawbacks, in that they either have limited application or produce undesirable side effects. Low-energy far-field stimulation has recently been proposed as a superior therapy. This proposed therapeutic method would exploit the phenomenon in which the application of low-energy far-field shocks induces a large number of activation sites ("virtual electrodes") in tissue. It has been found that the formation of such sites can lead to the termination of undesired states in the heart and the restoration of normal beating. In this study we investigate a particular aspect of this method. Here we seek to determine how the activation site density depends on the applied electric field through in vitro experiments carried out on neonatal rat cardiac tissue cultures. The results indicate that the activation site density increases exponentially as a function of the intracellular conductivity and the level of cell isotropy. Additionally, we report numerical results obtained from bidomain simulations of the Beeler-Reuter model that are quantitatively consistent with our experimental results. Also, we derive an intuitive analytical framework that describes the activation site density and provides useful information for determining the ratio of longitudinal to transverse conductivity in a cardiac tissue culture. The results obtained here should be useful in the development of an actual therapeutic method based on low-energy far-field pacing. In addition, they provide a deeper understanding of the intrinsic properties of cardiac cells.
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Affiliation(s)
- Marcel Hörning
- Department of Physics, Graduate School of Science, Kyoto University, Japan.
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37
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Cherubini C, Filippi S, Gizzi A. Electroelastic unpinning of rotating vortices in biological excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031915. [PMID: 22587131 DOI: 10.1103/physreve.85.031915] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2011] [Revised: 02/22/2012] [Indexed: 05/31/2023]
Abstract
Spiral waves in excitable biological media are associated with pathological situations. In the heart an action potential vortex pinned by an obstacle has to be removed through defibrillation protocols fine-tuned theoretically by using electrophysiological nonlinear mathematical models. Cardiac tissue, however, is an electroelastic medium whose electrical properties are strongly affected by large deformations. In this paper we specifically investigate the electroelastic pinning-unpinning mechanism in order to include cardiac contraction in the preexisting theoretically modeled defibrillation scenarios. Based on a two-dimensional minimal electromechanical model, we show numerically the existence of an unpinning band characterized by the size of the obstacle, the pacing site, and the frequency. Similar numerical simulations, performed in the absence of elastic coupling, show small differences in comparison with the electroelastic studies, suggesting for this specific scenario of pinning-unpinning dynamics a nonprominent role of elasticity.
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Affiliation(s)
- C Cherubini
- Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico, Rome, Italy
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Lou Q, Chen JX, Zhao YH, Shen FR, Fu Y, Wang LL, Liu Y. Control of turbulence in heterogeneous excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:026213. [PMID: 22463305 DOI: 10.1103/physreve.85.026213] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2011] [Revised: 01/05/2012] [Indexed: 05/31/2023]
Abstract
Control of turbulence in two kinds of typical heterogeneous excitable media by applying a combined method is investigated. It is found that local-low-amplitude and high-frequency pacing (LHP) is effective to suppress turbulence if the deviation of the heterogeneity is minor. However, LHP is invalid when the deviation is large. Studies show that an additional radial electric field can greatly increase the efficiency of LHP. The underlying mechanisms of successful control in the two kinds of cases are different and are discussed separately. Since the developed strategy of combining LHP with a radial electric field can terminate turbulence in excitable media with a high degree of inhomogeneity, it has the potential contribution to promote the practical low-amplitude defibrillation approach.
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Affiliation(s)
- Qin Lou
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
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39
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Li W, Janardhan AH, Fedorov VV, Sha Q, Schuessler RB, Efimov IR. Low-energy multistage atrial defibrillation therapy terminates atrial fibrillation with less energy than a single shock. Circ Arrhythm Electrophysiol 2011; 4:917-25. [PMID: 21980076 DOI: 10.1161/circep.111.965830] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
BACKGROUND Implantable device therapy of atrial fibrillation (AF) is limited by pain from high-energy shocks. We developed a low-energy multistage defibrillation therapy and tested it in a canine model of AF. METHODS AND RESULTS AF was induced by burst pacing during vagus nerve stimulation. Our novel defibrillation therapy consisted of 3 stages: stage (ST) 1 (1-4 low-energy biphasic [BP] shocks), ST2 (6-10 ultralow-energy monophasic [MP] shocks), and ST3 (antitachycardia pacing). First, ST1 testing compared single or multiple MP and BP shocks. Second, several multistage therapies were tested: ST1 versus ST1+ST3 versus ST1+ST2+ST3. Third, 3 shock vectors were compared: superior vena cava to distal coronary sinus, proximal coronary sinus to left atrial appendage, and right atrial appendage to left atrial appendage. The atrial defibrillation threshold (DFT) of 1 BP shock was <1 MP shock (0.55 ± 0.1 versus 1.38 ± 0.31 J, P=0.003). Two to 3 BP shocks terminated AF with lower peak voltage than 1 BP or 1 MP shock and with lower atrial DFT than 4 BP shocks. Compared with ST1 therapy alone, ST1+ST3 lowered the atrial DFT moderately (0.51 ± 0.46 versus 0.95 ± 0.32 J, P=0.036), whereas 3-stage therapy (ST1+ST2+ST3) dramatically lowered the atrial DFT (0.19 ± 0.12 versus 0.95 ± 0.32 J for ST1 alone, P=0.0012). Finally, the 3-stage therapy was equally effective for all studied vectors. CONCLUSIONS Three-stage electrotherapy significantly reduces the AF DFT and opens the door to low-energy atrial defibrillation at or below the pain threshold.
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Affiliation(s)
- Wenwen Li
- Department of Biomedical Engineering, Washington University School of Medicine, St Louis, MO 63130, USA
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40
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Abstract
Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult due to the nonlinear interaction of excitation waves within a heterogeneous anatomical substrate1–4. Lacking a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation5–7. Here, we establish the relation between the response of the tissue to an electric field and the spatial distribution of heterogeneities of the scale-free coronary vascular structure. We show that in response to a pulsed electric field E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E), and a characteristic time τ for tissue depolarization that obeys a power law τ∝Eα. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore efficient termination of fibrillation. Using this novel control strategy, we demonstrate, for the first time, low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and at the same time provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.
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41
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Konishi K, Takeuchi M, Shimizu T. Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh-Nagumo model. CHAOS (WOODBURY, N.Y.) 2011; 21:023101. [PMID: 21721743 DOI: 10.1063/1.3545162] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Elimination and control of nonlinear phenomena in excitable media are important for academic interests and practical applications. This paper provides a systematic procedure to design external forces for eliminating a traveling wave in a one-dimensional piecewise linear FitzHugh-Nagumo model. This procedure allows us to design nonfeedback and feedback control systems. The feedback control systems are designed using classical control theory. Furthermore, this procedure is extended to a two-dimensional model and verified using numerical simulation.
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Affiliation(s)
- Keiji Konishi
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan.
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42
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Ambrosi CM, Ripplinger CM, Efimov IR, Fedorov VV. Termination of sustained atrial flutter and fibrillation using low-voltage multiple-shock therapy. Heart Rhythm 2010; 8:101-8. [PMID: 20969974 DOI: 10.1016/j.hrthm.2010.10.018] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/20/2010] [Accepted: 10/12/2010] [Indexed: 10/18/2022]
Abstract
BACKGROUND Defibrillation therapy for atrial fibrillation (AF) and flutter (AFl) is limited by pain induced by high-energy shocks. Thus, lowering the defibrillation energy for AFl/AF is desirable. OBJECTIVE In this study we applied low-voltage multiple-shock defibrillation therapy in a rabbit model of atrial tachyarrhythmias comparing its efficacy to single shocks and antitachycardia pacing (ATP). METHODS Optical mapping was performed in Langendorff-perfused rabbit hearts (n = 18). Acetylcholine (7 ± 5 to 17 ± 16 μM) was administered to promote sustained AFl and AF, respectively. Single and multiple monophasic shocks were applied within 1 or 2 cycle lengths (CLs) of the arrhythmia. RESULTS We observed AFl (CL = 83 ± 15 ms, n = 17) and AF (CL = 50 ± 8 ms, n = 11). ATP had a success rate of 66.7% in the case of AFl, but no success with AF (n = 9). Low-voltage multiple shocks had 100% success for both arrhythmias. Multiple low-voltage shocks terminated AFl at 0.86 ± 0.73 V/cm (within 1 CL) and 0.28 ± 0.13 V/cm (within 2 CLs), as compared with single shocks at 2.12 ± 1.31 V/cm (P < .001) and AF at 3.46 ± 3 V/cm (within 1 CL), as compared with single shocks at 6.83 ± 3.12 V/cm (P =.06). No ventricular arrhythmias were induced. Optical mapping revealed that termination of AFl was achieved by a properly timed, local shock-induced wave that collides with the arrhythmia wavefront, whereas AF required the majority of atrial tissue to be excited and reset for termination. CONCLUSION Low-voltage multiple-shock therapy terminates AFl and AF with different mechanisms and thresholds based on spatiotemporal characteristics of the arrhythmias.
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Affiliation(s)
- Christina M Ambrosi
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri, USA
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43
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Hörning M, Takagi S, Yoshikawa K. Wave emission on interacting heterogeneities in cardiac tissue. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:021926. [PMID: 20866856 DOI: 10.1103/physreve.82.021926] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2010] [Revised: 07/27/2010] [Indexed: 05/29/2023]
Abstract
Cardiac arrhythmias, a precursor of fibrillationlike states in the beating heart, are associated with spiral waves, which are likely to become pinned to heterogeneities. Far-field pacing (FFP) is a promising method for terminating such waves by using heterogeneities in the tissue as internal pacing sites. In this study we investigated the role of multiple obstacles and their interaction during FFP. We show that a secondary nearby obstacle can significantly modulate the minimum electrical field in FFP. Further, we show that essentially the same effect can be observed in cardiac tissue culture, which is a powerful experimental model to simulate heart activity. Here, an isotropic cell distribution leads to domain formation of locally distributed depolarization sites. Both secondary obstacles and domain formation of local depolarization sites can modulate energy requirements to originate wave propagation on obstacles. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for the future application of FFP to a real beating heart.
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44
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Pumir A, Sinha S, Sridhar S, Argentina M, Hörning M, Filippi S, Cherubini C, Luther S, Krinsky V. Wave-train-induced termination of weakly anchored vortices in excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:010901. [PMID: 20365315 DOI: 10.1103/physreve.81.010901] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2008] [Revised: 08/24/2009] [Indexed: 05/07/2023]
Abstract
A free vortex in excitable media can be displaced and removed by a wave train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.
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Affiliation(s)
- Alain Pumir
- Laboratoire de Physique, ENS de Lyon and CNRS, 46 Allée d'Italie, 69007 Lyon, France
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45
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Krogh-Madsen T, Christini DJ. Pacing-induced spatiotemporal dynamics can be exploited to improve reentry termination efficacy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:021924. [PMID: 19792168 DOI: 10.1103/physreve.80.021924] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2009] [Revised: 05/30/2009] [Indexed: 05/25/2023]
Abstract
Some potentially fatal cardiac arrhythmias may be terminated by a series of premature stimuli. Monomorphic ventricular tachycardia, which may be modeled as an excitation wave traveling around in a ring, is one such arrhythmia. We investigated the mechanisms and requirements for termination of such reentry using an ionic cardiac ring model. Termination requires conduction block, which in turn is facilitated by spatial dispersion in repolarization and recovery time. When applying short series of two or three stimuli, we found that for conduction block to robustly occur, the magnitude of the spatial gradient in recovery time must exceed a critical value of 20 ms/cm. Importantly, the required spatial gradient can be induced in this homogeneous system by the dynamics of the stimulus-induced waves-we show analytically the necessary conditions. Finally, we introduce a type of pacing protocol, the "aggressive ramp," which increases the termination efficacy by exploiting such pacing-induced heterogeneities. This technique, which is straightforward to implement, may therefore have important clinical implications.
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Affiliation(s)
- Trine Krogh-Madsen
- Department of Medicine, Greenberg Division of Cardiology, Weill Cornell Medical College, New York, New York 10021, USA
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46
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Chen JX, Mao JW, Hu B, Xu JR, He YF, Li Y, Yuan XP. Suppression of spirals and turbulence in inhomogeneous excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:066209. [PMID: 19658585 DOI: 10.1103/physreve.79.066209] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2008] [Indexed: 05/28/2023]
Abstract
Suppression of spiral and turbulence in inhomogeneous media due to local heterogeneity with higher excitability is investigated numerically. When the inhomogeneity is small, control tactics by boundary periodic forcing (BPF) is effective against the existing spiral and turbulence. When the inhomogeneity of excitability is large, a rotating electric field (REF) is utilized to "smooth" regional heterogeneity based on driven synchronization. Consequently, a control approach combining BPF with REF is proposed to suppress the spiral and turbulence. The underlying mechanism of successful suppression is discussed in terms of dispersion relation.
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Affiliation(s)
- Jiang-Xing Chen
- Department of Physics, HangZhou Dianzi University, Hangzhou 310018, China.
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47
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Hörning M, Isomura A, Agladze K, Yoshikawa K. Liberation of a pinned spiral wave by a single stimulus in excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:026218. [PMID: 19391831 DOI: 10.1103/physreve.79.026218] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2009] [Indexed: 05/27/2023]
Abstract
The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.
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Affiliation(s)
- Marcel Hörning
- Department of Physics, Graduate School of Science, Kyoto University, and Spatio-Temporal Project, ICORP JST, Kyoto 606-8502, Japan.
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48
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Ripplinger CM, Lou Q, Li W, Hadley J, Efimov IR. Panoramic imaging reveals basic mechanisms of induction and termination of ventricular tachycardia in rabbit heart with chronic infarction: implications for low-voltage cardioversion. Heart Rhythm 2008; 6:87-97. [PMID: 18996057 DOI: 10.1016/j.hrthm.2008.09.019] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/03/2008] [Accepted: 09/17/2008] [Indexed: 11/24/2022]
Abstract
BACKGROUND Sudden cardiac death due to arrhythmia in the settings of chronic myocardial infarction (MI) is an important clinical problem. Arrhythmic risk post-MI continues indefinitely even if heart failure and acute ischemia are not present due to the anatomic substrate of the scar and border zone (BZ) tissue. OBJECTIVE The purpose of this study was to determine mechanisms of arrhythmia initiation and termination in a rabbit model of chronic MI. METHODS Ligation of the lateral division of the left circumflex artery was performed 72 +/- 29 days before acute experiments (n = 11). Flecainide (2.13 +/- 0.64 microM) was administered to promote sustained arrhythmias, which were induced with burst pacing or a multiple shock protocol (four pulses, 140-200 ms coupling interval). RESULTS Panoramic optical mapping with blebbistatin (5 microM) revealed monomorphic ventricular tachycardia (VT) maintained by a single mother rotor (cycle length [CL] = 174.7 +/- 38.4 ms) as the primary mechanism of arrhythmia. Mother rotors were anchored to the scar or BZ for 16 of the 19 rotor locations recorded. Cardioversion thresholds (CVTs) were determined at various phases throughout the VT CL from external shock electrodes. CVTs were found to be phase dependent, and the maximum versus minimum CVT was 7.8 +/- 1.9 vs. 4.1 +/- 1.6 V/cm, respectively (P = .005). Antitachycardia pacing was found to be effective in only 2.7% of cases in this model. CONCLUSIONS These results indicate that scar and BZ tissue heterogeneity provide the substrate for VT by attracting and stabilizing rotors. Additionally, a significant reduction in CVT may be achieved by appropriately timed shocks in which the shock-induced virtual electrode polarization interacts with the rotor to destabilize VT.
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Affiliation(s)
- Crystal M Ripplinger
- Department of Biomedical Engineering, Washington University, St Louis, Missouri 63130-4899, USA
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49
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Tang G, Deng M, Hu B, Hu G. Active and passive control of spiral turbulence in excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:046217. [PMID: 18517720 DOI: 10.1103/physreve.77.046217] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2007] [Revised: 10/08/2007] [Indexed: 05/26/2023]
Abstract
The influence of a spatially localized heterogeneity defect, defined by failure of the diffusion effect, on spiral turbulence suppression in two-dimensional excitable media is studied numerically, based on the Bär model. It is shown that in certain parameter regions spiral turbulence without the defect can be suppressed by a boundary periodic forcing (called active control) if the forcing frequency is properly chosen. However, with a sufficiently large defect this active control method no longer works due to the wake turbulence following the defect. We suggest an auxiliary method of enclosing the defect with a thin layer of material of high excitability (called passive control) to screen the interaction between the defect and the turbulence and to restore the global control effect of the periodic forcing. The possible application of the method in cardiac defibrillation is discussed.
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Affiliation(s)
- Guoning Tang
- College of Physics and Electronic Engineering, Guangxi Normal University, Guilin 541004, China
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Cysyk J, Tung L. Electric field perturbations of spiral waves attached to millimeter-size obstacles. Biophys J 2008; 94:1533-41. [PMID: 17921205 PMCID: PMC2212699 DOI: 10.1529/biophysj.107.116244] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2007] [Accepted: 09/26/2007] [Indexed: 11/18/2022] Open
Abstract
Reentrant spiral waves can become pinned to small anatomical obstacles in the heart and lead to monomorphic ventricular tachycardia that can degenerate into polymorphic tachycardia and ventricular fibrillation. Electric field-induced secondary source stimulation can excite directly at the obstacle, and may provide a means to terminate the pinned wave or inhibit the transition to more complex arrhythmia. We used confluent monolayers of neonatal rat ventricular myocytes to investigate the use of low intensity electric field stimulation to perturb the spiral wave. A hole 2-4 mm in diameter was created in the center to pin the spiral wave. Monolayers were stained with voltage-sensitive dye di-4-ANEPPS and mapped at 253 sites. Spiral waves were initiated that attached to the hole (n = 10 monolayers). Electric field pulses 1-s in duration were delivered with increasing strength (0.5-5 V/cm) until the wave terminated after detaching from the hole. At subdetachment intensities, cycle length increased with field strength, was sustained for the duration of the pulse, and returned to its original value after termination of the pulse. Mechanistically, conduction velocity near the wave tip decreased with field strength in the region of depolarization at the obstacle. In summary, electric fields cause strength-dependent slowing or detachment of pinned spiral waves. Our results suggest a means to decelerate tachycardia that may help to prevent wave degeneration.
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Affiliation(s)
- Joshua Cysyk
- Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, Maryland, USA
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