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Marta Varela, Roy A, Lee J. A survey of pathways for mechano-electric coupling in the atria. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2020; 159:136-145. [PMID: 33053408 PMCID: PMC7848589 DOI: 10.1016/j.pbiomolbio.2020.09.011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Revised: 09/09/2020] [Accepted: 09/29/2020] [Indexed: 11/26/2022]
Abstract
Mechano-electric coupling (MEC) in atrial tissue has received sparse investigation to date, despite the well-known association between chronic atrial dilation and atrial fibrillation (AF). Of note, no fewer than six different mechanisms pertaining to stretch-activated channels, cellular capacitance and geometric effects have been identified in the literature as potential players. In this mini review, we briefly survey each of these pathways to MEC. We then perform computational simulations using single cell and tissue models in presence of various stretch regimes and MEC pathways. This allows us to assess the relative significance of each pathway in determining action potential duration, conduction velocity and rotor stability. For chronic atrial stretch, we find that stretch-induced alterations in membrane capacitance decrease conduction velocity and increase action potential duration, in agreement with experimental findings. In the presence of time-dependent passive atrial stretch, stretch-activated channels play the largest role, leading to after-depolarizations and rotor hypermeandering. These findings suggest that physiological atrial stretches, such as passive stretch during the atrial reservoir phase, may play an important part in the mechanisms of atrial arrhythmogenesis. Passive strains caused by ventricular contraction need to be considered when incorporating mechano-electro feedback in atrial electrophysiology models. In chronic stretch, stretch-induced capacitance changes dominate. Chronic stretch leads to an increase in action potential duration and a reduction in conduction velocity, consistent with experimental studies. In the presence of passive stretch, stretch-activated channels can induce delayed after-depolarisations and lead to rotor hypermeandering. Mechano-electro feedback is thus likely to have implications for the genesis and maintenance of atrial arrhythmias.
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Affiliation(s)
- Marta Varela
- National Heart and Lung Institute, Faculty of Medicine, Imperial College London, London, UK; Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King's College London, London, UK.
| | - Aditi Roy
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King's College London, London, UK; Department of Computing, University of Oxford, Oxford, UK
| | - Jack Lee
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King's College London, London, UK
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2
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Adamatzky A. On interplay between excitability and geometry. Biosystems 2020; 187:104034. [DOI: 10.1016/j.biosystems.2019.104034] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2019] [Revised: 09/14/2019] [Accepted: 09/15/2019] [Indexed: 01/28/2023]
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3
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Spreckelsen F, Luther S, Parlitz U. Synchronization of viscoelastically coupled excitable oscillators. Phys Rev E 2019; 100:032214. [PMID: 31640069 DOI: 10.1103/physreve.100.032214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Indexed: 11/07/2022]
Abstract
Viscoelastically coupled excitable oscillators are used to model individually beating spatially separated cardiomyocytes surrounded by an extracellular matrix (ECM). We investigate how mechanical coupling via the ECM can synchronize two such oscillators with excitation contraction coupling and electromechanical feedback and how this synchronization depends on the rheological properties of the ECM. Extending our study to a linear chain of coupled oscillators we find a transition to synchronization as the ECM becomes stiffer. In the case of purely elastic coupling we observe antiphase chimera states.
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Affiliation(s)
- Florian Spreckelsen
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, D-37077 Göttingen, Germany.,University of Göttingen, Institute for the Dynamics of Complex Systems, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.,DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Robert-Koch-Straße 42a, D-37075 Göttingen, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, D-37077 Göttingen, Germany.,University of Göttingen, Institute for the Dynamics of Complex Systems, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.,DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Robert-Koch-Straße 42a, D-37075 Göttingen, Germany.,University Medical Center Göttingen (UMG), Institute of Pharmacology and Toxicology, Robert-Koch-Straße 40, D-37075 Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, D-37077 Göttingen, Germany.,University of Göttingen, Institute for the Dynamics of Complex Systems, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.,DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Robert-Koch-Straße 42a, D-37075 Göttingen, Germany
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Buccarello A, Azzarito M, Michoud F, Lacour SP, Kucera JP. Uniaxial strain of cultured mouse and rat cardiomyocyte strands slows conduction more when its axis is parallel to impulse propagation than when it is perpendicular. Acta Physiol (Oxf) 2018; 223:e13026. [PMID: 29282897 DOI: 10.1111/apha.13026] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Revised: 12/14/2017] [Accepted: 12/21/2017] [Indexed: 11/28/2022]
Abstract
AIM Cardiac tissue deformation can modify tissue resistance, membrane capacitance and ion currents and hence cause arrhythmogenic slow conduction. Our aim was to investigate whether uniaxial strain causes different changes in conduction velocity (θ) when the principal strain axis is parallel vs perpendicular to impulse propagation. METHODS Cardiomyocyte strands were cultured on stretchable custom microelectrode arrays, and θ was determined during steady-state pacing. Uniaxial strain (5%) with principal axis parallel (orthodromic) or perpendicular (paradromic) to propagation was applied for 1 minute and controlled by imaging a grid of markers. The results were analysed in terms of cable theory. RESULTS Both types of strain induced immediate changes of θ upon application and release. In material coordinates, orthodromic strain decreased θ significantly more (P < .001) than paradromic strain (2.2 ± 0.5% vs 1.0 ± 0.2% in n = 8 mouse cardiomyocyte cultures, 2.3 ± 0.4% vs 0.9 ± 0.5% in n = 4 rat cardiomyocyte cultures, respectively). The larger effect of orthodromic strain can be explained by the increase in axial myoplasmic resistance, which is not altered by paradromic strain. Thus, changes in tissue resistance substantially contributed to the changes of θ during strain, in addition to other influences (eg stretch-activated channels). Besides these immediate effects, the application of strain also consistently initiated a slow progressive decrease in θ and a slow recovery of θ upon release. CONCLUSION Changes in cardiac conduction velocity caused by acute stretch do not only depend on the magnitude of strain but also on its orientation relative to impulse propagation. This dependence is due to different effects on tissue resistance.
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Affiliation(s)
- A. Buccarello
- Department of Physiology; University of Bern; Bern Switzerland
| | - M. Azzarito
- Department of Physiology; University of Bern; Bern Switzerland
| | - F. Michoud
- Bertarelli Foundation Chair in Neuroprosthetic Technology; Laboratory for Soft Bioelectronic Interfaces; Institute of Microengineering; Institute of Bioengineering; Centre for Neuroprosthetics; École Polytechnique Fédérale de Lausanne (EPFL); Geneva Switzerland
| | - S. P. Lacour
- Bertarelli Foundation Chair in Neuroprosthetic Technology; Laboratory for Soft Bioelectronic Interfaces; Institute of Microengineering; Institute of Bioengineering; Centre for Neuroprosthetics; École Polytechnique Fédérale de Lausanne (EPFL); Geneva Switzerland
| | - J. P. Kucera
- Department of Physiology; University of Bern; Bern Switzerland
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Liu Y, Yuan L, Pan C, Gao J, Zhou W, Gao Q. Photoinduced Oscillations and Pulse Waves in the Hydrogen Peroxide–Sulfite–Ferrocyanide Reaction. J Phys Chem A 2018; 122:1175-1184. [DOI: 10.1021/acs.jpca.7b10025] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yang Liu
- College
of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, China
| | - Ling Yuan
- College
of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, China
| | - Changwei Pan
- College
of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, China
| | - Jianmin Gao
- Department
of Chemistry, Boston College, 2609 Beacon Street, Chestnut Hill, Massachusetts 02467-3860, United States
| | - Wenxiu Zhou
- College
of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, China
| | - Qingyu Gao
- College
of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, China
- Department
of Chemistry, Boston College, 2609 Beacon Street, Chestnut Hill, Massachusetts 02467-3860, United States
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Fast propagation regions cause self-sustained reentry in excitable media. Proc Natl Acad Sci U S A 2017; 114:1281-1286. [PMID: 28123066 DOI: 10.1073/pnas.1611475114] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.
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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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Kostin VA, Osipov GV. Transient and periodic spatiotemporal structures in a reaction-diffusion-mechanics system. CHAOS (WOODBURY, N.Y.) 2016; 26:013101. [PMID: 26826853 DOI: 10.1063/1.4938736] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We study transient spatiotemporal structures induced by a weak space-time localized stimulus in an excitable contractile fiber within a two-component globally coupled reaction-diffusion model. The model which we develop allows us to analyze various regimes of excitation spreading and determine origin of the induced structures for various contraction types (defined by the fiber fixation) and global coupling strengths. One of the most notable effects we observed is the after-excitation effect. It leads to emergence of multiple excitation pulses excited by a single external stimulus and can result in long-lasting transient activity and appearance of new oscillatory attractor regimes, including the ones with multiple phase clusters.
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Affiliation(s)
- V A Kostin
- University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia
| | - G V Osipov
- University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia
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9
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Li BW, Cai MC, Zhang H, Panfilov AV, Dierckx H. Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field. J Chem Phys 2015; 140:184901. [PMID: 24832300 DOI: 10.1063/1.4874645] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chirality is one of the most fundamental properties of many physical, chemical, and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the Belousov-Zhabotinsky reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.
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Affiliation(s)
- Bing-Wei Li
- Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
| | - Mei-Chun Cai
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
| | - Hans Dierckx
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
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10
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Quail T, Shrier A, Glass L. Spatial symmetry breaking determines spiral wave chirality. PHYSICAL REVIEW LETTERS 2014; 113:158101. [PMID: 25375745 DOI: 10.1103/physrevlett.113.158101] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2014] [Indexed: 05/27/2023]
Abstract
Chirality represents a fundamental property of spiral waves. Introducing obstacles into cardiac monolayers leads to the initiation of clockwise-rotating, counterclockwise-rotating, and pairs of spiral waves. Simulations show that the precise location of the obstacle and the pacing frequency determine spiral wave chirality. Instabilities predicted by curves relating the action potential duration and the pacing frequency at different spatial locations predict sites of wave break initiation and, hence, spiral wave chirality.
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Affiliation(s)
- Thomas Quail
- Department of Physiology, McGill University, Montreal, Canada H3G 1Y6
| | - Alvin Shrier
- Department of Physiology, McGill University, Montreal, Canada H3G 1Y6
| | - Leon Glass
- Department of Physiology, McGill University, Montreal, Canada H3G 1Y6
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11
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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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12
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Jiménez ZA, Zhang Z, Steinbock O. Electric-field-controlled unpinning of scroll waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052918. [PMID: 24329342 DOI: 10.1103/physreve.88.052918] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2013] [Indexed: 06/03/2023]
Abstract
Three-dimensional excitation vortices exist in systems such as chemical reactions and the human heart. Their one-dimensional rotation backbone can pin to unexcitable heterogeneities, which greatly affect the structure, dynamics, and lifetime of the vortex. In experiments with the Belousov-Zhabotinsky reaction, we demonstrate vortex unpinning from a pair of inert and impermeable spheres using externally applied electric fields. Unpinning occurs abruptly but is preceded by a slow reorientation and deformation of the initially circular vortex loop. Our experimental findings are reproduced by numerical simulations of an excitable reaction-diffusion-advection model.
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Affiliation(s)
- Zulma A Jiménez
- Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA
| | - 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
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13
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Weise LD, Panfilov AV. A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics. PLoS One 2013; 8:e59317. [PMID: 23527160 PMCID: PMC3602082 DOI: 10.1371/journal.pone.0059317] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2012] [Accepted: 02/13/2013] [Indexed: 11/24/2022] Open
Abstract
We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.
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Affiliation(s)
- Louis D Weise
- Department of Theoretical Biology, Utrecht University, Utrecht, The Netherlands.
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Borek B, Shajahan TK, Gabriels J, Hodge A, Glass L, Shrier A. Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture. CHAOS (WOODBURY, N.Y.) 2012; 22:033132. [PMID: 23020471 DOI: 10.1063/1.4747709] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Pacemaker interactions can lead to complex wave dynamics seen in certain types of cardiac arrhythmias. We use experimental and mathematical models of pacemakers in heterogeneous excitable media to investigate how pacemaker interactions can be a mechanism for wave break and reentrant wave dynamics. Embryonic chick ventricular cells are cultured in vitro so as to create a dominant central pacemaker site that entrains other pacemakers in the medium. Exposure of those cultures to a potassium channel blocker, E-4031, leads to emergence of peripheral pacemakers that compete with each other and with the central pacemaker. Waves emitted by faster pacemakers break up over the slower pacemaker to form reentrant waves. Similar dynamics are observed in a modified FitzHugh-Nagumo model of heterogeneous excitable media with two distinct sites of pacemaking. These findings elucidate a mechanism of pacemaker-induced reentry in excitable media.
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Affiliation(s)
- Bartłomiej Borek
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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