1
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Tyler SA, Mersing D, Fenton FH, Tinsley MR, Showalter K. Experimental studies of spiral wave teleportation in a light sensitive Belousov-Zhabotinsky system. CHAOS (WOODBURY, N.Y.) 2024; 34:093106. [PMID: 39226479 PMCID: PMC11374381 DOI: 10.1063/5.0216649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Accepted: 08/12/2024] [Indexed: 09/05/2024]
Abstract
Cardiac arrythmias are a form of heart disease that contributes toward making heart disease a significant cause of death globally. Irregular rhythms associated with cardiac arrythmias are thought to arise due to singularities in the heart tissue that generate reentrant waves in the underlying excitable medium. A normal approach to removing such singularities is to apply a high voltage electric shock, which effectively resets the phase of the cardiac cells. A concern with the use of this defibrillation technique is that the high-energy shock can cause lasting damage to the heart tissue. Various theoretical works have investigated lower-energy alternatives to defibrillation. In this work, we demonstrate the effectiveness of a low-energy defibrillation method in an experimental 2D Belousov-Zhabotinsky (BZ) system. When implemented as a 2D spatial reaction, the BZ reaction serves as an effective analog of general excitable media and supports regular and reentrant wave activity. The defibrillation technique employed involves targeted low-energy perturbations that can be used to "teleport" and/or annihilate singularities present in the excitable BZ medium.
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Affiliation(s)
- Shannyn A Tyler
- Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506, USA
| | - David Mersing
- Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Mark R Tinsley
- Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506, USA
| | - Kenneth Showalter
- Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506, USA
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2
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Stevenson WG, Tandri H, Roden DM. The Shape of Ventricular Tachycardia. Circulation 2023; 148:1368-1370. [PMID: 37903185 DOI: 10.1161/circulationaha.123.066574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/01/2023]
Affiliation(s)
- William G Stevenson
- Division of Cardiovascular Medicine, Vanderbilt University Medical Center, Nashville, TN
| | - Harikrishna Tandri
- Division of Cardiovascular Medicine, Vanderbilt University Medical Center, Nashville, TN
| | - Dan M Roden
- Division of Cardiovascular Medicine, Vanderbilt University Medical Center, Nashville, TN
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3
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Aron M, Lilienkamp T, Luther S, Parlitz U. Optimising low-energy defibrillation in 2D cardiac tissue with a genetic algorithm. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1172454. [PMID: 37555132 PMCID: PMC10406519 DOI: 10.3389/fnetp.2023.1172454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Accepted: 06/28/2023] [Indexed: 08/10/2023]
Abstract
Sequences of low-energy electrical pulses can effectively terminate ventricular fibrillation (VF) and avoid the side effects of conventional high-energy electrical defibrillation shocks, including tissue damage, traumatic pain, and worsening of prognosis. However, the systematic optimisation of sequences of low-energy pulses remains a major challenge. Using 2D simulations of homogeneous cardiac tissue and a genetic algorithm, we demonstrate the optimisation of sequences with non-uniform pulse energies and time intervals between consecutive pulses for efficient VF termination. We further identify model-dependent reductions of total pacing energy ranging from ∼4% to ∼80% compared to reference adaptive-deceleration pacing (ADP) protocols of equal success rate (100%).
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Affiliation(s)
- Marcel Aron
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
| | - Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Computational Physics for Life Science, Nuremberg Institute of Technology Georg Simon Ohm, Nuremberg, Germany
| | - Stefan Luther
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
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4
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Ramlugun GS, Kulkarni K, Pallares-Lupon N, Boukens BJ, Efimov IR, Vigmond EJ, Bernus O, Walton RD. A comprehensive framework for evaluation of high pacing frequency and arrhythmic optical mapping signals. Front Physiol 2023; 14:734356. [PMID: 36755791 PMCID: PMC9901579 DOI: 10.3389/fphys.2023.734356] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 01/09/2023] [Indexed: 01/24/2023] Open
Abstract
Introduction: High pacing frequency or irregular activity due to arrhythmia produces complex optical mapping signals and challenges for processing. The objective is to establish an automated activation time-based analytical framework applicable to optical mapping images of complex electrical behavior. Methods: Optical mapping signals with varying complexity from sheep (N = 7) ventricular preparations were examined. Windows of activation centered on each action potential upstroke were derived using Hilbert transform phase. Upstroke morphology was evaluated for potential multiple activation components and peaks of upstroke signal derivatives defined activation time. Spatially and temporally clustered activation time points were grouped in to wave fronts for individual processing. Each activation time point was evaluated for corresponding repolarization times. Each wave front was subsequently classified based on repetitive or non-repetitive events. Wave fronts were evaluated for activation time minima defining sites of wave front origin. A visualization tool was further developed to probe dynamically the ensemble activation sequence. Results: Our framework facilitated activation time mapping during complex dynamic events including transitions to rotor-like reentry and ventricular fibrillation. We showed that using fixed AT windows to extract AT maps can impair interpretation of the activation sequence. However, the phase windowing of action potential upstrokes enabled accurate recapitulation of repetitive behavior, providing spatially coherent activation patterns. We further demonstrate that grouping the spatio-temporal distribution of AT points in to coherent wave fronts, facilitated interpretation of isolated conduction events, such as conduction slowing, and to derive dynamic changes in repolarization properties. Focal origins precisely detected sites of stimulation origin and breakthrough for individual wave fronts. Furthermore, a visualization tool to dynamically probe activation time windows during reentry revealed a critical single static line of conduction slowing associated with the rotation core. Conclusion: This comprehensive analytical framework enables detailed quantitative assessment and visualization of complex electrical behavior.
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Affiliation(s)
- Girish S. Ramlugun
- IHU-Liryc, Fondation Bordeaux Université, Pessac-Bordeaux, France,Univ. Bordeaux, Inserm, Centre de Recherche Cardio-Thoracique, Bordeaux, France
| | - Kanchan Kulkarni
- IHU-Liryc, Fondation Bordeaux Université, Pessac-Bordeaux, France,Univ. Bordeaux, Inserm, Centre de Recherche Cardio-Thoracique, Bordeaux, France
| | - Nestor Pallares-Lupon
- IHU-Liryc, Fondation Bordeaux Université, Pessac-Bordeaux, France,Univ. Bordeaux, Inserm, Centre de Recherche Cardio-Thoracique, Bordeaux, France
| | - Bastiaan J. Boukens
- Department of Physiology, Cardiovascular Research Institute Maastricht, University Maastricht, Maastricht, Netherlands,Department of Medical Biology, Amsterdam Cardiovascular Sciences, Amsterdam University Medical Center, University of Amsterdam, Amsterdam, Netherlands
| | - Igor R. Efimov
- Department of Biomedical Engineering, The George Washington University, Washington, DC, United States,Department of Biomedical Engineering, Northwestern University, Chicago, IL, United States,Department of Medicine, Northwestern University, Chicago, IL, United States
| | - Edward J. Vigmond
- IHU-Liryc, Fondation Bordeaux Université, Pessac-Bordeaux, France,Univ. Bordeaux, Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux, UMR5251, Bordeaux, France
| | - Olivier Bernus
- IHU-Liryc, Fondation Bordeaux Université, Pessac-Bordeaux, France,Univ. Bordeaux, Inserm, Centre de Recherche Cardio-Thoracique, Bordeaux, France
| | - Richard D. Walton
- IHU-Liryc, Fondation Bordeaux Université, Pessac-Bordeaux, France,Univ. Bordeaux, Inserm, Centre de Recherche Cardio-Thoracique, Bordeaux, France,*Correspondence: Richard D. Walton,
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5
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Lilienkamp T, Parlitz U, Luther S. Taming cardiac arrhythmias: Terminating spiral wave chaos by adaptive deceleration pacing. CHAOS (WOODBURY, N.Y.) 2022; 32:121105. [PMID: 36587312 DOI: 10.1063/5.0126682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 10/26/2022] [Indexed: 06/17/2023]
Abstract
Sequences of weak electrical pulses are considered a promising alternative for terminating ventricular and atrial fibrillations while avoiding strong defibrillation shocks with adverse side effects. In this study, using numerical simulations of four different 2D excitable media, we show that pulse trains with increasing temporal intervals between successive pulses (deceleration pacing) provide high success rates at low energies. Furthermore, we propose a simple and robust approach to calculate inter-pulse spacing directly from the frequency spectrum of the dynamics (for instance, computed based on the electrocardiogram), which can be practically used in experiments and clinical applications.
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Affiliation(s)
- Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
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6
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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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7
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Lilienkamp T, Parlitz U, Luther S. Non-monotonous dose response function of the termination of spiral wave chaos. Sci Rep 2022; 12:12043. [PMID: 35835979 PMCID: PMC9283470 DOI: 10.1038/s41598-022-16068-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 07/04/2022] [Indexed: 11/15/2022] Open
Abstract
The conventional termination technique of life threatening cardiac arrhythmia like ventricular fibrillation is the application of a high-energy electrical defibrillation shock, coming along with severe side-effects. In order to improve the current treatment reducing these side-effects, the application of pulse sequences of lower energy instead of a single high-energy pulse are promising candidates. In this study, we show that in numerical simulations the dose-response function of pulse sequences applied to two-dimensional spiral wave chaos is not necessarily monotonously increasing, but exhibits a non-trivial frequency dependence. This insight into crucial phenomena appearing during termination attempts provides a deeper understanding of the governing termination mechanisms in general, and therefore may open up the path towards an efficient termination of cardiac arrhythmia in the future.
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Affiliation(s)
- Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, 37077, Germany. .,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, 37075, Germany.
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, 37077, Germany.,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, 37075, Germany.,Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, 37077, Göttingen, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, 37077, Germany. .,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, 37075, Germany. .,Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, 37077, Göttingen, Germany. .,University Medical Center Goettingen, Institute of Pharmacology and Toxicology, 37075, Göttingen, Germany.
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8
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Affiliation(s)
- Zhilin Qu
- Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, California.
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9
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Lebert J, Ravi N, Fenton FH, Christoph J. Rotor Localization and Phase Mapping of Cardiac Excitation Waves Using Deep Neural Networks. Front Physiol 2022; 12:782176. [PMID: 34975536 PMCID: PMC8718715 DOI: 10.3389/fphys.2021.782176] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 11/11/2021] [Indexed: 11/15/2022] Open
Abstract
The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting.
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Affiliation(s)
- Jan Lebert
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States
| | - Namita Ravi
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States.,Yale School of Medicine, Yale University, New Haven, CT, United States
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Jan Christoph
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States
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10
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Li TC, Zhong W, Ai BQ, Panfilov AV, Dierckx H. Control of the chirality of spiral waves and recreation of spatial excitation patterns through optogenetics. Phys Rev E 2022; 105:014214. [PMID: 35193299 DOI: 10.1103/physreve.105.014214] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
Spiral waves lead to dangerous arrhythmias in the cardiac system. In 2015 Burton et al. demonstrated the reversal of the spiral wave chirality through the rotating spiral-shaped illumination on the optogenetically modified cardiac monolayers. We show that this process entails the recreation of a spiral wave. We show how this methodology can be used to control and create the desired spatial excitation pattern. We found that the control is sensitive to the area of illuminated region but independent of the phase difference of the existing spiral wave and the applied spiral-shaped light. We also discovered that our methodology can temporarily resynchronize a turbulent system. The results offer numerical evidence for the control of spatial pattern in biological excitable systems with optogenetics.
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Affiliation(s)
- Teng-Chao Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Wei Zhong
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Alexander V Panfilov
- Ural Federal University, Biomed Laboratory, 620002 Ekaterinburg, Russia; Ghent University, 9000 Ghent, Belgium; and World-Class Research Center "Digital Biodesign and Personalized Healthcare," I. M. Sechenov First Moscow State Medical University, 119146 Moscow, Russia
| | - Hans Dierckx
- KU Leuven Campus Kortrijk-Kulak, Department of Mathematics, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium and iSi Health - KU Leuven Institute of Physics-based Modeling for In Silico Health, KU Leuven, Belgium
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11
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Abstract
The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).
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12
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Berman JP, Kaboudian A, Uzelac I, Iravanian S, Iles T, Iaizzo PA, Lim H, Smolka S, Glimm J, Cherry EM, Fenton FH. Interactive 3D Human Heart Simulations on Segmented Human MRI Hearts. COMPUTING IN CARDIOLOGY 2021; 48:10.23919/cinc53138.2021.9662948. [PMID: 35754523 PMCID: PMC9228622 DOI: 10.23919/cinc53138.2021.9662948] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Understanding cardiac arrhythmic mechanisms and developing new strategies to control and terminate them using computer simulations requires realistic physiological cell models with anatomically accurate heart structures. Furthermore, numerical simulations must be fast enough to study and validate model and structure parameters. Here, we present an interactive parallel approach for solving detailed cell dynamics in high-resolution human heart structures with a local PC's GPU. In vitro human heart MRI scans were manually segmented to produce 3D structures with anatomically realistic electrophysiology. The Abubu.js library was used to create an interactive code to solve the OVVR human ventricular cell model and the FDA extension of the model in the human MRI heart structures, allowing the simulation of reentrant waves and investigation of their dynamics in real time. Interactive simulations of a physiological cell model in a detailed anatomical human heart reveals propagation of waves through the fine structures of the trabeculae and pectinate muscle that can perpetuate arrhythmias, thereby giving new insights into effects that may need to be considered when planning ablation and other defibrillation methods.
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Affiliation(s)
- John P Berman
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
| | - Abouzar Kaboudian
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
| | - Ilija Uzelac
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
| | | | - Tinen Iles
- Medical School, University of Minnesota, Minneapolis, MN, USA
| | - Paul A Iaizzo
- Medical School, University of Minnesota, Minneapolis, MN, USA
| | | | | | | | - Elizabeth M Cherry
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
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13
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Anupong S, Schreiber I, Kheowan OU. Turbulent pattern in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. Phys Chem Chem Phys 2020; 22:28213-28221. [PMID: 33295367 DOI: 10.1039/d0cp04112b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Chemical turbulence was observed experimentally in the 1,4-cyclohexanedione Belousov-Zhabotinsky (CHD-BZ) reaction in a double layer consisting of a catalyst-loaded gel and uncatalyzed liquid on a Petri dish. The chemical patterns in the CHD-BZ reaction occur spontaneously in various forms as follows: the initial, regular, transient, and turbulent patterns, subsequently. These four patterns are characterized by using the two-dimensional Fourier transform (2D-FT). Mechanism of the onset of the turbulence in the CHD-BZ reaction is proposed. Turbulence in the CHD-BZ reaction is reproducible under a well defined protocol and it exists for a period of time of about 50 minutes, which is sufficiently long to offer a good opportunity to study and control the turbulence in the future. Two models of the BZ reaction were used to simulate the spiral breakup. Both are capable of producing spiral turbulence from initially regular patterns in each layer and reflect certain features of dynamics observed in experiments.
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Affiliation(s)
- Suparinthon Anupong
- Department of Chemistry, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand.
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14
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Glass L. Using mathematics to diagnose, cure, and predict cardiac arrhythmia. CHAOS (WOODBURY, N.Y.) 2020; 30:113132. [PMID: 33261334 DOI: 10.1063/5.0021844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 10/14/2020] [Indexed: 06/12/2023]
Abstract
Mathematics can be used to analyze and model cardiac arrhythmia. I discuss three different problems. (1) Diagnosis of atrial fibrillation based on the time intervals between subsequent beats. The probability density histograms of the differences of the intervals between consecutive beats have characteristic shapes for atrial fibrillation. (2) Curing atrial fibrillation by ablation of the core of rotors. Recent clinical studies have proposed that ablating the core of rotors in atrial tissue can cure atrial fibrillation. However, the claims are controversial. One problem that arises relates to difficulties associated with developing algorithms to identify the core of rotors. In model tissue culture systems, heterogeneity in the structure makes it difficult to unambiguously locate the core of rotors. (3) Risk stratification for sudden cardiac death (SCD). Despite numerous clinical studies, there is still a need for improved criteria to assess the risk of SCD. I discuss the possibility of using the dynamics of premature ventricular complexes to help make predictions. The development of wearable devices to record and analyze cardiac rhythms offers new prospects for the diagnosis and treatment of cardiac arrhythmia.
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Affiliation(s)
- Leon Glass
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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15
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Abstract
Optical mapping of electrical activity in the heart is based on voltage-sensitive and lipophilic fluorescence dyes. Optical signals recorded from cardiac cells correlate well with their transmembrane potentials. High spatiotemporal resolution, wide field mapping, and high sensitivity to transmembrane potential enable detailed characterization of action potential initiation and propagation. Optical mapping is used to study complex patterns of excitation propagation, including propagation across the sinoatrial and atrioventricular nodes and during atrial and ventricular arrhythmias.Optical mapping is used to study the role of reentrant activity in atrial and ventricular fibrillation.
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16
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Attuel G, Gerasimova-Chechkina E, Argoul F, Yahia H, Arneodo A. Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. Modeling. Front Physiol 2019; 10:480. [PMID: 31105585 PMCID: PMC6492055 DOI: 10.3389/fphys.2019.00480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2018] [Accepted: 04/05/2019] [Indexed: 11/13/2022] Open
Abstract
In a companion paper (I. Multifractal analysis of clinical data), we used a wavelet-based multiscale analysis to reveal and quantify the multifractal intermittent nature of the cardiac impulse energy in the low frequency range ≲ 2Hz during atrial fibrillation (AF). It demarcated two distinct areas within the coronary sinus (CS) with regionally stable multifractal spectra likely corresponding to different anatomical substrates. The electrical activity also showed no sign of the kind of temporal correlations typical of cascading processes across scales, thereby indicating that the multifractal scaling is carried by variations in the large amplitude oscillations of the recorded bipolar electric potential. In the present study, to account for these observations, we explore the role of the kinetics of gap junction channels (GJCs), in dynamically creating a new kind of imbalance between depolarizing and repolarizing currents. We propose a one-dimensional (1D) spatial model of a denervated myocardium, where the coupling of cardiac cells fails to synchronize the network of cardiac cells because of abnormal transjunctional capacitive charging of GJCs. We show that this non-ohmic nonlinear conduction 1D modeling accounts quantitatively well for the "multifractal random noise" dynamics of the electrical activity experimentally recorded in the left atrial posterior wall area. We further demonstrate that the multifractal properties of the numerical impulse energy are robust to changes in the model parameters.
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Affiliation(s)
- Guillaume Attuel
- Geometry and Statistics in Acquisition Data, Centre de Recherche INRIA, Talence, France
| | | | - Françoise Argoul
- Laboratoire Ondes et Matières d'Aquitaine, Université de Bordeaux, UMR 5798, CNRS, Talence, France
| | - Hussein Yahia
- Geometry and Statistics in Acquisition Data, Centre de Recherche INRIA, Talence, France
| | - Alain Arneodo
- Laboratoire Ondes et Matières d'Aquitaine, Université de Bordeaux, UMR 5798, CNRS, Talence, France
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17
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Mann I, Sandler B, Linton N, Kanagaratnam P. Drivers of Atrial Fibrillation: Theoretical Considerations and Practical Concerns. Arrhythm Electrophysiol Rev 2018; 7:49-54. [PMID: 29636973 DOI: 10.15420/aer.2017.40.3] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
Understanding the mechanisms responsible for driving AF is key to improving the procedural success for AF ablation. In this review, we look at some of the proposed drivers of AF, the disagreement between experts and the challenges confronted in attempting to map AF. Defining a 'driver' is also controversial, but for the purposes of this review we will consider an AF driver to be either a focal or localised source demonstrating fast, repetitive activity that propagates outward from this source, breaking down in to disorganisation further away from its origin.
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Affiliation(s)
- Ian Mann
- Imperial College Healthcare NHS TrustLondon, UK
| | | | - Nick Linton
- Imperial College Healthcare NHS TrustLondon, UK
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Saltiel P, d’Avella A, Tresch MC, Wyler K, Bizzi E. Critical Points and Traveling Wave in Locomotion: Experimental Evidence and Some Theoretical Considerations. Front Neural Circuits 2017; 11:98. [PMID: 29276476 PMCID: PMC5727018 DOI: 10.3389/fncir.2017.00098] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Accepted: 11/20/2017] [Indexed: 11/13/2022] Open
Abstract
The central pattern generator (CPG) architecture for rhythm generation remains partly elusive. We compare cat and frog locomotion results, where the component unrelated to pattern formation appears as a temporal grid, and traveling wave respectively. Frog spinal cord microstimulation with N-methyl-D-Aspartate (NMDA), a CPG activator, produced a limited set of force directions, sometimes tonic, but more often alternating between directions similar to the tonic forces. The tonic forces were topographically organized, and sites evoking rhythms with different force subsets were located close to the constituent tonic force regions. Thus CPGs consist of topographically organized modules. Modularity was also identified as a limited set of muscle synergies whose combinations reconstructed the EMGs. The cat CPG was investigated using proprioceptive inputs during fictive locomotion. Critical points identified both as abrupt transitions in the effect of phasic perturbations, and burst shape transitions, had biomechanical correlates in intact locomotion. During tonic proprioceptive perturbations, discrete shifts between these critical points explained the burst durations changes, and amplitude changes occurred at one of these points. Besides confirming CPG modularity, these results suggest a fixed temporal grid of anchoring points, to shift modules onsets and offsets. Frog locomotion, reconstructed with the NMDA synergies, showed a partially overlapping synergy activation sequence. Using the early synergy output evoked by NMDA at different spinal sites, revealed a rostrocaudal topographic organization, where each synergy is preferentially evoked from a few, albeit overlapping, cord regions. Comparing the locomotor synergy sequence with this topography suggests that a rostrocaudal traveling wave would activate the synergies in the proper sequence for locomotion. This output was reproduced in a two-layer model using this topography and a traveling wave. Together our results suggest two CPG components: modules, i.e., synergies; and temporal patterning, seen as a temporal grid in the cat, and a traveling wave in the frog. Animal and limb navigation have similarities. Research relating grid cells to the theta rhythm and on segmentation during navigation may relate to our temporal grid and traveling wave results. Winfree's mathematical work, combining critical phases and a traveling wave, also appears important. We conclude suggesting tracing, and imaging experiments to investigate our CPG model.
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Affiliation(s)
- Philippe Saltiel
- Department of Brain and Cognitive Sciences and McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, United States
- Département de Neurosciences, Faculté de Médecine, Université de Montréal, Montréal, QC, Canada
| | - Andrea d’Avella
- Department of Biomedical and Dental Sciences and Morphofunctional Imaging, University of Messina, Messina, Italy
- Laboratory of Neuromotor Physiology, Santa Lucia Foundation, Rome, Italy
| | - Matthew C. Tresch
- Departments of Biomedical Engineering, Physical Medicine and Rehabilitation, and Physiology, Northwestern University, Chicago, IL, United States
| | - Kuno Wyler
- Department of Brain and Cognitive Sciences and McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, United States
| | - Emilio Bizzi
- Department of Brain and Cognitive Sciences and McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, United States
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19
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Yang Y, Xiong D, Pipathsouk A, Weiner OD, Wu M. Clathrin Assembly Defines the Onset and Geometry of Cortical Patterning. Dev Cell 2017; 43:507-521.e4. [PMID: 29161594 PMCID: PMC5826602 DOI: 10.1016/j.devcel.2017.10.028] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2016] [Revised: 09/16/2017] [Accepted: 10/25/2017] [Indexed: 01/20/2023]
Abstract
Assembly of the endocytic machinery is a constitutively active process that is important for the organization of the plasma membrane, signal transduction, and membrane trafficking. Existing research has focused on the stochastic nature of endocytosis. Here, we report the emergence of the collective dynamics of endocytic proteins as periodic traveling waves on the cell surface. Coordinated clathrin assembly provides the earliest spatial cue for cortical waves and sets the direction of propagation. Surprisingly, the onset of clathrin waves, but not individual endocytic events, requires feedback from downstream factors, including FBP17, Cdc42, and N-WASP. In addition to the localized endocytic assembly at the plasma membrane, intracellular clathrin and phosphatidylinositol-3,4-bisphosphate predict the excitability of the plasma membrane and modulate the geometry of traveling waves. Collectively, our data demonstrate the multiplicity of clathrin functions in cortical pattern formation and provide important insights regarding the nucleation and propagation of single-cell patterns.
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Affiliation(s)
- Yang Yang
- Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore; Centre for Bioimaging Sciences, National University of Singapore, Singapore 117557, Singapore
| | - Ding Xiong
- Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore; Centre for Bioimaging Sciences, National University of Singapore, Singapore 117557, Singapore
| | - Anne Pipathsouk
- Cardiovascular Research Institute and Department of Biochemistry and Biophysics, University of California, San Francisco, CA 94158-9001, USA
| | - Orion D Weiner
- Cardiovascular Research Institute and Department of Biochemistry and Biophysics, University of California, San Francisco, CA 94158-9001, USA
| | - Min Wu
- Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore; Centre for Bioimaging Sciences, National University of Singapore, Singapore 117557, Singapore; Department of Biological Sciences, National University of Singapore, Singapore 117543, Singapore.
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20
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Marcotte CD, Grigoriev RO. Dynamical mechanism of atrial fibrillation: A topological approach. CHAOS (WOODBURY, N.Y.) 2017; 27:093936. [PMID: 28964130 DOI: 10.1063/1.5003259] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets' hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead, this complexity is maintained as a dynamical balance between wave coalescence-a unique, previously unidentified, topological process that increases the number of wavelets-and wave collapse-a different topological process that decreases their number.
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Affiliation(s)
- Christopher D Marcotte
- EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Devon, EX44QJ, United Kingdom
| | - Roman O Grigoriev
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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21
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Ng GA. Feasibility of selection of antiarrhythmic drug treatment on the basis of arrhythmogenic mechanism — Relevance of electrical restitution, wavebreak and rotors. Pharmacol Ther 2017; 176:1-12. [DOI: 10.1016/j.pharmthera.2016.10.002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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22
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Fibrosis and Atrial Fibrillation: Computerized and Optical Mapping; A View into the Human Atria at Submillimeter Resolution. JACC Clin Electrophysiol 2017; 3:531-546. [PMID: 29159313 DOI: 10.1016/j.jacep.2017.05.002] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
Recent studies strongly suggest that the majority of atrial fibrillation (AF) patients with diagnosed or subclinical cardiac diseases have established or even pre-existing fibrotic structural remodeling, which may lead to conduction abnormalities and reentrant activity that sustain AF. As conventional treatments fail to treat AF in far too many cases, an urgent need exists to identify specific structural arrhythmogenic fibrosis patterns, which may maintain AF, in order to identify effective ablation targets for AF treatment. However, the existing challenge is to define what exact structural remodeling within the complex 3D human atrial wall is arrhythmogenic, as well as linking arrhythmogenic fibrosis to an underlying mechanism of AF maintenance in the clinical setting. This review is focused on the role of 3D fibrosis architecture in the mechanisms of AF maintenance revealed by submillimeter, high-resolution ex-vivo imaging modalities directly of human atria, as well as from in-silico 3D computational techniques that can be able to overcome in-vivo clinical limitations. The systematic integration of functional and structural imaging ex-vivo may inform the necessary integration of electrode and structural mapping in-vivo. A holistic view of AF driver mechanisms may begin to identify the defining characteristics or "fingerprints" of reentrant AF drivers, such as 3D fibrotic architecture, in order to design optimal patient-specific ablation strategies.
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23
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Oprisan SA. Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve. Neural Comput 2017; 29:2030-2054. [PMID: 28562215 DOI: 10.1162/neco_a_00983] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
We used the phase-resetting method to study a biologically relevant three-neuron network in which one neuron receives multiple inputs per cycle. For this purpose, we first generalized the concept of phase resetting to accommodate multiple inputs per cycle. We explicitly showed how analytical conditions for the existence and the stability of phase-locked modes are derived. In particular, we solved newly derived recursive maps using as an example a biologically relevant driving-driven neural network with a dynamic feedback loop. We applied the generalized phase-resetting definition to predict the relative-phase and the stability of a phase-locked mode in open loop setup. We also compared the predicted phase-locked mode against numerical simulations of the fully connected network.
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Affiliation(s)
- Sorinel A Oprisan
- College of Charleston, Department of Physics and Astronomy, Charleston, SC 29424, U.S.A.
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24
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A Consistent Definition of Phase Resetting Using Hilbert Transform. INTERNATIONAL SCHOLARLY RESEARCH NOTICES 2017; 2017:5865101. [PMID: 28553658 PMCID: PMC5434474 DOI: 10.1155/2017/5865101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Accepted: 04/09/2017] [Indexed: 12/22/2022]
Abstract
A phase resetting curve (PRC) measures the transient change in the phase of a neural oscillator subject to an external perturbation. The PRC encapsulates the dynamical response of a neural oscillator and, as a result, it is often used for predicting phase-locked modes in neural networks. While phase is a fundamental concept, it has multiple definitions that may lead to contradictory results. We used the Hilbert Transform (HT) to define the phase of the membrane potential oscillations and HT amplitude to estimate the PRC of a single neural oscillator. We found that HT's amplitude and its corresponding instantaneous frequency are very sensitive to membrane potential perturbations. We also found that the phase shift of HT amplitude between the pre- and poststimulus cycles gives an accurate estimate of the PRC. Moreover, HT phase does not suffer from the shortcomings of voltage threshold or isochrone methods and, as a result, gives accurate and reliable estimations of phase resetting.
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25
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Oprisan SA, Austin DI. A generalized phase resetting method for phase-locked modes prediction. PLoS One 2017; 12:e0174304. [PMID: 28323894 PMCID: PMC5360347 DOI: 10.1371/journal.pone.0174304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Accepted: 03/07/2017] [Indexed: 11/23/2022] Open
Abstract
We derived analytically and checked numerically a set of novel conditions for the existence and the stability of phase-locked modes in a biologically relevant master-slave neural network with a dynamic feedback loop. Since neural oscillators even in the three-neuron network investigated here receive multiple inputs per cycle, we generalized the concept of phase resetting to accommodate multiple inputs per cycle. We proved that the phase resetting produced by two or more stimuli per cycle can be recursively computed from the traditional, single stimulus, phase resetting. We applied the newly derived generalized phase resetting definition to predicting the relative phase and the stability of a phase-locked mode that was experimentally observed in this type of master-slave network with a dynamic loop network.
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Affiliation(s)
- Sorinel A Oprisan
- Department of Physics and Astronomy, College of Charleston, Charleston, SC, United States of America
| | - Dave I Austin
- Department of Physics and Astronomy, College of Charleston, Charleston, SC, United States of America
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26
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Rossi S, Buccarello A, Ershler PR, Lux RL, Callegari S, Corradi D, Carnevali L, Sgoifo A, Miragoli M, Musso E, Macchi E. Effect of anisotropy on ventricular vulnerability to unidirectional block and reentry by single premature stimulation during normal sinus rhythm in rat heart. Am J Physiol Heart Circ Physiol 2016; 312:H584-H607. [PMID: 28011584 DOI: 10.1152/ajpheart.00366.2016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Revised: 12/05/2016] [Accepted: 12/20/2016] [Indexed: 11/22/2022]
Abstract
Single high-intensity premature stimuli when applied to the ventricles during ventricular drive of an ectopic site, as in Winfree's "pinwheel experiment," usually induce reentry arrhythmias in the normal heart, while single low-intensity stimuli barely do. Yet ventricular arrhythmia vulnerability during normal sinus rhythm remains largely unexplored. With a view to define the role of anisotropy on ventricular vulnerability to unidirectional conduction block and reentry, we revisited the pinwheel experiment with reduced constraints in the in situ rat heart. New features included single premature stimulation during normal sinus rhythm, stimulation and unipolar potential mapping from the same high-resolution epicardial electrode array, and progressive increase in stimulation strength and prematurity from diastolic threshold until arrhythmia induction. Measurements were performed with 1-ms cathodal stimuli at multiple test sites (n = 26) in seven rats. Stimulus-induced virtual electrode polarization during sinus beat recovery phase influenced premature ventricular responses. Specifically, gradual increase in stimulus strength and prematurity progressively induced make, break, and graded-response stimulation mechanisms. Hence unidirectional conduction block occurred as follows: 1) along fiber direction, on right and left ventricular free walls (n = 23), initiating figure-eight reentry (n = 17) and tachycardia (n = 12), and 2) across fiber direction, on lower interventricular septum (n = 3), initiating spiral wave reentry (n = 2) and tachycardia (n = 1). Critical time window (55.1 ± 4.7 ms, 68.2 ± 6.0 ms) and stimulus strength lower limit (4.9 ± 0.6 mA) defined vulnerability to reentry. A novel finding of this study was that ventricular tachycardia evolves and is maintained by episodes of scroll-like wave and focal activation couplets. We also found that single low-intensity premature stimuli can induce repetitive ventricular response (n = 13) characterized by focal activations.NEW & NOTEWORTHY We performed ventricular cathodal point stimulation during sinus rhythm by progressively increasing stimulus strength and prematurity. Virtual electrode polarization and recovery gradient progressively induced make, break, and graded-response stimulation mechanisms. Unidirectional conduction block occurred along or across fiber direction, initiating figure-eight or spiral wave reentry, respectively, and tachycardia sustained by scroll wave and focal activations.
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Affiliation(s)
- S Rossi
- Department of Life Sciences, Università degli Studi, Parma, Italy.,CERT, Center of Excellence for Toxicological Research, Department of Clinical and Experimental Medicine, Università degli Studi, Parma, Italy
| | - A Buccarello
- Department of Life Sciences, Università degli Studi, Parma, Italy
| | - P R Ershler
- Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, Utah
| | - R L Lux
- Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, Utah
| | - S Callegari
- Azienda Unità Sanitaria Locale, Unit of Cardiology, Parma, Italy
| | - D Corradi
- Department of Biomedical, Biotechnological, and Translational Sciences, Unit of Pathology, Università degli Studi, Parma, Italy.,CERT, Center of Excellence for Toxicological Research, Department of Clinical and Experimental Medicine, Università degli Studi, Parma, Italy
| | - L Carnevali
- Department of Life Sciences, Università degli Studi, Parma, Italy
| | - A Sgoifo
- Department of Life Sciences, Università degli Studi, Parma, Italy
| | - M Miragoli
- CERT, Center of Excellence for Toxicological Research, Department of Clinical and Experimental Medicine, Università degli Studi, Parma, Italy.,Humanitas Clinical and Research Center, Rozzano (Milan), Italy; and
| | - E Musso
- Department of Life Sciences, Università degli Studi, Parma, Italy.,Cardiac Stem Cell Interdepartmental Center "CISTAC," Università degli Studi, Parma, Italy
| | - E Macchi
- Department of Life Sciences, Università degli Studi, Parma, Italy; .,CERT, Center of Excellence for Toxicological Research, Department of Clinical and Experimental Medicine, Università degli Studi, Parma, Italy.,Cardiac Stem Cell Interdepartmental Center "CISTAC," Università degli Studi, Parma, Italy
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27
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Long-range synchrony and emergence of neural reentry. Sci Rep 2016; 6:36837. [PMID: 27874019 PMCID: PMC5118796 DOI: 10.1038/srep36837] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Accepted: 10/18/2016] [Indexed: 11/08/2022] Open
Abstract
Neural synchronization across long distances is a functionally important phenomenon in health and disease. In order to access the basis of different modes of long-range synchrony, we monitor spiking activities over centimetre scale in cortical networks and show that the mode of synchrony depends upon a length scale, λ, which is the minimal path that activity should propagate through to find its point of origin ready for reactivation. When λ is larger than the physical dimension of the network, distant neuronal populations operate synchronously, giving rise to irregularly occurring network-wide events that last hundreds of milliseconds to several seconds. In contrast, when λ approaches the dimension of the network, a continuous self-sustained reentry propagation emerges, a regular seizure-like mode that is marked by precise spatiotemporal patterns ('synfire chains') and may last many minutes. Termination of a reentry phase is preceded by a decrease of propagation speed to a halt. Stimulation decreases both propagation speed and λ values, which modifies the synchrony mode respectively. The results contribute to the understanding of the origin and termination of different modes of neural synchrony as well as their long-range spatial patterns, while hopefully catering to manipulation of the phenomena in pathological conditions.
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28
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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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29
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Vasserman IN, Matveenko VP, Shardakov IN, Shestakov AP. The mechanism of the initiation of cardiac arrhythmias due to a pathological distribution of myocardial conductivity. Biophysics (Nagoya-shi) 2016. [DOI: 10.1134/s0006350916020238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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30
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Proietti R, Roux JF, Verma A, Alturki A, Bernier ML, Essebag V. A Historical Perspective on the Role of Functional Lines of Block in the Re-entrant Circuit of Ventricular Tachycardia. PACING AND CLINICAL ELECTROPHYSIOLOGY: PACE 2016; 39:490-6. [PMID: 26852719 DOI: 10.1111/pace.12827] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Revised: 01/13/2016] [Accepted: 01/25/2016] [Indexed: 12/29/2022]
Abstract
The ablation strategy for ventricular tachycardia (VT) rapidly evolved from an entrainment mapping approach for identification of the critical isthmus of the re-entrant circuit during monomorphic VT, toward a substrate-based approach aiming to ablate surrogate markers of the circuit during sinus rhythm in hemodynamically nontolerated and polymorphic VT. The latter approach implies an assumption that the circuits responsible for the arrhythmia are anatomical or fixed, and present during sinus rhythm. Accordingly, the lines of block delimiting the channels of the circuits are often considered fixed, although there is evidence that they are functional or more frequently a combination of fixed and functional. The electroanatomical substrate-based approach to VT ablation performed during sinus rhythm is increasingly adopted in clinical practice and often described as scar homogenization, scar dechanneling, or core isolation. However, whether the surrogate markers of the VT circuit during sinus rhythm match the circuit during arrhythmias remains to be fully demonstrated. The myocardial scar is a heterogeneous electrophysiological milieu with complex arrhythmogenic mechanisms that potentially coexist simultaneously. Moreover, the scar consists of different areas of diverse refractoriness and conduction. It can be misleading to limit the arrhythmogenic perspective of the myocardial scar to fixed or anatomical barriers held responsible for the re-entry circuit. Greater understanding of the role of functional lines of block in VT and the validity of the surrogate targets being ablated is necessary to further improve the technique and outcome of VT ablation.
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Affiliation(s)
- Riccardo Proietti
- McGill University Health Center, Montreal, Quebec, Canada.,Cardiology Department, Luigi Sacco Hospital, Milan, Italy
| | - Jean-Francois Roux
- McGill University Health Center, Montreal, Quebec, Canada.,Centre Hospitalier Universite de Sherbrooke, Quebec, Canada
| | - Atul Verma
- McGill University Health Center, Montreal, Quebec, Canada.,Southlake Regional Health Centre, Newmarket, Ontario, Canada
| | - Ahmed Alturki
- McGill University Health Center, Montreal, Quebec, Canada
| | | | - Vidal Essebag
- McGill University Health Center, Montreal, Quebec, Canada.,Hôpital Sacré-Coeur de Montréal, Montreal, Quebec, Canada
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31
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Filgueiras-Rama D, Jalife J. STRUCTURAL AND FUNCTIONAL BASES OF CARDIAC FIBRILLATION. DIFFERENCES AND SIMILARITIES BETWEEN ATRIA AND VENTRICLES. JACC Clin Electrophysiol 2016; 2:1-3. [PMID: 27042693 DOI: 10.1016/j.jacep.2015.12.011] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Evidence accumulated over the last 25 years suggests that, whether in the atria or ventricles, fibrillation may be explained by the self-organization of the cardiac electrical activity into rapidly spinning rotors giving way to spiral waves that break intermittently and result in fibrillatory conduction. The dynamics and frequency of such rotors depend on the ion channel composition, excitability and refractory properties of the tissues involved, as well as on the thickness and respective three-dimensional fiber structure of the atrial and ventricular chambers. Therefore, improving the understanding of fibrillation has required the use of multidisciplinary research approaches, including optical mapping, patch clamping and molecular biology, and the application of concepts derived from the theory of wave propagation in excitable media. Moreover, translation of such concepts to the clinic has recently opened new opportunities to apply novel mechanistic approaches to therapy, particularly during atrial fibrillation ablation. Here we review the current understanding of the manner in which the underlying myocardial structure and function influence rotor initiation and maintenance during cardiac fibrillation. We also examine relevant underlying differences and similarities between atrial fibrillation and ventricular fibrillation and evaluate the latest clinical mapping technologies used to identify rotors in either arrhythmia. Altogether, the data being discussed have significantly improved our understanding of the cellular and structural bases of cardiac fibrillation and pointed toward potentially exciting new avenues for more efficient and effective identification and therapy of the most complex cardiac arrhythmias.
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Affiliation(s)
- David Filgueiras-Rama
- Fundación Centro Nacional de Investigaciones Cardiovasculares, Carlos III (CNIC)., Myocardial Pathophysiology Area, Madrid, Spain; Hospital Clínico San Carlos, Cardiology department, Madrid, Spain
| | - José Jalife
- Fundación Centro Nacional de Investigaciones Cardiovasculares, Carlos III (CNIC)., Myocardial Pathophysiology Area, Madrid, Spain; Center for Arrhythmia Research, Department of Internal Medicine, University of Michigan, Ann Arbor, Michigan, EEUU
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32
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Proietti R, Joza J, Essebag V. Therapy for ventricular arrhythmias in structural heart disease: a multifaceted challenge. J Physiol 2016; 594:2431-43. [PMID: 26621333 DOI: 10.1113/jp270534] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2015] [Accepted: 11/19/2015] [Indexed: 01/25/2023] Open
Abstract
The unpredictable nature and potentially catastrophic consequences of ventricular arrhythmias (VAs) have obligated physicians to search for therapies to prevent sudden cardiac death (SCD). At present, a low left ventricular ejection fraction (LVEF) has been used as a risk factor to predict SCD in patients with structural heart disease and has been consistently adopted as the predominant, and sometimes sole, indication for implantable cardioverter defibrillator (ICD) therapy. Although the ICD remains the mainstay life-saving therapy for SCD, it does not modify the underlying arrhythmic substrate and may be associated with adverse effects from perioperative and long-term complications. Preventative pharmacological therapy has been associated with limited benefits, but anti-arrhythmic medications have significant side effects profiles. Catheter ablation of VAs has greatly evolved over the last few decades. Substrate mapping in sinus rhythm has allowed haemodynamically unstable VAs to be successfully treated. Both LVEF as an indication for ICD therapy and electro-anatomical mapping for substrate modification identify static components of underlying myocardial arrhythmogenicity. They do not take into account dynamic factors, such as the mechanisms of arrhythmia initiation and development of new anatomical or functional lines of block, leading to the initiation and maintenance of VAs. Dynamic factors are difficult to evaluate and consequently are not routinely used in clinical practice to guide treatment. However, progress in the treatment of VAs should consider and integrate dynamic factors with static components to fully characterize the myocardial arrhythmic substrate.
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Affiliation(s)
- Riccardo Proietti
- McGill University Health Centre, Montreal, Quebec, Canada.,Cardiology Departments, Luigi Sacco Hospital, Milan, Italy
| | | | - Vidal Essebag
- McGill University Health Centre, Montreal, Quebec, Canada.,Hôpital Sacré-Coeur de Montréal, Montreal, Quebec, Canada
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33
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Abstract
Blood circulation is the result of the beating of the heart, which provides the mechanical force to pump oxygenated blood to, and deoxygenated blood away from, the peripheral tissues. This depends critically on the preceding electrical activation. Disruptions in the orderly pattern of this propagating cardiac excitation wave can lead to arrhythmias. Understanding of the mechanisms underlying their generation and maintenance requires knowledge of the ionic contributions to the cardiac action potential, which is discussed in the first part of this review. A brief outline of the different classification systems for arrhythmogenesis is then provided, followed by a detailed discussion for each mechanism in turn, highlighting recent advances in this area.
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Němec J, Kim JJ, Salama G. The link between abnormal calcium handling and electrical instability in acquired long QT syndrome--Does calcium precipitate arrhythmic storms? PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2015; 120:210-21. [PMID: 26631594 DOI: 10.1016/j.pbiomolbio.2015.11.003] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2015] [Revised: 11/17/2015] [Accepted: 11/19/2015] [Indexed: 12/19/2022]
Abstract
Release of Ca(2+) ions from sarcoplasmic reticulum (SR) into myocyte cytoplasm and their binding to troponin C is the final signal form myocardial contraction. Synchronous contraction of ventricular myocytes is necessary for efficient cardiac pumping function. This requires both shuttling of Ca(2+) between SR and cytoplasm in individual myocytes, and organ-level synchronization of this process by means of electrical coupling among ventricular myocytes. Abnormal Ca(2+) release from SR causes arrhythmias in the setting of CPVT (catecholaminergic polymorphic ventricular tachycardia) and digoxin toxicity. Recent optical mapping data indicate that abnormal Ca(2+) handling causes arrhythmias in models of both repolarization impairment and profound bradycardia. The mechanisms involve dynamic spatial heterogeneity of myocardial Ca(2+) handling preceding arrhythmia onset, cell-synchronous systolic secondary Ca(2+) elevation (SSCE), as well as more complex abnormalities of intracellular Ca(2+) handling detected by subcellular optical mapping in Langendorff-perfused hearts. The regional heterogeneities in Ca(2+) handling cause action potential (AP) heterogeneities through sodium-calcium exchange (NCX) activation and eventually overwhelm electrical coupling of the tissue. Divergent Ca(2+) dynamics among different myocardial regions leads to temporal instability of AP duration and - on the patient level - in T wave lability. Although T-wave alternans has been linked to cardiac arrhythmias, non-alternans lability is observed in pre-clinical models of the long QT syndrome (LQTS) and CPVT, and in LQTS patients. Analysis of T wave lability may provide a real-time window on the abnormal Ca(2+) dynamics causing specific arrhythmias such as Torsade de Pointes (TdP).
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Affiliation(s)
- Jan Němec
- Department of Medicine, Heart and Vascular Institute, University of Pittsburgh, Pittsburgh, PA 15261, USA
| | - Jong J Kim
- Department of Medicine, Heart and Vascular Institute, University of Pittsburgh, Pittsburgh, PA 15261, USA
| | - Guy Salama
- Department of Medicine, Heart and Vascular Institute, University of Pittsburgh, Pittsburgh, PA 15261, USA.
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35
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Gelens L, Huang KC, Ferrell JE. How Does the Xenopus laevis Embryonic Cell Cycle Avoid Spatial Chaos? Cell Rep 2015. [PMID: 26212326 DOI: 10.1016/j.celrep.2015.06.070] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022] Open
Abstract
Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally, and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells.
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Affiliation(s)
- Lendert Gelens
- Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, CA 94305-5174, USA; Applied Physics Research Group, Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium.
| | - Kerwyn Casey Huang
- Department of Bioengineering, Stanford University, Stanford, CA 94305-5444, USA; Department of Microbiology and Immunology, Stanford University School of Medicine, Stanford, CA 94305-5124, USA
| | - James E Ferrell
- Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, CA 94305-5174, USA; Department of Biochemistry, Stanford University School of Medicine, Stanford, CA 94305-5307, USA
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36
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Abstract
Formation of precipitation patterns and wave propagation in excitable media have attracted considerable scientific interest in the context of nonlinear chemical kinetics because of a new approach to micro and nanofabrication, in addition to some biological aspects. All precipitation patterns share common morphological characteristics, namely the formed patterns are stationary and no dynamical patterns can be observed in these classical precipitation systems (e.g., Liesegang phenomenon). However, it has been recently shown that in several circumstances dynamic patterns (chemical waves) can exist in purely inorganic precipitation systems similar to the well-known and studied (excitable) waves in Belousov-Zhabotinsky reaction. In this study, we show how to fine-tune the pattern characteristics in precipitation systems, such as the wavelength and the pattern morphology by changing the concentrations of the reagents, and we demonstrate chemical waves on a moving 3D spherical precipitation layer. We show that such precipitation waves have anomalous transport property, specifically superdiffusive nature, and it can be controlled by the initial concentration of the inner electrolyte. Moreover, we present several precipitation systems in which chemical wave propagation inside a moving precipitation layer can emerge. This observation points out the generality and robustness of similar behavior in diffusion-precipitation systems.
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Affiliation(s)
- Mahmoud M Ayass
- Department of Chemistry, American University of Beirut , P.O. Box 11-0236, Riad El-Solh 1107 2020, Beirut, Lebanon
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37
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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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38
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Das NP, Mahanta D, Dutta S. Unpinning of scroll waves under the influence of a thermal gradient. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022916. [PMID: 25215808 DOI: 10.1103/physreve.90.022916] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2014] [Indexed: 06/03/2023]
Abstract
Three-dimensional scroll waves of electrical activity are among the mechanisms believed to be responsible for the rapid, unsynchronized contraction of cardiac ventricles, thereby reducing the heart's ability to pump blood. Scroll waves can attach themselves to unexcitable obstacles, and this sometimes highly elongates their life span. Hence, the unpinning and annihilation of these vortices has attracted much attention in recent decades. In this work, we study the influence of a thermal gradient on scroll waves pinned to inert obstacles, in the Belousov-Zhabotinsky reaction. Under a temperature gradient, scroll rings were seen to unpin from these obstacles, thus strikingly reducing their lifetimes. These results were also reproduced by numerical simulations using the Barkley model.
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Affiliation(s)
- Nirmali Prabha Das
- Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - Dhriti Mahanta
- Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - Sumana Dutta
- Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
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39
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Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study. INTERNATIONAL SCHOLARLY RESEARCH NOTICES 2014; 2014:459675. [PMID: 27379274 PMCID: PMC4897501 DOI: 10.1155/2014/459675] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/11/2014] [Revised: 09/29/2014] [Accepted: 10/03/2014] [Indexed: 11/29/2022]
Abstract
The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.
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40
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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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41
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Weise LD, Panfilov AV. Emergence of spiral wave activity in a mechanically heterogeneous reaction-diffusion-mechanics system. PHYSICAL REVIEW LETTERS 2012; 108:228104. [PMID: 23003658 DOI: 10.1103/physrevlett.108.228104] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2012] [Indexed: 06/01/2023]
Abstract
We perform a numerical study of emergent spiral wave activity in a two-dimensional reaction-diffusion-mechanics medium with a regional inhomogeneity in active and passive mechanical properties. We find that self-sustaining spiral wave activity emerges for a wide range of mechanical parameters of the inhomogeneity via five mechanisms. We classify these mechanisms, relate them to parameters of the inhomogeneity, and discuss how these results can be applied to understand the onset of cardiac arrhythmias due to regional mechanical heterogeneity.
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Affiliation(s)
- L D Weise
- Department of Theoretical Biology, Utrecht University, Padualaan 8, Utrecht, 3584 CH, The Netherlands
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42
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Goryachev AB, Lichius A, Wright GD, Read ND. Excitable behavior can explain the "ping-pong" mode of communication between cells using the same chemoattractant. Bioessays 2012; 34:259-66. [PMID: 22271443 DOI: 10.1002/bies.201100135] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Here we elucidate a paradox: how a single chemoattractant-receptor system in two individuals is used for communication despite the seeming inevitability of self-excitation. In the filamentous fungus Neurospora crassa, genetically identical cells that produce the same chemoattractant fuse via the homing of individual cell protrusions toward each other. This is achieved via a recently described "ping-pong" pulsatile communication. Using a generic activator-inhibitor model of excitable behavior, we demonstrate that the pulse exchange can be fully understood in terms of two excitable systems locked into a stable oscillatory pattern of mutual excitation. The most puzzling properties of this communication are the sudden onset of oscillations with final amplitude, and the absence of seemingly inevitable self-excitation. We show that these properties result directly from both the excitability threshold and refractory period characteristic of excitable systems. Our model suggests possible molecular mechanisms for the ping-pong communication.
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43
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Weise LD, Panfilov AV. New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system. PLoS One 2011; 6:e27264. [PMID: 22114667 PMCID: PMC3215707 DOI: 10.1371/journal.pone.0027264] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2011] [Accepted: 10/12/2011] [Indexed: 11/21/2022] Open
Abstract
Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the “classical vulnerable zone.” Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM) model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material) to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the “classical,” and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the “classical vulnerable zone.” We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
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Affiliation(s)
- Louis D Weise
- Department of Theoretical Biology, Utrecht University, Utrecht, The Netherlands.
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44
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Shajahan TK, Borek B, Shrier A, Glass L. Scaling properties of conduction velocity in heterogeneous excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046208. [PMID: 22181246 DOI: 10.1103/physreve.84.046208] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2010] [Revised: 06/29/2011] [Indexed: 05/31/2023]
Abstract
Waves of excitation through excitable media, such as cardiac tissue, can propagate as plane waves or break up to form reentrant spiral waves. In diseased hearts reentrant waves can be associated with fatal cardiac arrhythmias. In this paper we investigate the conditions that lead to wave break, reentry, and propagation failure in mathematical models of heterogeneous excitable media. Two types of heterogeneities are considered: sinks are regions in space in which the voltage is fixed at its rest value, and breaks are nonconducting regions with no-flux boundary conditions. We find that randomly distributed heterogeneities in the medium have a decremental effect on the velocity, and above a critical density of such heterogeneities the conduction fails. Using numerical and analytical methods we derive the general relationship among the conduction velocity, density of heterogeneities, diffusion coefficient, and the rise time of the excitation in both two and three dimensions. This work helps us understand the factors leading to reduced propagation velocity and the formation of spiral waves in heterogeneous excitable media.
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Affiliation(s)
- T K Shajahan
- Department of Physiology, McGill University, Montreal, Canada
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45
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Abstract
Ventricular fibrillation (VF) is the leading cause of sudden cardiac death. This brief review addresses issues relevant to the dynamics of the rotors responsible for functional reentry and VF. It also makes an attempt to summarize present-day knowledge of the manner in which the dynamic interplay between inward and outward transmembrane currents and the heterogeneous cardiac structure establish a substrate for the initiation and maintenance of rotors and VF. The fragmentary nature of our current understanding of ionic VF mechanisms does not even allow an approach toward a "Theory of VF". Yet some hope is provided by recently obtained insight into the roles played in VF by some of the sarcolemmal ion channels that control the excitation-recovery process. For example, strong evidence supports the idea that the interplay between the rapid-inward sodium current and the inward-rectifier potassium current controls rotor formation, as well as rotor stability and frequency. Solid evidence also exists for an involvement of L-type calcium current in the control of rotor frequency and in determining VF-to-ventricular tachycardia conversion. Less clear, however, is whether or not time dependent outward currents through voltage-gated potassium channels affect the fibrillatory process. Hopefully, taking advantage of currently available approaches of structural, molecular and cellular biology, together with computational and imaging techniques, will afford us the opportunity to further advance knowledge on VF mechanisms.
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Affiliation(s)
- Sami F Noujaim
- Department of Pharmacology and Institute for Cardiovascular Research, SUNY Upstate Medical University, Syracuse, NY 13210, USA
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46
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Comtois P, Nattel S. Impact of tissue geometry on simulated cholinergic atrial fibrillation: a modeling study. CHAOS (WOODBURY, N.Y.) 2011; 21:013108. [PMID: 21456822 DOI: 10.1063/1.3544470] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Atrial fibrillation (AF), arising in the cardiac atria, is a common cardiac rhythm disorder that is incompletely understood. Numerous characteristics of the atrial tissue are thought to play a role in the maintenance of AF. Most traditional theoretical models of AF have considered the atrium to be a flat two-dimensional sheet. Here, we analyzed the relationship between atrial geometry, substrate size, and AF persistence, in a mathematical model involving heterogeneity. Spatially periodic properties were created by variations in times required for reactivation due to periodic acetylcholine concentration [ACh] distribution. The differences in AF maintenance between the sheet and the cylinder geometry are found for intermediate gradients of inexcitable time (intermediate [ACh]). The maximum difference in AF maintenance between geometry decreases with increasing tissue size, down to zero for a substrate of dimensions 20 × 10 cm. Generators have the tendency to be anchored to the regions of longer inexcitable period (low [ACh]). The differences in AF maintenance between geometries correlate with situations of moderate anchoring for which rotor-core drifts between low-[ACh] regions occur, favoring generator disappearance. The drift of generators increases their probability of disappearance at the tissue borders, resulting in a decreased maintenance rate in the sheet due to the higher number of no-flux boundaries. These interactions between biological variables and the role of geometry must be considered when selecting an appropriate model for AF in intact hearts.
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Affiliation(s)
- Philippe Comtois
- Department of Physiology and Institute of Biomedical Engineering, Université de Montréal, Montreal, Quebec, Canada.
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47
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Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu JY. Spiral wave dynamics in neocortex. Neuron 2011; 68:978-990. [PMID: 21145009 DOI: 10.1016/j.neuron.2010.11.007] [Citation(s) in RCA: 120] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/06/2010] [Indexed: 11/30/2022]
Abstract
Although spiral waves are ubiquitous features of nature and have been observed in many biological systems, their existence and potential function in mammalian cerebral cortex remain uncertain. Using voltage-sensitive dye imaging, we found that spiral waves occur frequently in the neocortex in vivo, both during pharmacologically induced oscillations and during sleep-like states. While their life span is limited, spiral waves can modify ongoing cortical activity by influencing oscillation frequencies and spatial coherence and by reducing amplitude in the area surrounding the spiral phase singularity. During sleep-like states, the rate of occurrence of spiral waves varies greatly depending on brain states. These results support the hypothesis that spiral waves, as an emergent activity pattern, can organize and modulate cortical population activity on the mesoscopic scale and may contribute to both normal cortical processing and to pathological patterns of activity such as those found in epilepsy.
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Affiliation(s)
- Xiaoying Huang
- Department of Physiology and Biophysics, Georgetown University Medical Center, Washington, DC 20057
| | - Weifeng Xu
- Department of Physiology and Biophysics, Georgetown University Medical Center, Washington, DC 20057
| | - Jianmin Liang
- Department of Physiology and Biophysics, Georgetown University Medical Center, Washington, DC 20057.,Department of Pediatrics, Jilin University First Hospital, Changchun, 130021, P.R. China
| | - Kentaroh Takagaki
- Department of Physiology and Biophysics, Georgetown University Medical Center, Washington, DC 20057.,Leibniz Institute for Neurobiology, Magdeburg, 39118, Germany
| | - Xin Gao
- Department of Physiology and Biophysics, Georgetown University Medical Center, Washington, DC 20057
| | - Jian-Young Wu
- Department of Physiology and Biophysics, Georgetown University Medical Center, Washington, DC 20057
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48
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Henao ÓA, Ferrero de Loma-Osorio JM, Sáiz J, Reynolds J. Arritmias potenciadas por isquemia sub-epicárdica en pared transmural heterogénea cardiaca: un estudio teórico de simulación. REVISTA COLOMBIANA DE CARDIOLOGÍA 2011. [DOI: 10.1016/s0120-5633(11)70164-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022] Open
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49
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Abstract
This brief review looks back to the major theoretical, experimental, and clinical work on the dynamics and mechanisms of atrial fibrillation (AF). Its goal is to highlight the most important issues, controversies, and advances that have driven the field of investigation into AF mechanisms at any given time during the last ∼100 years. It emphasizes that while the history of AF research has been full of controversies from the start, such controversies have led to new information, and individual scientists have learned from those that have preceded them. However, in the face of the most common sustained cardiac arrhythmia seen in clinical practice, we are yet to fully understand its fundamental mechanisms and learn how to treat it effectively. Future research into AF dynamics and mechanisms should focus on the development and validation of new numerical and animal models. Such models should be relevant to and accurately reproduce the important substrates associated with ageing and with diseases such as hypertension, heart failure, and ischaemic heart disease which cause AF in the vast majority of patients. Knowledge derived from such models may help to greatly advance the field and hopefully lead to more effective prevention and therapy.
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Affiliation(s)
- José Jalife
- Department of Internal Medicine/Cardiovascular Medicine, Center for Arrhythmia Research, University of Michigan, 5022 Venture Drive, Ann Arbor, MI 40108, USA.
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50
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The potential of microelectrode arrays and microelectronics for biomedical research and diagnostics. Anal Bioanal Chem 2010; 399:2313-29. [DOI: 10.1007/s00216-010-3968-1] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2010] [Accepted: 06/23/2010] [Indexed: 10/19/2022]
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