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Li J, Chen K, He L, Luo F, Wang X, Hu Y, Zhao J, Zhu K, Chen X, Zhang Y, Tao H, Dong J. Data-driven classification of left atrial morphology and its predictive impact on atrial fibrillation catheter ablation. J Cardiovasc Electrophysiol 2024; 35:811-820. [PMID: 38424601 DOI: 10.1111/jce.16228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/06/2024] [Revised: 02/11/2024] [Accepted: 02/14/2024] [Indexed: 03/02/2024]
Abstract
INTRODUCTION Various left atrial (LA) anatomical structures are correlated with postablative recurrence for atrial fibrillation (AF) patients. Comprehensively integrating anatomical structures, digitizing them, and implementing in-depth analysis, which may supply new insights, are needed. Thus, we aim to establish an interpretable model to identify AF patients' phenotypes according to LA anatomical morphology, using machine learning techniques. METHODS AND RESULTS Five hundred and nine AF patients underwent first ablation treatment in three centers were included and were followed-up for postablative recurrent atrial arrhythmias. Data from 369 patients were regarded as training set, while data from another 140 patients, collected from different centers, were used as validation set. We manually measured 57 morphological parameters on enhanced computed tomography with three-dimensional reconstruction technique and implemented unsupervised learning accordingly. Three morphological groups were identified, with distinct prognosis according to Kaplan-Meier estimator (p < .001). Multivariable Cox model revealed that morphological grouping were independent predictors of 1-year recurrence (Group 1: HR = 3.00, 95% CI: 1.51-5.95, p = .002; Group 2: HR = 4.68, 95% CI: 2.40-9.11, p < .001; Group 3 as reference). Furthermore, external validation consistently demonstrated our findings. CONCLUSIONS Our study illustrated the feasibility of employing unsupervised learning for the classification of LA morphology. By utilizing morphological grouping, we can effectively identify individuals at different risks of postablative recurrence and thereby assist in clinical decision-making.
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Affiliation(s)
- Jiaju Li
- Department of Cardiology, The First Affiliated Hospital of Zhengzhou University, Zhengzhou, China
| | - Ke Chen
- Department of Cardiology, Fuwai Central China Cardiovascular Hospital, Zhengzhou, China
| | - Liu He
- Department of Cardiology, Beijing Anzhen Hospital, Capital Medical University, Beijing, China
| | - Fangyuan Luo
- Graduate School of Peking Union Medical College, Chinese Academy of Medical Science, Beijing, China
- Department of Integrative Medicine Cardiology, China-Japan Friendship Hospital, Beijing, China
| | - Xianqing Wang
- Department of Cardiology, Fuwai Central China Cardiovascular Hospital, Zhengzhou, China
| | - Yucai Hu
- Department of Cardiology, The First Affiliated Hospital of Henan University of Chinese Medicine, Zhengzhou, China
| | - Jiangtao Zhao
- Department of Cardiology, The First Affiliated Hospital of Zhengzhou University, Zhengzhou, China
| | - Kui Zhu
- Department of Cardiology, The First Affiliated Hospital of Zhengzhou University, Zhengzhou, China
| | - Xiaowei Chen
- Department of Cardiology, The First Affiliated Hospital of Zhengzhou University, Zhengzhou, China
| | - Yuekun Zhang
- Department of Cardiology, Beijing Anzhen Hospital, Capital Medical University, Beijing, China
| | - Hailong Tao
- Department of Cardiology, The First Affiliated Hospital of Zhengzhou University, Zhengzhou, China
| | - Jianzeng Dong
- Department of Cardiology, The First Affiliated Hospital of Zhengzhou University, Zhengzhou, China
- Department of Cardiology, Beijing Anzhen Hospital, Capital Medical University, Beijing, China
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Cloet M, Arno L, Kabus D, Van der Veken J, Panfilov AV, Dierckx H. Scroll Waves and Filaments in Excitable Media of Higher Spatial Dimension. PHYSICAL REVIEW LETTERS 2023; 131:208401. [PMID: 38039450 DOI: 10.1103/physrevlett.131.208401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 08/30/2023] [Indexed: 12/03/2023]
Abstract
Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions. Numerical simulations are performed in four dimensions using the FitzHugh-Nagumo model, showing that the vortices rotate around a two-dimensional surface which we define as the superfilament. Evolution equations are derived for general superfilaments of codimension two in an N-dimensional space, and their equilibrium configurations are proven to be minimal surfaces. We suggest that biological excitable systems, such as the heart or brain which have nonlocal connections can be regarded, at least partially, as multidimensional excitable media and discuss further possible studies in this direction.
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Affiliation(s)
- Marie Cloet
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
| | - Louise Arno
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
| | - Desmond Kabus
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Leiden 2333 ZA, Netherlands
| | | | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620002, Russia
- World-Class Research Center "Digital biodesign and personalized healthcare," Sechenov University, Moscow 119991, Russia
| | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
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Maciunas K, Snipas M, Kraujalis T, Kraujalienė L, Panfilov AV. The role of the Cx43/Cx45 gap junction voltage gating on wave propagation and arrhythmogenic activity in cardiac tissue. Sci Rep 2023; 13:14863. [PMID: 37684404 PMCID: PMC10491658 DOI: 10.1038/s41598-023-41796-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2023] [Accepted: 08/31/2023] [Indexed: 09/10/2023] Open
Abstract
Gap junctions (GJs) formed of connexin (Cx) protein are the main conduits of electrical signals in the heart. Studies indicate that the transitional zone of the atrioventricular (AV) node contains heterotypic Cx43/Cx45 GJ channels which are highly sensitive to transjunctional voltage (Vj). To investigate the putative role of Vj gating of Cx43/Cx45 channels, we performed electrophysiological recordings in cell cultures and developed a novel mathematical/computational model which, for the first time, combines GJ channel Vj gating with a model of membrane excitability to simulate a spread of electrical pulses in 2D. Our simulation and electrophysiological data show that Vj transients during the spread of cardiac excitation can significantly affect the junctional conductance (gj) of Cx43/Cx45 GJs in a direction- and frequency-dependent manner. Subsequent simulation data indicate that such pulse-rate-dependent regulation of gj may have a physiological role in delaying impulse propagation through the AV node. We have also considered the putative role of the Cx43/Cx45 channel gating during pathological impulse propagation. Our simulation data show that Vj gating-induced changes in gj can cause the drift and subsequent termination of spiral waves of excitation. As a result, the development of fibrillation-like processes was significantly reduced in 2D clusters, which contained Vj-sensitive Cx43/Cx45 channels.
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Affiliation(s)
- Kestutis Maciunas
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
| | - Mindaugas Snipas
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania.
- Department of Mathematical Modelling, Kaunas University of Technology, Kaunas, Lithuania.
| | - Tadas Kraujalis
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
- Department of Applied Informatics, Kaunas University of Technology, Kaunas, Lithuania
| | - Lina Kraujalienė
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
- Department of Cardiology, Leiden University Medical Center, Leiden, The Netherlands
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Nampoothiri S. Preferential localization of a single spot in reaction-diffusion systems on non-spherical surfaces. SOFT MATTER 2023; 19:1977-1986. [PMID: 36847585 DOI: 10.1039/d2sm01287a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The present work systematically examines the effect of breaking the rotational symmetry of a surface on the spot positioning in reaction-diffusion (RD) systems. In particular, we study analytically and numerically the steady-state positioning of a single spot in RD systems on a prolate and an oblate ellipsoid. We adapt perturbative techniques to perform a linear stability analysis of the RD system on both ellipsoids. Furthermore, the spot positionings in the steady states of non-linear RD equations are obtained numerically on both ellipsoids. Our analysis suggests that preferential spot positioning can be observed on non-spherical surfaces. The present work may provide useful insights into the role of cell geometry on various symmetry-breaking mechanisms in cellular processes.
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Affiliation(s)
- Sankaran Nampoothiri
- Department of Physics, Gandhi Institute of Technology and Management (GITAM) University, Bengaluru, India.
- Dipartimento di Fisica e Astronomia G. Galilei - DFA, Sezione INFN, Universit di Padova, Via Marzolo 8, 35131 Padova, PD, Italy
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Hesaraghatta Hobli, Bengaluru North, 560089, India
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Xia YX, Zhi XP, Li TC, Pan JT, Panfilov AV, Zhang H. Spiral wave drift under optical feedback in cardiac tissue. Phys Rev E 2022; 106:024405. [PMID: 36109896 DOI: 10.1103/physreve.106.024405] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 06/01/2022] [Indexed: 06/15/2023]
Abstract
Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.
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Affiliation(s)
- Yuan-Xun Xia
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310027, China
| | - Xin-Pei Zhi
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310027, China
| | - Teng-Chao Li
- School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620002, Russia
- World-Class Research Center "Digital Biodesign and Personalized Healthcare", Sechenov University, Moscow 119146, Russia
| | - Hong Zhang
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310027, China
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6
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Nedios S, Sanatkhani S, Oladosu M, Seewöster T, Richter S, Arya A, Heijman J, J G M Crijns H, Hindricks G, Bollmann A, Menon PG. Association of low-voltage areas with the regional wall deformation and the left atrial shape in patients with atrial fibrillation: A proof of concept study. IJC HEART & VASCULATURE 2021; 33:100730. [PMID: 33718586 PMCID: PMC7933256 DOI: 10.1016/j.ijcha.2021.100730] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 01/03/2021] [Accepted: 01/30/2021] [Indexed: 11/30/2022]
Abstract
Background Left atrium (LA) remodeling is associated with atrial fibrillation (AF) and reduced success after AF ablation, but its relation with low-voltage areas (LVA) is not known. This study aimed to evaluate the relation between regional LA changes and LVAs in AF patients. Methods Pre-interventional CT data of patients (n = 24) with LA-LVA (<0.5 mV) in voltage mapping after AF ablation were analyzed (Surgery Explorer, QuantMD LLC). To quantify asymmetry (ASI = LA-A/LAV) a cutting plane parallel to the rear wall and along the pulmonary veins divided the LA-volume (LAV) into anterior (LA-A) and posterior parts. To quantify sphericity (LAS = 1-R/S), a patient-specific best-fit LA sphere was created. The average radius (R) and the mean deviation (S) from this sphere were calculated. The average local deviation (D) was measured for the roof, posterior, septum, inferior septum, inferior-posterior and lateral walls. Results The roof, posterior and septal regions had negative local deviations. There was a correlation between roof and septum (r = 0.42, p = 0.04), lateral and inferior-posterior (r = 0.48, p = 0.02) as well as posterior and inferior-septal deviations (r = −0.41, p = 0.046). ASI correlated with septum deformation (r = −0.43, p = 0.04). LAS correlated with dilatation (LAV, r = 0.49, p = 0.02), roof (r = 0.52, p = 0.009) and posterior deformation (r = −0.56, p = 0.005). Extended LVA correlated with local deformation of all LA walls, except the roof and the septum. LVA association with LAV, ASI and LAS did not reach statistical significance. Conclusion Extended LVA correlates with local wall deformations better than other remodeling surrogates. Therefore, their calculation could help predict LVA presence and deserve further evaluation in clinical studies.
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Key Words
- AF, atrial fibrillation
- AR, average radius
- ASI, asymmetry index
- Atrial fibrillation
- Atrial remodeling
- CA, catheter ablation
- CT, computed tomography
- Computer tomography
- IQR, inter-quartile range
- LA, left atrium
- LA-A, left atrial anterior (LA-A) partial volume
- LA-P, left atrial posterior (LA-P) partial volume
- LAA, left atrial appendage
- LAV, left atrial volume with anterior (LA-A) and posterior (LA-P) partial volumes
- LV, left ventricle
- LV-EF, left ventricular ejection fraction
- LVA, low-voltage area
- LVDD, left ventricular diastolic dysfunction
- MRI, magnetic resonance imaging
- PVI, pulmonary vein isolation
- S, mean deviation
- SD, standard deviation
- Sphericity
- Voltage mapping
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Affiliation(s)
- Sotirios Nedios
- Heart Center, University of Leipzig, Germany.,Cardiac Arrhythmia Service, Massachusetts General Hospital, Boston, MA, USA.,Department of Cardiology and Cardiovascular Research Institute Maastricht, Maastricht University Medical Center, the Netherlands
| | | | | | | | | | - Arash Arya
- Heart Center, University of Leipzig, Germany
| | - Jordi Heijman
- Department of Cardiology and Cardiovascular Research Institute Maastricht, Maastricht University Medical Center, the Netherlands
| | - Harry J G M Crijns
- Department of Cardiology and Cardiovascular Research Institute Maastricht, Maastricht University Medical Center, the Netherlands
| | | | | | - Prahlad G Menon
- University of Pittsburgh, Pittsburgh, PA, USA.,Duquesne University, Pittsburgh, PA, USA.,QuantMD LLC, Pittsburgh, PA, USA
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Roy A, Varela M, Chubb H, MacLeod R, Hancox JC, Schaeffter T, Aslanidi O. Identifying locations of re-entrant drivers from patient-specific distribution of fibrosis in the left atrium. PLoS Comput Biol 2020; 16:e1008086. [PMID: 32966275 PMCID: PMC7535127 DOI: 10.1371/journal.pcbi.1008086] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Revised: 10/05/2020] [Accepted: 06/22/2020] [Indexed: 11/18/2022] Open
Abstract
Clinical evidence suggests a link between fibrosis in the left atrium (LA) and atrial fibrillation (AF), the most common sustained arrhythmia. Image-derived fibrosis is increasingly used for patient stratification and therapy guidance. However, locations of re-entrant drivers (RDs) sustaining AF are unknown and therapy success rates remain suboptimal. This study used image-derived LA models to explore the dynamics of RD stabilization in fibrotic regions and generate maps of RD locations. LA models with patient-specific geometry and fibrosis distribution were derived from late gadolinium enhanced magnetic resonance imaging of 6 AF patients. In each model, RDs were initiated at multiple locations, and their trajectories were tracked and overlaid on the LA fibrosis distributions to identify the most likely regions where the RDs stabilized. The simulations showed that the RD dynamics were strongly influenced by the amount and spatial distribution of fibrosis. In patients with fibrosis burden greater than 25%, RDs anchored to specific locations near large fibrotic patches. In patients with fibrosis burden below 25%, RDs either moved near small fibrotic patches or anchored to anatomical features. The patient-specific maps of RD locations showed that areas that harboured the RDs were much smaller than the entire fibrotic areas, indicating potential targets for ablation therapy. Ablating the predicted locations and connecting them to the existing pulmonary vein ablation lesions was the most effective in-silico ablation strategy.
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Affiliation(s)
- Aditi Roy
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King’s College London, St Thomas’ Hospital, London, United Kingdom
| | - Marta Varela
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King’s College London, St Thomas’ Hospital, London, United Kingdom
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
| | - Henry Chubb
- Cardiothoracic Surgery, Stanford University, United States of America
| | - Robert MacLeod
- Bioengineering Department, University of Utah, Salt Lake City, Utah, United States of America
| | - Jules C. Hancox
- School of Physiology and Pharmacology, Cardiovascular Research Laboratories, University of Bristol, Bristol, United Kingdom
| | | | - Oleg Aslanidi
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King’s College London, St Thomas’ Hospital, London, United Kingdom
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8
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Anisotropic conduction in the myocardium due to fibrosis: the effect of texture on wave propagation. Sci Rep 2020; 10:764. [PMID: 31964904 PMCID: PMC6972912 DOI: 10.1038/s41598-020-57449-1] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Accepted: 12/16/2019] [Indexed: 11/22/2022] Open
Abstract
Cardiac fibrosis occurs in many forms of heart disease. It is well established that the spatial pattern of fibrosis, its texture, substantially affects the onset of arrhythmia. However, in most modelling studies fibrosis is represented by multiple randomly distributed short obstacles that mimic only one possible texture, diffuse fibrosis. An important characteristic feature of other fibrosis textures, such as interstitial and patchy textures, is that fibrotic inclusions have substantial length, which is suggested to have a pronounced effect on wave propagation. In this paper, we study the effect of the elongation of inexcitable inclusions (obstacles) on wave propagation in a 2D model of cardiac tissue described by the TP06 model for human ventricular cells. We study in detail how the elongation of obstacles affects various characteristics of the waves. We quantify the anisotropy induced by the textures, its dependency on the obstacle length and the effects of the texture on the shape of the propagating wave. Because such anisotropy is a result of zig-zag propagation we show, for the first time, quantification of the effects of geometry and source-sink relationship, on the zig-zag nature of the pathway of electrical conduction. We also study the effect of fibrosis in the case of pre-existing anisotropy and introduce a procedure for scaling of the fibrosis texture. We show that fibrosis can decrease or increase the preexisting anisotropy depending on its scaled texture.
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Dierckx H, Panfilov AV, Verschelde H, Biktashev VN, Biktasheva IV. Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves. Phys Rev E 2019; 99:022217. [PMID: 30934367 DOI: 10.1103/physreve.99.022217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/09/2023]
Abstract
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.
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Affiliation(s)
- Hans Dierckx
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - A V Panfilov
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620075, Russia
| | - H Verschelde
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - I V Biktasheva
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
- Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom
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Song JS, Kim J, Lim B, Lee YS, Hwang M, Joung B, Shim EB, Pak HN. Pro-Arrhythmogenic Effects of Heterogeneous Tissue Curvature - A Suggestion for Role of Left Atrial Appendage in Atrial Fibrillation. Circ J 2018; 83:32-40. [PMID: 30429429 DOI: 10.1253/circj.cj-18-0615] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
BACKGROUND The arrhythmogenic role of complex atrial morphology has not yet been clearly elucidated. We hypothesized that bumpy tissue geometry can induce action potential duration (APD) dispersion and wavebreak in atrial fibrillation (AF). Methods and Results: We simulated a 2D-bumpy atrial model by varying the degree of bumpiness, and 3D-left atrial (LA) models integrated by LA computed tomographic (CT) images taken from 14 patients with persistent AF. We also analyzed wave-dynamic parameters with bipolar electrograms during AF and compared them with LA-CT geometry in 30 patients with persistent AF. In the 2D-bumpy model, APD dispersion increased (P<0.001) and wavebreak occurred spontaneously when the surface bumpiness was greater, showing phase transition-like behavior (P<0.001). The bumpiness gradient 2D-model showed that spiral wave drifted in the direction of higher bumpiness, and phase singularity (PS) points were mostly located in areas with higher bumpiness. In the 3D-LA model, PS density was higher in the LA appendage (LAA) compared with other parts of the LA (P<0.05). In 30 persistent-AF patients, the surface bumpiness of LAA was 5.8-fold that of other LA parts (P<0.001), and exceeded critical bumpiness to induce wavebreak. Wave dynamics complexity parameters were consistently dominant in the LAA (P<0.001). CONCLUSIONS Bumpy tissue geometry promoted APD dispersion, wavebreak, and spiral wave drift in in-silico human atrial tissue, and corresponded to clinical electroanatomical maps.
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Roy A, Varela M, Aslanidi O. Image-Based Computational Evaluation of the Effects of Atrial Wall Thickness and Fibrosis on Re-entrant Drivers for Atrial Fibrillation. Front Physiol 2018; 9:1352. [PMID: 30349483 PMCID: PMC6187302 DOI: 10.3389/fphys.2018.01352] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2018] [Accepted: 09/06/2018] [Indexed: 12/19/2022] Open
Abstract
Introduction: Catheter ablation (CA) is a common treatment for atrial fibrillation (AF), but the knowledge of optimal ablation sites, and hence clinical outcomes, are suboptimal. Increasing evidence suggest that ablation strategies based on patient-specific substrates information, such as distributions of fibrosis and atrial wall thickness (AWT), may be used to improve therapy. We hypothesized that competing influences of large AWT gradients and fibrotic patches on conductive properties of atrial tissue can determine locations of re-entrant drivers (RDs) sustaining AF. Methods: Two sets of models were used: (1) a simple model of 3D atrial tissue slab with a step change in AWT and a synthetic fibrosis patch, and (2) 3D models based on patient-specific right atrial (RA) and left atrial (LA) geometries. The latter were obtained from four healthy volunteers and two AF patients, respectively, using magnetic resonance imaging (MRI). A synthetic fibrotic patch was added in the RA and fibrosis distributions in the LA were obtained from gadolinium-enhanced MRI of the same patients. In all models, 3D geometry was combined with the Fenton-Karma atrial cell model to simulate RDs. Results: In the slab, RDs drifted toward, and then along the AWT step. However, with additional fibrosis, the RDs were localized in regions between the step and fibrosis. In the RA, RDs drifted toward and anchored to a large AWT gradient between the crista terminalis (CT) region and the surrounding atrial wall. Without such a gradient, RDs drifted toward the superior vena cava (SVC) or the tricuspid valve (TSV). With additional fibrosis, RDs initiated away from the CT anchored to the fibrotic patch, whereas RDs initiated close to the CT region remained localized between the two structures. In the LA, AWT was more uniform and RDs drifted toward the pulmonary veins (PVs). However, with additional fibrotic patches, RDs either anchored to them or multiplied. Conclusion: In the RA, RD locations are determined by both fibrosis and AWT gradients at the CT region. In the LA, they are determined by fibrosis due to the absence of large AWT gradients. These results elucidate mechanisms behind the stabilization of RDs sustaining AF and can help guide ablation therapy.
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Affiliation(s)
| | | | - Oleg Aslanidi
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King’s College London, King’s Health Partners, St Thomas’ Hospital, London, United Kingdom
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12
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Dierckx H, Verschelde H, Panfilov AV. Measurement and structure of spiral wave response functions. CHAOS (WOODBURY, N.Y.) 2017; 27:093912. [PMID: 28964120 DOI: 10.1063/1.4999606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The rotating spiral waves that emerge in diverse natural and man-made systems typically exhibit a particle-like behaviour since their adjoint critical eigenmodes (response functions) are often seen to be localised around the spiral core. We present a simple method to numerically compute response functions for circular-core and meandering spirals by recording their drift response to many elementary perturbations. Although our method is computationally more expensive than solving the adjoint system, our technique is fully parallellisable, does not suffer from memory limitations and can be applied to experiments. For a cardiac tissue model with the linear spiral core, we find that the response functions are localised near the turning points of the trajectory.
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Affiliation(s)
- Hans Dierckx
- Department of Physics and Astronomy, Krijgslaan 281 S9, 9000 Gent, Belgium
| | - Henri Verschelde
- Department of Physics and Astronomy, Krijgslaan 281 S9, 9000 Gent, Belgium
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13
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Li TC, Gao X, Zheng FF, Pan DB, Zheng B, Zhang H. A theory for spiral wave drift induced by ac and polarized electric fields in chemical excitable media. Sci Rep 2017; 7:8657. [PMID: 28819226 PMCID: PMC5561252 DOI: 10.1038/s41598-017-09092-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2017] [Accepted: 07/21/2017] [Indexed: 11/09/2022] Open
Abstract
Spiral waves are shown to undergo directional drifts in the presence of ac and polarized electric fields when their frequencies are twice of the spiral frequencies. Here, we propose a quantitative description for the spiral wave drift induced by weak electric fields, and provide the explicit equations for the spiral wave drift speed and direction. Numerical simulations are performed to demonstrate the quantitative agreement with analytical results in both weakly and highly excitable media.
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Affiliation(s)
- Teng-Chao Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Xiang Gao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China
- Max-Planck Institute for Dynamics and Self-Organisation, Gottingen, D-37077, Germany
| | - Fei-Fei Zheng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, 310027, China
| | - De-Bei Pan
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Bo Zheng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, 310027, China.
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, 310027, China.
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14
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Varela M, Bisbal F, Zacur E, Berruezo A, Aslanidi OV, Mont L, Lamata P. Novel Computational Analysis of Left Atrial Anatomy Improves Prediction of Atrial Fibrillation Recurrence after Ablation. Front Physiol 2017; 8:68. [PMID: 28261103 PMCID: PMC5306209 DOI: 10.3389/fphys.2017.00068] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2016] [Accepted: 01/25/2017] [Indexed: 11/16/2022] Open
Abstract
The left atrium (LA) can change in size and shape due to atrial fibrillation (AF)-induced remodeling. These alterations can be linked to poorer outcomes of AF ablation. In this study, we propose a novel comprehensive computational analysis of LA anatomy to identify what features of LA shape can optimally predict post-ablation AF recurrence. To this end, we construct smooth 3D geometrical models from the segmentation of the LA blood pool captured in pre-procedural MR images. We first apply this methodology to characterize the LA anatomy of 144 AF patients and build a statistical shape model that includes the most salient variations in shape across this cohort. We then perform a discriminant analysis to optimally distinguish between recurrent and non-recurrent patients. From this analysis, we propose a new shape metric called vertical asymmetry, which measures the imbalance of size along the anterior to posterior direction between the superior and inferior left atrial hemispheres. Vertical asymmetry was found, in combination with LA sphericity, to be the best predictor of post-ablation recurrence at both 12 and 24 months (area under the ROC curve: 0.71 and 0.68, respectively) outperforming other shape markers and any of their combinations. We also found that model-derived shape metrics, such as the anterior-posterior radius, were better predictors than equivalent metrics taken directly from MRI or echocardiography, suggesting that the proposed approach leads to a reduction of the impact of data artifacts and noise. This novel methodology contributes to an improved characterization of LA organ remodeling and the reported findings have the potential to improve patient selection and risk stratification for catheter ablations in AF.
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Affiliation(s)
- Marta Varela
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London London, UK
| | - Felipe Bisbal
- Arrhythmia Unit-Heart Institute (iCor), Hospital Universitari Germans Trias i Pujol Badalona, Spain
| | - Ernesto Zacur
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College LondonLondon, UK; Department of Engineering Science, University of OxfordOxford, UK
| | - Antonio Berruezo
- Unitat de Fibrillació Auricular, Hospital Clínic, Universitat de Barcelona Barcelona, Spain
| | - Oleg V Aslanidi
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London London, UK
| | - Lluis Mont
- Unitat de Fibrillació Auricular, Hospital Clínic, Universitat de Barcelona Barcelona, Spain
| | - Pablo Lamata
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London London, UK
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15
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Abstract
We consider reaction-diffusion equations on a thin curved surface and obtain a set of effective reaction-diffusion (R-D) equations to O(ε^{2}), where ε is the surface thickness. We observe that the R-D systems on these curved surfaces can have space-dependent reaction kinetics. Further, we use linear stability analysis to study the Schnakenberg model on spherical and cylindrical geometries. The dependence of the steady state on the thickness is determined for both cases, and we find that a change in the thickness can stabilize the unstable modes, and vice versa. The combined effect of thickness and curvature can play an important role in the rearrangement of spatial patterns on thin curved surfaces.
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Affiliation(s)
- Sankaran Nampoothiri
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016, India
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16
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Drift of Scroll Wave Filaments in an Anisotropic Model of the Left Ventricle of the Human Heart. BIOMED RESEARCH INTERNATIONAL 2015; 2015:389830. [PMID: 26539486 PMCID: PMC4619794 DOI: 10.1155/2015/389830] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Accepted: 02/12/2015] [Indexed: 11/17/2022]
Abstract
Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias.
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17
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Gonzales MJ, Vincent KP, Rappel WJ, Narayan SM, McCulloch AD. Structural contributions to fibrillatory rotors in a patient-derived computational model of the atria. Europace 2015; 16 Suppl 4:iv3-iv10. [PMID: 25362167 DOI: 10.1093/europace/euu251] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
AIMS The aim of this study was to investigate structural contributions to the maintenance of rotors in human atrial fibrillation (AF) and possible mechanisms of termination. METHODS AND RESULTS A three-dimensional human biatrial finite element model based on patient-derived computed tomography and arrhythmia observed at electrophysiology study was used to study AF. With normal physiological electrical conductivity and effective refractory periods (ERPs), wave break failed to sustain reentrant activity or electrical rotors. With depressed excitability, decreased conduction anisotropy, and shorter ERP characteristic of AF, reentrant rotors were readily maintained. Rotors were transiently or permanently trapped by fibre discontinuities on the lateral wall of the right atrium near the tricuspid valve orifice and adjacent to the crista terminalis, both known sites of right atrial arrhythmias. Modelling inexcitable regions near the rotor tip to simulate fibrosis anchored the rotors, converting the arrhythmia to macro-reentry. Accordingly, increasing the spatial core of inexcitable tissue decreased the frequency of rotation, widened the excitable gap, and enabled an external wave to impinge on the rotor core and displace the source. CONCLUSION These model findings highlight the importance of structural features in rotor dynamics and suggest that regions of fibrosis may anchor fibrillatory rotors. Increasing extent of fibrosis and scar may eventually convert fibrillation to excitable gap reentry. Such macro-reentry can then be eliminated by extending the obstacle or by external stimuli that penetrate the excitable gap.
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Affiliation(s)
- Matthew J Gonzales
- Department of Bioengineering, University of California San Diego, Mail Code 0412, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA
| | - Kevin P Vincent
- Department of Bioengineering, University of California San Diego, Mail Code 0412, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California San Diego, La Jolla, CA, USA Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA, USA
| | - Sanjiv M Narayan
- Department of Medicine, University of California San Diego, La Jolla, CA, USA Cardiac Biomedical Science and Engineering Center, University of California San Diego, CA, USA VA San Diego Healthcare System, San Diego, CA, USA
| | - Andrew D McCulloch
- Department of Bioengineering, University of California San Diego, Mail Code 0412, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA Department of Medicine, University of California San Diego, La Jolla, CA, USA Cardiac Biomedical Science and Engineering Center, University of California San Diego, CA, USA
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18
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Dierckx H, Wellner M, Bernus O, Verschelde H. Generalized minimal principle for rotor filaments. PHYSICAL REVIEW LETTERS 2015; 114:178104. [PMID: 25978269 DOI: 10.1103/physrevlett.114.178104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2014] [Indexed: 06/04/2023]
Abstract
To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.
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Affiliation(s)
- Hans Dierckx
- Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - Marcel Wellner
- Physics Department, Syracuse University, Syracuse, New York 13244, USA
| | - Olivier Bernus
- L'Institut de Rythmologie et Modélisation Cardiaque, Université de Bordeaux, 33604 Pessac, France
| | - Henri Verschelde
- Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
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19
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Li BW, Cai MC, Zhang H, Panfilov AV, Dierckx H. Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field. J Chem Phys 2015; 140:184901. [PMID: 24832300 DOI: 10.1063/1.4874645] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chirality is one of the most fundamental properties of many physical, chemical, and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the Belousov-Zhabotinsky reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.
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Affiliation(s)
- Bing-Wei Li
- Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
| | - Mei-Chun Cai
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
| | - Hans Dierckx
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
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20
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Biktasheva IV, Dierckx H, Biktashev VN. Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations. PHYSICAL REVIEW LETTERS 2015; 114:068302. [PMID: 25723248 DOI: 10.1103/physrevlett.114.068302] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2014] [Indexed: 06/04/2023]
Abstract
A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behavior is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament tension and curvature-induced drifts described earlier. We outline a two-step asymptotic theory describing this effect, including asymptotics in the layer thickness and calculation of the drift of so-perturbed spiral waves using response functions. As specific examples, we consider drift of scrolls along thickness steps, ridges, ditches, and disk-shaped thickness variations. Asymptotic predictions agree with numerical simulations.
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Affiliation(s)
- I V Biktasheva
- Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom
| | - H Dierckx
- Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
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21
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Pravdin SF, Dierckx H, Katsnelson LB, Solovyova O, Markhasin VS, Panfilov AV. Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture. PLoS One 2014; 9:e93617. [PMID: 24817308 PMCID: PMC4015904 DOI: 10.1371/journal.pone.0093617] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2013] [Accepted: 02/27/2014] [Indexed: 11/19/2022] Open
Abstract
We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.
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Affiliation(s)
- Sergey F. Pravdin
- Function Approximation Theory Department, Institute of Mathematics and Mechanics, Ekaterinburg, Russia
- Laboratory of Mathematical Physiology, Institute of Immunology and Physiology, Ekaterinburg, Russia
- Department of Physics and Astronomy, Faculty of Sciences, Ghent University, Ghent, Belgium
- * E-mail: (SFP); (AVP)
| | - Hans Dierckx
- Department of Physics and Astronomy, Faculty of Sciences, Ghent University, Ghent, Belgium
| | - Leonid B. Katsnelson
- Laboratory of Mathematical Physiology, Institute of Immunology and Physiology, Ekaterinburg, Russia
- Ural Federal University, Ekaterinburg, Russia
| | - Olga Solovyova
- Laboratory of Mathematical Physiology, Institute of Immunology and Physiology, Ekaterinburg, Russia
- Ural Federal University, Ekaterinburg, Russia
| | - Vladimir S. Markhasin
- Laboratory of Mathematical Physiology, Institute of Immunology and Physiology, Ekaterinburg, Russia
- Ural Federal University, Ekaterinburg, Russia
| | - Alexander V. Panfilov
- Department of Physics and Astronomy, Faculty of Sciences, Ghent University, Ghent, Belgium
- Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region, Russia
- * E-mail: (SFP); (AVP)
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22
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Dierckx H, Verschelde H. Effective dynamics of twisted and curved scroll waves using virtual filaments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062907. [PMID: 24483531 DOI: 10.1103/physreve.88.062907] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2013] [Indexed: 06/03/2023]
Abstract
Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.
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Affiliation(s)
- Hans Dierckx
- Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281 S9 WE05, 9000 Ghent, Belgium
| | - Henri Verschelde
- Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281 S9 WE05, 9000 Ghent, Belgium
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