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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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Leenknegt L, Panfilov AV, Dierckx H. Impact of electrode orientation, myocardial wall thickness, and myofiber direction on intracardiac electrograms: numerical modeling and analytical solutions. Front Physiol 2023; 14:1213218. [PMID: 37492643 PMCID: PMC10364610 DOI: 10.3389/fphys.2023.1213218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 06/14/2023] [Indexed: 07/27/2023] Open
Abstract
Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R 2 (bipolar and parallel), and 1/R 3 (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters.
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Affiliation(s)
- Lore Leenknegt
- Department of Mathematics, KU Leuven Campus KULAK, KU Leuven, Kortrijk, Belgium
- iSi Health–KU Leuven Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | | | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus KULAK, KU Leuven, Kortrijk, Belgium
- iSi Health–KU Leuven Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
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Kabus D, Arno L, Leenknegt L, Panfilov AV, Dierckx H. Numerical methods for the detection of phase defect structures in excitable media. PLoS One 2022; 17:e0271351. [PMID: 35819963 PMCID: PMC9275727 DOI: 10.1371/journal.pone.0271351] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 06/12/2022] [Indexed: 11/19/2022] Open
Abstract
Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity. Recent analysis, however, showed that in many rotation regimes there exist phase discontinuities and the region of rotation must be defined not as a point of phase singularity, but as a phase defect line. In this paper, we use this novel methodology and perform a comparative study of three different phase definitions applied to in silico data and to experimental data obtained from optical voltage mapping experiments on monolayers of human atrial myocytes. We introduce new phase defect detection algorithms and compare them with those that appeared in literature already. We find that the phase definition is more important than the algorithm to identify sudden spatial phase variations. Sharp phase defect lines can be obtained from a phase derived from local activation times observed during one cycle of arrhythmia. Alternatively, similar quality can be obtained from a reparameterization of the classical phase obtained from observation of a single timeframe of transmembrane potential. We found that the phase defect line length was (35.9 ± 6.2)mm in the Fenton-Karma model and (4.01 ± 0.55)mm in cardiac human atrial myocyte monolayers. As local activation times are obtained during standard clinical cardiac mapping, the methods are also suitable to be applied to clinical datasets. All studied methods are publicly available and can be downloaded from an institutional web-server.
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Affiliation(s)
- Desmond Kabus
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Leiden, The Netherlands
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | - Louise Arno
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | - Lore Leenknegt
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | - Alexander V. Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg, Russia
- World-Class Research Center “Digital biodesign and personalized healthcare”, Sechenov University, Moscow, Russia
| | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
- * E-mail:
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Shibata N, Inada S, Nakazawa K, Ashihara T, Tomii N, Yamazaki M, Honjo H, Seno H, Sakuma I. Mechanism of Ventricular Fibrillation: Current Status and Problems. ADVANCED BIOMEDICAL ENGINEERING 2022. [DOI: 10.14326/abe.11.117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022] Open
Affiliation(s)
- Nitaro Shibata
- Department of Cardiology, Shinjuku Mitsui Building Clinic
| | - Shin Inada
- Faculty of Medical Science Technology, Morinomiya University of Medical Sciences
| | - Kazuo Nakazawa
- Faculty of Medical Science Technology, Morinomiya University of Medical Sciences
| | - Takashi Ashihara
- Department of Medical Informatics and Biomedical Engineering, Shiga University of Medical Science
| | - Naoki Tomii
- Department of Precision Engineering, The University of Tokyo
| | | | - Haruo Honjo
- Health Promotion Division, Toyota Autobody Co. Ltd
| | - Hiroshi Seno
- Department of Precision Engineering, The University of Tokyo
| | - Ichiro Sakuma
- Medical Device Development and Regulation Research Center, The University of Tokyo
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Arno L, Quan J, Nguyen NT, Vanmarcke M, Tolkacheva EG, Dierckx H. A Phase Defect Framework for the Analysis of Cardiac Arrhythmia Patterns. Front Physiol 2021; 12:690453. [PMID: 34630135 PMCID: PMC8494009 DOI: 10.3389/fphys.2021.690453] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 08/19/2021] [Indexed: 11/24/2022] Open
Abstract
During cardiac arrhythmias, dynamical patterns of electrical activation form and evolve, which are of interest to understand and cure heart rhythm disorders. The analysis of these patterns is commonly performed by calculating the local activation phase and searching for phase singularities (PSs), i.e., points around which all phases are present. Here we propose an alternative framework, which focuses on phase defect lines (PDLs) and surfaces (PDSs) as more general mechanisms, which include PSs as a specific case. The proposed framework enables two conceptual unifications: between the local activation time and phase description, and between conduction block lines and the central regions of linear-core rotors. A simple PDL detection method is proposed and applied to data from simulations and optical mapping experiments. Our analysis of ventricular tachycardia in rabbit hearts (n = 6) shows that nearly all detected PSs were found on PDLs, but the PDLs had a significantly longer lifespan than the detected PSs. Since the proposed framework revisits basic building blocks of cardiac activation patterns, it can become a useful tool for further theory development and experimental analysis.
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Affiliation(s)
- Louise Arno
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
| | - Jan Quan
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
| | - Nhan T Nguyen
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
| | | | - Elena G Tolkacheva
- Biomedical Engineering Department, University of Minnesota, Minneapolis, MN, United States
| | - Hans Dierckx
- KULeuven Campus KULAK, Department of Mathematics, Kortrijk, Belgium
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