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Duytschaever M, Van den Abeele R, Carlier N, Bezerra AS, Verstraeten B, Lootens S, Desplenter K, Okenov A, Nezlobinsky T, Shah D, Haas A, Luik A, Martens J, El Haddad M, De Smet M, De Becker B, Francois C, Le Polain de Waroux JB, Tavernier R, Knecht S, Hendrickx S, Vandersickel N. Atrial Topology for a Unified Understanding of Typical and Atypical Flutter. Circ Arrhythm Electrophysiol 2024; 17:e013102. [PMID: 39498566 DOI: 10.1161/circep.124.013102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/10/2024] [Accepted: 10/15/2024] [Indexed: 11/21/2024]
Abstract
BACKGROUND Macroreentry stands as the predominant mechanism of typical and atypical flutter. Despite advances in mapping, many aspects of macroreentrant atrial tachycardia remain unsolved. In this translational study, we applied principles of topology to understand the activation patterns, entrainment characteristics, and ablation responses in a large clinical macroreentrant atrial tachycardia database. METHODS Because the atrium can be topologically seen as a closed sphere with holes, we used a computational fixed spherical mesh model with a finite number of holes to induce and analyze macroreentrant atrial tachycardia. The ensuing insights were used to interpret high-density activation maps, postpacing interval-tachycardia cycle length values (difference between postpacing interval and tachycardia cycle length), and ablation response in 131 cases of typical and atypical flutter (n=106 left atrium, n=25 right atrium). RESULTS Modeling of macroreentrant atrial tachycardia revealed that reentry on closed surfaces consistently manifests itself as paired rotation and that an odd number of critical boundaries is mathematically impossible. Together with mathematical confirmation by the index theorem, this led to a unifying construct that could explain the number of loops, difference between postpacing interval and tachycardia cycle length values, and ablation outcomes (termination, no change, or prolongation in tachycardia cycle length) in all 131 cases. CONCLUSIONS Combining topology with the index theorem offers a novel and cohesive framework for understanding and managing typical and atypical flutter.
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Affiliation(s)
- Mattias Duytschaever
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Robin Van den Abeele
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Niels Carlier
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Arthur Santos Bezerra
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Bjorn Verstraeten
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Sebastiaan Lootens
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Karel Desplenter
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Arstanbek Okenov
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Timur Nezlobinsky
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Dipen Shah
- Department of Electrophysiology, University Hospital Geneva, Switzerland (D.S.)
| | - Annika Haas
- Department of Cardiology, Städtisches Klinikum Karlsruhe, Germany (A.H., A.L.)
| | - Armin Luik
- Department of Cardiology, Städtisches Klinikum Karlsruhe, Germany (A.H., A.L.)
| | - Jordi Martens
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Milad El Haddad
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Maarten De Smet
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Benjamin De Becker
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Clara Francois
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Jean-Benoit Le Polain de Waroux
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Rene Tavernier
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Sebastien Knecht
- Department of Cardiology, AZ Sint-Jan Brugge, Bruges, Belgium (M.D., J.M., M.E.H., M.D.S., B.D.B., C.F., J.-B.L.P.d.W., R.T., S.K.)
| | - Sander Hendrickx
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
| | - Nele Vandersickel
- Department of Physics and Astronomy, Ghent University, Belgium (R.V.d.A., N.C., A.S.B., B.V., S.L., K.D., A.O., T.N., S.H., N.V.)
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Lawson BA, dos Santos RW, Turner IW, Bueno-Orovio A, Burrage P, Burrage K. Homogenisation for the monodomain model in the presence of microscopic fibrotic structures. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION 2023; 116:None. [PMID: 37113591 PMCID: PMC10124103 DOI: 10.1016/j.cnsns.2022.106794] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Revised: 05/06/2022] [Accepted: 08/04/2022] [Indexed: 06/08/2023]
Abstract
Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to incorporate structural heterogeneities on small spatial scales, preventing a full understanding of the critical arrhythmogenic effects of conditions such as cardiac fibrosis. In this work, we explore the technique of homogenisation by volume averaging for the inclusion of non-conductive micro-structures into larger-scale cardiac meshes with minor computational overhead. Importantly, our approach is not restricted to periodic patterns, enabling homogenised models to represent, for example, the intricate patterns of collagen deposition present in different types of fibrosis. We first highlight the importance of appropriate boundary condition choice for the closure problems that define the parameters of homogenised models. Then, we demonstrate the technique's ability to correctly upscale the effects of fibrotic patterns with a spatial resolution of 10 µm into much larger numerical mesh sizes of 100- 250 µm . The homogenised models using these coarser meshes correctly predict critical pro-arrhythmic effects of fibrosis, including slowed conduction, source/sink mismatch, and stabilisation of re-entrant activation patterns. As such, this approach to homogenisation represents a significant step towards whole organ simulations that unravel the effects of microscopic cardiac tissue heterogeneities.
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Affiliation(s)
- Brodie A.J. Lawson
- Centre for Data Science, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
| | - Rodrigo Weber dos Santos
- Graduate Program on Computational Modelling, Universidade de Federal de Juiz de Fora, Rua Jose Lourenco Kelmer s/n, Juiz de Fora, 36036-900, Minas Gerais, Brazil
| | - Ian W. Turner
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
| | - Alfonso Bueno-Orovio
- Department of Computer Science, University of Oxford, Parks Rd, Oxford, OX1 3QD, Oxfordshire, United Kingdom
| | - Pamela Burrage
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
| | - Kevin Burrage
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, 4000, Queensland, Australia
- Department of Computer Science, University of Oxford, Parks Rd, Oxford, OX1 3QD, Oxfordshire, United Kingdom
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