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Kabus D, De Coster T, de Vries AAF, Pijnappels DA, Dierckx H. Fast creation of data-driven low-order predictive cardiac tissue excitation models from recorded activation patterns. Comput Biol Med 2024; 169:107949. [PMID: 38199206 DOI: 10.1016/j.compbiomed.2024.107949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Revised: 12/07/2023] [Accepted: 01/01/2024] [Indexed: 01/12/2024]
Abstract
Excitable systems give rise to important phenomena such as heat waves, epidemics and cardiac arrhythmias. Understanding, forecasting and controlling such systems requires reliable mathematical representations. For cardiac tissue, computational models are commonly generated in a reaction-diffusion framework based on detailed measurements of ionic currents in dedicated single-cell experiments. Here, we show that recorded movies at the tissue-level of stochastic pacing in a single variable are sufficient to generate a mathematical model. Via exponentially weighed moving averages, we create additional state variables, and use simple polynomial regression in the augmented state space to quantify excitation wave dynamics. A spatial gradient-sensing term replaces the classical diffusion as it is more robust to noise. Our pipeline for model creation is demonstrated for an in-silico model and optical voltage mapping recordings of cultured human atrial myocytes and only takes a few minutes. Our findings have the potential for widespread generation, use and on-the-fly refinement of personalised computer models for non-linear phenomena in biology and medicine, such as predictive cardiac digital twins.
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Affiliation(s)
- Desmond Kabus
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium; Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Tim De Coster
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Antoine A F de Vries
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Daniël A Pijnappels
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium.
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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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