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Dermul N, Dierckx H. Reconstruction of excitation waves from mechanical deformation using physics-informed neural networks. Sci Rep 2024; 14:16975. [PMID: 39043805 PMCID: PMC11266589 DOI: 10.1038/s41598-024-67597-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Accepted: 07/12/2024] [Indexed: 07/25/2024] Open
Abstract
Non-invasive assessment of the electrical activation pattern can significantly contribute to the diagnosis and treatment of cardiac arrhythmias, due to faster and safer diagnosis, improved surgical planning and easier follow-up. One promising path is to measure the mechanical contraction via echocardiography and utilize this as an indirect way of measuring the original activation pattern. To solve this demanding inversion task, we make use of physics-informed neural networks, an upcoming methodology to solve forward and inverse physical problems governed by partial differential equations. In this study, synthetic data sets were created, consisting of 2D excitation waves coupled to an isotropic and linearly deforming elastic medium. We show that for both focal and spiral patterns, the underlying excitation waves can be reconstructed accurately. We test the robustness of the method against Gaussian noise, reduced spatial resolution and projected tri-planar data. In situations where the data quality is heavily reduced, we show how to improve the reconstruction by additional regularization on the wave speed. Our findings suggest that physics-informed neural networks hold the potential to solve sparse and noisy bio-mechanical inversion problems and may offer a pathway to non-invasive assessment of certain cardiac arrhythmias.
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Affiliation(s)
- Nathan Dermul
- Department of Mathematics, KU Leuven, 8500, Kortrijk, Belgium.
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, 3000, Leuven, Belgium.
| | - Hans Dierckx
- Department of Mathematics, KU Leuven, 8500, Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, 3000, Leuven, Belgium
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2
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Liu W, Han JL, Tomek J, Bub G, Entcheva E. Simultaneous Widefield Voltage and Dye-Free Optical Mapping Quantifies Electromechanical Waves in Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes. ACS PHOTONICS 2023; 10:1070-1083. [PMID: 37096210 PMCID: PMC10119986 DOI: 10.1021/acsphotonics.2c01644] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Indexed: 05/03/2023]
Abstract
Coupled electromechanical waves define a heart's function in health and diseases. Optical mapping of electrical waves using fluorescent labels offers mechanistic insights into cardiac conduction abnormalities. Dye-free/label-free mapping of mechanical waves presents an attractive non-invasive alternative. In this study, we developed a simultaneous widefield voltage and interferometric dye-free optical imaging methodology that was used as follows: (1) to validate dye-free optical mapping for quantification of cardiac wave properties in human iPSC-cardiomyocytes (CMs); (2) to demonstrate low-cost optical mapping of electromechanical waves in hiPSC-CMs using recent near-infrared (NIR) voltage sensors and orders of magnitude cheaper miniature industrial CMOS cameras; (3) to uncover previously underexplored frequency- and space-varying parameters of cardiac electromechanical waves in hiPSC-CMs. We find similarity in the frequency-dependent responses of electrical (NIR fluorescence-imaged) and mechanical (dye-free-imaged) waves, with the latter being more sensitive to faster rates and showing steeper restitution and earlier appearance of wavefront tortuosity. During regular pacing, the dye-free-imaged conduction velocity and electrical wave velocity are correlated; both modalities are sensitive to pharmacological uncoupling and dependent on gap-junctional protein (connexins) determinants of wave propagation. We uncover the strong frequency dependence of the electromechanical delay (EMD) locally and globally in hiPSC-CMs on a rigid substrate. The presented framework and results offer new means to track the functional responses of hiPSC-CMs inexpensively and non-invasively for counteracting heart disease and aiding cardiotoxicity testing and drug development.
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Affiliation(s)
- Wei Liu
- Department
of Biomedical Engineering, George Washington
University, Washington, D.C. 20052, United States
| | - Julie L. Han
- Department
of Biomedical Engineering, George Washington
University, Washington, D.C. 20052, United States
| | - Jakub Tomek
- Department
of Pharmacology, University of California−Davis, Davis, California 95616, United States
| | - Gil Bub
- Department
of Physiology, McGill University, Montréal, Québec H3G 1Y6, Canada
| | - Emilia Entcheva
- Department
of Biomedical Engineering, George Washington
University, Washington, D.C. 20052, United States
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Stenger R, Herzog S, Kottlarz I, Rüchardt B, Luther S, Wörgötter F, Parlitz U. Reconstructing in-depth activity for chaotic 3D spatiotemporal excitable media models based on surface data. CHAOS (WOODBURY, N.Y.) 2023; 33:013134. [PMID: 36725654 DOI: 10.1063/5.0126824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Motivated by potential applications in cardiac research, we consider the task of reconstructing the dynamics within a spatiotemporal chaotic 3D excitable medium from partial observations at the surface. Three artificial neural network methods (a spatiotemporal convolutional long-short-term-memory, an autoencoder, and a diffusion model based on the U-Net architecture) are trained to predict the dynamics in deeper layers of a cube from observational data at the surface using data generated by the Barkley model on a 3D domain. The results show that despite the high-dimensional chaotic dynamics of this system, such cross-prediction is possible, but non-trivial and as expected, its quality decreases with increasing prediction depth.
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Affiliation(s)
- R Stenger
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - S Herzog
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - I Kottlarz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - B Rüchardt
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - S Luther
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - F Wörgötter
- Department for Computational Neuroscience, Third Institute of Physics-Biophysics, University of Göttingen, 37077 Göttingen, Germany
| | - U Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
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Lebert J, Mittal M, Christoph J. Reconstruction of three-dimensional scroll waves in excitable media from two-dimensional observations using deep neural networks. Phys Rev E 2023; 107:014221. [PMID: 36797900 DOI: 10.1103/physreve.107.014221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 01/17/2023] [Indexed: 02/03/2023]
Abstract
Scroll wave dynamics are thought to underlie life-threatening ventricular fibrillation. However, direct observations of three-dimensional electrical scroll waves remain elusive, as there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Here we study whether it is possible to reconstruct simulated scroll waves and scroll wave chaos using deep learning. We trained encoding-decoding convolutional neural networks to predict three-dimensional scroll wave dynamics inside bulk-shaped excitable media from two-dimensional observations of the wave dynamics on the bulk's surface. We tested whether observations from one or two opposing surfaces would be sufficient and whether transparency or measurements of surface deformations enhances the reconstruction. Further, we evaluated the approach's robustness against noise and tested the feasibility of predicting the bulk's thickness. We distinguished isotropic and anisotropic, as well as opaque and transparent, excitable media as models for cardiac tissue and the Belousov-Zhabotinsky chemical reaction, respectively. While we demonstrate that it is possible to reconstruct three-dimensional scroll wave dynamics, we also show that it is challenging to reconstruct complicated scroll wave chaos and that prediction outcomes depend on various factors such as transparency, anisotropy, and ultimately the thickness of the medium compared to the size of the scroll waves. In particular, we found that anisotropy provides crucial information for neural networks to decode depth, which facilitates the reconstructions. In the future, deep neural networks could be used to visualize intramural action potential wave patterns from epi- or endocardial measurements.
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Affiliation(s)
- Jan Lebert
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, California 94158, USA
| | - Meenakshi Mittal
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, California 94158, USA
- Department of Computer Science, University of California, Berkeley, Berkeley, California 94720, USA
| | - Jan Christoph
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, California 94158, USA
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Ryzhii M, Ryzhii E. Pacemaking function of two simplified cell models. PLoS One 2022; 17:e0257935. [PMID: 35404982 PMCID: PMC9000119 DOI: 10.1371/journal.pone.0257935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Accepted: 03/29/2022] [Indexed: 12/03/2022] Open
Abstract
Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.
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Affiliation(s)
- Maxim Ryzhii
- Complex Systems Modeling Laboratory, University of Aizu, Aizu-Wakamatsu, Japan
- * E-mail:
| | - Elena Ryzhii
- Department of Anatomy and Histology, Fukushima Medical University, Fukushima, Japan
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Christoph J, Lebert J. Inverse mechano-electrical reconstruction of cardiac excitation wave patterns from mechanical deformation using deep learning. CHAOS (WOODBURY, N.Y.) 2020; 30:123134. [PMID: 33380038 DOI: 10.1063/5.0023751] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 11/18/2020] [Indexed: 06/12/2023]
Abstract
The inverse mechano-electrical problem in cardiac electrophysiology is the attempt to reconstruct electrical excitation or action potential wave patterns from the heart's mechanical deformation that occurs in response to electrical excitation. Because heart muscle cells contract upon electrical excitation due to the excitation-contraction coupling mechanism, the resulting deformation of the heart should reflect macroscopic action potential wave phenomena. However, whether the relationship between macroscopic electrical and mechanical phenomena is well-defined and unique enough to be utilized for an inverse imaging technique in which mechanical activation mapping is used as a surrogate for electrical mapping has yet to be determined. Here, we provide a numerical proof-of-principle that deep learning can be used to solve the inverse mechano-electrical problem in phenomenological two- and three-dimensional computer simulations of the contracting heart wall, or in elastic excitable media, with muscle fiber anisotropy. We trained a convolutional autoencoder neural network to learn the complex relationship between electrical excitation, active stress, and tissue deformation during both focal or reentrant chaotic wave activity and, consequently, used the network to successfully estimate or reconstruct electrical excitation wave patterns from mechanical deformation in sheets and bulk-shaped tissues, even in the presence of noise and at low spatial resolutions. We demonstrate that even complicated three-dimensional electrical excitation wave phenomena, such as scroll waves and their vortex filaments, can be computed with very high reconstruction accuracies of about 95% from mechanical deformation using autoencoder neural networks, and we provide a comparison with results that were obtained previously with a physics- or knowledge-based approach.
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Affiliation(s)
- Jan Christoph
- Department of Cardiology and Pneumology, University Medical Center Göttingen, 37075 Göttingen, Germany
| | - Jan Lebert
- Department of Cardiology and Pneumology, University Medical Center Göttingen, 37075 Göttingen, Germany
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