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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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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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Yin J, Gao X, Wu M, Liang Y. A Method for the Reconstruction of Myocardial Fiber Structure in Diffusivity Adaptive Imaging Based on Particle Filter. INTERNATIONAL JOURNAL OF E-COLLABORATION 2022. [DOI: 10.4018/ijec.304033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
In order to explore the cause of characteristic change and pathological variation of myocardial fiber structure, the posterior probability distribution of fiber direction was described. To solve the problems of low computational efficiency and slow convergence of traditional particle filter, an adaptive particle filter myocardial fiber reconstruction algorithm based on diffusion anisotropy is proposed. This algorithm dynamically adjusts the number of particles and the disturbance intensity at the prediction stage according to the diffusion anisotropy values at different body elements. While ensuring the quality of state estimation, the computational complexity of the algorithm is reduced and the operating efficiency of the system is significantly improved. The experimental results show that the proposed method has strong anti-noise ability. While improving the accuracy of fiber reconstruction, the computational cost of the system decreases by 50%, which significantly improves the efficiency of the system. The proposed algorithm is good over traditional PF and STL approaches.
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Affiliation(s)
- Jun Yin
- Institute of Physical Education and Training, Capital University of Physical Education and Sports, China
| | - Xuan Gao
- School of Kinesiology and Health, Capital University of Physical Education and Sports, China
| | - Min Wu
- School of Sport and Health, Guangzhou Sport University, China
| | - Yan Liang
- School of Kinesiology and Health, Capital University of Physical Education and Sports, China
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Lebert J, Ravi N, Fenton FH, Christoph J. Rotor Localization and Phase Mapping of Cardiac Excitation Waves Using Deep Neural Networks. Front Physiol 2022; 12:782176. [PMID: 34975536 PMCID: PMC8718715 DOI: 10.3389/fphys.2021.782176] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 11/11/2021] [Indexed: 11/15/2022] Open
Abstract
The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting.
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Affiliation(s)
- Jan Lebert
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States
| | - Namita Ravi
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States.,Yale School of Medicine, Yale University, New Haven, CT, United States
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Jan Christoph
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States
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