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Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation. Proc Natl Acad Sci U S A 2022; 119:e2117568119. [PMID: 35679346 PMCID: PMC9214532 DOI: 10.1073/pnas.2117568119] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
Many chemical and biological systems can sustain complex spiral wave dynamics. In the heart, spiral waves of electrical activity induce deadly arrhythmias and must be eliminated with a large, system-wide perturbation to restore a healthy rhythm. However, the high-energy shocks required for defibrillation therapies are very painful and can even damage heart tissue. In this study, we demonstrate a method for eliminating spiral waves with what should be the minimal possible stimulus required in space for termination. To do this, we show how a localized perturbation can be designed to annihilate simultaneously all spiral waves both free and bound. This identified mechanism is applicable to any excitable system and, for the heart, may lead to more efficient defibrillation strategies. We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.
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2
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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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Li QH, Van Nieuwenhuyse E, Xia YX, Pan JT, Duytschaever M, Knecht S, Vandersickel N, Zhou C, Panfilov AV, Zhang H. Finding type and location of the source of cardiac arrhythmias from the averaged flow velocity field using the determinant-trace method. Phys Rev E 2021; 104:064401. [PMID: 35030872 DOI: 10.1103/physreve.104.064401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
Life threatening cardiac arrhythmias result from abnormal propagation of nonlinear electrical excitation waves in the heart. Finding the locations of the sources of these waves remains a challenging problem. This is mainly due to the low spatial resolution of electrode recordings of these waves. Also, these recordings are subjected to noise. In this paper, we develop a different approach: the AFV-DT method based on an averaged flow velocity (AFV) technique adopted from the analysis of optical flows and the determinant-trace (DT) method used for vector field analysis of dynamical systems. This method can find the location and determine all important types of sources found in excitable media such as focal activity, spiral waves, and waves rotating around obstacles. We test this method on in silico data of various wave excitation patterns obtained using the Luo-Rudy model for cardiac tissue. We show that the method works well for data with low spatial resolutions (up to 8×8) and is stable against noise. Finally, we apply it to two clinical cases and show that it can correctly identify the arrhythmia type and location. We discuss further steps on the development and improvement of this approach.
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Affiliation(s)
- Qi-Hao Li
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | | | - Yuan-Xun Xia
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | | | | | - Nele Vandersickel
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
| | - Changsong Zhou
- Department of Physics, Zhejiang University, Hangzhou 310027, China
- Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Research Centre, HKBU Institute of Research and Continuing Education, Shenzhen 518057, China
- Beijing Computational Science Research Center, Beijing 100084, China
| | - 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 119146, Russia
| | - Hong Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, China
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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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Abstract
The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).
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Glass L. Using mathematics to diagnose, cure, and predict cardiac arrhythmia. CHAOS (WOODBURY, N.Y.) 2020; 30:113132. [PMID: 33261334 DOI: 10.1063/5.0021844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 10/14/2020] [Indexed: 06/12/2023]
Abstract
Mathematics can be used to analyze and model cardiac arrhythmia. I discuss three different problems. (1) Diagnosis of atrial fibrillation based on the time intervals between subsequent beats. The probability density histograms of the differences of the intervals between consecutive beats have characteristic shapes for atrial fibrillation. (2) Curing atrial fibrillation by ablation of the core of rotors. Recent clinical studies have proposed that ablating the core of rotors in atrial tissue can cure atrial fibrillation. However, the claims are controversial. One problem that arises relates to difficulties associated with developing algorithms to identify the core of rotors. In model tissue culture systems, heterogeneity in the structure makes it difficult to unambiguously locate the core of rotors. (3) Risk stratification for sudden cardiac death (SCD). Despite numerous clinical studies, there is still a need for improved criteria to assess the risk of SCD. I discuss the possibility of using the dynamics of premature ventricular complexes to help make predictions. The development of wearable devices to record and analyze cardiac rhythms offers new prospects for the diagnosis and treatment of cardiac arrhythmia.
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Affiliation(s)
- Leon Glass
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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Li X, Almeida TP, Dastagir N, Guillem MS, Salinet J, Chu GS, Stafford PJ, Schlindwein FS, Ng GA. Standardizing Single-Frame Phase Singularity Identification Algorithms and Parameters in Phase Mapping During Human Atrial Fibrillation. Front Physiol 2020; 11:869. [PMID: 32792983 PMCID: PMC7386053 DOI: 10.3389/fphys.2020.00869] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Accepted: 06/29/2020] [Indexed: 12/03/2022] Open
Abstract
PURPOSE Recent investigations failed to reproduce the positive rotor-guided ablation outcomes shown by initial studies for treating persistent atrial fibrillation (persAF). Phase singularity (PS) is an important feature for AF driver detection, but algorithms for automated PS identification differ. We aim to investigate the performance of four different techniques for automated PS detection. METHODS 2048-channel virtual electrogram (VEGM) and electrocardiogram signals were collected for 30 s from 10 patients undergoing persAF ablation. QRST-subtraction was performed and VEGMs were processed using sinusoidal wavelet reconstruction. The phase was obtained using Hilbert transform. PSs were detected using four algorithms: (1) 2D image processing based and neighbor-indexing algorithm; (2) 3D neighbor-indexing algorithm; (3) 2D kernel convolutional algorithm estimating topological charge; (4) topological charge estimation on 3D mesh. PS annotations were compared using the structural similarity index (SSIM) and Pearson's correlation coefficient (CORR). Optimized parameters to improve detection accuracy were found for all four algorithms using F β score and 10-fold cross-validation compared with manual annotation. Local clustering with density-based spatial clustering of applications with noise (DBSCAN) was proposed to improve algorithms 3 and 4. RESULTS The PS density maps created by each algorithm with default parameters were poorly correlated. Phase gradient threshold and search radius (or kernels) were shown to affect PS detections. The processing times for the algorithms were significantly different (p < 0.0001). The F β scores for algorithms 1, 2, 3, 3 + DBSCAN, 4 and 4 + DBSCAN were 0.547, 0.645, 0.742, 0.828, 0.656, and 0.831. Algorithm 4 + DBSCAN achieved the best classification performance with acceptable processing time (2.0 ± 0.3 s). CONCLUSION AF driver identification is dependent on the PS detection algorithms and their parameters, which could explain some of the inconsistencies in rotor-guided ablation outcomes in different studies. For 3D triangulated meshes, algorithm 4 + DBSCAN with optimal parameters was the best solution for real-time, automated PS detection due to accuracy and speed. Similarly, algorithm 3 + DBSCAN with optimal parameters is preferred for uniform 2D meshes. Such algorithms - and parameters - should be preferred in future clinical studies for identifying AF drivers and minimizing methodological heterogeneities. This would facilitate comparisons in rotor-guided ablation outcomes in future works.
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Affiliation(s)
- Xin Li
- Department of Cardiovascular Science, University of Leicester, Leicester, United Kingdom
- School of Engineering, University of Leicester, Leicester, United Kingdom
| | - Tiago P. Almeida
- Department of Cardiovascular Science, University of Leicester, Leicester, United Kingdom
- School of Engineering, University of Leicester, Leicester, United Kingdom
- Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil
| | - Nawshin Dastagir
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | | | - João Salinet
- Centre for Engineering, Modelling and Applied Social Sciences, Federal University of ABC, Santo André, Brazil
| | - Gavin S. Chu
- Department of Cardiovascular Science, University of Leicester, Leicester, United Kingdom
| | - Peter J. Stafford
- National Institute for Health Research Leicester Cardiovascular Biomedical Research Centre, Glenfield Hospital, Leicester, United Kingdom
| | - Fernando S. Schlindwein
- School of Engineering, University of Leicester, Leicester, United Kingdom
- National Institute for Health Research Leicester Cardiovascular Biomedical Research Centre, Glenfield Hospital, Leicester, United Kingdom
| | - G. André Ng
- Department of Cardiovascular Science, University of Leicester, Leicester, United Kingdom
- National Institute for Health Research Leicester Cardiovascular Biomedical Research Centre, Glenfield Hospital, Leicester, United Kingdom
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Gagné S, Jacquemet V. Time resolution for wavefront and phase singularity tracking using activation maps in cardiac propagation models. CHAOS (WOODBURY, N.Y.) 2020; 30:033132. [PMID: 32237790 DOI: 10.1063/1.5133077] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 03/02/2020] [Indexed: 06/11/2023]
Abstract
The dynamics of cardiac fibrillation can be described by the number, the trajectory, the stability, and the lifespan of phase singularities (PSs). Accurate PS tracking is straightforward in simple uniform tissues but becomes more challenging as fibrosis, structural heterogeneity, and strong anisotropy are combined. In this paper, we derive a mathematical formulation for PS tracking in two-dimensional reaction-diffusion models. The method simultaneously tracks wavefronts and PS based on activation maps at full spatiotemporal resolution. PS tracking is formulated as a linear assignment problem solved by the Hungarian algorithm. The cost matrix incorporates information about distances between PS, chirality, and wavefronts. A graph of PS trajectories is generated to represent the creations and annihilations of PS pairs. Structure-preserving graph transformations are applied to provide a simplified description at longer observation time scales. The approach is validated in 180 simulations of fibrillation in four different types of substrates featuring, respectively, wavebreaks, ionic heterogeneities, fibrosis, and breakthrough patterns. The time step of PS tracking is studied in the range from 0.1 to 10 ms. The results show the benefits of improving time resolution from 1 to 0.1 ms. The tracking error rate decreases by an order of magnitude because the occurrence of simultaneous events becomes less likely. As observed on PS survival curves, the graph-based analysis facilitates the identification of macroscopically stable rotors despite wavefront fragmentation by fibrosis.
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Affiliation(s)
- Samuel Gagné
- Institut de Génie Biomédical, Département de Pharmacologie et Physiologie, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, Quebec H3C 3J7, Canada
| | - Vincent Jacquemet
- Institut de Génie Biomédical, Département de Pharmacologie et Physiologie, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, Quebec H3C 3J7, Canada
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