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Manche M, El Houari K, Kachenoura A, Albera L, Rochette M, Hernández A, Moussaoui S. A reduced complexity ECG imaging model for regularized inversion optimization. Comput Biol Med 2023; 167:107698. [PMID: 37956624 DOI: 10.1016/j.compbiomed.2023.107698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Revised: 10/27/2023] [Accepted: 11/07/2023] [Indexed: 11/15/2023]
Abstract
The resolution of the inverse problem of electrocardiography represents a major interest in the diagnosis and catheter-based therapy of cardiac arrhythmia. In this context, the ability to simulate several cardiac electrical behaviors was crucial for evaluating and comparing the performance of inversion methods. For this application, existing models are either too complex or do not produce realistic cardiac patterns. In this work, a low-resolution heart-torso model generating realistic whole heart cardiac mappings and electrocardiograms in healthy and pathological cases is designed. This model was built upon a simplified heart-torso geometry and implements the monodomain formalism by using the finite element method. In addition, a model reduction step through a sensitivity analysis was proposed where parameters were identified using an evolutionary optimization approach. Finally, the study illustrates the usefulness of the proposed model by comparing the performance of different variants of Tikhonov-based inversion methods for the determination of the regularization parameter in healthy, ischemic and ventricular tachycardia scenarios. First, results of the sensitivity analysis show that among 58 parameters only 25 are influent. Note also that the level of influence of the parameters depends on the heart region. Besides, the synthesized electrocardiograms globally present the same characteristic shape compared to the reference once with a correlation value that reaches 88%. Regarding inverse problem, results highlight that only Robust Generalized Cross Validation and Discrepancy Principle provide best performance, with a quasi-perfect success rate for both, and a respective relative error, between the generated electrocardiograms to the reference one, of 0.75 and 0.62.
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Affiliation(s)
- Maureen Manche
- University of Rennes (LTSI), Inserm - UMR 1099, Rennes, 35000, France; Nantes Université, Ecole Centrale Nantes, LS2N UMR CNRS 6004, Nantes, 44000, France
| | | | - Amar Kachenoura
- University of Rennes (LTSI), Inserm - UMR 1099, Rennes, 35000, France.
| | - Laurent Albera
- University of Rennes (LTSI), Inserm - UMR 1099, Rennes, 35000, France
| | | | - Alfredo Hernández
- University of Rennes (LTSI), Inserm - UMR 1099, Rennes, 35000, France
| | - Saïd Moussaoui
- Nantes Université, Ecole Centrale Nantes, LS2N UMR CNRS 6004, Nantes, 44000, France
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2
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Hernández-Romero I, Molero R, Fambuena-Santos C, Herrero-Martín C, Climent AM, Guillem MS. Electrocardiographic imaging in the atria. Med Biol Eng Comput 2023; 61:879-896. [PMID: 36370321 PMCID: PMC9988819 DOI: 10.1007/s11517-022-02709-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 10/26/2022] [Indexed: 11/13/2022]
Abstract
The inverse problem of electrocardiography or electrocardiographic imaging (ECGI) is a technique for reconstructing electrical information about cardiac surfaces from noninvasive or non-contact recordings. ECGI has been used to characterize atrial and ventricular arrhythmias. Although it is a technology with years of progress, its development to characterize atrial arrhythmias is challenging. Complications can arise when trying to describe the atrial mechanisms that lead to abnormal propagation patterns, premature or tachycardic beats, and reentrant arrhythmias. This review addresses the various ECGI methodologies, regularization methods, and post-processing techniques used in the atria, as well as the context in which they are used. The current advantages and limitations of ECGI in the fields of research and clinical diagnosis of atrial arrhythmias are outlined. In addition, areas where ECGI efforts should be concentrated to address the associated unsatisfied needs from the atrial perspective are discussed.
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Affiliation(s)
| | - Rubén Molero
- ITACA, Universitat Politècnica de València, Valencia, Spain
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Njeru DK, Athawale TM, France JJ, Johnson CR. Quantifying and Visualizing Uncertainty for Source Localization in Electrocardiographic Imaging. Comput Methods Biomech Biomed Eng Imaging Vis 2022; 11:812-822. [PMID: 37284179 PMCID: PMC10241371 DOI: 10.1080/21681163.2022.2113824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 08/12/2022] [Indexed: 06/08/2023]
Abstract
Electrocardiographic imaging (ECGI) presents a clinical opportunity to noninvasively understand the sources of arrhythmias for individual patients. To help increase the effectiveness of ECGI, we provide new ways to visualize associated measurement and modeling errors. In this paper, we study source localization uncertainty in two steps: First, we perform Monte Carlo simulations of a simple inverse ECGI source localization model with error sampling to understand the variations in ECGI solutions. Second, we present multiple visualization techniques, including confidence maps, level-sets, and topology-based visualizations, to better understand uncertainty in source localization. Our approach offers a new way to study uncertainty in the ECGI pipeline.
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Affiliation(s)
- Dennis K Njeru
- Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, USA
| | - Tushar M Athawale
- Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, USA
| | - Jessie J France
- Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, USA
| | - Chris R Johnson
- Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, USA
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4
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Caulier-Cisterna R, Sanromán-Junquera M, Muñoz-Romero S, Blanco-Velasco M, Goya-Esteban R, García-Alberola A, Rojo-Álvarez JL. Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (I): Preprocessing and Bipolar Potentials. Sensors (Basel) 2020; 20:E3131. [PMID: 32492938 PMCID: PMC7309141 DOI: 10.3390/s20113131] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Revised: 05/28/2020] [Accepted: 05/29/2020] [Indexed: 12/19/2022]
Abstract
During the last years, Electrocardiographic Imaging (ECGI) has emerged as a powerful and promising clinical tool to support cardiologists. Starting from a plurality of potential measurements on the torso, ECGI yields a noninvasive estimation of their causing potentials on the epicardium. This unprecedented amount of measured cardiac signals needs to be conditioned and adapted to current knowledge and methods in cardiac electrophysiology in order to maximize its support to the clinical practice. In this setting, many cardiac indices are defined in terms of the so-called bipolar electrograms, which correspond with differential potentials between two spatially close potential measurements. Our aim was to contribute to the usefulness of ECGI recordings in the current knowledge and methods of cardiac electrophysiology. For this purpose, we first analyzed the basic stages of conventional cardiac signal processing and scrutinized the implications of the spatial-temporal nature of signals in ECGI scenarios. Specifically, the stages of baseline wander removal, low-pass filtering, and beat segmentation and synchronization were considered. We also aimed to establish a mathematical operator to provide suitable bipolar electrograms from the ECGI-estimated epicardium potentials. Results were obtained on data from an infarction patient and from a healthy subject. First, the low-frequency and high-frequency noises are shown to be non-independently distributed in the ECGI-estimated recordings due to their spatial dimension. Second, bipolar electrograms are better estimated when using the criterion of the maximum-amplitude difference between spatial neighbors, but also a temporal delay in discrete time of about 40 samples has to be included to obtain the usual morphology in clinical bipolar electrograms from catheters. We conclude that spatial-temporal digital signal processing and bipolar electrograms can pave the way towards the usefulness of ECGI recordings in the cardiological clinical practice. The companion paper is devoted to analyzing clinical indices obtained from ECGI epicardial electrograms measuring waveform variability and repolarization tissue properties.
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Affiliation(s)
- Raúl Caulier-Cisterna
- Department of Signal Theory and Communications, Telematics and Computing Systems, Rey Juan Carlos University, Fuenlabrada, 28943 Madrid, Spain; (R.C.-C.); (M.S.-J.); (S.M.-R.); (R.G.-E.)
| | - Margarita Sanromán-Junquera
- Department of Signal Theory and Communications, Telematics and Computing Systems, Rey Juan Carlos University, Fuenlabrada, 28943 Madrid, Spain; (R.C.-C.); (M.S.-J.); (S.M.-R.); (R.G.-E.)
| | - Sergio Muñoz-Romero
- Department of Signal Theory and Communications, Telematics and Computing Systems, Rey Juan Carlos University, Fuenlabrada, 28943 Madrid, Spain; (R.C.-C.); (M.S.-J.); (S.M.-R.); (R.G.-E.)
- Center for Computational Simulation, Universidad Politécnica de Madrid, Boadilla, 28223 Madrid, Spain
| | - Manuel Blanco-Velasco
- Department of Signal Theory and Communications, Universidad de Alcalá, Alcalá de Henares, 28805 Madrid, Spain;
| | - Rebeca Goya-Esteban
- Department of Signal Theory and Communications, Telematics and Computing Systems, Rey Juan Carlos University, Fuenlabrada, 28943 Madrid, Spain; (R.C.-C.); (M.S.-J.); (S.M.-R.); (R.G.-E.)
| | - Arcadi García-Alberola
- Arrhythmia Unit, Hospital Clínico Universitario Virgen de la Arrixaca de Murcia, El Palmar, 30120 Murcia, Spain;
| | - José Luis Rojo-Álvarez
- Department of Signal Theory and Communications, Telematics and Computing Systems, Rey Juan Carlos University, Fuenlabrada, 28943 Madrid, Spain; (R.C.-C.); (M.S.-J.); (S.M.-R.); (R.G.-E.)
- Center for Computational Simulation, Universidad Politécnica de Madrid, Boadilla, 28223 Madrid, Spain
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5
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Karoui A, Bear L, Migerditichan P, Zemzemi N. Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data. Front Physiol 2018; 9:1708. [PMID: 30555347 PMCID: PMC6281950 DOI: 10.3389/fphys.2018.01708] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Accepted: 11/13/2018] [Indexed: 11/13/2022] Open
Abstract
The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.
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Affiliation(s)
- Amel Karoui
- Institute of Mathematics, University of Bordeaux, Bordeaux, France.,INRIA Bordeaux Sud-Ouest, Bordeaux, France.,IHU Lyric, Bordeaux, France
| | | | | | - Nejib Zemzemi
- Institute of Mathematics, University of Bordeaux, Bordeaux, France.,INRIA Bordeaux Sud-Ouest, Bordeaux, France.,IHU Lyric, Bordeaux, France
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6
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Abstract
BACKGROUND This study estimates atrial repolarization activities (Ta waves), which are typically hidden most of the time from body surface electrocardiography when diagnosing cardiovascular diseases. The morphology of Ta waves has been proven to be an important marker for the early sign of inferior injury, such as acute atrial infarction, or arrhythmia, such as atrial fibrillation. However, Ta waves are usually unseen except during conduction system malfunction, such as long QT interval or atrioventricular block. Therefore, justifying heart diseases based on atrial repolarization becomes impossible in sinus rhythm. METHODS We obtain TMPs in the atrial part of the myocardium which reflects the correct excitation sequence starting from the atrium to the end of the apex. RESULTS The resulting TMP shows the hidden atrial part of ECG waves. CONCLUSIONS This extraction makes many diseases, such as acute atrial infarction or arrhythmia, become easily diagnosed.
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Affiliation(s)
- Wei-Hua Tang
- Division of Cardiology, Department of Internal Medicine, National Yang-Ming University Hospital, Yilan, Taiwan
| | - Wen-Hsien Ho
- Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, 100 Shin-Chuan 1st Road, Kaohsiung, 807, Taiwan. .,Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, Taiwan.
| | - Yenming J Chen
- Department of Logistics Management, National Kaohsiung University of Science and Technology, 1 University Road, Yenchao, Kaohsiung, 824, Taiwan.
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7
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Janssen AM, Potyagaylo D, Dössel O, Oostendorp TF. Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart. Med Biol Eng Comput 2018. [PMID: 29130137 DOI: 10.1007/sll517-017-1715-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.
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Affiliation(s)
- Arno M Janssen
- The Netherlands Heart Institute, Utrecht, The Netherlands
- The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
| | - Danila Potyagaylo
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
| | - Olaf Dössel
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Thom F Oostendorp
- The Netherlands Heart Institute, Utrecht, The Netherlands
- The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
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8
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Janssen AM, Potyagaylo D, Dössel O, Oostendorp TF. Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart. Med Biol Eng Comput 2017; 56:1013-1025. [PMID: 29130137 PMCID: PMC5978848 DOI: 10.1007/s11517-017-1715-x] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Accepted: 08/17/2017] [Indexed: 12/25/2022]
Abstract
Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.
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Affiliation(s)
- Arno M Janssen
- The Netherlands Heart Institute, Utrecht, The Netherlands.,The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
| | - Danila Potyagaylo
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
| | - Olaf Dössel
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Thom F Oostendorp
- The Netherlands Heart Institute, Utrecht, The Netherlands.,The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
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9
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Barnes JP, Johnston PR. Application of robust Generalised Cross-Validation to the inverse problem of electrocardiology. Comput Biol Med 2016; 69:213-25. [PMID: 26773942 DOI: 10.1016/j.compbiomed.2015.12.011] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2015] [Revised: 12/14/2015] [Accepted: 12/17/2015] [Indexed: 11/22/2022]
Abstract
Robust Generalised Cross-Validation was proposed recently as a method for determining near optimal regularisation parameters in inverse problems. It was introduced to overcome a problem with the regular Generalised Cross-Validation method in which the function that is minimised to obtain the regularisation parameter often has a broad, flat minimum, resulting in a poor estimate for the parameter. The robust method defines a new function to be minimised which has a narrower minimum, but at the expense of introducing a new parameter called the robustness parameter. In this study, the Robust Generalised Cross-Validation method is applied to the inverse problem of electrocardiology. It is demonstrated that, for realistic situations, the robustness parameter can be set to zero. With this choice of robustness parameter, it is shown that the robust method is able to obtain estimates of the regularisation parameter in the inverse problem of electrocardiology that are comparable to, or better than, many of the standard methods that are applied to this inverse problem.
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10
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Lopez Rincon A, Bendahmane M, Ainseba B. Two-step genetic algorithm to solve the inverse problem in electrocardiography for cardiac sources. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization 2014. [DOI: 10.1080/21681163.2013.814295] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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11
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Wang D, Kirby RM, MacLeod RS, Johnson CR. Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution. J Comput Phys 2013; 250:403-424. [PMID: 23913980 PMCID: PMC3727301 DOI: 10.1016/j.jcp.2013.05.027] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem's specific structure. Our simulations used realistic, fiber-included heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization.
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Affiliation(s)
- Dafang Wang
- School of Computing, University of Utah, Salt Lake City, UT, USA
- Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA
| | - Robert M. Kirby
- School of Computing, University of Utah, Salt Lake City, UT, USA
- Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA
| | - Rob S. MacLeod
- Department of Bioengineering, University of Utah, Salt Lake City, UT, USA
- Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA
| | - Chris R. Johnson
- School of Computing, University of Utah, Salt Lake City, UT, USA
- Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA
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12
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Wang L, Dawoud F, Yeung SK, Shi P, Wong KCL, Liu H, Lardo AC. Transmural imaging of ventricular action potentials and post-infarction scars in swine hearts. IEEE Trans Med Imaging 2013; 32:731-47. [PMID: 23288331 DOI: 10.1109/tmi.2012.2236567] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The problem of using surface data to reconstruct transmural electrophysiological (EP) signals is intrinsically ill-posed without a unique solution in its unconstrained form. Incorporating physiological spatiotemporal priors through probabilistic integration of dynamic EP models, we have previously developed a Bayesian approach to transmural electrophysiological imaging (TEPI) using body-surface electrocardiograms. In this study, we generalize TEPI to using electrical signals collected from heart surfaces, and we test its feasibility on two pre-clinical swine models provided through the STACOM 2011 EP simulation Challenge. Since this new application of TEPI does not require whole-body imaging, there may be more immediate potential in EP laboratories where it could utilize catheter mapping data and produce transmural information for therapy guidance. Another focus of this study is to investigate the consistency among three modalities in delineating scar after myocardial infarction: TEPI, electroanatomical voltage mapping (EAVM), and magnetic resonance imaging (MRI). Our preliminary data demonstrate that, compared to the low-voltage scar area in EAVM, the 3-D electrical scar volume detected by TEPI is more consistent with anatomical scar volume delineated in MRI. Furthermore, TEPI could complement anatomical imaging by providing EP functional features related to both scar and healthy tissue.
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Affiliation(s)
- Linwei Wang
- Computational Biomedicine Laboratory, Golisano College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA.
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13
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Wang D, Kirby RM, Macleod RS, Johnson CR. An optimization framework for inversely estimating myocardial transmembrane potentials and localizing ischemia. Annu Int Conf IEEE Eng Med Biol Soc 2012; 2011:1680-3. [PMID: 22254648 DOI: 10.1109/iembs.2011.6090483] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
By combining a static bidomain heart model with a torso conduction model, we studied the inverse electrocardiographic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to localize myocardial ischemia. Our main contribution is solving the inverse problem within a constrained optimization framework, which is a generalization of previous methods for calculating transmembrane potentials. The framework offers ample flexibility for users to apply various physiologically-based constraints, and is well supported by mature algorithms and solvers developed by the optimization community. By avoiding the traditional inverse ECG approach of building the lead-field matrix, the framework greatly reduces computation cost and, by setting the associated forward problem as a constraint, the framework enables one to flexibly set individualized resolutions for each physical variable, a desirable feature for balancing model accuracy, ill-conditioning and computation tractability. Although the task of computing myocardial TMPs at an arbitrary time instance remains an open problem, we showed that it is possible to obtain TMPs with moderate accuracy during the ST segment by assuming all cardiac cells are at the plateau phase. Moreover, the calculated TMPs yielded a good estimate of ischemic regions, which was of more clinical interest than the voltage values themselves. We conducted finite element simulations of a phantom experiment over a 2D torso model with synthetic ischemic data. Preliminary results indicated that our approach is feasible and suitably accurate for the common case of transmural myocardial ischemia.
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Affiliation(s)
- Dafang Wang
- Scientific Computing and Imaging Institute, University of Utah, USA.
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14
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Abstract
We evaluated the theoretical aspects of monitoring the deep body temperature distribution with the inverse modeling method. A two-dimensional model was built based on anatomical structure to simulate the human abdomen. By integrating biophysical and physiological information, the deep body temperature distribution was estimated from cutaneous surface temperature measurements using an inverse quasilinear method. Simulations were conducted with and without the heat effect of blood perfusion in the muscle and skin layers. The results of the simulations showed consistently that the noise characteristics and arrangement of the temperature sensors were the major factors affecting the accuracy of the inverse solution. With temperature sensors of 0.05 °C systematic error and an optimized 16-sensor arrangement, the inverse method could estimate the deep body temperature distribution with an average absolute error of less than 0.20 °C. The results of this theoretical study suggest that it is possible to reconstruct the deep body temperature distribution with the inverse method and that this approach merits further investigation.
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Affiliation(s)
- Ming Huang
- The University of Aizu, Tsuruga, Ikki-machi, Aizu-wakamatsu, Fukushima 965-8580, Japan
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15
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Wang L, Qin J, Wong TT, Heng PA. Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection. Phys Med Biol 2011; 56:6291-310. [PMID: 21896965 DOI: 10.1088/0031-9155/56/19/009] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
The epicardial potential (EP)-targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a well-known ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But the L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using the L1-norm penalty function, however, may greatly increase computational complexity due to its non-differentiability. We propose an L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1-norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a bound-constrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1-norm regularization methods, especially when the noises are large.
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Affiliation(s)
- Liansheng Wang
- Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong.
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Wang D, Kirby RM, Johnson CR. Finite-element-based discretization and regularization strategies for 3-D inverse electrocardiography. IEEE Trans Biomed Eng 2011; 58:1827-38. [PMID: 21382763 DOI: 10.1109/tbme.2011.2122305] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L(2) norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.
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Affiliation(s)
- Dafang Wang
- Scientific Computing and Imaging (SCI) Institute and the School of Computing, University of Utah, Salt Lake City, UT 84112, USA.
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