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Ondrusova B, Tino P, Svehlikova J. A two-step inverse solution for a single dipole cardiac source. Front Physiol 2023; 14:1264690. [PMID: 37745249 PMCID: PMC10513503 DOI: 10.3389/fphys.2023.1264690] [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] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 08/25/2023] [Indexed: 09/26/2023] Open
Abstract
Introduction: The inverse problem of electrocardiography noninvasively localizes the origin of undesired cardiac activity, such as a premature ventricular contraction (PVC), from potential recordings from multiple torso electrodes. However, the optimal number and placement of electrodes for an accurate solution of the inverse problem remain undetermined. This study presents a two-step inverse solution for a single dipole cardiac source, which investigates the significance of the torso electrodes on a patient-specific level. Furthermore, the impact of the significant electrodes on the accuracy of the inverse solution is studied. Methods: Body surface potential recordings from 128 electrodes of 13 patients with PVCs and their corresponding homogeneous and inhomogeneous torso models were used. The inverse problem using a single dipole was solved in two steps: First, using information from all electrodes, and second, using a subset of electrodes sorted in descending order according to their significance estimated by a greedy algorithm. The significance of electrodes was computed for three criteria derived from the singular values of the transfer matrix that correspond to the inversely estimated origin of the PVC computed in the first step. The localization error (LE) was computed as the Euclidean distance between the ground truth and the inversely estimated origin of the PVC. The LE obtained using the 32 and 64 most significant electrodes was compared to the LE obtained when all 128 electrodes were used for the inverse solution. Results: The average LE calculated for both torso models and using all 128 electrodes was 28.8 ± 11.9 mm. For the three tested criteria, the average LEs were 32.6 ± 19.9 mm, 29.6 ± 14.7 mm, and 28.8 ± 14.5 mm when 32 electrodes were used. When 64 electrodes were used, the average LEs were 30.1 ± 16.8 mm, 29.4 ± 12.0 mm, and 29.5 ± 12.6 mm. Conclusion: The study found inter-patient variability in the significance of torso electrodes and demonstrated that an accurate localization by the inverse solution with a single dipole could be achieved using a carefully selected reduced number of electrodes.
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Affiliation(s)
- Beata Ondrusova
- Institute of Measurement Science, Slovak Academy of Sciences, Bratislava, Slovakia
- Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia
| | - Peter Tino
- School of Computer Science, University of Birmingham, Birmingham, United Kingdom
| | - Jana Svehlikova
- Institute of Measurement Science, Slovak Academy of Sciences, Bratislava, Slovakia
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Bear LR, Bergquist JA, Abell E, Cochet H, MacLeod RS, Dubois R, Serinagaoglu Y. Investigation into the importance of using natural PVCs and pathological models for potential-based ECGI validation. Front Physiol 2023; 14:1198002. [PMID: 37275229 PMCID: PMC10232953 DOI: 10.3389/fphys.2023.1198002] [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] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 04/28/2023] [Indexed: 06/07/2023] Open
Abstract
Introduction: Premature ventricular contractions (PVCs) are one of the most commonly targeted pathologies for ECGI validation, often through ventricular stimulation to mimic the ectopic beat. However, it remains unclear if such stimulated beats faithfully reproduce spontaneously occurring PVCs, particularly in the case of the R-on-T phenomenon. The objective of this study was to determine the differences in ECGI accuracy when reconstructing spontaneous PVCs as compared to ventricular-stimulated beats and to explore the impact of pathophysiological perturbation on this reconstruction accuracy. Methods: Langendorff-perfused pig hearts (n = 3) were suspended in a human torso-shaped tank, and local hyperkalemia was induced through perfusion of a high-K+ solution (8 mM) into the LAD. Recordings were taken simultaneously from the heart and tank surfaces during ventricular pacing and during spontaneous PVCs (including R-on-T), both at baseline and high K+. Epicardial potentials were reconstructed from torso potentials using ECGI. Results: Spontaneously occurring PVCs were better reconstructed than stimulated beats at baseline in terms of electrogram morphology [correlation coefficient (CC) = 0.74 ± 0.05 vs. CC = 0.60 ± 0.10], potential maps (CC = 0.61 ± 0.06 vs. CC = 0.51 ± 0.12), and activation time maps (CC = 0.86 ± 0.07 vs. 0.76 ± 0.10), though there was no difference in the localization error (LE) of epicardial origin (LE = 14 ± 6 vs. 15 ± 11 mm). High K+ perfusion reduced the accuracy of ECGI reconstructions in terms of electrogram morphology (CC = 0.68 ± 0.10) and AT maps (CC = 0.70 ± 0.12 and 0.59 ± 0.23) for isolated PVCs and paced beats, respectively. LE trended worse, but the change was not significant (LE = 17 ± 9 and 20 ± 12 mm). Spontaneous PVCs were less well when the R-on-T phenomenon occurred and the activation wavefronts encountered a line of block. Conclusion: This study demonstrates the differences in ECGI accuracy between spontaneous PVCs and ventricular-paced beats. We also observed a reduction in this accuracy near regions of electrically inactive tissue. These results highlight the need for more physiologically realistic experimental models when evaluating the accuracy of ECGI methods. In particular, reconstruction accuracy needs to be further evaluated in the presence of R-on-T or isolated PVCs, particularly when encountering obstacles (functional or anatomical) which cause line of block and re-entry.
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Affiliation(s)
- Laura R. Bear
- IHU-Liryc, Heart Rhythm Disease Institute, Foundation Bordeaux Université, Bordeaux, France
- University Bordeaux, CRCTB, Bordeaux, France
- INSERM, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France
| | - Jake A. Bergquist
- Scientific Computing and Imaging Institute, University of Utah, Salt LakeCity, UT, United States
- Norra Eccles Harrison Cardiovascular Research and Training Institute (CVRTI), University of Utah, Salt LakeCity, UT, United States
- Department of Biomedical Engineering, University of Utah, Salt LakeCity, UT, United States
| | - Emma Abell
- IHU-Liryc, Heart Rhythm Disease Institute, Foundation Bordeaux Université, Bordeaux, France
- University Bordeaux, CRCTB, Bordeaux, France
- INSERM, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France
| | - Hubert Cochet
- IHU-Liryc, Heart Rhythm Disease Institute, Foundation Bordeaux Université, Bordeaux, France
- University Bordeaux, CRCTB, Bordeaux, France
- INSERM, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France
- Bordeaux University Hospital (CHU), Pessac, France
| | - Rob S. MacLeod
- Scientific Computing and Imaging Institute, University of Utah, Salt LakeCity, UT, United States
- Norra Eccles Harrison Cardiovascular Research and Training Institute (CVRTI), University of Utah, Salt LakeCity, UT, United States
- Department of Biomedical Engineering, University of Utah, Salt LakeCity, UT, United States
| | - Remi Dubois
- IHU-Liryc, Heart Rhythm Disease Institute, Foundation Bordeaux Université, Bordeaux, France
- University Bordeaux, CRCTB, Bordeaux, France
- INSERM, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France
| | - Yesim Serinagaoglu
- Electrical-Electronics Engineering Department, Middle East Technical University, Ankara, Türkiye
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van der Waal JG, Meijborg VMF, Belterman CNW, Streekstra GJ, Oostendorp TF, Coronel R. Ex vivo Validation of Noninvasive Epicardial and Endocardial Repolarization Mapping. Front Physiol 2021; 12:737609. [PMID: 34744778 PMCID: PMC8569864 DOI: 10.3389/fphys.2021.737609] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [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: 07/07/2021] [Accepted: 09/21/2021] [Indexed: 11/17/2022] Open
Abstract
Background: The detection and localization of electrophysiological substrates currently involve invasive cardiac mapping. Electrocardiographic imaging (ECGI) using the equivalent dipole layer (EDL) method allows the noninvasive estimation of endocardial and epicardial activation and repolarization times (AT and RT), but the RT validation is limited to in silico studies. We aimed to assess the temporal and spatial accuracy of the EDL method in reconstructing the RTs from the surface ECG under physiological circumstances and situations with artificially induced increased repolarization heterogeneity. Methods: In four Langendorff-perfused pig hearts, we simultaneously recorded unipolar electrograms from plunge needles and pseudo-ECGs from a volume-conducting container equipped with 61 electrodes. The RTs were computed from the ECGs during atrial and ventricular pacing and compared with those measured from the local unipolar electrograms. Regional RT prolongation (cooling) or shortening (pinacidil) was achieved by selective perfusion of the left anterior descending artery (LAD) region. Results: The differences between the computed and measured RTs were 19.0 ± 17.8 and 18.6 ± 13.7 ms for atrial and ventricular paced beats, respectively. The region of artificially delayed or shortened repolarization was correctly identified, with minimum/maximum RT roughly in the center of the region in three hearts. In one heart, the reconstructed region was shifted by ~2.5 cm. The total absolute difference between the measured and calculated RTs for all analyzed patterns in selectively perfused hearts (n = 5) was 39.6 ± 27.1 ms. Conclusion: The noninvasive ECG repolarization imaging using the EDL method of atrial and ventricular paced beats allows adequate quantitative reconstruction of regions of altered repolarization.
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Affiliation(s)
- Jeanne G van der Waal
- Department of Experimental and Clinical Cardiology, Amsterdam University Medical Centers, Location Academic Medical Center, Amsterdam, Netherlands
| | - Veronique M F Meijborg
- Department of Experimental and Clinical Cardiology, Amsterdam University Medical Centers, Location Academic Medical Center, Amsterdam, Netherlands
| | - Charly N W Belterman
- Department of Experimental and Clinical Cardiology, Amsterdam University Medical Centers, Location Academic Medical Center, Amsterdam, Netherlands
| | - Geert J Streekstra
- Department of Biomedical Engineering and Physics, Amsterdam University Medical Centers, Location Academic Medical Center, Amsterdam, Netherlands
| | - Thom F Oostendorp
- Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, Netherlands
| | - Ruben Coronel
- Department of Experimental and Clinical Cardiology, Amsterdam University Medical Centers, Location Academic Medical Center, Amsterdam, Netherlands.,IHU Liryc, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, Pessac-Bordeaux, France
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Roudijk RW, Boonstra MJ, Brummel R, Kassenberg W, Blom LJ, Oostendorp TF, Te Riele ASJM, van der Heijden JF, Asselbergs FW, van Dam PM, Loh P. Comparing Non-invasive Inverse Electrocardiography With Invasive Endocardial and Epicardial Electroanatomical Mapping During Sinus Rhythm. Front Physiol 2021; 12:730736. [PMID: 34671274 PMCID: PMC8521153 DOI: 10.3389/fphys.2021.730736] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [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: 06/25/2021] [Accepted: 09/01/2021] [Indexed: 01/04/2023] Open
Abstract
This study presents a novel non-invasive equivalent dipole layer (EDL) based inverse electrocardiography (iECG) technique which estimates both endocardial and epicardial ventricular activation sequences. We aimed to quantitatively compare our iECG approach with invasive electro-anatomical mapping (EAM) during sinus rhythm with the objective of enabling functional substrate imaging and sudden cardiac death risk stratification in patients with cardiomyopathy. Thirteen patients (77% males, 48 ± 20 years old) referred for endocardial and epicardial EAM underwent 67-electrode body surface potential mapping and CT imaging. The EDL-based iECG approach was improved by mimicking the effects of the His-Purkinje system on ventricular activation. EAM local activation timing (LAT) maps were compared with iECG-LAT maps using absolute differences and Pearson’s correlation coefficient, reported as mean ± standard deviation [95% confidence interval]. The correlation coefficient between iECG-LAT maps and EAM was 0.54 ± 0.19 [0.49–0.59] for epicardial activation, 0.50 ± 0.27 [0.41–0.58] for right ventricular endocardial activation and 0.44 ± 0.29 [0.32–0.56] for left ventricular endocardial activation. The absolute difference in timing between iECG maps and EAM was 17.4 ± 7.2 ms for epicardial maps, 19.5 ± 7.7 ms for right ventricular endocardial maps, 27.9 ± 8.7 ms for left ventricular endocardial maps. The absolute distance between right ventricular endocardial breakthrough sites was 30 ± 16 mm and 31 ± 17 mm for the left ventricle. The absolute distance for latest epicardial activation was median 12.8 [IQR: 2.9–29.3] mm. This first in-human quantitative comparison of iECG and invasive LAT-maps on both the endocardial and epicardial surface during sinus rhythm showed improved agreement, although with considerable absolute difference and moderate correlation coefficient. Non-invasive iECG requires further refinements to facilitate clinical implementation and risk stratification.
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Affiliation(s)
- Robert W Roudijk
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Machteld J Boonstra
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Rolf Brummel
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Wil Kassenberg
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Lennart J Blom
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Thom F Oostendorp
- Radboud University Nijmegen Medical Centre, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, Netherlands
| | - Anneline S J M Te Riele
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Jeroen F van der Heijden
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
| | - Folkert W Asselbergs
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands.,Faculty of Population Health Sciences, Institute of Cardiovascular Science, University College London, London, United Kingdom.,Health Data Research UK, Institute of Health Informatics, University College London, London, United Kingdom
| | - Peter M van Dam
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands.,ECG Excellence BV, Nieuwerbrug, Netherlands
| | - Peter Loh
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands
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Gander L, Krause R, Multerer M, Pezzuto S. Space-time shape uncertainties in the forward and inverse problem of electrocardiography. Int J Numer Method Biomed Eng 2021; 37:e3522. [PMID: 34410040 PMCID: PMC9285968 DOI: 10.1002/cnm.3522] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Revised: 06/27/2021] [Accepted: 08/13/2021] [Indexed: 06/08/2023]
Abstract
In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded two-dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem, the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an H1/2 regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.
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Affiliation(s)
- Lia Gander
- Center for Computational Medicine in CardiologyEuler Institute, Università della Svizzera italianaLuganoSwitzerland
| | - Rolf Krause
- Center for Computational Medicine in CardiologyEuler Institute, Università della Svizzera italianaLuganoSwitzerland
| | - Michael Multerer
- Center for Computational Medicine in CardiologyEuler Institute, Università della Svizzera italianaLuganoSwitzerland
| | - Simone Pezzuto
- Center for Computational Medicine in CardiologyEuler Institute, Università della Svizzera italianaLuganoSwitzerland
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Xu J, Dehaghani AR, Gao F, Wang L. Noninvasive transmural electrophysiological imaging based on minimization of total-variation functional. IEEE Trans Med Imaging 2014; 33:1860-74. [PMID: 24846557 PMCID: PMC6476190 DOI: 10.1109/tmi.2014.2324900] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
While tomographic imaging of cardiac structure and kinetics has improved substantially, electrophysiological mapping of the heart is still restricted to the surface with little or no depth information beneath. The progress in reconstructing 3-D action potential from surface voltage data has been hindered by the intrinsic ill-posedness of the problem and the lack of a unique solution in the absence of prior assumptions. In this work, we propose a novel adaption of the total-variation (TV) prior to exploit the unique spatial property of transmural action potential of being piecewise smooth with a steep boundary (gradient) separating depolarized and repolarized regions. We present a variational TV-prior instead of a common discrete TV-prior for improved robustness to mesh resolution, and solve the TV-minimization by a sequence of weighted, first-order L2-norm minimization. In a large set of phantom experiments, the proposed method is shown to outperform existing quadratic methods in preserving the steep gradient of action potential along the border of infarcts, as well as in capturing the disruption to the normal path of electrical wavefronts. Real-data experiments also further demonstrate the potential of the proposed method in revealing the location and shape of infarcts when quadratic methods fail to do so.
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Affiliation(s)
- Jingjia Xu
- Computational Biomedicine Laboratory, Golisano College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, NY 14623 USA ()
| | - Azar Rahimi Dehaghani
- Computational Biomedicine Laboratory, Golisano College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, NY 14623 USA
| | - Fei Gao
- Molecular Imaging Division, Siemens Medical Solutions, Knoxville, TN 37932 USA
| | - Linwei Wang
- Computational Biomedicine Laboratory, Golisano College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, NY 14623 USA
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