TY - JOUR
T1 - Electrocardiographic Imaging
T2 - A Comparison of Iterative Solvers
AU - Borràs, Marta
AU - Chamorro-Servent, Judit
N1 - Funding Information:
We would like to acknowledge the availably of the EDGAR data (Cluitmans et al., 2014; Aras et al., 2015; Bear et al., 2015), as well as the experiments performed by the Cardiovascular Research and Training Institute (CVRTI) and the Scientific Computing and Imaging (SCI) Institute at the University of Utah with funding from the Nora Eccles Treadwell Foundation and the NIH/NIGMS Center of Integrative Biomedical Computing under grant P41 GM103545-17). We would also like to thank Ana González Suárez and Jaume Coll-Font, who externally reviewed the master’s thesis of MB compiling some of the results compiled here. Their comments had helped to improve the work behind this manuscript.
Funding Information:
We would like to acknowledge the availably of the EDGAR data (Cluitmans et al., 2014 ; Aras et al., 2015 ; Bear et al., 2015), as well as the experiments performed by the Cardiovascular Research and Training Institute (CVRTI) and the Scientific Computing and Imaging (SCI) Institute at the University of Utah with funding from the Nora Eccles Treadwell Foundation and the NIH/NIGMS Center of Integrative Biomedical Computing under grant P41 GM103545-17). We would also like to thank Ana Gonz?lez Su?rez and Jaume Coll-Font, who externally reviewed the master?s thesis of MB compiling some of the results compiled here. Their comments had helped to improve the work behind this manuscript. Funding. This work compiles part of the master?s thesis of MB, JC-S could supervise this thesis thanks to the funded project from the European Union?s Horizon 2020 Research and Innovation Program under the Marie Sk?odowska-Curie grant agreement no. 794370.
Funding Information:
This work compiles part of the master’s thesis of MB, JC-S could supervise this thesis thanks to the funded project from the European Union’s Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie grant agreement no. 794370.
Publisher Copyright:
© Copyright © 2021 Borràs and Chamorro-Servent.
PY - 2021/2/3
Y1 - 2021/2/3
N2 - Cardiac disease is a leading cause of morbidity and mortality in developed countries. Currently, non-invasive techniques that can identify patients at risk and provide accurate diagnosis and ablation guidance therapy are under development. One of these is electrocardiographic imaging (ECGI). In ECGI, the first step is to formulate a forward problem that relates the unknown potential sources on the cardiac surface to the measured body surface potentials. Then, the unknown potential sources on the cardiac surface are reconstructed through the solution of an inverse problem. Unfortunately, ECGI still lacks accuracy due to the underlying inverse problem being ill-posed, and this consequently imposes limitations on the understanding and treatment of many cardiac diseases. Therefore, it is necessary to improve the solution of the inverse problem. In this work, we transfer and adapt four inverse problem methods to the ECGI setting: algebraic reconstruction technique (ART), random ART, ART Split Bregman (ART-SB) and range restricted generalized minimal residual (RRGMRES) method. We test all these methods with data from the Experimental Data and Geometric Analysis Repository (EDGAR) and compare their solution with the recorded epicardial potentials provided by EDGAR and a generalized minimal residual (GMRES) iterative method computed solution. Activation maps are also computed and compared. The results show that ART achieved the most stable solutions and, for some datasets, returned the best reconstruction. Differences between the solutions derived from ART and random ART are almost negligible, and the accuracy of their solutions is followed by RRGMRES, ART-SB and finally the GMRES (which returned the worst reconstructions). The RRGMRES method provided the best reconstruction for some datasets but appeared to be less stable than ART when comparing different datasets. In conclusion, we show that the proposed methods (ART, random ART, and RRGMRES) improve the GMRES solution, which has been suggested as inverse problem solution for ECGI.
AB - Cardiac disease is a leading cause of morbidity and mortality in developed countries. Currently, non-invasive techniques that can identify patients at risk and provide accurate diagnosis and ablation guidance therapy are under development. One of these is electrocardiographic imaging (ECGI). In ECGI, the first step is to formulate a forward problem that relates the unknown potential sources on the cardiac surface to the measured body surface potentials. Then, the unknown potential sources on the cardiac surface are reconstructed through the solution of an inverse problem. Unfortunately, ECGI still lacks accuracy due to the underlying inverse problem being ill-posed, and this consequently imposes limitations on the understanding and treatment of many cardiac diseases. Therefore, it is necessary to improve the solution of the inverse problem. In this work, we transfer and adapt four inverse problem methods to the ECGI setting: algebraic reconstruction technique (ART), random ART, ART Split Bregman (ART-SB) and range restricted generalized minimal residual (RRGMRES) method. We test all these methods with data from the Experimental Data and Geometric Analysis Repository (EDGAR) and compare their solution with the recorded epicardial potentials provided by EDGAR and a generalized minimal residual (GMRES) iterative method computed solution. Activation maps are also computed and compared. The results show that ART achieved the most stable solutions and, for some datasets, returned the best reconstruction. Differences between the solutions derived from ART and random ART are almost negligible, and the accuracy of their solutions is followed by RRGMRES, ART-SB and finally the GMRES (which returned the worst reconstructions). The RRGMRES method provided the best reconstruction for some datasets but appeared to be less stable than ART when comparing different datasets. In conclusion, we show that the proposed methods (ART, random ART, and RRGMRES) improve the GMRES solution, which has been suggested as inverse problem solution for ECGI.
KW - ART
KW - ART-SB
KW - ECGI
KW - GMRES
KW - inverse problem
KW - iterative methods
KW - MFS
KW - RRGMRES
KW - Kaczmarz method
KW - meshless methods
KW - Regularization
KW - algebraic reconstruction technique
KW - split Bregman
KW - ECG
KW - Applied mathematics
UR - http://www.scopus.com/inward/record.url?scp=85100876584&partnerID=8YFLogxK
U2 - 10.3389/fphys.2021.620250
DO - 10.3389/fphys.2021.620250
M3 - Article
C2 - 33613311
AN - SCOPUS:85100876584
SN - 1664-042X
VL - 12
JO - Frontiers in physiology
JF - Frontiers in physiology
M1 - 620250
ER -