Inverse problem of electrocardiography
About this article
DOI:
https://doi.org/10.14419/ijet.v7i4.18181Keywords:
ECG, Electric Potential, Epicardium, Ill-Posedness, Inverse Problem.Abstract
Inverse problem in Electrocardiography (ECG) is the mathematical formulation of the electrical activity of the heart surface from the measured body surface potential. This paper presents a state of art review of the inverse problem in ECG and the recent development in the solution of the mathematical model.
References
Ahmad GF, Brookes DH. and Macleod RS. An Admissible Solution Approach to Inverse Electrocardiography. Annals of Biomedical En-gineering, Vol. 26, (1998) 278-292. https://doi.org/10.1114/1.56.
Chambolle A, Caselles V, Novaga M, Cremers D and Pock T. An introduction to total Variation for Image Analysis. 2009.
Colli-Franzone P, Guerri L, Tentoni S et al.. A mathematical proce-dure for solving the inverse potential problem of Electrocardiog-raphy-Analysis of the time space Accuracy from In Vitro Experi-mental Data, Mathematical Biosciences 77 (1985), 353-396, 1985.
Costabel M and Darmstadt TH. Principles of Boundary Element Methods. https://perso.univ-rennes1.fr/martin.costabel/publis/Co_PrinciplesBEM.pdf.
Denisov AM, Zakharov EV, Kalinin AV and Kalinin VV. Numeri-cal Methods for Some Inverse Problems of Heart Electrophysiology. Differential Equations 2009, Vol. 45 No. 7. 1034-1043. https://doi.org/10.1134/S0012266109070106.
View more references (31)
Gantumur T. Adaptive boundary element methods with convergence rates. Math.NA, Dec. 2012.
Gerald CF and Wheatley PO. Applied Numerical Analysis. Pearson 7th edition.
Ghosh S and Rudy Y. Accuracy of Quadratic versus Linear Interpo-lation in Noninvasive Electrocardiographic Imaging (ECGI), Ann. Biomedical Eng., 2005. https://doi.org/10.1007/s10439-005-5537-x.
Hansen PC. The truncated SVD as a method for regularization, NA-86-36, (1986).
Horacek BM, Wang L, Dawoud F, Xu J and Sapp JL. Noninvasive electrocardiographic imaging of chronic myocardial infarct scar. Journal of Electrocardiology 48 (2015), 952-958. https://doi.org/10.1016/j.jelectrocard.2015.08.035.
Hullerum M. The inverse Problem of Electrocardiography: Explana-tion based on a simple Example. August 2012.
Intini A, Goldstein RN, Jia P et. al. Electrocardiographic imaging (ECGI), a novel diagnostic modality used for mapping of focal left ventricular tachycardia in a young athlete. Heart Rhythm 2005 Nov; 2(11) 250-1252. https://doi.org/10.1016/j.hrthm.2005.08.019.
Johnson CR and MacLeod RS. Adaptive Local Regularization Methods for the Inverse ECG Problem. Prog Biophys Mol Biol, 69(2-3), (1998), 405-23. https://doi.org/10.1016/S0079-6107(98)00017-0.
Liesen J, Rozloznik M and Strakos Z. Least Squares Residuals and Minimal Residual Methods. SIAM J. SCI.Comput. Vol. 23, No. 5, 1503-1525. https://doi.org/10.1137/S1064827500377988.
Macfarlane PW, Oosterom AV, Pahlm O, Kligfield P, Janse M and Camm J. Comprehensive Electrocardiography, Springer.
Milan Horacek B and John. C. Clements. The inverse problem of Electrocardiography: A Solution in Terms of Single- and Double-Layer Sources on the Epicardial surface. Mathematical Biosciences 144, 1997, 119-154. https://doi.org/10.1016/S0025-5564(97)00024-2.
Milanic M, Jazbinsek V, Macleod RS. Assessment of Regularization Techniques for electrocardiographic Imaging. Journal of Electrocar-diology 47 (2014). https://doi.org/10.1016/j.jelectrocard.2013.10.004.
Mocanu D, Morega M, Eisenberg SR, Morega AM. Nonsmooth Regularization in Electrocardiographic Imaging. Rev. Round. Sci. Tech.-Electotechn. et Energ., 48, I,p, Bucarest, 2003.
Pullan AJ, Cheng LK, Nash MP, Ghodrati A, MacLeod R and Brooks D. The Inverse Problem of Electrocardiography. Compre-hensive Electrocardiology 299-344.
Ramanathan C and Rudy Y. Electrocardiographic Imaging: II. Effect of Torso Inhomogeneties on Noninvasive Reconstruction of Epicar-dial Potentials, Electrograms and Isochrones. Journal of Cardiovas-cular Electrophysiology, Volume 12, No. 2, February 2001. https://doi.org/10.1046/j.1540-8167.2001.00241.x.
Ramanathan C, Jia P, Ghanem R and Calvetti D and Rudy Y. Non-invasive Electrocardiographic Imaging (ECGI): Application of the Generalized Minimal Residual (GMRes) Method. Annals of Biomed Eng Vol. 31, pp. 981–994, 2003. https://doi.org/10.1114/1.1588655.
Ramanathan C, Jia P, Ghanem R and Calvetti D and Rudy Y. Non-invasive Electrocardiographic Imaging (ECGI)”. Annals of Biomed Eng 2007 December 24.
Shewchuk JR. An Introduction to the Conjugate Gradient Method without the Agonizing Pain, Edition 1(1/ 4), (1994). https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf.
Shou G, Xia L, Jiang M, Liu F and Crozier S. Forward and Inverse Solutions of Electrocardiography Problem Using an Adaptive BEM Method. In proceeding “FIMH 2007”, LNCS 4466 (2007), 290-299.
Smidth BF, Domain Decomposition Methods for Partial Differential Equations. Parallel Numeric Algorithms, Springer (1997).
Stenroos M and Haueisen J. Boundary Element Computations in the Forward and Inverse Problems of Electrocardiography: Comparison of Collocation and Galerkin Weightings. IEEE transaction of Bio-medical Engineering, vol. 55 Issue 9. https://doi.org/10.1109/TBME.2008.923913.
Verfürth P. Reconstruction of the Epicardial Potential from Body Surface Potential Maps. 2011.
Wang Y and Rudy Y. Application of the method of fundamental So-lutions to Potential based Inverse Electrocardiography. Ann Biomed Eng. 2006 August: 34(8). 1272-1288. https://doi.org/10.1007/s10439-006-9131-7.
Wang D, Kirby RM and Johnson CR. Resolution Strategies for the Finite-Element-Based solution of the ECG Inverse problem. IEEE Transactions on Biomedical Engineering, Vol. 57, No. 2, Feb. 2010.
Wang L. Computational reduction for noninvasive transmural elec-trophysiological imaging. Computers in Biology and Medicine 43 (2013), 184-199. https://doi.org/10.1016/j.compbiomed.2012.12.003.
Zemzemi N. An Iterative Method for Solving the Inverse Problem in Electrocardiography in Normal and Fibrillation Conditions: A simu-lation study. Proceeding of “Electrography 2014: 41st International Congress on Electrocardiography”.
Zemzemi N, Bourenane H, Cochet H. An Iterative Method for Solv-ing the Inverse Problem in Electrocardiography Imaging: From Body Surface to Heart Potential. Computing in Cardiology 2014, 717-720.
Zemzemi N. A Domain Decomposition Approach in the Electrocar-diography Inverse Problem. Domain decomposition methods in Sci-ence and Engineering XXII, Lecture Notes in Computational Sci-ence and Engineering. 641-647.
http://www.mit.edu/~9.520/scribe-notes/cl7.pdf (tikhonov cl17).