Inverse problem of electrocardiography

  • Authors

    • Benaki Lairenjam MITS, college
    • Satyendra Satyendra Singh BT College
    2019-02-26
    https://doi.org/10.14419/ijet.v7i4.18181
  • 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

    1. [1] Ahmad GF, Brookes DH. and Macleod RS. An Admissible Solution Approach to Inverse Electrocardiography. Annals of Biomedical Engineering, Vol. 26, (1998) 278-292. https://doi.org/10.1114/1.56.

      [2] Chambolle A, Caselles V, Novaga M, Cremers D and Pock T. An introduction to total Variation for Image Analysis. 2009.<hal-00437581>

      [3] Colli-Franzone P, Guerri L, Tentoni S et al.. A mathematical procedure for solving the inverse potential problem of Electrocardiography-Analysis of the time space Accuracy from In Vitro Experimental Data, Mathematical Biosciences 77 (1985), 353-396, 1985.

      [4] Costabel M and Darmstadt TH. Principles of Boundary Element Methods. https://perso.univ-rennes1.fr/martin.costabel/publis/Co_PrinciplesBEM.pdf.

      [5] Denisov AM, Zakharov EV, Kalinin AV and Kalinin VV. Numerical Methods for Some Inverse Problems of Heart Electrophysiology. Differential Equations 2009, Vol. 45 No. 7. 1034-1043. https://doi.org/10.1134/S0012266109070106.

      [6] Gantumur T. Adaptive boundary element methods with convergence rates. Math.NA, Dec. 2012.

      [7] Gerald CF and Wheatley PO. Applied Numerical Analysis. Pearson 7th edition.

      [8] Ghosh S and Rudy Y. Accuracy of Quadratic versus Linear Interpolation in Noninvasive Electrocardiographic Imaging (ECGI), Ann. Biomedical Eng., 2005. https://doi.org/10.1007/s10439-005-5537-x.

      [9] Hansen PC. The truncated SVD as a method for regularization, NA-86-36, (1986).

      [10] 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.

      [11] Hullerum M. The inverse Problem of Electrocardiography: Explanation based on a simple Example. August 2012.

      [12] 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.

      [13] 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.

      [14] 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.

      [15] Macfarlane PW, Oosterom AV, Pahlm O, Kligfield P, Janse M and Camm J. Comprehensive Electrocardiography, Springer.

      [16] 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.

      [17] Milanic M, Jazbinsek V, Macleod RS. Assessment of Regularization Techniques for electrocardiographic Imaging. Journal of Electrocardiology 47 (2014). https://doi.org/10.1016/j.jelectrocard.2013.10.004.

      [18] 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.

      [19] Pullan AJ, Cheng LK, Nash MP, Ghodrati A, MacLeod R and Brooks D. The Inverse Problem of Electrocardiography. Comprehensive Electrocardiology 299-344.

      [20] Ramanathan C and Rudy Y. Electrocardiographic Imaging: II. Effect of Torso Inhomogeneties on Noninvasive Reconstruction of Epicardial Potentials, Electrograms and Isochrones. Journal of Cardiovascular Electrophysiology, Volume 12, No. 2, February 2001. https://doi.org/10.1046/j.1540-8167.2001.00241.x.

      [21] Ramanathan C, Jia P, Ghanem R and Calvetti D and Rudy Y. Noninvasive 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.

      [22] Ramanathan C, Jia P, Ghanem R and Calvetti D and Rudy Y. Noninvasive Electrocardiographic Imaging (ECGI)â€. Annals of Biomed Eng 2007 December 24.

      [23] 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.

      [24] 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 2007â€, LNCS 4466 (2007), 290-299.

      [25] Smidth BF, Domain Decomposition Methods for Partial Differential Equations. Parallel Numeric Algorithms, Springer (1997).

      [26] 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 Biomedical Engineering, vol. 55 Issue 9. https://doi.org/10.1109/TBME.2008.923913.

      [27] Verfürth P. Reconstruction of the Epicardial Potential from Body Surface Potential Maps. 2011.

      [28] Wang Y and Rudy Y. Application of the method of fundamental Solutions to Potential based Inverse Electrocardiography. Ann Biomed Eng. 2006 August: 34(8). 1272-1288. https://doi.org/10.1007/s10439-006-9131-7.

      [29] 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.

      [30] Wang L. Computational reduction for noninvasive transmural electrophysiological imaging. Computers in Biology and Medicine 43 (2013), 184-199. https://doi.org/10.1016/j.compbiomed.2012.12.003.

      [31] Zemzemi N. An Iterative Method for Solving the Inverse Problem in Electrocardiography in Normal and Fibrillation Conditions: A simulation study. Proceeding of “Electrography 2014: 41st International Congress on Electrocardiographyâ€.

      [32] Zemzemi N, Bourenane H, Cochet H. An Iterative Method for Solving the Inverse Problem in Electrocardiography Imaging: From Body Surface to Heart Potential. Computing in Cardiology 2014, 717-720.

      [33] Zemzemi N. A Domain Decomposition Approach in the Electrocardiography Inverse Problem. Domain decomposition methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering. 641-647.

      [34] http://www.mit.edu/~9.520/scribe-notes/cl7.pdf (tikhonov cl17).

      [35] https://www.medicalnewstoday.com/articles/237191.php.

      [1] https://www.tutorialspoint.com/sdlc/sdlc_v_model.htm.

  • Downloads

  • How to Cite

    Lairenjam, B., & Satyendra Singh, S. (2019). Inverse problem of electrocardiography. International Journal of Engineering & Technology, 7(4), 4819-4822. https://doi.org/10.14419/ijet.v7i4.18181

    Received date: 2018-08-24

    Accepted date: 2018-12-03

    Published date: 2019-02-26