Inverse Problem of Electrocardiography: Estimating the Location of Cardiac Ischemia in a 3D Realistic Geometry

  • Carlos Eduardo ChávezEmail author
  • Nejib Zemzemi
  • Yves Coudière
  • Felipe Alonso-Atienza
  • Diego Álvarez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9126)


The inverse problem of electrocardiography (IPE) has been formulated in different ways in order to non invasively obtain valuable informations about the heart condition. Most of the formulations solve the IPE neglecting the dynamic behavior of the electrical wave propagation in the heart. In this work we take into account this dynamic behavior by constraining the cost function with the monodomain model. We use an iterative algorithm combined with a level set formulation and the use of a simple phenomenological model. This method has been previously presented to localize ischemic regions in a 2D cardiac tissue. In this work, we analyze the performance of this method in different 3D geometries. The inverse procedure exploits the spatiotemporal correlations contained in the observed data, which is formulated as a parametric adjust of a mathematical model that minimizes the misfit between the simulated and the observed data. Numerical results over 3D geometries show that the algorithm is capable of identifying the position and the size of the ischemic regions. For the experiments with a realistic anatomical geometry, we reconstruct the ischemic region with roughly a 47 % of false-positive rate and a 13 % false-negative rate under 10 % of input noise. The correlation coefficient between the reconstructed ischemic region and the ground truth exceeds the value of 0.70).


Cardiac Tissue Ischemic Region Concentric Sphere Remote Measurement Spatiotemporal Correlation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by Spanish MINECO grants TEC-2013-46067-R, FIS2013-41802-R and by Carlos III of Madrid University PIF grant to Carlos E. Chavez.


  1. 1.
    Álvarez, D., Alonso-Atienza, F., Rojo-Álvarez, J.L., García-Alberola, A., Moscoso, M.: Shape reconstruction of cardiac ischemia from non-contact intracardiac recordings: a model study. Math. Comput. Model. 55, 1770–1781 (2012)zbMATHCrossRefGoogle Scholar
  2. 2.
    Berger, T., Fischer, G., Pfeifer, B., Modre, R., Hanser, F., Trieb, T., Roithinger, F.X., Stuehlinger, M., Pachinger, O., Tilg, B., Hintringer, F.: Single-beat noninvasive imaging of cardiac electrophysiology of ventricular pre-excitation. J. Am. Coll. Cardiol. 48(10), 2045–2052 (2006). Focus issue: Cardiac. ImagingCrossRefGoogle Scholar
  3. 3.
    Brooks, D.H., Ahmad, G.F., MacLeod, R.S., Maratos, G.M.: Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE Trans. Biomed. Eng. 46(1), 3–18 (1999)CrossRefGoogle Scholar
  4. 4.
    Chávez, C., Alonzo-Atienza, F., Alvarez, D.: Avoiding the inverse crime in the inverse problem of electrocardiography: estimating the shape and location of cardiac ischemia. In: Computing in Cardiology Conference (CinC), pp. 687–690, September 2013Google Scholar
  5. 5.
    Farina, D., Dossel, O.: Model-based approach to the localization of infarction. In: Computers in Cardiology, pp. 173–176, 30 September 2007–3 October 2007Google Scholar
  6. 6.
    Geuzaine, C., Remacle, J.F.: Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309–1331 (2009). zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Greensite, F., Huiskamp, G.: An improved method for estimating epicardial potentials from the body surface. IEEE Trans. Biomed. Eng. 45(1), 98–104 (1998)CrossRefGoogle Scholar
  8. 8.
    Gulrajani, R.M.: The forward and inverse problems of electrocardiography. IEEE Eng. Med. Biol. Mag. 17(5), 84–101 (1998)CrossRefGoogle Scholar
  9. 9.
    Huiskamp, G., Van Oosterom, A.: The depolarization sequence of the human heart surface computed from measured body surface potentials. IEEE Trans. Biomed. Eng. 35(12), 1047–1058 (1988)CrossRefGoogle Scholar
  10. 10.
    Lazzara, R., El-Sherif, N., Hope, R.R., Scherlag, B.J.: Ventricular arrhythmias and electrophysiological consequences of myocardial ischemia and infarction. Circ. Res. 42(6), 740–749 (1978). CrossRefGoogle Scholar
  11. 11.
    Li, G., He, B.: Non-invasive estimation of myocardial infarction by means of a heart-model-based imaging approach: a simulation study. Med. Biol. Eng. Comput. 42(1), 128–136 (2004)CrossRefGoogle Scholar
  12. 12.
    MacLachlan, M.C., Nielsen, B.F., Lysaker, M., Tveito, A.: Computing the size and location of myocardial ischemia using measurements of ST-segment shift. IEEE Trans. Biomed. Eng. 53(6), 1024–1031 (2006)CrossRefGoogle Scholar
  13. 13.
    Malmivuo, J., Plonsey, R.: Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields, 1st edn. Oxford University Press, Oxford (1995)CrossRefGoogle Scholar
  14. 14.
    Mitchell, C.C., Schaeffer, D.G.: A two-current model for the dynamics of cardiac membrane. Bull. Math. Biol. 65(5), 767–793 (2003)CrossRefGoogle Scholar
  15. 15.
    Nielsen, B., Lysaker, M., Grottum, P.: Computing ischemic regions in the heart with the bidomain model; first steps towards validation. IEEE Trans. Med. Imaging 32(6), 1085–1096 (2013)CrossRefGoogle Scholar
  16. 16.
    van Oosterom, A., Jacquemet, V.: Genesis of the P wave: atrial signals as generated by the equivalent double layer source model. Europace 7(s2), S21–S29 (2005)CrossRefGoogle Scholar
  17. 17.
    Rudy, Y.: Noninvasive electrocardiographic imaging of arrhythmogenic substrates in humans. Circ. Res. 112(5), 863–874 (2013)CrossRefGoogle Scholar
  18. 18.
    Ruud, T., Nielsen, B., Lysaker, M., Sundnes, J.: A computationally efficient method for determining the size and location of myocardial ischemia. IEEE Trans. Biomed. Eng. 56(2), 263–272 (2009)CrossRefGoogle Scholar
  19. 19.
    Shah, A.J., Hocini, M., Pascale, P., Roten, L., Komatsu, Y., Daly, M., Ramoul, K., Denis, A., Derval, N., Sacher, F., Dubois, R., Bokan, R., Eliatou, S., Strom, M., Ramanathan, C., Jais, P., Ritter, P., Haissaguerre, M.: Body surface electrocardiographic mapping for non-invasive identification of arrhythmic sources. Arrhythm. Electrophysiol. Rev. 2(1), 16–22 (2013)CrossRefGoogle Scholar
  20. 20.
    Tokuda, M., Tedrow, U.B., Inada, K., Reichlin, T., Michaud, G.F., John, R.M., Epstein, L.M., Stevenson, W.G.: Direct comparison of adjacent endocardial and epicardial electrograms: implications for substrate mapping. J. Am. Hear. Assoc. 2(2), e000215 (2013). Google Scholar
  21. 21.
    Trénor, B., Romero, L., Ferrero Jr., J.M., Sáiz, J., Moltó, G., Alonso, J.M.: Vulnerability to reentry in a regionally ischemic tissue: a simulation study. Ann. Biomed. Eng. 35(10), 1756–1770 (2007)CrossRefGoogle Scholar
  22. 22.
    Wang, D., Kirby, R.M., MacLeod, R.S., Johnson, C.R.: Inverse electrocardiographic source localization of ischemia: an optimization framework and finite element solution. J. Comput. Phys. 250, 403–424 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Carlos Eduardo Chávez
    • 1
    Email author
  • Nejib Zemzemi
    • 2
    • 3
  • Yves Coudière
    • 2
    • 3
  • Felipe Alonso-Atienza
    • 4
  • Diego Álvarez
    • 1
  1. 1.University Carlos III of MadridLeganésSpain
  2. 2.INRIA Bordeaux - Soud-OuestBordeauxFrance
  3. 3.Electrophysiology and Heart Modeling Institute (IHU LIRYC)BordeauxFrance
  4. 4.University Rey Juan CarlosFuenlabradaSpain

Personalised recommendations