A Method to Reconstruct Activation Wavefronts Without Isotropy Assumptions Using a Level Sets Approach

  • Felipe Calderero
  • Alireza Ghodrati
  • Dana H. Brooks
  • Gilead Tadmor
  • Rob MacLeod
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3504)


We report on an investigation into using a Level Sets based method to reconstruct activation wavefronts at each time instant from measured potentials on the body surface. The potential map on the epicardium is approximated by a two level image and the inverse problem is solved by evolving a boundary, starting from an initial region, such that a filtered residual error is minimized. The advantage of this method over standard activation-based solutions is that no isotropy assumptions are required. We discuss modifications of the Level Sets method used to improve accuracy, and show the promise of this method via simulation results using recorded canine epicardial data.


Time Instant Residual Error Singular Vector Isotropy Assumption Speed Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brooks, D.H., MacLeod, R.S.: Electrical Imaging of the Heart: Electrophysical Underpinnings and Signal Processing Opportunities. IEEE Sig. Proc. Mag. 14(1), 24–42 (1997)CrossRefGoogle Scholar
  2. 2.
    Rudy, Y., Messinger-Rapport, B.: The inverse problem of electrocardiography. Solutions in terms of epicardial potentials. CRC Crit. Rev. Biomed. Eng. 16, 215–268 (1988)Google Scholar
  3. 3.
    Huiskamp, G.J.M., van Oosterom, A.: The depolarization sequence of the human heart surface computed from measured body surface potentials. IEEE Trans. Biomed. Eng. BME35, 1047–1058 (1988)CrossRefGoogle Scholar
  4. 4.
    Huiskamp, G.J.M., Greensite, F.S.: A new method for myocardial activation imaging. IEEE Trans. Biomed. Eng. 44, 433–446 (1997)CrossRefGoogle Scholar
  5. 5.
    Pullan, A.J., Cheng, L.K., Nash, M.P., Bradley, C.P., Paterson, D.J.: Noninvasive electrical imaging of the heart: theory and model development. Annals of Biomedical Eng. 29(10), 817–836 (2001)CrossRefGoogle Scholar
  6. 6.
    Oostendorp, T., Macleod, R.S., van Oosterom, A.: Non-invasive determination of the activation sequence of the heart: Validation with invasive data. In: Proc. IEEE Int. Conf. Eng. in Med. and Biol. Soc. (1997)Google Scholar
  7. 7.
    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
  8. 8.
    Messnarz, B., Tilg, B., Modre, R., Fischer, G., Hanser, F.: A new spatiotemporal regularization approach for reconstruction of cardiac transmembrane potential patterns. IEEE Trans. Biomed. Eng. 51(2), 273–281 (2004)CrossRefGoogle Scholar
  9. 9.
    Santosa, F.: A Level-Set Approach for Inverse Problems Involving Obstacles. ESAIM: Control, Optimisation and Calculus of Variations 1, 17–33 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Osher, S., Sethian, J.A.: Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. Journal of Computational Physics 79, 12–49 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods, 2nd edn. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  12. 12.
    MacLeod, R.S., Ni, Q., Punske, B., Ershler, P.R., Yilmaz, B., Taccardi, B.: Effects of Heart Position on the Body-Surface ECG. J. Electrocardiol. 33(suppl.), 229–237 (2000)CrossRefGoogle Scholar
  13. 13.
    MacLeod, R.S., Johnson, C.R.: Map3d: Interactive scientific visualization for bioengineering data. In: Proc. Int. Conf. IEEE Eng. Med. Bio. Soc., pp. 30–31 (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Felipe Calderero
    • 1
  • Alireza Ghodrati
    • 2
  • Dana H. Brooks
    • 2
  • Gilead Tadmor
    • 2
  • Rob MacLeod
    • 3
  1. 1.Department of Signal Theory and CommunicationsTechnical University of Catalonia (UPC)BarcelonaSpain
  2. 2.Department of Electrical and Computer EngineeringNortheastern UniversityBostonUSA
  3. 3.Nora Eccles Harrison Cardiovascular Research and Training Institute (CVRTI)University of UtahSalt Lake CityUSA

Personalised recommendations