Advertisement

Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

  • M. Boulakia
  • J-F. Gerbeau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6666)

Abstract

We consider the problem of estimating some parameters (like ionic models or parameters involved in the initial stimulation) of a model of electrocardiograms (ECG) from the data of the Einthoven leads. This problem can be viewed as a first attempt to identify or to locate a pathology. The direct model is based on the bidomain equations in the heart and a Poisson equation in the torso and. To keep the computational time reasonable, the evaluation of the direct problem is approximated with a reduced order model based on Proper Orthogonal Decomposition (POD). The optimization problem is solved using a genetic algorithm. Numerical tests show that, with noisy synthetic data, the proposed procedure allows to recover ionic parameters and initial activation regions with a fair accuracy.

References

  1. 1.
    Amsallem, D., Farhat, C.: Interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA Journal-American Institute of Aeronautics and Astronautics 46(7), 1803–1813 (2008)CrossRefGoogle Scholar
  2. 2.
    Boulakia, M., Cazeau, S., Fernández, M.A., Gerbeau, J.-F., Zemzemi, N.: Mathematical modeling of electrocardiograms: a numerical study. Ann. Biomed. Eng. 38(3), 1071–1097 (2010)CrossRefGoogle Scholar
  3. 3.
    Goldberg, D.E.: Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading (1989)zbMATHGoogle Scholar
  4. 4.
    Kunisch, K., Volkwein, S.: Galerkin proper orthogonal decomposition methods for parabolic problems. Numerische Mathematik 90(1), 117–148 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Mitchell, C.C., Schaeffer, D.G.: A two-current model for the dynamics of cardiac membrane. Bulletin Math. Bio. 65, 767–793 (2003)CrossRefzbMATHGoogle Scholar
  6. 6.
    Rathinam, M., Petzold, L.R.: A new look at proper orthogonal decomposition. SIAM Journal on Numerical Analysis 41(5), 1893–1925 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Sachse, F.B.: Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. Springer, Heidelberg (2004)CrossRefzbMATHGoogle Scholar
  8. 8.
    Sundnes, J., Lines, G.T., Cai, X., Nielsen, B.F., Mardal, K.-A., Tveito, A.: Computing the Electrical Activity in the Heart. Springer, Heidelberg (2006)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. Boulakia
    • 1
  • J-F. Gerbeau
    • 2
  1. 1.Université Pierre et Marie Curie-Paris 6, LJLLParisFrance
  2. 2.INRIA Paris-RocquencourtLe Chesnay CedexFrance

Personalised recommendations