Effective Estimation in Cardiac Modelling

  • Philippe Moireau
  • Dominique Chapelle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4466)


We present a novel strategy to perform estimation for a mechanical system defined to feature the same essential characteristics as a heart model, using measurements of a type that is available in medical imaging. We adopt a sequential approach, and the joint state-parameter estimation procedure is constructed based on a robust and effective state estimator inspired from collocated feedback control. The convergence of the resulting joint estimator can be mathematically established, and we demonstrate its effectiveness by identifying localized contractility and stiffness parameters in a test problem representative of cardiac behavior and using synthetic –albeit realistic –measurements.


State Estimation Adjoint State Parameter Convergence Contractility Parameter Cardiac Modelling 
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  1. 1.
    Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice-Hall, Englewood Cliffs (1979)zbMATHGoogle Scholar
  2. 2.
    Augenstein, K.F., Cowan, B.R., LeGrice, I.J., Young, A.A.: Estimation of cardiac hyperelastic material properties from MRI tissue tagging and diffusion tensor imaging. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 628–635. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Bardos, C., Lebeau, G., Rauch, J.: Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30(5), 1024–1065 (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bensoussan, A.: Filtrage optimal des systèmes linéaires. Dunod (1971)Google Scholar
  5. 5.
    Collet, M., Walter, V., Delobelle, P.: Active damping of a micro-cantilever piezo-composite beam. J. Sound Vibration 260(3), 453–476 (2003)CrossRefGoogle Scholar
  6. 6.
    Cox, S., Zuazua, E.: The rate at which energy decays in a damped string. Comm. Partial Differential Equations 19(1-2), 213–243 (1994)zbMATHCrossRefGoogle Scholar
  7. 7.
    Duan, Q., Moireau, P., Angelini, E., Chapelle, D.: Simulation of 3D ultrasound with a realistic electro-mechanical model of the heart. In: Sachse, F.B., Seemann, G. (eds.) FIMH 2007. LNCS, vol. 4466, pp. 463–473. Springer, Berlin Heidelberg (2007)Google Scholar
  8. 8.
    Hunter, P.J., McCulloch, A.D., ter Keurs, H.E.D.: Modelling the mechanical properties of cardiac muscle. Progress in Biophysics and Molecular Biology. 69, 289–331 (1998)CrossRefGoogle Scholar
  9. 9.
    Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory. ASME Trans.–Journal of Basic Engineering 83(Series D), 95–108 (1961)Google Scholar
  10. 10.
    Lions, J.-L.: Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. (Tome 1), of Recherches en Mathématiques Appliquées [Research in Applied Mathematics]. Masson, Paris, vol. 8 (1988)Google Scholar
  11. 11.
    Moireau, Ph., Chapelle, C., Le Tallec, P.: Joint state and parameter estimation for distributed mechanical systems. Submitted to CMAME.Google Scholar
  12. 12.
    Pham, D.T., Verron, J., Roubeaud, M.C.: A singular evolutive interpolated kalman filter for data assimilation in oceanography. J. Marine Systems 16, 323–341 (1997)CrossRefGoogle Scholar
  13. 13.
    Preumont, A.: Vibration Control of Active Structures, An Introduction, 2nd edn. Kluwer Academic Publishers, Boston (2002)zbMATHGoogle Scholar
  14. 14.
    Sainte-Marie, J., Chapelle, D., Cimrman, R., Sorine, M.: Modeling and estimation of the cardiac electromechanical activity. Comp. & Struct. 84, 1743–1759 (2006)CrossRefGoogle Scholar
  15. 15.
    Tong, S., Shi, P.: Cardiac motion recovery: Continuous dynamics, discrete measurements, and optimal estimation. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 744–751. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Zhang, Q., Clavel, A.: Adaptive observer with exponential forgetting factor for linear time varying systems. In: Decision and Control, 2001. Proceedings of the 40th IEEE Conference on, vol. 4, Orlando, FL, USA, pp. 3886–3891 (2001)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Philippe Moireau
    • 1
  • Dominique Chapelle
    • 1
  1. 1.INRIA, MACS team, B.P.105, 78153 Le Chesnay cedexFrance

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