Personalization of Cardiac Fiber Orientations from Image Data Using the Unscented Kalman Filter

  • Andreas Nagler
  • Cristóbal Bertoglio
  • Michael Gee
  • Wolfgang Wall
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7945)


In this work, we propose to estimate rule-based myocardial fiber model (RBM) parameters from measured image data, with the goal of personalizing the fiber architecture for cardiac simulations. We first describe the RBM, which is based on a space-dependent angle distribution on the heart surface and then extended to the whole domain through an harmonic lifting of the fiber vectors. We then present a static Unscented Kalman Filter which we use for estimating the degrees of freedom of the fiber model. We illustrate the methodology using noisy synthetic data on a real heart geometry, as well as real DT-MRI-derived fiber data. We also show the impact of different fiber distributions on cardiac contraction simulations.


Unscented Kalman Filter Fiber Distribution Rule Base Model Fiber Model Contraction Pattern 
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.
    Streeter, D.D., Spotnitz, H.M., Patel, D.P., Ross, J., Sonnenblick, E.H.: Fiber orientation in the canine left ventricle during diastole and systole. Circulation Research 24(3), 339–347 (1969)CrossRefGoogle Scholar
  2. 2.
    Armour, J., Randall, W.: Structural basis for cardiac function. American Journal of Physiology – Legacy Content 218(6), 1517–1523 (1970)Google Scholar
  3. 3.
    Greenbaum, R.A., Ho, S.Y., Gibson, D.G., Becker, A.E., Anderson, R.H.: Left ventricular fibre architecture in man. British Heart Journal 45(3), 248–263 (1981)CrossRefGoogle Scholar
  4. 4.
    LeGrice, I.J., Smaill, B.H., Chai, L.Z., Edgar, S.G., Gavin, J.B., Hunter, P.J.: Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. American Journal of Physiology - Heart and Circulatory Physiology 269(2), H571–H582 (1995)Google Scholar
  5. 5.
    Potse, M., Dube, B., Richer, J., Vinet, A., Gulrajani, R.: A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng. 53, 2425–2435 (2006)CrossRefGoogle Scholar
  6. 6.
    Chapelle, D., Fernández, M.A., Gerbeau, J.-F., Moireau, P., Sainte-Marie, J., Zemzemi, N.: Numerical simulation of the electromechanical activity of the heart. In: Ayache, N., Delingette, H., Sermesant, M. (eds.) FIMH 2009. LNCS, vol. 5528, pp. 357–365. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Wong, J., Kuhl, E.: Generating fibre orientation maps in human heart models using poisson interpolation. Computer Methods in Biomechanics and Biomedical Engineering, 1–10, PMID: 23210529 (2012)Google Scholar
  8. 8.
    Bayer, J., Blake, R., Plank, G., Trayanova, N.: A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Annals of Biomedical Engineering 40, 2243–2254 (2012)CrossRefGoogle Scholar
  9. 9.
    Goektepe, S., Kuhl, E.: Electromechanics of the heart: a unified approach to the strongly coupled excitation contraction problem. Computational Mechanics 45, 227–243 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Chabiniok, R., Moireau, P., Lesault, P.F., Rahmouni, A., Deux, J.F., Chapelle, D.: Estimation of tissue contractility from cardiac cine-mri using a biomechanical heart model. Biomechanics and Modeling in Mechanobiology, 1–22 (2011), doi:10.1007/s10237-011-0337-8Google Scholar
  11. 11.
    Xi, J., Lamata, P., Niederer, S., Land, S., Shi, W., Zhuang, X., Ourselin, S., Duckett, S.G., Shetty, A.K., Rinaldi, C.A., Rueckert, D., Razavi, R., Smith, N.P.: The estimation of patient-specific cardiac diastolic functions from clinical measurements. Medical Image Analysis (2012)Google Scholar
  12. 12.
    Lafortune, P., Ars, R., Vázquez, M., Houzeaux, G.: Coupled electromechanical model of the heart: Parallel finite element formulation. International Journal for Numerical Methods in Biomedical Engineering 28(1), 72–86 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Basser, P., Mattiello, J., Lebihan, D.: Estimation of the effective self-diffusion tensor from the nmr spin echo. Journal of Magnetic Resonance, Series B 103(3), 247–254 (1994)CrossRefGoogle Scholar
  14. 14.
    Hsu, E.W., Muzikant, A.L., Matulevicius, S.A., Penland, R.C., Henriquez, C.S.: Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. American Journal of Physiology - Heart and Circulatory Physiology 274(5), H1627–H1634 (1998)Google Scholar
  15. 15.
    Scollan, D.F., Holmes, A., Winslow, R., Forder, J.: Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. American Journal of Physiology - Heart and Circulatory Physiology 275(6), H2308–H2318 (1998)Google Scholar
  16. 16.
    Helm, P., Beg, M.F., Miller, M.I., Winslow, R.L.: Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging. Annals of the New York Academy of Sciences 1047(1), 296–307 (2005)Google Scholar
  17. 17.
    Helm, P.A., Tseng, H.J., Younes, L., McVeigh, E.R., Winslow, R.L.: Ex vivo 3D diffusion tensor imaging and quantification of cardiac laminar structure. Magnetic Resonance in Medicine 54(4), 850–859 (2005)Google Scholar
  18. 18.
    Lombaert, H., Peyrat, J., Croisille, P., Rapacchi, S., Fanton, L., Cheriet, F., Clarysse, P., Magnin, I., Delingette, H., Ayache, N.: Human atlas of the cardiac fiber architecture: study on a healthy population. IEEE Transactions on Medical Imaging 31(7), 1436–1447 (2012)CrossRefGoogle Scholar
  19. 19.
    Gamper, U., Boesiger, P., Kozerke, S.: Diffusion imaging of the in vivo heart using spin echoes considerations on bulk motion sensitivity. Magnetic Resonance in Medicine 57(2), 331–337 (2007)CrossRefGoogle Scholar
  20. 20.
    Toussaint, N., Sermesant, M., Stoeck, C.T., Kozerke, S., Batchelor, P.G.: in vivo human 3D cardiac fibre architecture: Reconstruction using curvilinear interpolation of diffusion tensor images. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010, Part I. LNCS, vol. 6361, pp. 418–425. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Moireau, P., Chapelle, D.: Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems. COCV 17, 380–405 (2011), doi:10.1051/cocv/2010006Google Scholar
  22. 22.
    Julier, S., Uhlmann, J., Durrant-Whyte, H.: A new approach for filtering nonlinear systems. In: American Control Conference, pp. 1628–1632 (1995)Google Scholar
  23. 23.
    Julier, S., Uhlmann, J., Durrant-Whyte, H.: A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control 45(3), 477–482 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Pham, D.-T., Verron, J., Gourdeau, L.: Filtres de Kalman singuliers évolutifs pour l’assimilation de données en océanographie. Comptes Rendus de l’Académie des Sciences - Series IIA 326(4), 255–260 (1998)Google Scholar
  25. 25.
    Hoteit, I., Pham, D.-T., Blum, J.: A simplified reduced order Kalman filtering and application to altimetric data assimilation in Tropical Pacific. Journal of Marine Systems 36(1–2), 101–127 (2002)CrossRefGoogle Scholar
  26. 26.
    Geuzaine, C., Remacle, J.F.: Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 79(11), 1309–1331 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Sainte-Marie, J., Chapelle, D., Cimrman, R., Sorine, M.: Modeling and estimation of the cardiac electromechanical activity. Computers & Structures 84(28), 1743–1759 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andreas Nagler
    • 1
  • Cristóbal Bertoglio
    • 1
  • Michael Gee
    • 2
  • Wolfgang Wall
    • 1
  1. 1.Institute for Computational MechanicsTechnische Universität MünchenGermany
  2. 2.Mechanics & High Performance Computing GroupTechnische Universität MünchenGermany

Personalised recommendations