Advertisement

Geometrical Modelling of the Fibre Organization in the Human Left Ventricle

  • Ayman Mourad
  • Luc Biard
  • Denis Caillerie
  • Pierre-Simon Jouk
  • Annie Raoult
  • Nicolas Szafran
  • Yves Usson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2230)

Abstract

The aim of the present study is to check, by means of elementary mathematical tools, a conjecture according to which myocardial fibres are geodesic curves running on some surfaces. This conjecture was first stated and experimentally checked by Streeter (1979) for the equatorial part of the left ventricle free wall. Quantitative polarized light microscopy provides measurements on fibre orientation that could lead to evidence that the conjecture remains true for the whole of the left ventricle. Study of the right ventricle is under progress.

Keywords

Left Ventricle Geodesic Curve Fibre Organization Regular Curve Periodic Geodesic 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Cai H. (1998)-Loi de comportement en grandes déformations du muscle à fibres actives. Application à la mécanique du coeur humain et à sa croissance, Thèse de l’Université de Savoie.Google Scholar
  2. [2]
    Do Carmo M.P. (1976)-Differential geometry of curves and surfaces, Prentice-Hall.Google Scholar
  3. [3]
    Hutchins G.M. et al (1978)-Shape of the human cardiac ventricles, Am. J. Cardiol., Vol. 41, pp. 646–654.CrossRefGoogle Scholar
  4. [4]
    Jouk P.S., Usson Y., Michalowicz G., and Parazza F. (1995)-Mapping of the orientation of myocardial cells by means of polarized light and confocal scanning laser microscopy, Microsc. Res. Tech., Vol. 30, pp. 480–490.CrossRefGoogle Scholar
  5. [5]
    Jouk P.S., Usson Y., Michalowicz G., and Grossi L. (2000)-Three-dimensional cartography of the pattern of the myofibres in the second trimester fetal human heart, Anat. Embryol., Vol. 202, pp. 103–118.CrossRefGoogle Scholar
  6. [6]
    Hopf H., Rinow W. (1931)-Über den Begriff der vollständigen differentialgeometrischen Flächen, Comm. Math. Helv., Vol. 3, pp. 209–225.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Ohayon J., Usson Y., Jouk P.S., and Cai H. (1998)-Fibre orientation in human fetal heart and ventricular mechanics: A small perturbation analysis, Comput. Methods Biomechanics Biomedic. Eng., Vol. 2, pp. 83–105.CrossRefGoogle Scholar
  8. [8]
    Sanchez-Quintana D., Garcia-Martinez V., Climent V., and Hurle J.M. (1995)-Morphological changes in the normal pattern of ventricular myoarchitecture in the developing human heart, Anat. Rec., Vol. 243, pp. 483–495.CrossRefGoogle Scholar
  9. [9]
    Streeter D.D. (1979)-Gross morphology and fiber geometry of the heart, in Handbook of Physiology. The cardiovascular system, Berne R.M., Sperelakis N., Geiger S.R. eds, Am. Phys. Soc., Williams & Wilkins, Baltimore.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ayman Mourad
    • 1
    • 2
  • Luc Biard
    • 2
  • Denis Caillerie
    • 1
  • Pierre-Simon Jouk
    • 3
    • 4
  • Annie Raoult
    • 2
  • Nicolas Szafran
    • 2
  • Yves Usson
    • 3
  1. 1.Laboratoire Sols, Solides, StructuresGrenoble Cedex 9France
  2. 2.Laboratoire de Modélisation et Calcul/IMAGGrenoble Cedex 9France
  3. 3.Laboratoire TIMCDomaine de de la MerciLa Tronche CedexFrance
  4. 4.Unité fonctionnelle Biologie du développement et Génétique cliniqueGrenoble Cedex 9France

Personalised recommendations