Advertisement

Biophysics

, Volume 60, Issue 6, pp 977–982 | Cite as

Mathematical modeling of the stretching-induced elongation of the embryonic epithelium layer in the absence of an external load

  • S. A. LogvenkovEmail author
  • A. A. Stein
Biophysics of Complex Systems

Abstract

The problem of deformation of a planar embryonic epithelium layer that is unloaded after a short period of uniaxial stretching with subsequent fixation in the stretched state for different periods of time is solved. The initial conditions for solving this problem are derived from the previously discussed problem of the uniform stretching of a tissue fragment (explant) with subsequent fixation of the obtained length. In this study we used the previously developed continuum model that describes the stress–strain state of epithelial tissue taking the parameters that characterize the shape of the cells and their stress state into account, as well as the active stresses they exert when they interact with each other. The experimentally observed continuation of the deformation of a stretched tissue after the external force has ceased to act is described theoretically as a result of active cell reactions to mechanical stress. The duration of explant fixation is shown to have a strong effect on its further elongation and on the pattern of cell activity.

Keywords

cell systems active media embryonic epithelium 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. A. Davidson, S. D. Joshi, H. Y. Kim, et al., J. Biomech. 43 (1), 63 (2010).CrossRefGoogle Scholar
  2. 2.
    N. N. Luchinskaya, L. V. Beloussov, and A. A. Shtein, Russ. J. Dev. Biol. 28 (2), 81 (1997).Google Scholar
  3. 3.
    L. V. Beloussov, N. N. Louchinskaia, and A. A. Stein, Dev. Gen. Evol. 210, 92 (2000).CrossRefGoogle Scholar
  4. 4.
    L. A. Taber, Biomech. Model. Mechanobiol. 7 (6), 427 (2008).CrossRefGoogle Scholar
  5. 5.
    L. A. Taber, Phil. Trans. R. Soc. A 367, 3555 (2009).CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. 6.
    P. Ciarletta, M. Amar, and M. Labouesse, Phil. Trans. R. Soc. A 367, 3379 (2009).CrossRefADSzbMATHGoogle Scholar
  7. 7.
    L. V. Beloussov, S. A. Logvenkov, and A. A. Shtein, Fluid Dyn., 50 (1) 1 (2015).CrossRefMathSciNetGoogle Scholar
  8. 8.
    L. E. Sedov, Introduction to the Mechanics of a Continuous Medium (Fizmatlit, Moscow, 1962; Addison–Wesley, Reading, MA, 1965).Google Scholar
  9. 9.
    A. N. Mansurov, A. A. Stein, and L. V. Beloussov, Biomech. Model. Mechanobiol. 11 (8) 1123 (2012).CrossRefGoogle Scholar
  10. 10.
    L. V. Beloussov, Phys. Biol. 5 (1) 015009 (2008).CrossRefADSGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Department of Higher MathematicsNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Institute of MechanicsMoscow State UniversityMoscowRussia

Personalised recommendations