Model of Mechanical Interaction of Mesenchyme and Epithelium in Living Tissues

  • Jiří Kroc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3994)

Abstract

Developmental biology describes how tissues, organs, and bodies are made from living cells. There exists a large body of biological data about developmental processes but there is still not ultimate understanding of how the whole orchestra of all involved processes is working. It is the place where mathematical modelling could help to create biologically relevant models of morphological development. The morphological development could be mathematically decomposed into three distinct but mutually interconnected parts, namely to mechanical response of tissues, signalling by chemicals, and switching of cells into different types by a gene regulatory network. This paper is focussed to the part dealing with mechanical interaction of growing mesenchyme and epithelium within a living tissue modelled by a set of nodes interconnected by deformable bars as in tensegrity models.

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References

  1. 1.
    Toffoli, T., Margolus, N.: Cellular Automata Theory. MIT Press, Cambridge (1987)Google Scholar
  2. 2.
    Ilachinski, A.: Cellular Automata: A Discrete Universe. World Scientific Publishing Co. Pte. Ltd., New Jersey (2001)MATHGoogle Scholar
  3. 3.
    Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champaign (2002)MATHGoogle Scholar
  4. 4.
    Ingber, D.E.: The architecture of life. Scientific American 278(1), 48–57 (1998)CrossRefGoogle Scholar
  5. 5.
    Ingber, D.E., Heidemann, S.R., Lamoreux, P., Buxbaum, R.E.: Opposing views on tensegrity as a structural framework for understanding cell mechanics. J. Appl. Physiol. 89(4), 1663–1670 (2000)Google Scholar
  6. 6.
    Lamoreux, P., Heidemann, S.R., Buxbaum, R.E.: Opposing views on tensegrity as a structural framework for understanding cell mechanics. J. Appl. Physiol. 89, 1670–1674 (2000)Google Scholar
  7. 7.
    Ingber, D.E.: Opposing views on tensegrity as a structural framework for understanding cell mechanics - rebuttals. J. Appl. Physiol. 89, 1674–1677 (2000)Google Scholar
  8. 8.
    Ingber, D.E., Heidemann, S.R., Lamoreux, P., Buxbaum, R.E.: Opposing views on tensegrity as a structural framework for understanding cell mechanics - rebuttals. J. Appl. Physiol. 89, 1677–1678 (2000)Google Scholar
  9. 9.
    Hajela, P., Kim, B.: On the use of energy minimization for ca based analysis in elasticity. Struct. Multidisc. Optim. 23, 24–33 (2001)CrossRefGoogle Scholar
  10. 10.
    Kita, E., Toyoda, T.: Structural design using cellular automata. Struct. Multidisc. Optim. 19, 64–73 (2000)CrossRefGoogle Scholar
  11. 11.
    Gurdal, Z., Tatting, B.: Cellular automata for design of truss structures with linear and nonlinear response. In: 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, September 2000, pp. 1–11. American Institute for Aeronautics and Astronautics (2000)Google Scholar
  12. 12.
    Pilot, F., Lecuit, T.: Compartmentalized morphogenesis in epithelia: From cell to tissue shape. Developmental Dynamics 232(3), 685–694 (2005)CrossRefGoogle Scholar
  13. 13.
    Hay, E.D.: The mesenchymal cell, its role in the embryo, and the remarkable signaling mechanisms that create it. Developmental Dynamics 233(3), 706–720 (2005)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Ball, E.M.A., Risbridger, G.P.: Activins as regulators of branching morphogenesis. Developmental Biology 238(1), 1–12 (2001)CrossRefGoogle Scholar
  15. 15.
    Heidemann, S.R., Wirtz, D.: Towards a regional approach to cell mechanics. TRENDS in Cell Biology 14(4), 160–166 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jiří Kroc
    • 1
  1. 1.Department of MechanicsUniversity of West Bohemia in PilsenPilsenCzech Republic

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