Acta Biotheoretica

, Volume 43, Issue 4, pp 373–386 | Cite as

Spatio-temporal self-organization of bone mineral metabolism and trabecular structure of primary bone

  • B. Courtin
  • A. -M. Perault-Staub
  • J. -F. Staub


A nonlinear two-variable reaction-diffusion model of bone mineral metabolism, built from an overall self-oscillatory compartmental model of calcium metabolism in vivo, has been studied for its ability to generate spatial and spatio-temporal self-organizations in a two-dimensional space. Analytical and numerical results confirm the theoretical properties previously described for this kind of model. In particular, it is shown that, for a given set of reactional parameter values and certain values of the ratio of the two diffusion coefficients, there exists a set of unstable wavenumbers leading spontaneously to the development, from the homogeneous steady state, of either different types of stationary spatial patterns (hexagonal, striped and re-entrant hexagonal patterns) or more or less complex spatio-temporal expressions. We discuss the relevance of analogies established between some spatial or spatio-temporal structures predicted by the model and some peculiar features of the primary bone trabecular architecture which appear during embryonic ossification.


Diffusion Coefficient Spatial Pattern Compartmental Model Reactional Parameter Peculiar Feature 
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.


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • B. Courtin
    • 1
  • A. -M. Perault-Staub
    • 1
  • J. -F. Staub
    • 1
  1. 1.CNRS URA 1432LRO, Faculté de Médecine Lariboisière-Saint-LouisParisFrance

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