Spatio-temporal self-organization of bone mineral metabolism and trabecular structure of primary bone.
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.
Courtin
B
B
Faculte de Medecine Lariboisiere-Saint-Louis, Paris, France.
Perault-Staub
A M
AM
Staub
J F
JF
D000818:Animals; D015519:Bone Density / Q000502:physiology*; D001842:Bone and Bones / Q000033:anatomy & histology*; D002118:Calcium / Q000378:metabolism; D004058:Diffusion; D007091:Image Processing, Computer-Assisted; D016014:Linear Models; D010012:Osteogenesis / Q000502:physiology; D051381:Rats
D002118:Calcium