Accepted:
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/vol04/STAUB-paper1/ | © Copyright 1997 | |||
| Volume 04 | Received: Accepted: |
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A Reaction-Diffusion Model for Trabecular Architecture of Embryonic Periosteal Long Bone
Bruno Courtin, Anne-M. Perault-Staub, Jean-F. Staub |
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| Abstract | |
| Numerical study of a reaction-diffusion model related to bone mineral metabolism reveals complex spatio-temporal behaviour in the vicinity of a Turing bifurcation. When these nonstationary patterns are explored in numerical experiments chosen for their biological relevance (size, geometry and growth of the two-dimensional reaction-diffusion space, random variations in parameter values), 3-D images and 2-D cross-sections of predicted spatial self-organisations can be produced as a time-record of the dynamic behaviour of the model with time being assimilated as an additional space dimension. Such images present striking analogies with the internal architecture of primary periosteal long bone. Our results suggest that dynamic properties of solute mineral species, intermediary between crystalline solid phase and solute parent ions, may play a major role not only, as previously reported, in the temporal self-organisation of bone mineral metabolism, but also in the emergence of the heterogeneous trabecular architecture typical of periosteal bone, at least during the first steps of embryonic bone development. | |
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