Origin of the pattern of trabecular bone: an experiment and a model

As a result of an experiment in which the development of a mineral phase in the rabbit embryo was observed, a model is proposed to explain the mechanism that controls the place of precipitation of crystals in mineralizing tissue. The reaction-diffusion equations for the specified compounds are formulated and solved. Among a variety of compounds the concentrations of carbon dioxide, oxygen, HCO-3 ions, H+ ions, calcium, and inorganic phosphorus are evaluated. CO2, HCO-3 ions, and H+ ions, are distinguished due to their key role in the maintenance of the pH value. The local concentration of oxygen is the pivot factor that controls the metabolic rate, i.e., production of CO2. Next the supersaturation was estimated on the basis of the calculated values of pH and the concentrations of calcium and inorganic phosphorus. It is assumed that the synthesis of the organic matrix breaks the metastable equilibrium with respect to spontaneous precipitation and leads to the deposition of minerals. It was found that the geometry of the vasculature determines the shape of primitive trabecular bone (woven bone) while the value of the diffusion coefficient may be the key factor indicating the possibility of mineralization under the control of a living organism.