Theory of osteogenesis behavior based on calcium diffusion theory

Osteogenesis is completed by the nucleation mechanism on crystal nuclei formation and growth after amorphous calcium phostate accretion to collagen fibers. For nuclei formation, it is necessary to have preliminary ionic diffusion such as that of Ca²⁺ and PO₄³⁻ ions to this part. Therefore, promotion of ionic diffusion to this part is the first essential condition for osteogenesis. We have considered this phenomenon as the nucleation mechanism accompanied by preliminary diffusion behavior and shown the optimum mechanical condition on promoting this ionic diffusion.Furthermore, we noticed callus by callotasis as the typical example which fits this mechanical condition and investigated its histology. However, necking occurs at the site of callus sandwiched by cortical bones due to tensile stress, three axial tensile stress in radial and tangential directions, in addition to the tensile stress occurs at the netsection of the callus due to the constraint of cortical bones. Therefore, the size of pore along the collagen lamination and hole zone becomes large under this mechanical condition and ionic diffusion such as Ca²⁺, PO₄³⁻ is liable to occur at this part. By solving the partial differential equation of the stress-induced diffusion, diffusive particles are shown to concentrate at the high three axial tensile stress region. Therefore, a high concentrated region of Ca, PO⁴ is achieved and selective osteogenesis due to hydroxyapatite nucleation is considered to progress in this region. Histological investigation of the callus of rabbit showed that mineralization occurs at this site and supports the theory of stress-induced diffusion on osteogenesis behavior.