Comparative Evaluation of Mathematical Model and In Vivo Study of Calcium Phosphate Bone Grafts

One of the key factors of the interaction ‘osteoplastic material—organism’ is the state of the implant surface. Taking into account the fact that the equilibrium in regeneration conditions is reached only after the reparative histogenesis process is completed, the implant surface is constantly modified. This work is devoted to the numerical description of the dynamic bilateral material–medium interaction under close to physiological conditions, as well as to the assessment of the comparability of the model with in vitro and in vivo experimental results. The semi-empirical model obtained on the basis of chemical kinetics allows us to describe numerically the processes occurring in the in vitro systems and extrapolates well to assess the behavior of dicalcium phosphate dihydrate (DCPD) material under conditions of ectopic (subcutaneous) implantation in Wistar rats. It is shown that an experiment conducted using a perfusion–diffusion bioreactor in a cell culture medium with the addition of fetal bovine serum (FBS) allows for achieving morphologically and chemically identical changes in the surface of the material in comparison with the real organism. This fact opens up wide possibilities for the creation of an analog of a ‘laboratory-on-a-chip’ and the transition from classical in vivo models to more controlled and mathematically based in vitro systems.