Stochastic porous model of a bone-implant healing process using polynomial chaos expansion

Porous material is used in engineering and biomedical structures, where the solid phase is the frame of the material and dissipation effects occur in the pores of the material. This work proposes a stochastic model of porous material to predict the bone tissue healing process in the early period after the implantation surgery. The bone implant is assumed to be axisymmetric and the healing process is evaluated up to 8 weeks after the implantation, which is validated by the canine experiments. The porous dynamic model is coupled with biochemical equations to take into account the osteoblast cells migration and the growth factors diffusion. Using the polynomial chaos expansion method, the effects of uncertain biochemical factors on the distribution of the new-formed tissue around the bone implant are examined. Compared with Monte Carlo simulations, the stochastic model can obtain high accuracy with greatly improved computational cost. The spatial-temporal model presented here provides a tool to evaluate the highly complex implant healing process and the influences of different biochemical factors.