A stochastic model is proposed to predict the intramembranous process in periprosthetic healing in the early post-operative period. The methodology was validated by a canine experimental model. In this first part, the effects of each individual uncertain biochemical factor on the bone-implant healing are examined, including the coefficient of osteoid synthesis, the coefficients of haptotactic and chemotactic migration of osteoblastic population and the radius of the drill hole. A multi-phase reactive model solved by an explicit finite difference scheme is combined with the polynomial chaos expansion to solve the stochastic system. In the second part, combined biochemical factors are considered to study a real configuration of clinical acts.