ABSTRACT
After an alteration of the physiological stress whithin bone, experimental studies reported some time-delay in bone adaptation. To study this phenomenon, a bone adaptation model including the stress history was developed. The model consisted in a first-order nonlinear integro-differential equation, coupled to the equilibrium partial differential equation. Existence, unicity and stability of the solutions were investigated and established. A finite element code was used to solve the equilibrium equation and a third order accuracy numerical scheme was developed to integrate the evolution law. The unknown parameters of the model were identified by using published clinical data. The model was then applied to analyse adaptation of bone after Total Hip Arthroplasty (THA). Two situations were compared: with and without stress history. In both cases, the density evolution converged approximately to the same values after one year but were notably different during the first two months. During this period, the use of the stress history induced a smooth and delayed bone response, which was more conform to clinical data.
