Long term durability of osseointegrated implants depends on bone adaptation to stress and strain occurring in proximity of the prosthesis. Mechanical overloading, as well as disuse, may reduce the stability of implants by provoking bone resorption. However, an appropriate mechanical environment can improve integration. Several studies have focused on the definition of numerical methods to predict bone peri-implant adaptation to the mechanical environment. Existing adaptation models differ notably in the type of mechanical variable adopted as stimulus but also in the bounds and shape of the adaptation rate equation. However, a general comparison of the different approaches on a common benchmark case is still missing and general guidelines to determine physically sound parameters still need to be developed. This current work addresses these themes in two steps. Firstly, the histograms of effective stress, strain and strain energy density are compared for rat tibiae in physiological (homeostatic) conditions. According to the Mechanostat, the ideal stimulus should present a clearly defined, position and tissue invariant lazy zone in homeostatic conditions. Our results highlight that only the octahedral shear strain presents this characteristic and can thus be considered the optimal choice for implementation of a continuum level bone adaptation model. Secondly, critical modeling parameters such as lazy zone bounds, type of rate equation and bone overloading response are classified depending on their influence on the numerical predictions of bone adaptation. Guidelines are proposed to establish the dominant model parameters based on experimental and simulated data.