The objective of this research was to develop a purely biomechanical model, intended to predict the long-term secondary stability of the implant starting from the biomechanical stability immediately after the operation. A continuous rule- based adaptation scheme was formulated as a dynamic system, and the work verified if such a model produced unique and clinically meaningful solutions. It also investigated whether this continuous model provided results comparable with those of a simpler, discrete-states model used in a previous study. The proposed model showed stable convergence behaviour with all investigated initial conditions, with oscillatory behaviour limited to the first steps of the simulation. The results obtained with the wide range of initial conditions support the hypothesis of the existence and uniqueness of the solution for all initial conditions. The differences between the continuous model and the simpler and more efficient finite-states model were found to be extremely modest (less than 4% over the predicted bonded area). Because of these minimal differences, the use of the much faster finite-states model is recommended to investigate asymptotic conditions, and the continuous model described should be used to investigate the evolution over time of the adaptive process.
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