A bone-remodelling scheme based on principal strains applied to a tooth during translation

This paper investigates the role of principal strains within the periodontal ligament (PDL) during bone remodelling in orthodontics and particularly in the case of bodily motion (pure translation). Using analytical formulas of stress and strains within the PDL for the particular case of a paraboloidal central incisor during translation, the strains are directly related to the motion of the interface between the alveolar bone and the PDL, called bone surface. It is shown that both normal and shear strains within the PDL are of the same importance for bone surface motion. Moreover, both "mean average" and "geometrical average" of principal strains within the PDL play a significant role in the bone remodelling process, as they contribute with the same proportionality. In summary, the proposed formulas differ than previous ones that had been successfully applied to describe remodelling within long bones. The proposed theory is also sustained by a linear finite element analysis.