Optimum force magnitude for orthodontic tooth movement: A mathematic model

The aim of this study was to develop a mathematic model to describe the relationship between magnitude of applied force and rate of orthodontic tooth movement. Initially, data were extracted from experimental studies in dogs (beagles), in which controlled, standardized forces were used to move mandibular second premolars distally. Curve-fitting by nonlinear regression analysis provided an equation describing the relationship between force magnitude and rate of tooth movement in beagles. A similar equation was subsequently used to analyze the limited available data from the literature on human canine retraction. The maximum rates of tooth movement in humans and dogs are very similar. A threshold for force magnitude that would switch on tooth movement could not be defined. The model showed that a wide range of forces can be identified, all of which lead to a maximum rate of tooth movement.