Mechanical in-silico modeling of orthodontic tooth movement: A review of the boundary value problem

Orthodontic tooth movement allows clinicians to modify tooth position and functionality using a mechanical stimulus, which makes reliable mechanical models highly beneficial for predictive tasks and virtual parameter studies. Several individual advancements over the last few decades have identified challenges within this system of multiple constituents. This work aims at providing a thorough review from the mechanical perspective. It specifically reviews and discusses the mechanical boundary value problem in terms of geometry, loads, and material behavior. Characteristic values of the involved loads and material models are summarized. Clinical key features of the treatment process then highlight the link between the mechanical and the clinical perspective, underlining the relevance of variability in patients and treatment. Future perspectives can be guided by practical assessment of model sensitivity, data uncertainty, and the coupling to non-mechanical fields.