Time-related PDL: viscoelastic response during initial orthodontic tooth movement of a tooth with functioning interproximal contact—A mathematical model

Most anteroposterior orthodontic movements of posterior teeth have to overcome the “resistance” of adjacent teeth with functioning interproximal contacts. The aim of this study was to develop a mathematical model describing initial posterior tooth movement associated with functioning interproximal contacts in relation to the viscoelastic mechanical behavior of the human periodontal ligament (PDL). A linear viscoelastic 2D mathematical model was modified to depict tipping movement around the center of rotation (Crot) of a premolar where tipping is restrained by adjacent teeth. Equilibrium equations were applied taking into account the sagittal moment developed around the Crot. The constants of the model were analyzed and applied to a numerical model that can simulate short-term tooth creep movement caused by a tipping force. Changes in force magnitude (0.5–3 N) and crown length (6–10 mm) were analyzed until no movement was observed (steady state). Premolar displacement in contact with adjacent teeth showed a non-linear progression over time with an initial sharp tipping movement followed by a transient period of 2.6–7.1 min. As tipping force increased the transient period increased. A similar but smaller effect was observed with an increase in crown length. The premolar initial displacement within the arch (3.2–19.5 μm) is about seven-fold smaller than retraction/protraction movement of an incisor. These suggest reduction in tooth displacement when functioning interproximal contact is present and clinically recommend establishing a space in the direction of tooth displacement before tooth movement.