Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: a case study

Objectives The objective of this study was to investigate the optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar to determine tooth movements during orthodontic treatment using hydrostatic stress and logarithmic strain on the periodontal ligament (PDL) as indicators by numerical simulations. Material and methods Teeth, PDL and alveolar bone numerical models were constructed as analytical objects based on computed tomography (CT) images. Teeth were assumed to be rigid bodies, and rotational moments ranging from 1.0 to 4.0 Nmm were exerted on the crowns. PDL was defined as a hyperelastic–viscoelastic material with a uniform thickness of 0.25 mm. The alveolar bone model was constructed using a non-uniform material with varied mechanical properties determined based on Hounsfield unit (HU) values calculated using CT images, and its bottom was fixed completely. The optimal range values of PDL compressive and tensile stress were set as 0.47–12.8 and 18.8–51.2 kPa, respectively, whereas that of PDL logarithmic strain was set as 0.15–0.3%. Results The rotational tendency of PDL was around the long axis of teeth when loaded. The optimal range values of rotational moment for the mandibular lateral incisor, canine and first premolar were 2.2–2.3, 3.0–3.1 and 2.8–2.9 Nmm, respectively, referring to the biomechanical responses of loaded PDL. Primarily, the optimal range of rotational moment was quadratically dependent on the area of PDL internal surface (i.e. area of PDL internal surface was used to indicate PDL size), as described by the fitting formula. Conclusions Biomechanical responses of PDL can be used to estimate the optimal range of rotational moment for teeth. These rotational moments were not consistent for all teeth, as demonstrated by numerical simulations. Clinical Relevance The quantitative relationship between the area of PDL internal surface and the optimal orthodontic moment can help orthodontists to determine a more reasonable moment and further optimise clinical treatment.