Influence of elastic modulus of periodontal ligament on the centers of rotation of incisors : finite element analysis

Abstract

Consideration of the physical properties of the periodontium is important in diagnosis and treatment planning of orthodontic treatment. Moreover, periodontal ligament (PDL) is the most important tissue in proceeding of tooth movement under orthodontic loading. The elastic modulus of periodontal ligament (E) used in previous studies has quite wide range of value from 0.07 to 1,750 MPa. The objective of this study was to measure the changes of the centers of rotation (Crot) of upper central incisors and evaluate the influence of physical properties on orthodontic tooth movement, in response to single horizontal force applied at different vertical levels with regard to various elastic modulus of PDL using finite element analysis (FEA). A 3-dimensional finite element model was constructed from a 3D laser scan of a maxillary anteriors of a Nissin dental model by the sample survey of adults with normal occlusion. In this study, PDL was designed with 4 layers of fine tetrahedron solid elements to estimate the influence of the elastic properties of PDL on orthodontic teeth movement precisely. The variables of the elasticity of PDL (0.07 to 1,750 MPa) were consulted previous studies. The conclusions are as follows: 1. The vertical position of Crot of upper central incisors was displaced apically with increase of E at same vertical force application level. 2. Centers of resistance (Cres) of upper central incisors was changed according to the elastic modulus of PDL. On non-rigid bone/tooth model, Cres of upper central incisors relocated apically at E 50.0 and 68.9 MPa and shifted more incisally from E 171.9 to 1750 MPa. On rigid bone/tooth model, Cres of upper central incisors moved apically with increase of E. On non-rigid bone/rigid tooth model, Cres of upper central incisors tended to move incisally. 3. The 'functional axes' (traces of the measured Crot) of the upper central incisors were formulized in accordance with various E. The Crot distributed on a line under given E in relation to the horizontal forces applied to the various vertical level. The different linear equations could be evaluated with coefficients in accordance with various E, which slopes turn counterclockwise direction gradually with increase of E. The absollute quantity of displacement and the tendency of rotation of teeth used to decrease with increased E, when compared the characteristics of teeth movement according to E. Consideration of the physical properties of the PDL might be an important factor in diagnosis and treatment planning of orthodontic treatment.