Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth. A study of autopsy specimens and their conversion into finite element models

Material and Methods: The aim of this study was to determine the elasticity parameters of the human periodontal ligament by measuring three-dimensionally the initial buccolingual tooth displacements of eight single-rooted teeth in human jaw specimens, using a noninvasive method. Subsequently the specimens were used to develop finite element models presenting the same individual geometry as the respective autopsy material. These models formed the basis for computerized movement simulations, whose characteristic was brought into line with the experimentally registered movements by adapting the elasticity parameters of the periodontal ligament. Using the individual elasticity parameters determined in this way, with which the displacement of the computer models could be realistically calculated, the centers of resistance of the examined teeth were determined by simulating the effects of different force systems. Results: The nonlinear character of the initial tooth movement could be effectively simulated by using a bilinear parameter set for the elasticity of the periodontal ligament and by determining a critical expansion value for the transition from the validity range of the first Young's modulus to the second. The mean Young's modulus of the first phase of movement was 0.05 MPa, that of the second phase 0.28 MPa, and the critical expansion 7.5% (Poisson's ratio μ = 0.3). The centers of resistance of single-rooted teeth were found to be at approximately 42% of the alveolar height from the alveolar crest to the apex, irrespective of root length and direction of loading. Conclusion: The elasticity parameters were found to be on a similar scale to those determined in previous studies on multi-rooted pig teeth.