A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading

The stressed state of the periodontal ligament (PDL) is understood to play a critical role in the tooth movement initiated by orthodontic treatment. Finite element simulations have been used to describe PDL stresses for orthodontic loading; however, these models have predominantly assumed linear mechanical properties for the PDL. The present study sought to determine the importance of using nonlinear mechanical properties and nonuniform geometric data in computer predictions of periodontal ligament stresses and tooth movements. A 2-dimensional plane-strain finite element model of a mandibular premolar was constructed based on anatomic data of transverse sections of tooth, PDL, and bone from a 24-year-old cadaveric man. A second model was constructed of the same tooth but with a PDL of uniform thickness. Each of these was prescribed linear or nonlinear elastic mechanical properties, as obtained in our own experiments. Predictions of the maximum and minimum principal stresses and von Mises stresses in the PDL were determined for extrusive and tipping forces. The results indicated that biofidelic finite element models predicted substantially different stresses in the PDL for extrusive loading than did the uniform thickness model, suggesting that incorporation of the hourglass shape of the PDL is warranted. In addition, incorporation of nonlinear mechanical properties for the PDL resulted in dramatic increases in the stresses at the apex and cervical margin as compared with the linear models.