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.

Quasi-linear viscoelastic behavior of the human periodontal ligament.

Previous studies have not produced a comprehensive mathematical description of the nonlinear viscoelastic stress-strain behavior of the periodontal ligament (PDL). In the present study, the quasi-linear viscoelastic (QLV) model was applied to mechanical tests of the human PDL. Transverse sections of cadaveric premolars were subjected to relaxation tests and loading to failure perpendicular to the plane of section. Distinct and repeatable toe and linear regions of stress-strain behavior were observed. The amount of strain associated with the toe region differed as a function of anatomical location along the tooth root. Stress relaxation behavior was comparable for different anatomical locations. Model predicted peak tissue stresses for cyclic loading were within 11% of experimental values, demonstrating that the QLV approach provided an improved, accurate quantification of PDL mechanical response. The success of the QLV approach supports its usefulness in future efforts of experimental characterization of PDL mechanical behavior.

Nonlinear stress-strain behavior of periodontal ligament under orthodontic loading.

Previous studies of the periodontal ligament (PDL) have applied high forces to the dental units to examine the stress-strain behavior of this soft tissue. In this study, cadaveric specimens of mandibular premolars from 2 young adult and 2 elderly adult donors were tested to determine the biomechanical behavior of the PDL over an orthodontic force range. Transverse specimens were prepared from 9 premolars and subjected to loading in intrusion and extrusion. Stress-strain curves for both loading directions had distinct toe and linear regions, demonstrating nonlinear behavior of the PDL. The average linear shear modulus was higher for intrusion than for extrusion. The toe extrusive modulus was higher for the young group, and extrusive toe size was larger for the elderly group. In extrusion, the average modulus was higher for the cervical margin and the apex regions than for the midroot regions. The size of the toe region was smaller for intrusion than extrusion. The results indicate age-dependent, location-dependent, and load-direction-dependent nonlinear properties of the human PDL and suggest that analytical computer simulations of orthodontic tooth movements might benefit from incorporating the nonlinear material properties of the PDL.