Estimation of periodontal ligament's equivalent mechanical parameters for finite element modeling

Young's modulus (E) and Poisson's ratio (v) of the periodontal ligament are needed in a finite element analysis for investigating the biomechanical behavior of a tooth, periodontal ligament, and bone complex. However, large discrepancies in E (0.01-1,750 MPa) and v (0.28-0.49) were reported previously. The objective of this study was to narrow the ranges and to provide equivalent E and v pairs suitable for finite element modeling of a tooth, periodontal ligament, and bone complex by using a reported crown load-displacement relationship as the criterion.

A 3-dimensional finite element model of a 3-tooth, periodontal ligament, and bone complex, consisting of a maxillary central incisor with 2 adjacent teeth, from a cone-beam computed tomography scan was created. The dimensions, constraints, and loading condition were kept similar to those reported in the human study. With the load applied to the crown, both v and E were adjusted independently, and the corresponding crown displacements were calculated. The resulting load-displacement curves were compared with those reported in the human study. The mean absolute displacement difference method was used to find the best fit. The E and v pairs that generated the minimum mean absolute displacement difference were identified.

The finite element model with 1 of the 3 E and v pairs (v = 0.35, E = 0.87 MPa; v = 0.4, E = 0.71 MPa; and v = 0.45, E = 0.47 MPa) simulated the tooth, periodontal ligament, and bone complex well. The mean absolute displacement differences were 0.0135, 0.0138, and 0.0138 mm, respectively; these are less than 8% of 0.175 mm, which was the crown displacement of the tooth, periodontal ligament, and bone complex under the load of 500 cN.

The E and v values close to the 3 pairs might be used for finite element modeling of the tooth, periodontal ligament, and bone complex.