Estimation of Periodontal Ligament’s Mechanical Parameters for Finite Element Modeling

Objectives: The Young’s modulus, E, and Poisson’s ratio, v, of periodontal ligament (PDL) are needed in a finite element analysis for investigating biomechanical behavior of a tooth-PDL-bone-complex (TPBC). However, large discrepancies in E (0.01 – 1750 MPa) and v (0.28 – 0.49) were reported previously. The objective of this study is to narrow the ranges using a reported human crown load-displacement relationship as the criterion.

Methods: A three-dimensional finite element model (FEM) of a TPBC based on cone-beam CT image of a human maxillary left lateral incisor was created and analyzed using ANSYS 12.1 (Canonsburg, PA), finite element analysis software.  The dimensions, constraints, and the loading condition were kept similar to these reported in the human study. The PDL was considered homogeneous and isotropic. The tooth, PDL, and bone were meshed with ten-node tetrahedral (SOLID187) elements with the numbers of the elements equaled to 14,555, 4,899, and 22,069 respectively. 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 the one reported in the human study. The mean absolute displacement difference (MADD) method was used to find the best fit to that reported. The E and v pairs that generated the minimum MADD were identified.

Results: The FEMs using three E and v pairs (v=0.35, E=3 MPa; v=0.4, E=2.55 MPa; v=0.45, E=1.95 MPa) simulated the human TPBC well. The MADDs are 0.0136, 0.0139, and 0.0137 mm respectively, which are less than 8% of 0.175 mm, the crown displacement of the human TPBC under the load of 500 cN.

Conclusion: The E and v close to the three pairs may be used for finite element modeling of TPBC.