The Importance of Boundary Conditions and Failure Criterion in Finite Element Analysis Accuracy—A Comparative Assessment of Periodontal Ligament Biomechanical Behavior

Abstract

(1) Background: Herein, finite element analysis (FEA) of the periodontal ligament (PDL) was used to assess differences between Tresca (T-non-homogenous) and Von Mises (VM-homogenous) criterion, by simulating a 0–8 mm periodontal breakdown under five orthodontic movements (extrusion, intrusion, rotation, tipping, and translation) and three loads (0.6, 1.2, and 2.4 N). Additionally, we addressed the issues of proper boundary condition selection for more than 1 N loads and correlated the results with the maximum hydrostatic pressure (MHP) and available knowledge, evaluating ischemic and resorptive risks for more than 1 N orthodontic loads. (2) Methods: Eighty-one models of the second lower premolar (nine patients) with intact and 1–8 mm reduced periodontia were created. The assumed boundary conditions were isotropy, homogeneity, and linear elasticity. A total of 486 FEA simulations were performed in Abaqus. (3) Results: Both criteria displayed similar qualitative results, with T being quantitatively 15% higher and better suited. The assumed boundary conditions seem to be correct up to 2.4 N of the applied load. (4) Conclusions: Both criteria displayed constant deformations and displacements manifested in the same areas independently of the load’s amount, the only difference being their intensity (doubling—1.2 N; quadrupling—2.4 N). Moreover, 2.4 N seems safe for intact periodontium, while, after a 4 mm loss (seen as the reference point), a load of more than 1 N seems to have significant ischemic and resorptive risks.

Keywords

• boundary conditions
• finite element analysis
• periodontal ligament (PDL)
• orthodontic movements
• periodontal breakdown