The mechanical function of the periodontal ligament in the macaque mandible: a validation and sensitivity study using finite element analysis

Abstract

Whilst the periodontal ligament (PDL) acts as an attachment tissue between bone and tooth, hypotheses regarding the role of the PDL as a hydrodynamic damping mechanism during intraoral food processing have highlighted its potential importance in finite element (FE) analysis. Although experimental and constitutive models have correlated the mechanical function of the PDL tissue with its anisotropic, heterogeneous, viscoelastic and non-linear elastic nature, in many FE simulations the PDL is either present or absent, and when present is variably modelled. In addition, the small space the PDL occupies and the inability to visualize the PDL tissue using μCT scans poses issues during FE model construction and so protocols for the PDL thickness also vary. In this paper we initially test and validate the sensitivity of an FE model of a macaque mandible to variations in the Young's modulus and the thickness of the PDL tissue. We then tested the validity of the FE models by carrying out experimental strain measurements on the same mandible in the laboratory using laser speckle interferometry. These strain measurements matched the FE predictions very closely, providing confidence that material properties and PDL thickness were suitably defined. The FE strain results across the mandible are generally insensitive to the absence and variably modelled PDL tissue. Differences are only found in the alveolar region adjacent to the socket of the loaded tooth. The results indicate that the effect of the PDL on strain distribution and/or absorption is restricted locally to the alveolar bone surrounding the teeth and does not affect other regions of the mandible.

Fig. 1

The models used in the FEA analyses of this study. PDL Model A: PDL thickness segmented out as a three to four voxel structure towards the alveolar bone. PDL Model B: PDL thickness segmented out as a four to five voxel structure towards the alveolar bone. PDL Model C: PDL thickness segmented out as a three to four voxel structure towards the tooth root. PDL Model D: PDL thickness segmented out as a four to five voxel structure towards the tooth root. No PDL Model: PDL is not modelled.

Fig. 2

(A) Position of the mandible on the testing rig resting on the medial aspect of both condyles and on the occlusal surface of the P₃ on both sides. The Dantec sensor is attached to the right mandibular corpus and ramus. (B) Location of the mean ε₁ and ε₃ values and orientation of ε₁ strain values on the ex vivo experiment. (C) Location of the mean ε₁ and ε₃ values and orientation of ε₁ strain values on each of the FE models.

Fig. 3

ε₁, ε₃ and γ_max strain magnitudes during physiological unilateral biting were computed from 15 strain locations on each FE model.

Fig. 4

Comparison of the mean ε₁ (positive axis) and ε₃ (negative axis) values from six different strain locations on the right corpus and ramus from the experimental study and the FE models using different E values for the PDL tissue.

Fig. 5

Physiological FE models with different E values for the PDL. (A) ε₁, ε₃ and (B) γ_max values during unilateral biting on the P_3; (C) ε₁, ε₃ and (D) γ_max values during unilateral biting on the M_3.

Fig. 6

Comparison of the mean ε₁ (positive axis) and ε₃ (negative axis) values from six different strain locations on the right corpus and ramus from the experimental study and the FE models with different PDL geometry.

Fig. 7

ε₁ strain orientations between (A) the FE model without PDL, (B) the FE model with PDL (PDL Model A), and (C) the experimental ex vivo model.

Fig. 8

Mean ε₁ (positive axis)_,ε₃ (negative axis) and γ_max strain magnitudes from 15 strain locations during unilateral physiological biting on (A) the P₃ and (B) the M₃.

Fig. 9

The spatial arrangement of γ_max between (A) the PDL Model A and (B) the No PDL Model.