A Nonlinear Hyperelastic Behavior for Mechanical Properties of Bovine PDL

Objectives: The dental periodontal ligament (PDL) is important for orthodontic tooth movement, yet the biomechanical characteristics of the PDL have not been validated. The PDL is a viscoelastic material whose mechanical property is affected by anatomic location. We hypothesize that the PDL stress-strain behavior can be constituted by a hyperelastic model with heterogeneous elastic modulus varied by the location.
Methods: Samples from mandibular bovine incisors were obtained from longitudinal locations: apical and middle, and circumferential locations: mesial, distal, facial and lingual. Uniaxial tension test using a ramp force of 0.5N/min to 0.5N was applied to 52 PDL samples utilizing a dynamic mechanical analyzer (DMA), which detects force resolution of 0.002N. Young’s modulus (E) values calculated from the initial slope of experimental data were compared to investigate the effects of anatomic location. Stress-strain data were further used to fit into the Mooney-Rivlin Hyperelastic (MRH) model.
Results: The modulus of the PDL was approximately 37% greater for apical than middle regions of roots (p<0.05). Mean (SD) elastic moduli were 0.55(0.09) GPa, 0.83(0.10) GPa, 0.77(0.11) GPa, and 0.89(0.09) GPa for mesial, distal, lingual, and facial surfaces, respectively. The MRH model fits well the non-linear stress-strain curve of PDL (r=0.99), which can be further utilized to accurately predict tooth movement in a computer simulation.
Conclusions: The PDL biomechanical parameters are dependent on anatomic location and the constitutive law of the PDL stress-strain relationship favors the Mooney-Rivlin model.