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The analysis of the non-linear and time-dependent viscoelasticity of the periodontal ligament (PDL) enables a better understanding of the biomechanical features of the key regulator tissue for tooth movement. This is of great significance in the field of orthodontics as targeted tooth movement remains still one of the main goals to accomplish. The investigation of biomechanical aspects of the PDL function, a difficult area of research, helps towards this direction. After analysing the time-dependent biomechanical properties of pig PDL specimens in an in vitro experimental study, it was possible to confirm that PDL has a viscoelastic anisotropic behaviour. Three-dimensional finite element models of mini-pig mandibular premolars with surrounding tissues were developed, based on micro-computed tomography (μCT) data of the experimental specimens. Tooth mobility was numerically analysed under the same force systems as used in the experiment. A bilinear material parameter set was assumed to simulate tooth displacements. The numerical force/displacement curves were fitted to the experimental curves by repeatedly calculating tooth displacements of 0.2mm varying the loading velocities and the parameters, which describe the nonlinearity. The experimental results showed a good agreement with the numerical calculations. Mean values of Young's moduli E1, E2 and ultimate strain ε12 were derived for the elastic behaviour of the PDL for all loading velocities. E1 and E2 values increased with increasing the velocity, while ε12 remained relatively stable. A bilinear approximation of material properties of the PDL is a suitable description of measured force/displacement diagrams. The numerical results can be used to describe mechanical processes, especially stress-strain distributions in the PDL, accurately. Further development of suitable modelling assumptions for the response of PDL under load would be instrumental to orthodontists and engineers for designing more predictable orthodontic force systems and appliances.

Biomechanical time dependency of the periodontal ligament: a combined experimental and numerical approach