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

Abstract

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.

Time-dependent behavior of porcine periodontal ligament: A combined experimental, numeric in-vitro study

“…The process of freezing and slowly thawing (before measurement was started) did not have a significant influence on the biomechanical behavior of the PDLs. 16,17 Furthermore, intraoral force measurements 18 and subsequent FE simulations 19,20 to determine the timedependent constitutional behavior of the PDL in vivo did not show relevant differences when compared with in-vitro results. Values are stated individually for each sample and as a mean value with standard deviations for all loading times above 2 seconds.…”

Types of tooth movement, bodily or tipping, do not affect the displacement of the tooth's center of resistance but do affect the alveolar bone resorption

“…[14][15][16] The periodontal ligament was set to be nonlinear elastic, and its width was set to be 0.2 mm. 17,18 All Poisson ratios were set to be 0.3. [14][15][16] The position of CR was determined following the method reported previously.…”

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

“…Toms and Eberhardt (2003) reported that linear elastic models can underestimate PDL stresses at the apex and overestimate them in the midroot locations. Although the bilinear elastic model with two different elastic moduli can be considered as a simple nonlinear one, it cannot describe (Qian et al 2009;Papadopoulou et al 2013). In order to capture well the nonlinear elastic behavior of the PDL, it is necessary for us to use hyperelastic models in the FEA.…”