Time-dependent mechanical behaviour of the periodontal ligament

The process of tooth displacement in response to orthodontic forces is thought to be induced by the stresses and strains in the periodontium. The mechanical force on the tooth is transmitted to the alveolar bone through a layer of soft connective tissue, the periodontal ligament. Stress and/or strain distribution in this layer must be derived from mathematical models, such as the finite element method, because it cannot be measured directly in a non-destructive way. The material behaviour of the constituent tissues is required as an input for such a model. The purpose of this study was to determine the time-dependent mechanical behaviour of the periodontal ligament due to orthodontic loading of a tooth. Therefore, in vivo experiments were performed on beagle dogs. The experimental configuration was simulated in a finite element model to estimate the poroelastic material properties for the periodontal ligament. The experiments showed a two-step response: an instantaneous displacement of 14.10±3.21 μm within 4 s and a more gradual (creep) displacement reaching a maximum of 60.00±9.92 μm after 5 h. This response fitted excellently in the finite element model when 21 per cent of the ligament volume was assigned a permeability of 1.0×10^-14 m⁴/N S, the remaining 97 per cent was assigned a permeability of 2.5×10^-17 m⁴/N s. A tissue elastic modulus of 0.015±0.001 MPa was estimated. Our results indicate that fluid compartments within the periodontal ligament play an important role in the transmission and damping of forces acting on teeth.