Numerical simulation of the biomechanical behaviour of multi-rooted teeth

The elastic properties of the periodontal ligament (PDL) in eight multi-rooted teeth were examined in a combined experimental and numerical study in six minipigs. The initial tooth movement of the mandibular primary molars surrounded by the periodontium was registered three-dimensionally (3D) in an optomechanical measuring system. The dissections were then embedded in resin and cut in transverse sections. Based on these sections, 3D finite element (FE) models were constructed and numerically loaded with the same force systems as used in the experiment. The material behaviour of the PDL registered in the experiment was non-linear and could be approximated with a bilinear parameter set consisting of two Young's moduli, E1 and E2, and one ultimate strain, epsilon12, separating both elastic regimes. When a deficient congruence existed between the experimental and numerical force/deflection curves the material parameters were varied to obtain a satisfactory congruence. The material behaviour determined for these specimens delivered mean values of E1 = 0.05 MPa, E2 = 0.18 MPa and epsilon12 = 6.4 per cent for the elastic behaviour of the multi-rooted minipig teeth. There was no significant difference in the material parameters determined for specimens with two, four or six roots. The results were in close agreement with the material parameters of the PDL, determined in previous investigations of single-rooted human and pig teeth.