Validation of a heterogeneous elastic-biphasic model for the numerical simulation of the PDL

Abstract

An elastic-biphasic model for the simulation of the periodontal ligament (PDL) and the adjacent tooth is presented and investigated. The PDL is modelled as a biphasic material following the work of Ehlers and Markert (2001), whereas the tooth is modelled as a linear elastic body. A spatial discretisation scheme is proposed based on mixed finite elements for the spatial discretisation. Due to nonlinearity in the model, a predictor–corrector scheme is employed as a temporal discretisation scheme. In order to validate the PDL model, in vitro measurements are compared with numerical simulations. The numerical simulations are performed using geometries resulting from micro-CT scanner of the same porcine tooth, which was employed for the invitro measurements.

Keywords::

• finite elements
• biphasic theory
• periodontal ligament
• elastic-biphasic coupling
• partial differential equation

Acknowledgements

This study was in part supported by the German Research Foundation (DFG, Clinical Research Unit KFO208). We also thank Johannes Steiner (University of Lugano) for his help in creating the PDL and tooth geometry.