Assessment of parameters of a fractional relaxation kernel modelling viscoelastic properties of the periodontal ligament

The periodontal ligament (PDL) is a thin layer of soft connective tissue located between the hard surfaces of the tooth root and the dental alveolar bone. As many of biological tissues the PDL possesses viscoelastic properties. It is considered as a physiological mechanism mainly responsible for the movement of teeth and the reaction of teeth to stress and plays a key role in tooth mobility due to its low stiffness. The aim of study is an analytic modeling of the viscoelastic behaviour of the PDL in the case of an asymmetric tooth root tipping. For this model a fractional relaxation kernel is used whose parameters are determined by experimental data. One of the advantages of the proposed model is the ability to change the time intervals for the phase transition of the PDL at the same maximal displacements of the tooth root in the PDL. Increase in the fractional parameter leads to simultaneous increase in the phase transition duration and the maximal displacement of the tooth root.