# Towards a reduced order model of the periodontal ligament

## TL;DR

This paper presents a model to simulate how the periodontal ligament responds to forces during tooth movement, using a combination of poro-visco-hyperelastic properties.

## Contribution

The study introduces a reduced order model and optimal interpolation metamodel for parameter identification in periodontal ligament simulations.

## Key findings

- The periodontal ligament shows high initial compressibility, likely due to its vascular system.
- Poroelastic behavior diminishes as viscoelastic relaxation progresses, confirmed through simulations.
- Alveolar bone permeability significantly affects fluid flow in the periodontium.

## Abstract

Based on previous in vitro experiments with specimens of porcine mandibular premolars, the simulation of the periodontal ligament response to force in the initial phase of orthodontic tooth movement is described. The initial response of the periodontal ligament can be simulated with a poro-visco-hyperelastic model. For the ground substance a hyperelastic constitutive model for compressible material was used. To facilitate parameter identification a reduced order model and an optimal interpolation metamodel were used. Parameters for the constitutive model identified herein are in good agreement with published values. They indicate a high initial compressibility of the periodontal ligament, which may be attributed to the compressibility of the vascular system within the periodontal ligament. Dimensionless analysis suggests that poroelastic behaviour will gradually cease when viscoelastic relaxation progresses. This was observed as well in the simulation and confirmed by varying the poroelastic model parameters within physically justified limits. Alveolar bone permeability has a significant influence on the flow of pore fluid in the periodontium due to poroelasticity. It is argued that in vivo alveolar bone perforation may adapt locally to optimise for the predominant load situation. A strain rate hardening effect was observed, which is not covered by the simulation, and may be the subject of further investigations.