Mesh management methods in finite element simulations of orthodontic tooth movement

An in-silico approach to modeling orthodontic tooth movement using stimulus-induced external bone adaptation

Bone remodeling process has been used in orthodontics to treat malposition of teeth in patients by applying stimuli outside of usual everyday loads to promote tooth movement by affecting equilibrium state of the surrounding bone tissue. Accurate modeling of long term orthodontic tooth movement (OTM) is crucial in the field of dental biomechanical research since it allows to predict the behavior and interaction of bone-tooth environment in a non-destructive way, and helps to gain more insight on how exactly tooth motion progresses over time. Existence of such predictive tools might help to avoid the adverse effects of OTM on teeth and the surrounding tissues during this clinical procedure. In this study a new numerical approach to simulating long-term OTM is proposed, that involves external bone adaptation with strain energy density of the bone taken as the stimulus parameter and bone adaptation modeled by nodal movements at the bone-tooth interface using Abaqus UMESHMOTION subroutine. Contrary to conventional re-meshing algorithms, where the mesh of resorbed-apposed bone region is constantly updated and element deletion/creation is performed for each increment, the proposed method only moves nodes without changing the initial mesh topology. For this study, a 3D model of right central maxillary incisor tooth and its surrounding maxillary bone was used for the modeling of OTM for a duration of 1 week. Two test cases were performed and the results from induced tooth motion were investigated. Results indicate tooth movement values that were quite close to clinical values provided in the literature and this method is easily applicable to validate various postulates of OTM via adapting the stimulus-adaption rate relation and patient-specific planning of orthodontic patients as well.

Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations

This scoping review is intended to synthesize the techniques proposed to model the tooth-periodontal ligament-bone complex (TPBC), while also evaluating the suggested periodontal ligament (PDL) material properties. It is concentrated on the recent advancements on the PDL and TPBC models, while identifying the advantages and limitations of the proposed approaches. Systematic searches were conducted up to December 2020 for articles that proposed PDL models to assess orthodontic tooth movement in Compendex, Web of Science, EMBASE, MEDLINE, PubMed, ScienceDirect, Google Scholar and Scopus databases. Although there have been many studies focused on the evaluation of PDL material properties through numerous modelling approaches, only a handful of approaches have been identified to investigate the interface properties of the PDL as a complete dynamical system (TPBC models). Past reviews on the analytical and experimental determination of the PDL properties already show a concerning range in reported output values-some nearly six orders of magnitude in difference-that strongly suggested the need for further investigation. Surprisingly, it has not yet been possible to determine a narrower range of values for the PDL material properties. Moreover, very few scientific approaches address the TPBC as an integrated complex system model. In consequence, current methods for capturing the PDL material behaviour in a clinical setting are limited and inconclusive. This synthesis encourages more systematic, pragmatic and phenomenological research in this area.

Biomechanical investigation of orthodontic treatment planning based on orthodontic force measurement and finite element method before implementation: A case study

BACKGROUND

Orthodontic treatment planning (OTP) is primarily depended on clinical experiences of orthodontists at present, while equivocal OTP would increase the possibility of treatment failure.

OBJECTIVE

The objective was to investigate a methodology for quantitatively evaluating OTP, using theoretical analyses, orthodontic forces measurement (OFM) and finite element method (FEM).

METHODS

An OTP was theoretically designed based on a clinical case and forces on incisors in OTP were measured on a specialized platform. Further, FEM simulations were performed on the designed OTP and control group. At last, an 18-month tracking was carried out to observe treatment effects of the designed OTP.

RESULTS

The moving tendencies of incisors were in keeping with ideal treatment from the designed OTP through FEM; the maximal hydrostatic stress and logarithmic strain in periodontal ligament (PDL) decreased by 26.81% and 32.60% compared to the control group. Clinical feedback indicated that a controllable correction of incisors was realized after 18 months, which was in accord with the FEM result and root/bone resorption by reason of stress/strain reduction on PDL did not occur.

CONCLUSIONS

Biomechanical responses of periodontium can be quantitatively estimated using OTM and FEM. This study provided an alternative technological mean for the predictability and optimization of clinical OTP.