Numerical Methods for Clear Aligner Therapy

Abstract

Clear Aligner Therapy (CAT) was introduced by Invisalign➤ in 1999. However, their original patents have expired, opening up a huge and growing market for clear aligners. Advanced manufacturing techniques and computer systems enable this appliance technology.

This thesis investigates three aspects of the computer systems side of CAT. The first aspect is modelling the interaction between the aligner and the crown. The second aspect is computer-assisted treatment planning. The third aspect is modelling the interaction of the tooth root with the jaw. As these three areas are broad, only one aspect of each is explored.

The first part presents a novel algorithm for modelling the contact between a rigid tooth and a deformable plastic aligner. The rigid body is modelled by a Signed Distance Function (SDF) image, whilst a regular triangle mesh models the deformable plastic aligner. It is found that this algorithm works. It is also found that the results are sensitive to the resolution of the SDF image.

The second part focuses on automatically determining a target dentition. Here the definitions for the ideal dentition are researched, and an algorithm is presented. The algorithm works by packing the teeth onto a curve so that they touch each other. This packing works best when the full crown geometries are used to calculate the contact between the teeth. In addition, using one of the industry standard archwires as the curve works better than a fitted polynomial. The algorithm provides the foundation for further algorithms.

The third part of this thesis focussed on the material properties of the Periodontal Ligament (PDL). First, a simple bi-linear elastic material model characterises the effect of non-linearity in the PDL. It is found that the non-linearity in the material changes the relationship between the Centre of Rotation (Crot) and the Centre of Force (Cf ). However, the change in the position of the Centre of Resistance (Cres) is found to be negligible over an extensive range of materials. Finally, an inverse modelling method was proposed to fit material models to the PDL. This inverse modelling approach was tested in a synthetic experiment, where the PDL was modelled using a non-linear material, and two simple material models were fitted using the force-displacement response. The linear and bi-linear material models were used. For the inverse modelling to succeed, the fitted material models should accurately capture the force vs displacement and force vs stress relationships within the PDL. The linear material is adequate if the loading is dominated by translation. Unfortunately, typical load cases are dominated by tipping. The bi-linear material model effectively captures both relationships. However, the enhanced flexibility of this model requires richer data to achieve a suitable fitting. These results proved that the inverse modelling method proposed could be used with in vivo measurements data to find the material properties of the PDL. Although this thesis merely scratches the surface of the field, it provides three frameworks that may be built on: for contact modelling using SDF images, for automatic determining of the target dentition and inverse modelling of the PDL.