Mathematical Methods & Models for Computer Aided Design of Medical Devices

The Ph.D. project aimed at the development of a CAE method to support the design of orthodontic removable thermoplastic appliances (RTA). Treatments based on RTAs are composed of a set of thermoformed templates having different shapes, which are sequentially worn by the patient. Each RTA is shaped a bit different than the real teeth position in the mouth in order to force teeth to move in the correct position. A set of distinct templates is usually required to achieve the final desired outcome since each RTA can perform only a limited rotation and/or translation. Even if orthodontic treatments based on the use of clear aligners are commonly used in clinical practice there is no technical literature describing how the loads are transferred from the thermoformed aligner to the patient dentition. Since both design and production processes involve many clinical and technological skills (knowledge), the optimization of aligners features represents one of the most challenging aspects of this kind of orthodontic treatments. The design of customized and optimized templates would be of utmost importance to obtain more effective treatment plans and accurate prediction of the achievable results. The first year focused mainly on the study of the state of art and the feasibility of a finite element model to simulate a treatment with RTAs. Several methods to reconstruct the geometries of the dental tissue to use within the FEM was analyzed in order to compare results and establish the best solution. The development of the FEM represented the main activity all over the second year. Three different models with 3/5/7 teeth respectively was developed. The effect of attachment on the orthodontic movement was also analyzed. The third and last year the research was conducted at the Center for Dental Research at Loma Linda University, in California. The FEM was improved by modeling a full maxillary arch model. The study of attachments was also improved analyzing different movements. Moreover with the support of the Dentists an accurate study on the orthodontic movement was performed, with the aim at analyzing tooth movement in response to different force systems. This allowed for a better understanding of the FEM result.