Mathematical Modeling and Digital Simulation of Teeth Dynamics for the Approximation of Orthodontic Treatment Duration

Abstract

The paper presents an original solution for modeling and simulation of the teeth movement biomedical processes which occur in the case of orthodontic treatments. The direct application of this method consists in the possibility to approximate, with high precision, the orthodontic treatment duration, depending on the physical characteristics of each patient. This aspect represents a novelty element in the biomedical processes’ domain since, until now, the research activities in the mentioned field did not generate a solution for the approximation of the orthodontic treatment’s duration. Analog modeling of the biomedical process operates with a fictional shaft defined to highlight the tooth symmetry axis. The tooth considered as an example is approximated as having a parabolic shape with an elliptical section. The digital simulation refers to the spatial-temporal evolution of this fictional shaft in the orthodontic dynamics, being made through the run of four computer programming algorithms. Interpretation of the obtained performance indicators will lead to an interesting study regarding the dynamics’ process in orthodontics, having a pronounced unitary and systematic characteristic. Using the developed programs for obtaining the simulations results presented in the four tables and in the 18 figures shown in the paper, several case studies can be elaborated, associated with a wide variety of orthodontic treatments.

Keywords

• digital simulation
• mathematical modeling
• orthodontic treatment
• teeth dynamics