Simulation of Uncontrolled Orthodontic Tipping in Single Rooted Teeth

Abstract

Quantitative analysis of system behavior represents a mandatory step in order to completely define and understand the evolution of time-dependant processes. The purpose of our study has been to model and simulate orthodontic force distribution during uncontrolled tipping of single rooted teeth. A mathematical model has been developed to simulate a system composed of an orthodontic force applied at crown level of a single rooted tooth, implanted and connected by periodontal ligament fibers in its bone socket.  The equation model includes several flexible features regarding anatomic variations of tooth size, mass and volume, its periodontal estate, as well as possible types of orthodontic force systems applied to the tooth. It simulates the dynamics of tooth tipping over time, focusing on identifying the exact position of the rotation center in the implanted part of the root as well as calculating the pressures appearing around the root surface during orthodontic loading of single rooted teeth.