An Efficient Spring Model for an Integrated Orthodontic Tooth Movement: A Verified Mathematical Model

Abstract

Orthodontic tooth movement is of interest to both the medical and the engineering communities. Recent studies focused their attention mainly on the stress distribution within the periodontal ligament and the surrounding alveolar bone prior to the remodeling stage. Yet, although motion is indeed triggered by the exerted stress distribution, these remodeling processes are the main driver for significant (and permanent) tooth movements. Other studies attempted to provide such a holistic mechanical model for both the stress distribution and the remodeling processes to describe the movement of the tooth along an orthodontic treatment. Nevertheless, these methods are cumbersome and slow to run, and therefore, are unlikely to provide a clinical decision support platform. This paper aims to bridge this gap by providing a relaxed, simplified numerical model. The scheme is described, and its limitations and main assumptions are stated. The model is then optimized to accommodate clinical accuracy needs. Lastly, validation is provided by comparing the model to a recent study, which demonstrates the good agreement between the model and actual real-world clinical cases.