A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth

Summary

This study outlines the necessary tools for utilizing low-dose three-dimensional cone beam-based patient images of the maxilla and maxillary teeth to obtain finite element models. These patient models are then used to accurately locate the C_RES of all the maxillary teeth.

Abstract

The center of resistance (C_RES) is regarded as the fundamental reference point for predictable tooth movement. The methods used to estimate the C_RES of teeth range from traditional radiographic and physical measurements to in vitro analysis on models or cadaver specimens. Techniques involving finite element analysis of high-dose micro-CT scans of models and single teeth have shown a lot of promise, but little has been done with newer, low-dose, and low resolution cone beam computed tomography (CBCT) images. Also, the C_RES for only a few select teeth (i.e., maxillary central incisor, canine, and first molar) have been described; the rest have been largely ignored. There is also a need to describe the methodology of determining the C_RES in detail, so that it becomes easy to replicate and build upon.

This study used routine CBCT patient images for developing tools and a workflow to obtain finite element models for locating the C_RES of maxillary teeth. The CBCT volume images were manipulated to extract three-dimensional (3D) biological structures relevant in determining the C_RES of the maxillary teeth by segmentation. The segmented objects were cleaned and converted into a virtual mesh made up tetrahedral (tet4) triangles having a maximum edge length of 1 mm with 3matic software. The models were further converted into a solid volumetric mesh of tetrahedrons with a maximum edge length of 1 mm for use in finite element analysis. The engineering software, Abaqus, was used to preprocess the models to create an assembly and set material properties, interaction conditions, boundary conditions, and load applications. The loads, when analyzed, simulated the stresses and strains on the system, aiding in locating the C_RES. This study is the first step in accurate prediction of tooth movement.

Introduction

The center of resistance (C_RES) of a tooth or segment of teeth is analogous to the center of mass of a free body. It is a term borrowed from the field of mechanics of rigid bodies. When a single force is applied at the C_RES, translation of the tooth in the direction of the line of action of the force occurs^1,2. The position of the C_RES depends not only on the tooth's anatomy and properties but also on its environment (e.g., periodontal ligament, surrounding bone, adjacent teeth). The tooth is a restrained body, making its C_RES similar to the center of mass of a f....

Protocol

An institutional review board exemption was obtained for evaluating CBCT volumes archived in the Division of Oral and Maxillofacial Radiology (IRB No. 17-071S-2).

1. Volume selection and criteria

1. Acquire a CBCT image of the head and face¹⁶.
2. Examine the image for tooth alignment, missing teeth, voxel size, field of view, and overall quality of the image.
3. Make sure the voxel size is not larger than 350 µm (0.35 mm).

Discussion

This study shows a set of tools to establish a consistent workflow for finite element analysis (FEA) of models of maxillary teeth derived from CBCT images of patients to determine their C_RES. For the clinician, a clear and straightforward map of the C_RES of the maxillary teeth would be an invaluable clinical tool to plan tooth movements and predict side effects. The finite element method (FEM) was introduced in dental biomechanical research in 1973¹⁷, and since then has been .......

Materials

Name	Company	Catalog Number	Comments
3-matic software	Materialise, Leuven, Belgium.		Cleaning and meshing
Abaqus/CAE software, version 2017	Dassault Systèmes Simulia Corp., Johnston, RI, USA.		Finite Element Analysis
Mimics software, version 17.0	Materialise, Leuven, Belgium.		Segmentation of teeth and bone