Name: a finite element approach for locating the center of resistance of maxillary teeth
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Description: Watch this Scientific Journal Video about A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth at JoVE.com

The authors would like to acknowledge the Charles Burstone Foundation Award for supporting the project.

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
<ol>
	<li>Acquire a CBCT image of the head and face16.</li>
	<li>Examine the image for tooth alignment, missing teeth, voxel size, field of view, and overall quality of the image.</li>
	<li>Make sure the voxel size is not larger than 350 &#181;m (0.35 mm).</li>
</ol>
<p class...

<ol>
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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 CRES. For the clinician, a clear and straightforward map of the CRES 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 ...

The center of resistance (CRES) 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 CRES, translation of the tooth in the direction of the line of action of the force occurs1,2. The position of the CRES depends not only on the tooth&#39;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 CRES similar to the center of mass of a free body. In the manipulation of appliances, most orthodontists consider the relationship of the force vector to the CRES of a tooth or a group of teeth. Indeed, whether an object will display tipping or bodily movement when submitted to a single force is mainly determined by the location of the CRES of the object and the distance between the force vector and the CRES. If this can be accurately predicted, treatment results will be greatly improved. Thus, an accurate estimation of CRES can greatly enhance the efficiency of orthodontic tooth movement.
For decades, the orthodontic field has been revisiting research regarding the location of the CRES of a given tooth, segment, or arch1,2,3,4,5,6,7,8,9,10,11,12. However, these studies have been limited in their approach in many ways. Most studies have determined the CRES for only a few teeth, leaving out the majority. For example, the maxillary central incisor and the maxillary incisor segment have been evaluated quite extensively. On the other hand, there are only a few studies on the maxillary canine and first molar and none for the remaining teeth. Also, many of these studies have determined the location of the CRES based on generic anatomical data for teeth, measurements from two-dimensional (2D) radiographs, and calculations on 2D drawings8. In addition, some of the current literature uses generic models or three-dimensional (3D) scans of dentiform models rather than human data4,8. As orthodontics shifts into 3D technology for planning tooth movement, it is crucial to revisit this concept to develop a 3D, scientific understanding of tooth movement.
With technological advancements resulting in increased computational power and modeling capabilities, the ability to create and study more complex models has increased. The introduction of computed tomography scanning and cone-beam computed tomography (CBCT) scanning has thrust models and calculations from the 2D world into 3D. Simultaneous increases in computing power and software complexity have allowed researchers to use 3D radiographs to extract accurate anatomical models for use in advanced software to segment the teeth, bone, periodontal ligament (PDL), and various other structures7,8,9,10,13,14,15. These segmented structures can be converted into a virtual mesh for use in engineering software to calculate the response of a system when a given force or displacement is applied to it.
This study proposes a specific, replicable methodology that can be utilized to examine hypothetical orthodontic force systems applied on models derived from CBCT images of live patients. In utilizing this methodology, investigators can then estimate the CRES of various teeth and take into consideration the biological morphology of dental structures, such as tooth anatomy, number of roots and their orientation in 3D space, mass distribution, and structure of periodontal attachments. A general outline of this process is shown in Figure 1. This is to orient the reader to the logical process involved in generation of 3D tooth models for locating the CRES.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>3-matic software</td>
			<td>Materialise, Leuven, Belgium.</td>
			<td></td>
			<td>Cleaning and meshing</td>
		</tr>
		<tr>
			<td>Abaqus/CAE software, version 2017</td>
			<td>Dassault Syst&#232;mes Simulia Corp., Johnston, RI, USA.</td>
			<td></td>
			<td>Finite Element Analysis</td>
		</tr>
		<tr>
			<td>Mimics software, version 17.0</td>
			<td>Materialise, Leuven, Belgium.</td>
			<td></td>
			<td>Segmentation of teeth and bone</td>
		</tr>
	</tbody>
</table>

a finite element approach for locating the center of resistance of maxillary teeth

The center of resistance (CRES) is regarded as the fundamental reference point for predictable tooth movement. The methods used to estimate the CRES 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 CRES 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 CRES 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 CRES of maxillary teeth. The CBCT volume images were manipulated to extract three-dimensional (3D) biological structures relevant in determining the CRES 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 CRES. This study is the first step in accurate prediction of tooth movement.

In order to verify segmentation and manual outlining as described in the Procedures section (step 2), a maxillary first molar was extracted from a dry skull, and a CBCT image was taken. The image processing and editing software Mimics was used for manually outlining the tooth as described in step 2. Subsequently, meshing was performed, the segmented models were cleaned with 3matic software, and they were imported to Abaqus for analysis. We did not find any significant difference in the li...

Watch this Scientific Journal Video about A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth at JoVE.com

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

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 CRES of all the maxillary teeth.

The center of resistance (CRES) is regarded as the fundamental reference point for predictable tooth movement. The methods used to estimate the CRES of ...

Now this is for the first time that a work has been done that presents a step-by-step guide on how to figure out the center of resistance. And this is really important because any research that intends to build on it does not have to now go back to the drawing board, kind of reinvent the wheel again, and then move forward. And it takes off an enormous amount of burden off any research that intends to build on this center of resistance concept.This step-by-step method will empower the scientific community to obtain a 3D location of the center of mass for a tooth or a set of teeth in a standardized manner. This technique can be applied both maxillary as well as mandibular dentition. It would be interesting to apply this concept to similar complex tooth movement with multi-bracket assembly.For segmentation of the teeth and bone, load the raw DICOM files of the cone beam computed tomography image into an appropriate medical imaging software program, and crop the image to include only the teeth and bones of interest. Right-click on the tab for Mask, and create a new mask for the image. Click on the Multiple Slice Edit tool, and select the axial, coronal, or sagittal view.Manually highlight some of the slices as necessary, and select the Interpolate tool to fill up the volume for the skipped slices. Then click Apply, and right-click on the mask to generate the 3D volume for the tooth. When a 3D volume has been generated for each tooth of interest, select all of the 3D teeth, and right-click to select Smoothing.To segment the bones, right-click on the tab for Mask, and create a new mask for the image. To fill the large holes visible in the mask, click the Dynamic Region Growing tool. Then right-click on the mask to generate the 3D volume for the bone.For cleaning and meshing of the images, open an appropriate data optimization software program, and paste in the selected 3D objects. For the duplicated teeth in group one, click the Curve Module and the Create Curve option, and manually draw a curve around the cementoenamel junction for all of the duplicated teeth. Duplicate the 3D objects from group one to generate the objects for group two, and in the Object Tree box, click Object.From the Surface list, delete the crown surface for each object in group two, and click Design Module and Hollow to apply the desired parameters. In group one, from the Object Tree box, click Object, and delete the root surface for each group one object. Select the Fill Hole Normal option, and click the Add Contour and Apply.The entire space will be filled. Select the Design Module and Local Offset, and select the entire crown surface. Check Design and the Offset Distance and Diminishing Distance options, and click Apply.In the Remesh Module, Create Non-Manifold Assembly, Main Entity, and Maxilla from the Object Tree and select intersecting entity for all objects. Then split the non-manifold assembly. Split the non-manifold assembly two more times using an intersecting entity as all of the objects from group one and all of the objects from group two and click Apply after each split.Click Adaptive Remesh and select all of the intersecting entities and click Apply. Then click Split Non-Manifold Assembly. Click Create Non-Manifold Assembly, Main Entity, and Individual Object from group two from the Object Tree and select Intersecting Entity and select Respective Object corresponding to the tooth type.Click Adaptive Remesh and select the Intersecting Entity. Then click Create Non-Manifold Assembly. To generate a 0.2 millimeter uniform width of periodontal ligament using the non-manifold technique, it is critical to follow the same order for the main and intersecting entities as demonstrated.When each tooth has been processed as demonstrated, click Create Volume Mesh and select the mesh parameters. In Abacus, click File and Run Script and select Model_setup_Part1.py. Click Simulation, Parts, Maxilla, and Surfaces.Enter the surface name and Under Select the Region of the Surface, select By Angle and set 15 as the angle. Click Simulation and Parts and select UL1 and Surfaces. Name the surface UL1.Under Select the Region of the Surface, select Individually, select the tooth on the screen, and click Done. When all of the tooth surfaces have been processed, click Models, Simulation, and Parts and select UL1_PDL and Surfaces. Name the surface UL1_PDL_Inner.Under Select the Region of the Surface, select By Angle and enter 15 as the angle. Select UL1_PDL and Surfaces and name the surface UL1_PDL_Outer. Under Select the Region of the Surface, select By Angle and set 15 as the angle.When all of the periodontal ligaments have been processed, click File and Run Script and select Model_setup_Part2.py. Click Simulation and BCs. Enter BC All for the name and set the step as initial.Click Simulation, Assembly, Sets, and name the set U1_y_force. Select a node at the center of the crown on the buckle surface of the upper central incisor and in Select the Nodes for the Set, select Individually. Then click Sets and Create Set and name the set U1_z_force.To set up the model, click File and Run Script and select Model_setup_Part3.py. Then click File and Run Script and select Functions.py. To process the model, click File and Run Script and select Job_submission.py.In the Suppress All dialog box, enter the sides of the teeth based on the constraints and click Okay. In the Job Submission dialog box, enter Y to run the analysis for the specified tooth or teeth and click Okay. Then, in the Directions for Analysis dialog box, enter Y to specify the force application and click Okay.To estimate the center of resistance, select File, Run Script, and Bulk_process.py. In the Analyze Multiple Jobs dialog box, enter Y for the specified tooth or teeth and click Okay. In the Directions for Analysis dialog box, enter Y for the specifying force application and click Okay.In the Get Input dialog box, enter the specific tooth number as outlined in the named instances and click Okay. Then check the coordinates for the Force About Point and Estimated Location in the Command box. To verify the segmentation and manual outlining as demonstrated, a maxillary first molar was extracted from a dry skull and a cone beam computed tomography image was taken.Meshing was then performed. No significant difference in the linear and volumetric measurements made on the finite element model of the tooth and the actual tooth as measured in the lab were observed. To verify the validity of the user defined algorithm in determining the center of resistance of an object, a simplified model of a beam encased within a sheath can be used in the initial stages of script creation.By following the defined algorithm and its calculations, the center of resistance of the model beam can be predicted. Here, the material properties assigned to the structures can be observed. Differences in the modeling of the material properties of the periodontal ligament and bone can affect the final location of the center of resistance of a tooth.To standardize the force vectors and to locate the position of the center of resistance, a Cartesian coordinate system can be constructed by the X, Y, and Z orientations as indicated. The R point specific for every tooth is defined as the geometric center on the buckle surface of the crown and is chosen to approximate the closest location at which an operator might place a bracket to apply orthodontic forces. In this representative analysis, the locations of the center of resistance obtained along the X coordinate when a force system was applied along the Y and Z coordinates were different, but the average differences were small.Finite element analyses can be very tedious for new users. Take care to be patient and methodical the first few times you perform the pre-processing steps. So this research is a foundation research.Some of the applications of this can be predicting tooth movement, which is very, very crucial for companies which work in the field of aligners. It can be used to figure out the center of resistance of many teeth, segments of teeth, et cetera, the side effects that are generated during tooth movement, and very, very important perhaps in figuring out how to accelerate tooth movement.

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