Name: a finite element approach for locating the center of resistance of maxillary teeth
Uploaded: 2020-04-08T13:00:00
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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F., Budiman, A., Burstone, C. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Axes+of+resistance+for+tooth+movement:+Does+the+Cres+exist+in+3-dimensional+space?.">Axes of resistance for tooth movement: Does the Cres exist in 3-dimensional space?.</a> American Journal of Orthodontics and Dentofacial Orthopedics. 143 (2), 163-172 (2013).</li><li>Ammar, H. H., Ngan, P., Crout, R. J., Mucino, V. H., Mukdadi, O. 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Y., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effect+of+play+between+bracket+and+archwire+on+anterior+tooth+movement+in+sliding+mechanics:+A+three-dimensional+finite+element+study.">Effect of play between bracket and archwire on anterior tooth movement in sliding mechanics: A three-dimensional finite element study.</a> Journal of Dental Biomechanics. 3, 1758736012461269 (2012).</li><li>Cai, Y., Yang, X., He, B., Yao, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Finite+element+method+analysis+of+the+periodontal+ligament+in+mandibular+canine+movement+with+transparent+tooth+correction+treatment.">Finite element method analysis of the periodontal ligament in mandibular canine movement with transparent tooth correction treatment.</a> BMC Oral Health. 15 (106), (2015).</li><li>Pauwels, R., Araki, K., Siewerdsen, J. H., Thongvigitmanee, S. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Technical+aspects+of+dental+CBCT:+state+of+the+art.">Technical aspects of dental CBCT: state of the art.</a> Dentomaxillofacial Radiology. 44 (1), 20140224 (2015).</li><li>Farah, J. W., Craig, R. G., Sikarskie, D. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photoelastic+and+finite+element+stress+analysis+of+a+restored+axisymmetric+first+molar.">Photoelastic and finite element stress analysis of a restored axisymmetric first molar.</a> Journal of Biomechanics. 6 (5), 511-520 (1973).</li><li>van Driel, W. D., van Leeuwen, E. J., Von den Hoff, J. W., Maltha, J. C., Kuijpers-Jagtman, A. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Time-dependent+mechanical+behavior+of+the+periodontal+ligament.">Time-dependent mechanical behavior of the periodontal ligament.</a> Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine. 214 (5), 497-504 (2000).</li><li>Bourauel, C., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Simulation+of+orthodontic+tooth+movements.+A+comparison+of+numerical+models.">Simulation of orthodontic tooth movements. A comparison of numerical models.</a> Journal of Orofacial Orthopedics. 60 (2), 136-151 (1999).</li><li>Schneider, J., Geiger, M., Sander, F. G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Numerical+experiments+on+longtime+orthodontic+tooth+movement.">Numerical experiments on longtime orthodontic tooth movement.</a> American Journal of Orthodontics and Dentofacial Orthopedics. 121 (3), 257-265 (2002).</li><li>Ten Cate, A. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Oral histology, development, structure and function (5th ed). , (1998).</li><li>McCormack, S. W., Witzel, U., Watson, P. J., Fagan, M. J., Gr&#246;ning, F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Biomechanical+Function+of+Periodontal+Ligament+Fibres+in+Orthodontic+Tooth+Movement.">The Biomechanical Function of Periodontal Ligament Fibres in Orthodontic Tooth Movement.</a> PLoS One. 9 (7), e102387 (2014).</li><li>Huang, H., Tang, W., Yan, B., Wu, B., Cao, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mechanical+responses+of+the+periodontal+ligament+based+on+an+exponential+hyperelastic+model:+a+combined+experimental+and+finite+element+method.">Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method.</a> Computer Methods in Biomechanics and Biomedical Engineering. 19 (2), 188-198 (2016).</li><li>Yang, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+new+device+for+measuring+density+of+jaw+bones.">A new device for measuring density of jaw bones.</a> Dentomaxillofacial Radiology. 31 (5), 313-316 (2002).</li><li>Gradl, R., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mass+density+measurement+of+mineralized+tissue+with+grating-based+X-ray+phase+tomography.">Mass density measurement of mineralized tissue with grating-based X-ray phase tomography.</a> PLoS One. 11 (12), e01677979 (2016).</li><li>Jiang, F., Kula, K., Chen, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Estimating+the+location+of+the+center+of+resistance+of+canines.">Estimating the location of the center of resistance of canines.</a> Angle Orthodontics. 86 (3), 365-371 (2016).</li><li>Nyashin, Y., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Center+of+resistance+and+center+of+rotation+of+a+tooth:+experimental+determination,+computer+simulation+and+the+effect+of+tissue+nonlinearity.">Center of resistance and center of rotation of a tooth: experimental determination, computer simulation and the effect of tissue nonlinearity.</a> Computer Methods in Biomechanics and Biomedical Engineering. 19, 229-239 (2016).</li><li>Toms, S. 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M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+caveat+concerning+center+of+resistance.">A caveat concerning center of resistance.</a> Journal of Dental Biomechanics. 4, 1758736013499770 (2013).</li><li>Hohmann, A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Influence+of+different+modeling+strategies+for+the+periodontal+ligament+on+finite+element+simulation+results.">Influence of different modeling strategies for the periodontal ligament on finite element simulation results.</a> American Journal of Orthodontics and Dentofacial Orthopedics. 139 (6), 775-783 (2011).</li></ol>

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 ...

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