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>
2. Segmentation of the teeth and bone
<ol>
	<li>Load the raw DICOM files of the CBCT image into Mimics software for segmentation (Figure 2). Click Image &#62; Crop Project. Crop the image to include only the maxilla and maxillary teeth. 
	NOTE: The field of view should be large enough to capture the maxilla and maxillary teeth. Make sure the image includes the tooth crowns, the hard palate up to the nasal floor, maxillary sinuses, facial surfaces of the maxillary teeth, and the posterior extent of the hard palate and maxillary tuberosity.</li>
	<li>Right click on the tab for Mask and create a New Mask for the image. Rename the mask as UL1, UL2, &#8230;, UL7 for the left side and UR1, UR2, &#8230;, UR7 for the right side, based on the tooth of interest.</li>
	<li>Identify the tooth of interest on the masked CBCT image (see views). Use the Clear Mask tool to erase the mask. The software might be unable to distinguish between the teeth and bone because the gray values of the two are similar. 
	NOTE: The thresholding tool in Mimics is unable to segment the teeth and bone separately. Therefore, a different method for segmentation is required.</li>
	<li>Click on the Multiple Slice Edit tool (Ctrl + M). Select the view (Axial, Coronal, or Sagittal). Manually highlight (i.e., draw) some of the slices as deemed necessary. 
	NOTE: Highlighting more slices adds more detail to the structure.</li>
	<li>Click the Interpolate tool to fill up the volume for the skipped slices and apply.</li>
	<li>Generate the 3D volume for the tooth by right-clicking on the mask and selecting the option to calculate the 3D volume.</li>
	<li>Repeat steps 2.2-2.6 for each tooth of the maxillary arch.</li>
	<li>Select all the 3D maxillary teeth, UL7-UR7. Right-click to select Smoothing. Set the smoothing factor to 0.4 and iterations to 4.</li>
	<li>To segment the maxillary bones right-click on the tab for Mask. Create a new mask for the image.</li>
	<li>From the drop-down menu for predefined threshold sets, select Custom. Adjust the threshold value to include the complete maxillary bone. Be sure to check the Fill Holes box before applying the threshold. 
	NOTE: Small holes of &#8804;1 mm in the cortical bone are acceptable, because they can be removed easily in later stages.</li>
	<li>Click on the Dynamic Region Growing Tool to fill the large holes visible in the mask. Select the maxillary bone mask as the target for the tool in addition to selecting the Multiple Layer box. Use 50 for the Min and 150 for Max values. Hold down the Control key while clicking on the areas of cortical bone that were not highlighted in the mask.</li>
	<li>Right-click on the maxillary bone mask for the Smooth Mask function. Repeat this step 3x for best results.</li>
	<li>Generate the 3D volume for the maxilla by right-clicking on the mask and selecting the option to calculate the 3D volume.</li>
	<li>Select the 3D maxillary bone. Right-click to select smoothing. Set the smoothing factor to ~0.4 and iterations to 4.</li>
	<li>Select the 3D maxillary bone and right-click to select Wrap. Set 0.2 mm for the smallest detail and 1 mm for the gap closing distance. Check the Protect Thin Walls option. Press Ok.</li>
	<li>Rename the 3D maxillary bone &#34;Maxilla&#34;.</li>
</ol>
3. Cleaning and meshing
<ol>
	<li>Select the 3D objects and copy (Ctrl + C).</li>
	<li>Open the 3matic software, and paste (Ctrl + V) the selected 3D objects. They will appear in the object tree and work area of 3matic as a 3D structure (Figure 3).</li>
	<li>Click the Fix tab from the tool bar and use the Smooth option. Under the Operations box select the desired 3D object(s) or entities and Apply the default parameters.</li>
	<li>Click the Finish tab from the tool bar and use the Local Smoothing option. Under the Operations Box select the desired 3D object(s) or entities. Use the cursor to manually smoothen out the desired regions.</li>
	<li>Duplicate the teeth. On the object tree select all teeth, right-click, and select Duplicate.</li>
	<li>Select All Duplicated Teeth, group, and name the folder &#34;group 1&#34;. The original set will serve as the final teeth for analysis.</li>
	<li>For the duplicated teeth in group 1, click the Curve Module and the Create Curve option. Manually draw a curve around the cementoenamel junction (CEJ) for all duplicated teeth.</li>
	<li>Select the Curve, Contour, and Border entities under the Smooth Curve option.</li>
	<li>Separate the crown and root surfaces into their own parts by selecting the Split Surfaces by Curves option and left-clicking on the 3D object to select.</li>
	<li>Generate the PDL from the root structure of the tooth by splitting the tooth into root and crown at the CEJ.
	<ol>
		<li>Duplicate the 3D objects from group 1 (generated in step 3.6) as group 2. For group 2, in the object tree box, click on the Object. From the surface list delete the crown surface. Perform this step for all objects in group 2.</li>
		<li>For group 2, click on Design Module &#62; Hollow. Apply the desired parameters (Table 1).</li>
		<li>Click on the Fix Module &#62; Fix Wizard. Click on the individual parts, update, and follow the given directions.</li>
		<li>Repeat step 3.10.3 for all parts. Rename all parts in the group 2 as &#34;UL1_PDL&#34; to &#34;UL7_PDL&#34; and &#34;UR1_PDL&#34; to &#34;UR7_PDL&#34;.</li>
	</ol>
	</li>
	<li>In group 1, from the object tree box, click on Object. From the surface list delete the root surface.</li>
	<li>Select Fill Hole Normal option and select the contour. Click on Bad Contour and Apply. The entire space will be filled.</li>
	<li>Select the Design Module &#62; Local Offset and select the entire crown surface. Check the following options: Direction (select external), Offset Distance (select 0.5), and Diminishing Distance (select 2.0). Apply.</li>
	<li>Repeat step 3.13.</li>
	<li>Repeat steps 3.11-3.14 for each tooth of the maxillary arch.</li>
	<li>Remesh (Figure 3)
	<ol>
		<li>Click the Remesh Module &#62; Create Non-Manifold Assembly &#62; Main Entity &#62; Maxilla from the object tree. Select intersecting entity for all objects from 3.4 (original teeth) and select Apply.</li>
		<li>Click the Remesh Module. Split the non-manifold assembly.</li>
		<li>Repeat steps 3.16.1-3.16.2 using an intersecting entity as all objects from group 1 and Apply.</li>
		<li>As an optional step, only if required, select the Finish Module &#62; Trim &#62; Entity &#62; Maxilla. Select the excess structure (i.e., noise) and Apply.</li>
		<li>Click the Fix Module &#62; Fix Wizard &#62; Maxilla &#62; Update. Follow the directions given.</li>
		<li>Repeat step 3.16.1 using an intersecting entity as all objects from group 2 and Apply.</li>
		<li>Click the Remesh Module &#62; Adaptive Remesh. Select all intersecting entities from 3.16.6 and Apply.</li>
		<li>Click the Remesh Module &#62; Split Non-manifold Assembly.</li>
		<li>Click the Remesh Module &#62; Create Non-manifold Assembly &#62; Main Entity &#62; Individual Object (PDL) from group 2 from the object tree. Select Intersecting Entity &#62; Select Respective Object from step 3.4 (corresponding to that tooth type) and Apply.</li>
		<li>Click Remesh Module &#62; Adaptive Remesh. Select the intersecting entity from 3.16.9 and Apply.</li>
		<li>Click Remesh Module &#62; Split Non-manifold Assembly.</li>
		<li>Repeat steps 3.16.9-3.16.11 for each tooth.</li>
	</ol>
	</li>
	<li>Click the Remesh Module &#62; Quality Preserving Reduce Triangles. In the object tree select all entities (i.e., teeth, PDLs, and Maxilla) and Apply.</li>
	<li>Click Remesh Module &#62; Create Volume Mesh &#62; Select Entity. Choose Mesh Parameters.</li>
	<li>Repeat step 3.18 for all entities (i.e., teeth, PDLs, and Maxilla).</li>
	<li>Manually export the input(.inp) files from 3Matic to Abaqus (Figure 4).</li>
</ol>
4. Finite element analysis
NOTE: All custom Python scripts can be found in the supplemental attachments. They have been generated using the macro manager function in Abaqus.
<ol>
	<li>Preprocessing setup
	<ol>
		<li>Open Abaqus and select Standard Model. Click File &#62; Set the Work Directory &#62; Select Location for File Storage.</li>
		<li>Click File &#62; Run Script and select Model_setup_Part1.py</li>
		<li>In the Model Directory specify the file path to load .inp files on Abaqus.</li>
		<li>Click on Models &#62; Simulation &#62; Parts &#62; Maxilla &#62; Surfaces.</li>
		<li>Name the surface in the dialog box &#34;UL1 _socket&#34;.</li>
		<li>Under Select the Region of the Surface choose By Angle. Add &#34;15&#34; as the angle.</li>
		<li>Make sure all areas of the socket are selected. Press Done when completed.</li>
		<li>Repeat steps 4.1.4-4.1.7 for the individual sockets.</li>
		<li>Click on Models &#62; Simulation &#62; Parts. Then select UL1 &#62; Surfaces. Name the surface &#34;UL1&#34;.</li>
		<li>Under Select the Region of the Surface opt for &#34;Individually&#34;. Select the tooth on the screen and press Done.</li>
		<li>Repeat steps 4.1.9-4.1.10 for all teeth.</li>
		<li>Click on Models &#62; Simulation &#62; Parts. Then select UL1_PDL &#62; Surfaces. Name the surface &#34;UL1_PDL_inner&#34;.</li>
		<li>Under Select the Region of the Surface choose By Angle. Add &#34;15&#34; as the angle. 
		NOTE: If an error is found during the final simulation, reduce the angle and reselect the surface.</li>
		<li>Make sure the entire inner surface area of the PDL is selected. Press Done when completed.</li>
		<li>Select UL1_PDL &#62; Surfaces. Name the surface &#34;UL1_PDL_outer&#34;.</li>
		<li>Under Select the Region of the Surface choose By Angle. Add &#34;15&#34; as the angle. 
		NOTE: If an error is found during the final simulation, reduce the angle and reselect the surface.</li>
		<li>Make sure the entire outer surface area of the PDL is selected. Press Done when completed.</li>
		<li>Repeat steps 4.1.13-4.1.19 for all PDLs.</li>
		<li>Click on File &#62; Run Script and select Model_setup_Part2.py</li>
		<li>Click on Models &#62; Simulation &#62; BCs. Name BC_all, then select Step as Initial. Under category, select &#34;Mechanical&#34;, and under &#34;Types of Selected Step&#34; select &#34;Displacement/Rotation&#34;. Press Continue.</li>
		<li>Under Select Regions for the Boundary Condition select By Angle. Add &#34;15&#34; as the angle. Check Create Set. Select individual sockets for the 14 teeth. Press Done. 
		NOTE: This helped simulate instantaneous tooth movement.</li>
		<li>Click on Models &#62; Simulation &#62; Assembly &#62; Sets &#62; Create Set. Name the set &#34;U1_y_force&#34;.</li>
		<li>In Select the Nodes for the Set choose Individually. 
		NOTE: A one Newton concentrated force was applied on a randomly selected tooth node in either the positive Y direction (simulating a distalization force) or the positive Z direction (simulating an intrusive force).</li>
		<li>Select a node at the center of the crown on the buccal surface of the upper central incisor (U1) and press Done.</li>
		<li>Click Sets &#62; Create Set. Name the set &#34;U1_z_force&#34;.</li>
		<li>Repeat steps 4.1.23-4.1.24.</li>
		<li>Repeat steps 4.1.22-4.1.26 for all teeth. 
		NOTE: Before a set is generated for a particular tooth as in 4.1.25, go to Instance &#62; Resume for that tooth.</li>
	</ol>
	</li>
	<li>Model set up
	<ol>
		<li>Click on Models &#62; Simulation &#62; Assembly &#62; Instances. Select All Instances and click Resume.</li>
		<li>Click on Tools &#62; Query &#62; Point/Node. Select a node at the center of a randomly selected central incisor and press Done.</li>
		<li>Under the command center at the bottom of the page, copy the X, Y, and Z coordinates of the node selected in step 4.2.2.</li>
		<li>Under the vertical tool bar select Translate Instance and select the entire assembly (i.e., all instances) on the screen. Press Done.</li>
		<li>In the Select a Start Point for the Translation Vector box, paste the copied coordinates in step 4.2.3 or enter the X, Y, and Z values. Click Enter.</li>
		<li>Under Select an End Point for the Translation Vector or enter X,Y,Z: enter the coordinates &#34;0.0&#34;, &#34;0.0&#34;, and &#34;0.0&#34;. Click Enter.</li>
		<li>For Position of Instance, press Ok.</li>
		<li>Click on Tools &#62; Query &#62; Point/Node and select a node directly above the midline of the center incisors. Enter Done.</li>
		<li>Under the command center at the bottom of the page, copy the X, Y, and Z coordinates of the node selected in step 4.2.8.</li>
		<li>Under the vertical tool bar select Translate Instance and select the entire assembly (i.e., all instances) on the screen. Enter Done.</li>
		<li>Paste the copied coordinates into the Select a Start Point for the Translation Vector - or Enter X,Y,Z box. Click Enter.</li>
		<li>Under Select an End Point for the Translation Vector - or enter X,Y,Z: insert the coordinates as copied in step 4.2.9. Change the X coordinate to 0.0. Click Enter.</li>
		<li>For Position of Instance, press Ok.</li>
		<li>Click on File &#62; Run Script and select Model_setup_Part3.py. Insert or change material properties.</li>
		<li>Click on Models &#62; Simulation &#62; Materials and click Bone/PDL/Tooth. Insert tissue specific properties.</li>
		<li>Click on File &#62; Run Script and select Functions.py.</li>
	</ol>
	</li>
	<li>Processing the model
	<ol>
		<li>Click on File &#62; Run Script and select Job_submission.py. 
		NOTE: The job module is where the user sets up one or more actions on the model, and job manager is where model analysis is started, progress is shown, and completion is noted.</li>
		<li>In the dialog box titled Suppress All, enter the sides (L or R) of the teeth based on constraints (Under Models &#62; Simulation &#62; Constraints). Press Ok.</li>
		<li>In the dialog box titled Job Submission enter &#34;Y&#34; to run the analysis for the specified tooth/teeth. Press Ok.</li>
		<li>In the dialog box titled Directions for Analysis enter &#34;Y&#34; to specify force application. Press Ok.</li>
	</ol>
	</li>
	<li>Post processing for C RES estimation
	<ol>
		<li>Choose File &#62; Run Script &#62; Bulk_process.py.</li>
		<li>In the dialog box titled Analyze Multiple Jobs enter &#34;Y&#34; for the specified tooth/teeth. Press Ok.</li>
		<li>In the dialog box titled Directions for Analysis enter &#34;Y&#34; for specifying force application. Press Ok.</li>
		<li>In the dialog box titled Get Input enter Specific Tooth Number as outlined named Instances (e.g., UL1 or UL5, etc.). Press Ok.</li>
		<li>Check coordinates for the Force About Point and Estimated Location in the command box. If they are not similar, then repeat steps 4.3.1-4.4.4. 
		NOTE: After the jobs for each step were run, a user-defined algorithm created in Python was run within the Abaqus interface to analyze the reaction force system and subsequent moments created as a result of load application. The algorithm automatically suggests a new node location to apply the load such that a moment of near-zero magnitude is created within the force system. This proceeds in an iterative process, until the node location that creates a moment closest to zero when a force is applied through it is found or estimated. The algorithm is described in detail in the Discussion section.</li>
	</ol>
	</li>
</ol>

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<li>Bourauel, C., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Simulation+of+orthodontic+tooth+movements.+A+comparison+of+numerical+models%5BTitle%5D)+AND+%22Journal+of+Orofacial+Orthopedics%22%5BJournal%5D)">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/pubmed?term=((Numerical+experiments+on+longtime+orthodontic+tooth+movement%5BTitle%5D)+AND+%22American+Journal+of+Orthodontics+and+Dentofacial+Orthopedics%22%5BJournal%5D)">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://scholar.google.com/scholar?hl=en&safe=off&q=author%3aTen+Cate%2C+AR+%22Oral+histology%2C+development%2C+structure+and+function+%285th+ed%29%22">Oral histology, development, structure and function (5th ed)</a>. , St. Louis Mosby. (1998).</li>
<li>McCormack, S. W., Witzel, U., Watson, P. J., Fagan, M. J., Gröning, F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((The+Biomechanical+Function+of+Periodontal+Ligament+Fibres+in+Orthodontic+Tooth+Movement%5BTitle%5D)+AND+%22PLoS+One%22%5BJournal%5D)">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/pubmed?term=((Mechanical+responses+of+the+periodontal+ligament+based+on+an+exponential+hyperelastic+model%3A+a+combined+experimental+and+finite+element+method%5BTitle%5D)+AND+%22Computer+Methods+in+Biomechanics+and+Biomedical+Engineering%22%5BJournal%5D)">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/pubmed?term=((A+new+device+for+measuring+density+of+jaw+bones%5BTitle%5D)+AND+%22Dentomaxillofacial+Radiology%22%5BJournal%5D)">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/pubmed?term=((Mass+density+measurement+of+mineralized+tissue+with+grating-based+X-ray+phase+tomography%5BTitle%5D)+AND+%22PLoS+One%22%5BJournal%5D)">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/pubmed?term=((Estimating+the+location+of+the+center+of+resistance+of+canines%5BTitle%5D)+AND+%22Angle+Orthodontics%22%5BJournal%5D)">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/pubmed?term=((Center+of+resistance+and+center+of+rotation+of+a+tooth%3A+experimental+determination%2C+computer+simulation+and+the+effect+of+tissue+nonlinearity%5BTitle%5D)+AND+%22Computer+Methods+in+Biomechanics+and+Biomedical+Engineering%22%5BJournal%5D)">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. R., Eberhardt, A. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((A+nonlinear+finite+element+analysis+of+the+periodontal+ligament+under+orthodontic+tooth+loading%5BTitle%5D)+AND+%22American+Journal+of+Orthodontics+and+Dentofacial+Orthopedics%22%5BJournal%5D)">A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading.</a> American Journal of Orthodontics and Dentofacial Orthopedics. 123 (6), 657-665 (2003).</li>
<li>Osipenko, M. A., Nyashin, M. Y., Nyashin, Y. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Centre+of+resistance+and+centre+of+rotation+of+a+tooth%3A+the+definitions%2C+conditions+of+existence%2C+properties%5BTitle%5D)+AND+%22Russian+Journal+of+Biomechanics%22%5BJournal%5D)">Centre of resistance and centre of rotation of a tooth: the definitions, conditions of existence, properties.</a> Russian Journal of Biomechanics. 3 (1), 5-15 (1999).</li>
<li>Dathe, H., Nägerl, H., Dietmar, K. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((A+caveat+concerning+center+of+resistance%5BTitle%5D)+AND+%22Journal+of+Dental+Biomechanics%22%5BJournal%5D)">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/pubmed?term=((Influence+of+different+modeling+strategies+for+the+periodontal+ligament+on+finite+element+simulation+results%5BTitle%5D)+AND+%22American+Journal+of+Orthodontics+and+Dentofacial+Orthopedics%22%5BJournal%5D)">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>

The authors have nothing to disclose.

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><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&amp;egrave;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...

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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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9.6K Views.  University of Connecticut Health. 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.

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

Choice and No-Choice Assays for Testing the Resistance of A. thaliana to Chewing Insects

Larvae of the small white cabbage butterfly are a pest in agricultural settings. This caterpillar species feeds from plants in the cabbage family, which include many crops such as cabbage, broccoli, Brussel sprouts etc. Rearing of the insects takes place on cabbage plants in the greenhouse. At least two cages are needed for the rearing of Pieris rapae. One for the larvae and the other to contain the adults, the butterflies. In order to investigate the role of plant hormones and toxic plant chemicals in resistance to this insect pest, we demonstrate two experiments. First, determination of the role of jasmonic acid (JA - a plant hormone often indicated in resistance to insects) in resistance to the chewing insect Pieris rapae. Caterpillar growth can be compared on wild-type and mutant plants impaired in production of JA. This experiment is considered "No Choice", because larvae are forced to subsist on a single plant which synthesizes or is deficient in JA. Second, we demonstrate an experiment that investigates the role of glucosinolates, which are used as oviposition (egg-laying) signals. Here, we use WT and mutant Arabidopsis impaired in glucosinolate production in a "Choice" experiment in which female butterflies are allowed to choose to lay their eggs on plants of either genotype. This video demonstrates the experimental setup for both assays as well as representative results.

Plant resistance to chewing insect herbivores can be tested in several ways. Here, we demonstrate how to set-up a choice and a no-choice experiment with the model plant Arabidopsis thaliana to identify resistance against the pest species Pieris rapae.

Larvae of the small white cabbage butterfly are a pest in agricultural settings. This caterpillar species feeds from plants in the cabbage family, which ...

Methods for the Study of the Zebrafish Maxillary Barbel

Barbels are skin sensory appendages found in fishes, reptiles and amphibians. The zebrafish, Danio rerio, develops two pairs of barbels- a short nasal pair and a longer maxillary pair. Barbel tissue contains cells of ectodermal, mesodermal and neural crest origin, including skin cells, glands, taste buds, melanocytes, circulatory vessels and sensory nerves. Unlike most adult tissue, the maxillary barbel is optically clear, allowing us to visualize the development and maintenance of these tissue types throughout the life cycle. 
This video shows early development of the maxillary barbel (beginning approximately one month post-fertilization) and demonstrates a surgical protocol to induce regeneration in the adult appendage (&gt;3 months post-fertilization). Briefly, the left maxillary barbel of an anesthetized fish is elevated with sterile forceps just distal to the caudal edge of the maxilla. A fine, sterile spring scissors is positioned against the forceps to cut the barbel shaft at this level, establishing an anatomical landmark for the amputation plane. Regenerative growth can be measured with respect to this plane, and in comparison to the contralateral barbel. Barbel tissue regenerates rapidly, reaching maximal regrowth within 2 weeks of injury.
Techniques for analyzing the regenerated barbel include dissecting and embedding matched pairs of barbels (regenerate and control) in the wells of a standard DNA electrophoresis gel. Embedded specimens are conveniently photographed under a stereomicroscope for gross morphology and morphometry, and can be stored for weeks prior to downstream applications such as paraffin histology, cryosectioning, and/or whole mount immunohistochemistry. These methods establish the maxillary barbel as a novel in vivo tissue system for studying the regenerative capacity of multiple cell types within the genetic context of zebrafish.

The zebrafish maxillary barbel is an integumentary sense organ containing ectodermal, mesodermal and neural crest derivatives. Importantly, the adult barbel can regenerate after proximal amputation. This video introduces maxillary barbel development and demonstrates a surgical protocol to induce regeneration, followed by collection, embedding and downstream imaging of barbel specimens.

Barbels are skin sensory appendages found in fishes, reptiles and amphibians.  The zebrafish, Danio rerio, develops two pairs of barbels- a short nasal ...

Bioassays for Monitoring Insecticide Resistance

Pest resistance to pesticides is an increasing problem because pesticides are an integral part of high-yielding production agriculture. When few products are labeled for an individual pest within a particular crop system, chemical control options are limited. Therefore, the same product(s) are used repeatedly and continual selection pressure is placed on the target pest. There are both financial and environmental costs associated with the development of resistant populations. The cost of pesticide resistance has been estimated at approximately $ 1.5 billion annually in the United States. This paper will describe protocols, currently used to monitor arthropod (specifically insects) populations for the development of resistance. The adult vial test is used to measure the toxicity to contact insecticides and a modification of this test is used for plant-systemic insecticides. In these bioassays, insects are exposed to technical grade insecticide and responses (mortality) recorded at a specific post-exposure interval. The mortality data are subjected to Log Dose probit analysis to generate estimates of a lethal concentration that provides mortality to 50% (LC50) of the target populations and a series of confidence limits (CL's) as estimates of data variability. When these data are collected for a range of insecticide-susceptible populations, the LC50 can be used as baseline data for future monitoring purposes. After populations have been exposed to products, the results can be compared to a previously determined LC50 using the same methodology.

This manuscript demonstrates and discusses techniques used to survey pesticide susceptibility and detect resistance to contact and systemic pesticides in arthropod pests.

Pest resistance to pesticides is an increasing problem because pesticides are an integral part of high-yielding production agriculture. When few products ...

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires

A proper understanding of the force system created by various orthodontic appliances can make treatment of patients efficient and predictable. Reducing the complicated multi-bracket appliances to a simple two-bracket system for the purpose of force system evaluation will be the first step in this direction. However, much of the orthodontic biomechanics in this regard is confined to 2D experimental studies, computer modeling/analysis or theoretical extrapolation of existing models. The objective of this protocol is to design, construct and validate an in vitro 3D model capable of measuring the forces and moments generated by an archwire with a V-bend placed between two brackets. Additional objectives are to compare the force system generated by different types of archwires among themselves and to previous models. For this purpose, a 2 x 4 appliance representing a molar and an incisor has been simulated. An orthodontic wire tester (OWT) is constructed consisting of two multi-axis force transducers or load cells (nanosensors) to which the orthodontic brackets are attached. The load cells are capable of measuring the force system in all the three planes of space. Two types of archwires, stainless-steel and beta-titanium of three different sizes (0.016 x 0.022 inch, 0.017 x 0.025 inch and 0.019 x 0.025 inch), are tested. Each wire receives a single vertical V-bend systematically placed at a specific position with a predefined angle. Similar V-bends are replicated on different archwires at 11 different locations between the molar and incisor attachments. This is the first time an attempt has been made in vitro to simulate an orthodontic appliance utilizing V-bends on different archwires.

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires

The method presented here is designed to construct and validate an in vitro 3D model capable of measuring the force system generated by different archwires with V-bends placed between two brackets. Additional objectives are to compare this force system with different types of archwires and to previous models.

A proper understanding of the force system created by various orthodontic appliances can make treatment of patients efficient and predictable. Reducing ...

Bioengineering

Designing CAD/CAM Surgical Guides for Maxillary Reconstruction Using an In-house Approach

Computer-aided design/computer-assisted manufacturing (CAD/CAM) is now being evaluated as a preparative technique for maxillofacial surgery. Because this technique is expensive and available in only limited areas of the world, we developed a novel CAD/CAM surgical guide using an in-house approach. By using the CAD software, the maxillary resection area and cutting planes and the fibular cutting planes and angles are determined. Once the resection area is decided, the necessary faces are extracted using a Boolean modifier. These superficial faces are united to fit the surface of the bones and thickened to stabilize the solids. Not only the cutting guides for the fibula and maxilla but also the location arrangement of the transferred bone segments is defined by thickening the superficial faces. The CAD design is recorded as .stl files and three-dimensionally (3-D) printed as actual surgical guides. To check the accuracy of the guides, model surgery using 3-D-printed facial and fibular models is performed. These methods may be used to assist surgeons where commercial guides are not available.

Methods for designing a computer-aided design/computer-aided manufacturing (CAD/CAM) surgical guide are shown. Cutting planes are separated, united, and thickened to easily visualize the necessary bone transfer. These designs can be three-dimensional printed and checked for accuracy.

Computer-aided design/computer-assisted manufacturing (CAD/CAM) is now being evaluated as a preparative technique for maxillofacial surgery. Because this ...

Medicine

Analysis of Expansion Patterns from SARPE Using Finite Element Models

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion

Surgically assisted rapid palatal expansion (SARPE) was introduced to release bony resistance to facilitate skeletal expansion in skeletally mature patients. However, asymmetric expansion between the left and right sides has been reported in 7.52% of all SARPE patients, of which 12.90% had to undergo a second surgery for correction. The etiologies leading to asymmetric expansion remain unclear. Finite element analysis has been used to evaluate the stress associated with SARPE in the maxillofacial structures. However, as a collision of the bone at the LeFort I osteotomy sites occurs only after a certain amount of expansion, most of the existing models do not truly represent the force distribution, given that the expansion amount of these existing models rarely exceeds 1 mm. Therefore, there is a need to create a novel finite element model of SARPE that could perform a clinically required amount of expander activation for further analysis of the expansion patterns of the hemimaxillae in all three dimensions. A three-dimensional (3D) skull model from cone beam computed tomography (CBCT) was imported into Mimics and converted into mathematical entities to segment the maxillary complex, maxillary first premolars, and maxillary first molars. These structures were transferred into Geomagic for surface smoothing and cancellous bone and periodontal ligament creation. The right half of the maxillary complex was then retained and mirrored to create a perfectly symmetrical model in SolidWorks. A Haas expander was constructed and banded to the maxillary first premolars and first molars. Finite element analysis of various combinations of buccal osteotomies at different angles with 1 mm clearance was performed in Ansys. A convergence test was conducted until the desired amount of expansion on both sides (at least 6 mm in total) was achieved. This study lays the foundation for evaluating how buccal osteotomy angulation influences the expansion patterns of SARPE.

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques 

A set of novel finite element models of surgically assisted rapid palatal expansion (SARPE) that could perform a clinically required amount of expander activation with various angles of buccal osteotomy was created for further analysis of the expansion patterns of the hemimaxillae in all three dimensions.

Surgically assisted rapid palatal expansion (SARPE) was introduced to release bony resistance to facilitate skeletal expansion in skeletally mature ...

3D Cephalometric Landmark Annotation Demonstration on Human CBCT Scans

Three-Dimensional Cephalometric Landmark Annotation Demonstration on Human Cone Beam Computed Tomography Scans

Craniofacial cephalometric analysis is a diagnostic tool used for the assessment of the relationship of various bones and soft tissues in the head and face. Cephalometric analysis has been traditionally conducted with the use of 2D radiographs and landmark sets and restricted to size, linear and angular measurements, and 2D relationships. The increasing use of 3D cone beam computed tomography (CBCT) scans in the dental field dictates the need for the evolution to 3D cephalometric analysis, which incorporates shape and a more realistic analysis of longitudinal development in all three planes. This study is a demonstration of 3D cephalometric analysis with the use of a validated set of skeletal tissue landmarks on human CBCT scans. Detailed instructions for the annotation of each landmark on a 3D volume are provided as part of a step-by-step protocol. The generated measurements and 3D coordinates of the landmarks can be exported and used both for clinical and research purposes. The introduction of 3D cephalometric analysis in basic and clinical craniofacial studies will lead to future advancements in the field of craniofacial growth and development.

Author Spotlight: Three-Dimensional Cephalometric Landmark Annotation Demonstration on Human Cone Beam Computed Tomography Scans  

Presented here is a detailed protocol for the conduction of three-dimensional cephalometric analysis with the use of human cone beam computed tomography scans.

Craniofacial cephalometric analysis is a diagnostic tool used for the assessment of the relationship of various bones and soft tissues in the head and ...

A Murine Maxillary Orthodontic Model Guide to Bone Remodeling Analysis

The Establishment of a Murine Maxillary Orthodontic Model

Due to the lack of reproducible protocols for establishing a murine maxillary orthodontic model, we present a reliable and reproducible protocol to provide researchers with a feasible tool to analyze mechanical loading-associated bone remodeling. This study presents a detailed flowchart in addition to different types of schematic diagrams, operation photos, and videos. We performed this protocol on 11 adult wide-type C57/B6J mice and harvested samples on postoperative days 3, 8, and 14. The micro-CT and histopathological data have proven the success of tooth movements coupled with bone remodeling using this protocol. Furthermore, according to the micro-CT results on days 3, 8, and 14, we have divided bone modeling into three stages: preparation stage, bone resorption stage, and bone formation stage. These stages are expected to help researchers concerned with different stages to set sample collection time reasonably. This protocol can equip researchers with a tool to carry out regenerative analysis of bone remodeling.

Author Spotlight: Insights into an Efficient Murine Maxillary Orthodontic Model Protocol

Here we demonstrate step-by-step a manageable, orthodontic tooth movement protocol operated on a murine maxillary model. With the explicit explanation of each step and visual demonstration, researchers can master this model and apply it to their experimental needs with a few modifications.

Due to the lack of reproducible protocols for establishing a murine maxillary orthodontic model, we present a reliable and reproducible protocol to ...

Evaluation of Maxillary Posterior Tooth Movement Using Digital Superimposition

Measuring Maxillary Posterior Tooth Movement: A Model Assessment using Palatal and Dental Superimposition

Since the introduction of Invisalign by Align Technology, Inc. in 1999, questions and debates have persisted regarding the precision of Invisalign (clear aligner) therapy, particularly when compared to the use of traditional fixed appliances. This becomes particularly significant in cases involving anteroposterior, vertical, and transverse corrections, where precise comparisons are of paramount importance. To address these inquiries, this study introduces a meticulously devised protocol, placing a primary emphasis on digitally superimposing the movement of maxillary posterior teeth to facilitate accurate analysis. The sample included 25 patients who had completed their first series of Invisalign (clear) aligners. Four maxillary digital models (pre-treatment, post-treatment, ClinCheck-initial, and final models) were digitally superimposed using the palate rugae and dentitions as stable references. A software combination was used for model superimposition and tooth segmentation. Transformation matrices then expressed the differences between the achieved and predicted tooth positions. Thresholds for clinically relevant differences were at &plusmn;0.25 mm for linear displacement and &plusmn;2&#176; for rotation. Differences were assessed using Hotelling's T-squared tests with Bonferroni correction. The mean differences in rotation (2.036&#176; &plusmn; 4.217&#176;) and torque (-2.913&#176; &plusmn; 3.263&#176;) were significant statistically and clinically, with p-values of 0.023 and 0.0003 respectively. De-rotation of premolars and torque control for all posterior teeth were less predictable. All mean differences for the linear measurements were statistically and clinically insignificant, except that the first molars seemed slightly (0.256 mm) more intruded than their predicted position. The clear aligner system appears to meet its prediction for most translational tooth movements and mesial-distal tipping in maxillary posterior teeth for non-extraction cases with mild to moderate malocclusions.

Author Spotlight: 3D Movement Assessment of Maxillary Posterior Teeth in Clear Aligner Treatment

This manuscript presents a comprehensive protocol to evaluate the three-dimensional (3D) movement of maxillary posterior teeth with clear aligners using digital model superimposition, an invaluable tool in orthodontics and dentofacial orthopedics.

Since the introduction of Invisalign by Align Technology, Inc. in 1999, questions and debates have persisted regarding the precision of Invisalign (clear ...

Investigating Orthodontic Tooth Movement and Bone Adaptation Mechanisms in Mice

Studying Orthodontic Tooth Movement in Mice

Orthodontic tooth movement (OTM) represents a dynamic process in which the alveolar bone undergoes resorption at compression sites and deposition at tension sites, orchestrated by osteoclasts and osteoblasts, respectively. This mechanism serves as a valuable model for studying various aspects of bone adaptation, including root resorption and the cellular response to mechanical force stimuli. The protocol outlined here offers a straightforward approach to investigate OTM, establishing 0.35 N as the optimal force in a mouse model employing a nickel-titanium (NiTi) coil spring. Utilizing micro-computed tomography analysis, we quantified OTM by assessing the discrepancy in the linear distance at the cement-enamel junction. The evaluation also included an analysis of orthodontic-induced inflammatory root resorption, assessing parameters such as root mineral density and the percentage of root volume per total volume. This comprehensive protocol contributes to advancing our understanding of bone remodeling processes and enhancing the ability to develop effective orthodontic treatment strategies.

Here, we present a protocol for studying orthodontic tooth movement (OTM), serving as a suitable model for investigating the mechanisms of bone adaptation, root resorption, and the response of bone cells to mechanical stimuli. This comprehensive guide provides detailed information on the OTM model, micro-computed tomography acquisition, and subsequent analysis.

Orthodontic tooth movement (OTM) represents a dynamic process in which the alveolar bone undergoes resorption at compression sites and deposition at ...

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

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