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

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.