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

Summary

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.

Abstract

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 ±0.25 mm for linear displacement and ±2° for rotation. Differences were assessed using Hotelling's T-squared tests with Bonferroni correction. The mean differences in rotation (2.036° ± 4.217°) and torque (-2.913° ± 3.263°) 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.

Introduction

In 1999, digitally fabricated removable orthodontic appliances were made commercially available by Align (Align Technology Inc., Tempe, AZ). Originally, this system was designed to solve non-growing cases with mild to moderate crowding or close small spaces as an aesthetic alternative to traditional fixed edgewise appliances. With decades of improvements in computer-aided design and manufacturing (CAD/CAM), dental materials, and treatment planning, clear aligner therapy (CAT) has since been used to treat over 10 million patients with various malocclusions worldwide¹. A recent retrospective study suggested that CAT is as effective as fixed appliance therapy for the teenage population with mild malocclusions, with significantly improved results in tooth alignment, occlusal relations, and overjet². The number of appointments, emergency visits, and overall treatment time also had better outcomes for clear aligner therapy patients. Although CAT can be used to treat non-extraction, mild-to-moderate malocclusions in non-growing patients^3,4, and shorten treatment duration and chair time⁵, it remains unclear whether the treatment is as effective as the gold standard of conventional labial braces^4,6,7,8,9, especially for anteroposterior and vertical correction¹⁰.

ClinCheck is a software platform developed by Align to provide clinicians with virtual three-dimensional (3D) simulations of prospective tooth movements. Primarily concerned with the patient's initial status and the clinician's prescribed treatment plan, it can also be a visual communication tool for the patient. Any mismatch between the predicted and achieved results may require a mid-course correction, refinement, or conversion to fixed appliance therapy. Consequently, the reliability of software predictions has drawn increasing attention from investigators. Since Lagravere and Flores-Mir's systematic review published in 2005¹¹, investigations into the concordance between predicted models and post-treatment models have been measured in different ways, measurement methods including arch-length, inter-canine distance, overbite, overjet, midline deviation¹², the American Board of Orthodontics objective grading system (ABO-OGS) reduction score¹³, upper and lower interdental width¹⁴, and measures derived from cone-beam computed tomography¹⁵.

Comparisons have also been made by superimposing 3D models^{16,17,18,19,20,21}. For example, many current software platforms, such as ToothMeasure (internal software developed by Align Technology), can reproducibly superimpose two digital models using user-selected reference points on untreated teeth, palatal rugae, or dental implants. Since the predicted and achieved models usually do not include the palatal surfaces, many previous studies^15,16,17,18 have used the untreated posterior teeth as references for superimposition, including the possibility of adding errors due to the relative movements of these teeth. These studies have been confined to anterior regions of the arch in relatively simple cases with spacing or mild to moderate crowding.

Grünheid et al. used mathematical superimposition to quantify the discrepancies between virtual treatment plans and actual treatment outcomes to evaluate the accuracy of full-dentition CAT without stable anatomic structures in digital models²⁰. Haouili et al. used the same method in a best-fit algorithm within the Compare software to conduct a prospective follow-up study on the efficacy of tooth movement with CAT²¹. The aim was to provide an update on the accuracy associated with emerging technology, i.e., SmartForce, SmartTrack aligner materials, and digital scans. Their findings of an improved overall accuracy from 41%¹⁷ to 50%²¹ were encouraging but do not negate the possibility that some tooth movements are still not satisfactorily achievable with the clear aligner system.

When predicted and achieved, digital models include a common 3D reference independent of the dentition, such as palatal rugae, dental implants, or tori; they can be co-registered within the coordinate system of many suitable software platforms. If a tooth of interest is then segmented from one and transformed mathematically to match its displaced version in the other, the transformation matrix contains the complete information needed to describe the entire 3D transposition. Its content can be expressed as three translations and three rotations described by a formal convention. An example is found on the Invisalign ClinCheck Pro 3D control software, where the numerical parameters indicating the 3D tooth movements needed to move teeth to their predicted positions are shown in a tooth movement table.

While the initial and final (predicted) models from the planning software share a common coordinate system provided by the same software platform, their absence of palates restricts the possibility of co-registering with any other digital dentition model unless they possess identical dentition. In this context, it was hypothesized that the superimposition of software-predicted and post-treatment (achieved) models would be feasible. This feasibility arises from the availability of two pairs: initial and final (automatically superimposed during export from planning software) and another pair of pre-treatment and achieved models (superimposed using palatal rugae). These pairs could be registered using the pre-treatment dentition as a reference to align them with the Invisalign-initial model. Subsequently, the segmentation of individual teeth could be performed to assess differences in their positions and orientations. This assessment involves transposing teeth between the models, and the transformation matrices would enable a numerical quantification of the translations and re-orientations.

In this protocol, an approach to evaluate the effectiveness of CAT in addressing mild to moderate malocclusions in both adolescents and adults was introduced, specifically focusing on the maxillary posterior teeth. The null hypothesis was that there was no difference between the achieved and the planning software-predicted tooth position in the maxillary posterior teeth after the first series of clear aligners.

Protocol

This study received ethical approval from the Institutional Review Board at the University of British Columbia (No. H19-00787). To uphold confidentiality, all samples utilized in the study underwent de-identification procedures. Furthermore, prior to their inclusion in the research, informed consent was appropriately obtained from all participating patients.

NOTE: Each participant contributed four maxillary digital models, which encompassed the following:

1. Pre-treatment digital model, with the palate scanned using iTero
2. Post-treatment digital model, with the palate scanned using iTero
3. Pre-treatment model, exported from the planning software.
4. Predicted model, exported from the planning software.

This protocol leveraged a combination of several software tools, which included CloudCompare, Meshmixer, and Rhinoceros. These software platforms played a pivotal role in facilitating the registration process and enabling the segmentation of individual teeth for the purpose of analyzing their movements and orientations. It is worth noting that these software tools may be replicable with other open-source software options, provided that they can achieve similar objectives. A workflow illustrating the software sequence is presented in Figure 1.

1. Preparation

1. Obtain the initial and final (predicted) models as stereolithographic (STL) files from the planning software by clicking on Tools > Export > STL.
   NOTE: Models exported from the planning software present only clinical crowns and virtual gingiva without the palate.
2. Obtain the pre-treatment and post-treatment digital models as STL files from the scanned model software (OrthoCAD) by selecting the scan, clicking and choosing Export > Export Type (open shell), Data Format (File per Arch [arches oriented in occlusion]).
   ​NOTE: Models exported from the model scanning software include not only dentition but also gingiva and the whole palate.

2. Palatal superimposition of pre- and post-treatment digital models in CloudCompare

1. Open the software and drag and drop the STL files of the pre-treatment and post-treatment digital models.
2. Select each model and click Edit > Colors > Set Unique to change the colors of the selected models.
3. Select the post-treatment digital model and click the Translate/Rotate icon. Right-click to drag the model so they are side by side. Click the Green Checkmark.
4. Select the pre-treatment digital model and click the Segment icon.
5. Click four points on the palatal rugae and right-click to deselect. Click Segment In, then click the Green Checkmark. Repeat steps 2.4 to 2.5 for the post-treatment digital model.
6. Hide the PostTreatModel.remaining and PreTreatModel.remaining models and select both the PostTreatModel.part and PreTreatModel.part models.
7. Click the Rough Registration alignment icon (point pair picking) and place at least three corresponding landmarks on the palate on each side of the midline for both the pre- and post-treatment palates. Click Align, then click the Green Checkmark.
8. Unhide the meshes for both models and move the untransformed PostTreatModel.remaining model by copying the transformation matrix, clicking Edit > Apply Transformation, and pasting the transformation matrix.
   NOTE: The transformation matrix outputs are shown in the console.
9. Hide the PostTreatModel.remaining and PreTreatModel.remaining models and select the PostTreatModel.part and PreTreatModel.part models.
10. Click the Fine Registration alignment icon and make sure the PreTreatModel.part model is selected as the reference. Click Ok.
    NOTE: Confirm the resulting root mean square (RMS) in the registration information window. A deviation of ≤ 0.05 RMS is acceptable.
11. Unhide the meshes for both models and move the untransformed PostTreatModel.remaining model by copying the transformation matrix, clicking Edit > Apply Transformation, and pasting the transformation matrix.
12. Save the superimposed PostTreatModel.remaining and PreTreatModel.remaining models as STL files.

3. Software-model preparation for superimposition with Rhinoceros software

1. Import the STL files of the planning software pre-treatment and predicted models separately.
   NOTE: When importing software models into measurement software such as Rhinoceros or CloudCompare, the orientation and models' registration are preserved
2. Select the simulated gingiva and press Delete to remove it.
3. Click MeshTools, select Meshplane. Draw a plane around the teeth and move the plane to the occlusal 1/3 of the tooth crowns. This wil improve the superimposition precision.
4. Double click the button Right to expand the right view.
5. Enter the command MeshBooleanSplit and select the plane and all the teeth then press Enter.
6. Delete the plane and cervical portions of the teeth leaving the 1/3 occlusal tooth crowns.
7. Save the split model as an STL file.
8. Repeat all steps for the other model.

4. Superimposition of software-predicted and post-treatment digital models with CloudCompare

1. Drag and drop the STL files of the previously palatally superimposed pre-treatment and post-treatment digital models, and the split pre-treatment and split predicted models.
2. Select each model and click Edit > Colors > Set Unique to change the colors of the selected models.
3. Select both the pre-treatment and post-treatment digital models and click the Translate/Rotate icon. Right-click to drag the models so they are side by side.
4. Request the software hide the split predicted model and post-treatment digital model by uncheckmarking the corresponding boxes. Select the split pre-treatment model and pre-treatment digital model.
5. Click the Rough Registration alignment icon and place corresponding landmarks on the crowns' cusps on both the split pre-treatment model and the pre-treatment digital model. Click Align, then click the Green Checkmark.
6. Unhide the split predicted model and post-treatment model and move the untransformed post-treatment model by copying the transformation matrix, clicking Edit > Apply Transformation, and pasting the transformation matrix.
7. Hide the post-treatment and split predicted models. Select the pre-treatment and split pre-treatment models. Click the Fine Registration alignment icon for the best fit between the split pre-treatment model and the pre-treatment digital model.
8. Unhide the meshes and move the untransformed model by copying the transformation matrix, clicking Edit > Apply Transformation, and pasting the transformation matrix.
9. Unhide the split predicted and post-treatment digital models, then Hide the split pre-treatment model and pre-treatment digital model to display the superimposition (Figure 2).
10. Save the models as STL files.

5. Crown segmentation using Meshmixer

1. Import the split predicted model and post-treatment digital model to Meshmixer.
2. Click Edit > Duplicate to duplicate the models for the number of teeth to be segmented. Label each model with the corresponding tooth number to be segmented.
3. Hide the split predicted model by clicking the Eye icon, keeping the post-treatment digital model visible.
4. On the post-treatment model, click Select and adjust the size of the Brush. To segment the selected crown, drag the Brush tool on the occlusal surface of the selected tooth, paying close attention to the cusp tips.
5. Click Modify > Invert, then Edit > Discard to delete the rest of the model, leaving the segmented crown.
6. Unhide the split predicted model and hide the post-treatment model by clicking the corresponding Eye icons.
7. Repeat steps 5.4-5.5 for the split predicted model.
8. Export each selected crown as STL files.
9. Repeat all steps for each tooth segmentation.

6. Dental superimposition with CloudCompare

1. Import the segmented post-treatment digital crowns and split software-predicted crowns into the software. Ensure that the orientation and cloud registration remain consistent. Establish the World Coordinate Grid to standardize the orientation of both right and left teeth, enhancing the reliability of the methodology. The grid's center should represent the (0,0,0,0,0,0) coordinate of the CloudCompare software cloud.
2. Select both crowns and click Edit > Normals > Compute > Per-Vertex.
3. Select each tooth and click Edit > Colors > Set Unique to change the colors of the selected models.
4. Hide the post-treatment tooth by unchecking the box and select both the hidden post-treatment tooth and the visible predicted tooth.
5. Select the bottom view, click the Translate/Rotate icon, and use the planes X, Y, and Z to rotate the tooth such that the buccal cusp lines up with the vertical line.
6. Select the left side view, click the Translate/Rotate icon, and line the buccal and lingual cusps with the horizontal line.
7. Select the back view, click the Translate/Rotate icon, and line the buccal and lingual cusps with the horizontal line.
   NOTE: Aim to align its occlusal and facial surfaces with the world axes and planes. Ensure the bounding box center of the tooth is positioned at the world origin. By adhering to the World Coordinate Grid, the positions of all teeth will be standardized. This step ensures a consistent and accurate conversion of X, Y, and Z translations across all axes, irrespective of an individual tooth's specific position.
8. Once all the cusps line up, click the Translate/Rotate icon to center the tooth on the grid in all views.
9. Unhide the post-treatment tooth and select the predicted tooth and post-treatment tooth.
10. Click the Fine Registration alignment icon to register the post-treatment tooth over the predicted tooth. Click OK.
    NOTE: Upon completion, CloudCompare will show the registration information, including superimposition RMS (Figure 3).
11. To determine the positional and rotational differences between the two teeth, select the post-treatment tooth, copy the transformation matrix, click Edit > Apply Transformation, and paste the transformation matrix.
12. Select the Euler Angles icon to display the rotational and linear movements between the predicted tooth and the post-treatment tooth.
13. Document all translation and rotation measurements in a spreadsheet. Repeat this process for all remaining posterior teeth.
    NOTE: Use the American Board of Orthodontics (ABO) model grading system¹² to identify clinically significant measurement differences. Differences greater than 0.5 mm linearly and 2 degrees angularly are considered clinically relevant.
14. Adjust measurement values for the anterior-posterior direction of right-side teeth in a spreadsheet. This adjustment accounts for the standardized orientation of right-side teeth to left-side teeth.

7. Measurement specifications

1. Understand the sequence of rotation and measurement conventions: CloudCompare employs the Tait-Bryan ZYX extrinsic (world origin) convention for its measurements.
   NOTE: For translation, the axes represent X (buccolingual direction), Y (mesiodistal direction), and Z (vertical direction: intrusion/extrusion). Angular movements are represented by the X-axis (Psi - mesiodistal tipping), the Y-axis (Theta - buccolingual torque), and the Z-axis (Phi - mesiodistal rotation)²². Tooth movements are expressed in terms of the tooth's anatomy, regardless of its position in the arch. The sign of measures (+, -) indicates the direction from the world origin and rotation around its axes.
2. Importance of contextual relevance: Note that the directional terms describing tooth movements (e.g., mesial, distal, buccolingual) reference the specific tooth and do not account for alterations relative to the dental arch.

8. Statistical analysis

1. Use the R statistical package (v 3.2.3, RStudio Inc.) via RStudio (version 1.4.1103) for all the analyses.
2. Select 32 teeth at random and perform duplicate measurements at a 1 month interval.
3. Test intra-examiner reliability with Intra-class correlation coefficients (ICC) and Bland Altman analyses for both sets of measurements.
4. Apply Hotelling's T-squared tests to test mean prediction differences between the predicted and achieved tooth positions for both angular and linear parameters.
5. Adjust for multiple tooth comparisons using a Bonferroni correction on p-values, aiming for a family-wise error rate of 0.05.
6. Conduct a post-hoc Hotelling's T-squared test if any significant differences are detected to determine if prediction differences for each tooth type and movement parameter are significant. Consider discrepancies of 0.25 mm or more in linear measurements and 2° or above for angular measurements as clinically relevant.

Results

A minimum sample size of 24 cases was required to detect an effect change of 0.6° for the average tip and torque angles, with an 80% power and an alpha of 0.05²³. The inclusion criteria were as follows: (1) full permanent dentition through the first molars, (2) Class I malocclusions, or less than 2 mm Class II /III malocclusions with spacing, or mild to moderate crowding that had undergone non-extraction Invisalign treatment, (3) completion of the first series of Invisalign aligners at least,...

Discussion

The palatal rugae have a unique configuration at adolescence; they remain constant during growth, are authentic markers for personal identification, and are considered stable anatomic references for maxillary model superimposition^24,25,26,27. Dai et al. used this method to compare the achieved and predicted tooth movement of maxillary first molars and central incisors with clear aligners after ...

Materials

Name	Company	Catalog Number	Comments
CloudCompare	GPL software	Version 2.11	open-source software (https://www.cloudcompare.net/)
Meshmixer software	Autodesk, Inc.
Rhinoceros 5.0	Robert McNeel & Associates	Version 5.0