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: Pre-treatment digital mo…

Representative 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

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