Clinical Evaluation of Digital Dental Articulation for One-Piece Maxillary Surgery

Abstract

Purpose:

Digital dental alignment is not readily available to automatically articulate the upper and lower models. The purpose of this study was to assess the accuracy of our newly developed 3-stage automatic digital articulation approach by comparing it to the gold standard of orthodontist-articulated occlusion.

Materials and methods:

Thirty pairs of stone dental models from double-jaw orthognathic surgery patients who had undergone a one-piece Le Fort I osteotomy were used. Two experienced orthodontists together, hand articulated the models to their perceived final occlusion for surgery. Each pair of the models was then scanned twice: while they were in orthodontist-determined occlusion, and while the upper and lower models were separated and positioned randomly. The separately scanned models were automatically articulated to the final occlusion using our 3-stage algorithm, resulting in an algorithm-articulated occlusion (experimental group). The models scanned together represented the hand-articulated occlusion (control group). The qualitative evaluation was completed using a 3-point categorical scale by the same orthodontists, who were blinded from the methods used to articulate the models. A quantitative evaluation was also completed to determine whether there was a difference in midline, canine and molar relationship between the algorithm- and hand-articulated occlusions using repeated measures analysis of variance (ANOVA). Finally, means and standard deviations were used to present the differences between the 2 methods.

Results:

The results of the qualitative evaluation revealed that all the algorithm-articulated occlusions were as good as the hand-articulated ones. The results of repeated measures ANOVA showed that there was no statistically significant difference between the two methods (F(1,28)=0.03, P=0.87). The mean differences between the two methods were all within 0.2mm.

Conclusions:

The results of our study have demonstrated that the dental models can be accurately, reliably and automatically articulated using our 3-stage algorithm approach to the standards of orthodontists.

INTRODUCTION

An important step in computer-aided surgical simulation (CASS) is to reestablish an ideal final dental occlusion. Traditionally, surgeons and orthodontists hand articulate upper and lower stone dental models to the final occlusion for 1-piece maxillary surgery. The instant tactile response and cognitive insight help doctors to quickly achieve the ideal position of the dental models, i.e., midline alignment, Class I canine relationship, Class I molar relationship, and maximized contacts between the upper and lower teeth. However, it is completely different in the digital world. The digital upper and lower dental models are represented by point clouds or triangulated surfaces that lack a tactile response. When they are in contact, they can still be moved towards each other, while they never penetrate each other in reality.

There is no automatic method of digitally articulating upper and lower dental models to the final occlusion. In the current protocol of virtual surgical planning using CASS, the stone models are first hand articulated to the final occlusion, then scanned together using a cone-beam computed tomography (CBCT) scanner or a surface scanner. The resultant digital teeth model serves as the template for articulating the upper and lower dental models to the final occlusion during the planning. This process is time-consuming and cost-inefficient. When an intraoral scanner is used, the upper and lower digital dental models are often printed using a three-dimensional (3D) printer for hand articulation. This completely defeats the purpose of using an intraoral scanner. In order to solve this problem, some commercial service providers and clinicians have started to align the digital upper and lower teeth manually based on visual clues in the computer.¹ However, it is almost impossible and time consuming to visually achieve a perfect occlusion due to any irregularity in the shape of the teeth.² In addition, based on our observation, it is also nearly impossible to visually determine whether the best possible maximal contacts between the upper and lower teeth are achieved, and therefore, might require more occlusal adjustments to achieve this goal.

There have been attempts on digital dental occlusion. Nadjmi et al proposed a “spring connection” method between at least 3 pairs of manually indicated corresponding landmarks.² The result showed that the mean difference between the hand-articulated and a virtual-articulated occlusion was 0.6 mm. Wu et al proposed a complex graphics processing unit (GPU)-based haptic simulation framework for determining virtual dental occlusion.³ Despite the use of additional hardware of the GPU and haptic device, the mean difference between the hand- and algorithm-articulated occlusion were between 0.4 and 0.6 mm in three dimensions.

In the past, we have also developed a method of digitally articulating the upper and lower dental models into maximum intercuspation (MI), without considering the other important clinical criteria.^4–6 However, this method requires labor-intensive human intervention to extract the occlusal surface. Moreover, it is computationally inefficient. Even after the occlusal surface is manually extracted, it takes more than an hour to complete the computation. Due to these problems, we have not been able to utilize it clinically.

Recently, we developed a new automatic three-stage approach to digitally align the dental models for 1-piece maxillary orthognathic surgery.^{7, 8} In the first stage, point cloud of the occlusal surface, the peaks and valleys of the teeth anatomy, and key teeth landmarks are automatically extracted from the digital dental model (Table 1). In the second stage, the upper and lower teeth are aligned to a clinically desired Midline-Canine-Molar relationship with the help of a group of teeth landmarks (Table 1). In the third stage, the upper and lower teeth are finally aligned to a best possible maximum contact. The computational time for each articulation is within 3 minutes. The aim of this study was to assess the accuracy of our new method by comparing it to the gold standard of manually articulated occlusion determined by orthodontists.

Table 1:

Teeth landmarks used in digital articulation

Landmark Name	Description
U0*	Central upper dental midline, located between the upper right and left
	central incisal edges
U3Cusp-R (or -L)*	Cusp of the upper canine, right or left
U6MPCusp-R (or -L) **	Mesiopalatal cusp of the upper first molar, right or left
L0*	Central lower dental midline, located between the lower right and left
	central incisal edges
L34Embr-R (or -L)**	Embrasure between the lower canine and the first premolar, right or left
L6CF-R (or -L)**	Central fossa of the lower first molar, right or left

^*Landmarks are routinely used during the surgical planning (manually digitized by the planner)

^**Landmarks are not routinely used during the surgical planning (automatically extracted by our approach)

MATERIALS AND METHODS

Study Design and Subjects

This was a mixed-designed study with a prospective study conducted on retrospective data of orthognathic surgeries completed between November 2016 and August 2018. All models were obtained from the digital archive of the Houston Methodist Department of Oral and Maxillofacial Surgery using a random table. Institutional review board (IRB) approval was obtained prior to the data collection (IRB#: Pro00003644). The inclusion criteria were: 1) the stone models were from patients who had undergone double-jaw orthognathic surgery; 2) the maxillary surgery was a one-piece non-segmental Le Fort I osteotomy; and 3) the occlusion was stable without rocking between the upper and lower dental models. Partially edentulous models were not excluded. Finally, the data used during the algorithm development and optimization^{7, 8} were not used in this study.

The evaluation was completed at Department of Orthodontics at The University of Texas Houston Health Science Center School of Dentistry. IRB approval was exempted from the University after the identity was removed from the data (IRB#: HSC-DB-18–0104).

Data Collection

Two experienced orthodontists (F.G. and R.E.) together mounted and articulated the thirty models manually on a Galetti articulator to their perceived idea of ideal post-surgical occlusion. To allow standardization, the following criteria were used during the articulation: 1) coincident upper and lower dental midlines and a bilateral Class I canine relationship were the main basis for the ideal occlusion, 2) overjet, overbite and molar relationship were weighted less, and 3) best possible maximum contacts between the upper and lower teeth after achieving the above clinical criteria. The orthodontist’s clinical decision-making parameters were recorded in our automatic articulation algorithm later.

Once the final articulated occlusion was determined by both orthodontists, a paper thin bite registration was immediately fabricated using Blu-Mousse to maintain this position without creating an artificial open-bite. The articulated stone models were then removed from the Galetti articulator and scanned using a cone-beam computed tomography (CBCT) scanner (iCAT, Hatfield, PA) with a dental model scanning protocol (0.2mm isotropically). Each pair of models was scanned twice: one was scanned while they were in final occlusion with the thin bite registration in place and tied with rubber bands, and the other was scanned while the upper and lower models were separated and positioned randomly. Three digital models were created subsequently: a final occlusal template model from the models scanned together, and a separate upper and lower model. In order to ensure the corresponding models were identical, the threshold for the image segmentation and the parameters for 3D reconstruction algorithm were identical for each patient using AnatomicAligner software.⁹

The separately scanned upper dental models were digitally duplicated. To generate the control group, the final occlusal template was first registered to the lower dental model using the same registration method in the CASS planning protocol.⁹ Then one of the two duplicated upper models was registered to the final occlusal template, resulting in a hand-articulated occlusion.

To generate the experimental group, the other upper dental model was automatically articulated to the lower model using our 3-stage algorithm, which was programmed and compiled in an executable MATLAB program (The MathWorks, Inc, Natick, MA). The recorded orthodontist’s decision-making parameters were keyed into a built-in user-friendly interface, allowing the algorithm to automatically articulate the upper model to the lower one, without human intervention. During the articulation, the sole operator (H.D.) was blinded from the hand-articulated occlusion in the control group. The resultant articulated models, the algorithm-articulated occlusion, served as the experimental group. Finally, the accuracy evaluation was completed qualitatively and quantitatively.

Evaluation

Qualitative Evaluation

The same orthodontists together evaluated the outcomes of the hand- and algorithm-articulated occlusions. They were blinded from the methods of the articulation. Both algorithm- and hand-articulated final occlusions were displayed on a large computer monitor, side by side, in a random order. The evaluators were able to rotate, zoom in/out and hide/display the models freely. They could also use the stone dental models to check the occlusion as needed.

The same criteria used for the hand articulation were used again for the evaluation. The evaluation was completed using 3-point categorical scale (1: the occlusion on the left side of the monitor was better than the one on right side; 2: they were equal; and 3: the occlusion on the left side was worse). Only one scale was assigned to each set of the models.

Quantitative Evaluation

The quantitative evaluation was to compare the difference in midline, canine and first molar regions between the two methods. It was completed using our local coordinate system-based method that was developed on the lower dental model (Fig. 1).⁸ The measurements were performed on 5 pairs of landmarks (Tables 1 and 2). The differences in the upper and lower midline, canine and first molar relationships were calculated three dimensionally in local x, y and z axes.

Fig. 1:

Local Coordinate System. A local coordinate system was established on the corresponding lower teeth landmark used in each measurement. Specifically, the occlusal plane P for the lower dental model was first calculated with Principle Component Analysis (PCA) using the lower landmarks L0, L34Embr-R, L34Embr-L, and the mesiobuccal cusps of the lower right and left first molar. The normal vector of P was then calculated in the direction from the tooth root to the crown. This was defined as the z-axis of the local coordinates for all the landmarks. The lower landmarks was then projected onto the plane P and a fitting curve C was created on the plane P. The tangent line of C for each projected landmark, pointing from left to right, was defined as the x-axis of the (original) lower landmark. The local y-axis was then calculated as the cross product of the z- and the x-axes for each landmark. Finally, the origin of each local coordinate system was translated to the teeth landmarks: L0, L34Embr-R, L34Embr-L, L6CF-R and L6CF-L.

Table 2.

Paired landmarks used in the measurements

Relationship	Paired Landmarks
	Upper	Lower
Midline	U0	L0
Right Canine	U3Cusp-R	L34Embr-R
Left Canine	U3Cusp-L	L34Embr-L
Right 1st Molar	U6MPCusp-R	L6CF-R
Left 1st Molar	U6MPCusp-L	L6CF-L

There were two upper dental models for each patient, one for each articulation method. In order to avoid the human error during the landmark digitization, the landmarks were only digitized on one randomly selected model. Then, the surface-best-fit method was used to automatically “copy” the landmarks to the other upper dental model.^{10, 11}

Statistical Analysis

After all the models were evaluated, the results were unblinded, paired and tabulated in Excel spreadsheet (Microsoft Corp, Redmond, WA). For the result of the qualitative evaluation, Wilcoxon signed-rank test would be used to detect if there was a statistically significant difference between the two methods. For the quantitative evaluation results, repeated measures analysis of variance (ANOVA) was first used to detect whether there was a statistically significant difference between the two methods. Responding variable was the distance between the paired landmarks. Between-factor was the 2 methods (algorithm- and hand- articulations). Within-factors were the 3 dimensions (x, y, and z), and 5 locations (midline, right and left canines, and right and left 1^st molars). The assumption for the repeated measures ANOVA was tested and could not be rejected. If there was a statistically significant difference between the 2 methods, the within contrast would be further computed and the results would be reported separately. If there was no statistically significant difference, the differences between the two methods would be descriptively presented using means and standard deviations.

RESULTS

The qualitative evaluation results showed that the algorithm-articulated occlusion was as good as the hand-articulated occlusion in all 30 pairs of models. Fig. 2 shows a comparison between the algorithm- and hand-articulated occlusions from a randomly selected subject. Therefore, Wilcoxon signed-rank test was not further performed. The results of repeated measures ANOVA showed there was no statistically significant difference of occlusion between the two methods (F(1,28)=0.03, P=0.87). Therefore, within contrast was not further computed. The mean differences and their standard deviations between the two methods are presented in Table 3. The mean differences between the two methods were less than 0.2 mm in all three dimensions.

Fig. 2:

A comparison of the algorithm- and hand-articulated occlusions from a randomly selected subject. (A): algorithm-articulated occlusion, (B): hand-articulated occlusion.

Table 3.

Descriptive Results (Differences between two articulation methods)

Relationship	Measurement	Mean (mm)	Standard Deviation (mm)
Midline	x-axis	0.2	0.3
	y-axis	0.0	0.5
	z-axis	0.0	0.4
Right Canine	x-axis	0.1	0.5
	y-axis	0.1	0.5
	z-axis	0.0	0.3
Left Canine	x-axis	0.1	0.5
	y-axis	0.1	0.5
	z-axis	0.0	0.4
Right Molar	x-axis	0.0	0.4
	y-axis	0.2	0.6
	z-axis	0.1	0.3
Left Molar	x-axis	0.1	0.5
	y-axis	0.2	0.5
	z-axis	0.0	0.2

Note: x-axis: mediolaterally, y-axis: buccolingually, z-axis: superoinferiorly

DISCUSSION

Our new 3-stage dental articulation method automatically extracts the anatomy of dental occlusal surface (i.e., the peaks and valleys), and key teeth landmarks from the digital dental models, aligns the upper and lower teeth to a clinically desired Midline-Canine-Molar relationship, and finally aligns the upper and lower teeth to a best possible maximum contact without altering Midline-Canine-Molar relationship. The results of this study further confirm that the algorithm-articulated occlusion is as good as the gold standard of the hand-articulated occlusion for 1-piece Le Fort I osteotomy after orthodontists have completed the presurgical orthodontic treatment.

The new method works in real-world orthodontic tooth set up. It solves a major problem that was associated with our previously developed method, in which only MI was considered during the articulation. During presurgical orthodontics, the clinical criteria is always prioritized to MI. Therefore, our new method is designed to utilize any specific clinical parameters, e.g., midline, Class I canine and molar relationships, overbite and overjet, as if an orthodontist determines the final occlusion using stone models. This is especially important to handle Bolton discrepancies. The algorithm will automatically take care of small Bolton discrepancies by balancing overjet, canine, and molar relationships. However, if Bolton discrepancies are large, users are able to adjust the weights of overjet, Class I canine relationship, and Class I molar relationship during automatic articulation.

Our new method is also capable of articulating partially edentulous upper and lower dental arches. In our experiments, 8 out of 30 cases had at least one or more teeth extracted or missing. Our method is capable of articulating partial edentulous upper and lower arches. Dental extraction treatment is important in achieving Class I canine relationship. This is because the canine relationship is more important than the molar relationship for the final occlusion, and the molar relationship can be changed due to different extraction patterns of teeth. In most cases, the missing teeth were upper and/or lower premolars. There was an extreme case in this study where two upper premolars were used to substitute two upper canines as the canines were used to substitute for the lateral incisors. The same case was also intentionally treated to a Class II molar relationship in order to create a Class I canine relationship using the premolar and to help with surgical decompensation. Another extreme case had a missing upper first molar. Therefore, the paired upper and lower second molars were used to achieve a Class I molar relationship on one side, and standard Class I relationship for the first molars on the other side, maintaining bilateral Class I canine relationship. Two other cases had missing upper second molars, however, it was not used for calculation purposes. Nonetheless, in both extreme cases, the desired final occlusions were established using our method uneventfully.

Unlike the previous method, this new method is fully automatic. The occlusal surface is extracted automatically, unlike the manual extraction required in the previous method. The teeth landmarks, other than the routinely used ones during surgical planning, are also automatically extracted. The entire articulation process for a pair of dental models is within 3 minutes.

One limitation of this algorithm is that it was only applicable to one-piece maxillary surgery. Currently, we are working on digital dental articulation for multi-piece maxillary surgery. Another limitation is that the accuracy of the digital enameloplasty was not tested, even though our algorithm is capable of detecting first tooth contact. In this study, we used historical stone models that belong to patients who have already had orthognathic surgery and occlusal equilibration done. Currently, we are testing the algorithm prospectively on new patient models before the occlusal adjustment is performed.

In conclusion, the results of this evaluation show that digital dental models can be accurately and efficiently articulated according to the standards chosen by the orthodontists for one-piece maxillary orthognathic surgery. The mean differences between the algorithm-articulated and the hand-articulated occlusions were within 0.2 mm. This provides a step closer to a stone-less and a complete virtual planning for orthognathic surgery. Ultimately, the automatic algorithm-articulated occlusions will replace the ones derived from hand-articulated physical dental models and become a module for our AnatomicAligner software.