Treatment of class II malocclusion with Invisalign®: A pilot study using digital model-integrated maxillofacial cone beam computed tomography

Background/purpose The treatment effects of Invisalign® are still obscure due to methodological limitations of previous studies. We introduced a method to comprehensively evaluate the dental and skeletal changes of Class II malocclusion treated non-extraction with Invisalign® and compare with the virtual simulation of ClinCheck® using digital models integrated into maxillofacial cone-beam computed tomography (CBCT). Materials and methods The pretreatment (T1) and posttreatment (T2) scanned digital images of actual dentitions were integrated into maxillofacial CBCT images. To evaluate three-dimensional movement of maxillary teeth and change of mandible position, T1 and T2 digital model-integrated maxillofacial CBCT images were superimposed using voxel-based registrations of stable cranial base structures. To evaluate movement of mandibular teeth, model-integrated mandibular CBCT superimposition was registered on mandibular basal bone. To compare achieved and predicted tooth movements, the actual dental images and the virtual digital models created by ClinCheck® were registered on the T1 dentitions. Results For simulated upper first molar (U6) distalization of more than 1 mm, treatment accuracy ranged from 31.1% to 40.1%, which was significantly less than virtual planning and previous reports. In unilateral Class II subjects, the amount of U6 distalization on the Class II side was not significantly different from contralateral side, indicating efficacy of sequential distalization was questionable. Those with favorable overjet correction showed evidence of condylar distraction. Conclusion Digital model-integrated CBCT superimpositions reflected the actual treatment changes in comparison with the virtual simulation, and showed that ideal occlusion was not achieved in mild to moderate Class II adult patients treated non-extraction with Invisalign®.

Abstract Background/purpose: The treatment effects of Invisalignâ are still obscure due to methodological limitations of previous studies. We introduced a method to comprehensively evaluate the dental and skeletal changes of Class II malocclusion treated non-extraction with Invisalignâ and compare with the virtual simulation of ClinCheckâ using digital models integrated into maxillofacial cone-beam computed tomography (CBCT). Materials and methods: The pretreatment (T1) and posttreatment (T2) scanned digital images of actual dentitions were integrated into maxillofacial CBCT images. To evaluate threedimensional movement of maxillary teeth and change of mandible position, T1 and T2 digital model-integrated maxillofacial CBCT images were superimposed using voxel-based registrations of stable cranial base structures. To evaluate movement of mandibular teeth, modelintegrated mandibular CBCT superimposition was registered on mandibular basal bone. To compare achieved and predicted tooth movements, the actual dental images and the virtual digital models created by ClinCheckâ were registered on the T1 dentitions. Results: For simulated upper first molar (U6) distalization of more than 1 mm, treatment accuracy ranged from 31.1% to 40.1%, which was significantly less than virtual planning and previous reports. In unilateral Class II subjects, the amount of U6 distalization on the Class II side was not significantly different from contralateral side, indicating efficacy of sequential distalization was questionable. Those with favorable overjet correction showed evidence of condylar distraction.

Introduction
Since its development in 1997, Invisalignâ has gained popularity because of improved esthetics and easier oral hygiene than conventional fixed orthodontic appliances. 1,2 The combination of Invisalignâ and Class II elastics has been established as a treatment option for Class II malocclusion. 3 The manufacturer claims that Invisalignâ effectively achieves distalization by using the sequential distalization protocol in combination with composite attachments and Class II elastics. Meta-analysis has shown more effective molar distalization using skeletal anchorage; on the contrary, premolar mesial movement was observed when using conventional anchorage. 4 Theoretically, during sequential distalization, Invisalignâ does not provide more distalization force/anchorage than other conventional devices; and after sequential distalization, the distalized teeth are prone to move mesially again to close the space created during distalization. It is dubitable whether the efficacy of distalization using Invisalignâ is as high as claimed.
Studies have assessed the efficacy of clear aligners to achieve the expected/predicted goals of tooth movement in different directions, the differences of posttreatment results from that of fixed orthodontic devices, or the success of treatment using the American Board of Orthodontics (ABO) objective grading system (OGS). 5 It is generally concluded that Invisalignâ may achieve the treatment goals of non-extraction treatment for mild to moderate malocclusion in adults and the distalization of upper molars are highly predictable. 6,7 However, studies using OGS have shown that clear aligners scores were consistently lower than braces scores in occlusal contacts, occlusal relationships, and overjet. 8 No significant Class II correction or overjet reduction was observed for Class II adult patients treated with elastics at the end of first set of active aligners and all posttreatment occlusions failed to meet ABO standards. 9 If distalization of maxillary molars with Invisalignâ is highly predictable, how come OGS results show no significant Class II correction and overjet reduction? At present, no standard method exists for determining the efficacy of invisible orthodontic tooth movement. 6 Most studies have compared the efficacy of tooth movement using superimposition of digital models. The references/registration of the superimposition included the occlusal plane, 10,11 the teeth with less movement, 12,13 and best-fit surface-based registration with software. 14 These references are not stationary and may change after treatment. Simon et al. reported 88.4% accuracy for a planned upper molar distalization of 2.7 mm. 12 The authors used the 'untreated' teeth as reference for superimposition. In the real-world scenario, the distal movement of the molars is balanced against the mesial movement of the teeth anterior to the molars. In the figure that the authors showed how they superimposed the digital scans, the incisors on the same side of molar distalization were retracted/distalized as well. There is a high possibility that the study has overestimated the efficacy of molar distalization. By using lateral cephalometric superimposition, Ravera et al. reported that non-extraction treatment of Class II malocclusion with Invisalignâ and Class II elastics resulted in 2.25 mm distalization of maxillary first molars (U6). 15 However, in the figure that the authors demonstrated their cephalometric superimposition, the posttreatment tracing (including the oribital rim, pterygomandibular fissure, coronoid process, and condylar head) all appeared to be more distally and superiorly positioned than the pretreatment cephalometric tracing. There is a high possibility of superimposition error and the amount of molar distalization and intrusion in that study may be overestimated. Another limitation of the cephalometric method is that the predicted virtual tooth movement cannot be superimposed with a lateral cephalogram; therefore the efficacy of tooth movement in directions other than anteroposterior cannot be determined.
Considering the aforementioned limitations of previous studies and that the Class II treatment effects of Invisalignâ are still obscure, we aimed to analyze the nonextraction treatment outcomes of Class II adult patients treated with Invisalignâ and Class II elastics after completion of the treatment with the initial set of clear aligners by using digital models integrated into maxillofacial cone beam computed tomography (CBCT). We investigated the changes in the upper and lower dentitions and mandible position, and compared with the virtual tooth movement in ClinCheckâ. We further grouped the patients into good and bad responders of overjet correction and identified the associated variables that differentiated the two groups. We also examined the correlations between these variables and the amount of overjet correction.

Materials and methods
This retrospective study included patients who had started treatment from January 2017 to December 2018 and completed the first series of Invisalignâ performed by a sole orthodontist with approximately 10 years of Invisalignâ experiences. The ethical approval was obtained from the Research Ethic Committee of National Taiwan University Hospital (approval number: 202108032RIND). All the methods were performed in accordance with the relevant guidelines and regulations. All clinical records used in this study were obtained from archives of the patients, from which informed consent forms were signed before any intervention, highlighting the possible use of materials from their records for research purposes.
The inclusion criteria were as follows: 1 bilateral/unilateral Class II molar relationship as defined by the ABO, 2 aged 18 years and older, 3 non-extraction (except for the third molars), 4 upper molar distalization with Class II elastics planned in ClinCheckâ, and 5 complete records of intraoral digital scans and maxillofacial CBCT images before (T1) and after (T2) treatment (the end of the first set of active aligners). The exclusion criteria were as follows: 1 signs/symptoms of temporomandibular joint disorder, 2 periodontal problems, 3 congenital missing or impacted teeth (except for the third molar), and 4 medication that could affect tooth movement.
The CBCT datasets at T1 and T2 in DICOM format were evaluated with Amira ver. 2020.3 (Thermo Fisher Scientific, Dallas, TX, USA). The overall superimposition was performed with the voxel-based method using the anterior cranial base, the frontal bone, and the periorbital bone as the registration structures. The scanned digital images of the actual maxillary dentitions at T1 and T2 in Stereo-Lithography (STL) format were incorporated into the CBCT images at T1 and T2, respectively, via surface-based registration. The virtual pretreatment and posttreatment maxillary digital models created by ClinCheckâ were exported in STL format. The virtual pretreatment and actual T1 maxillary dentitions were registered on the dental arch since they had the same dentition, and the final superimposition of the T1, T2, and the virtual posttreatment models of the maxillary dentition could be obtained (Fig. 1AeD). To evaluate the change of mandible position, segmentation of the T1 and T2 mandibles was performed while maintaining the voxel-based registrations of the cranial base surface (Fig. 1EeG). To evaluate the movement of the mandibular teeth, mandibular superimposition was performed by registration on the mandibular basal bone. The actual T1 and T2 digital models of the mandibular dentitions were incorporated into the CBCT images at T1 and T2, respectively. The virtual pretreatment and actual T1 mandibular dentitions were registered on the dental arch to obtain the final superimposition of the T1, T2, and virtual posttreatment models of the lower dentition (Fig. 1HeK).
After superimposition, the STL format of the superimposed images of T1, T2, and virtual post-treatment models were imported into Dolphin imaging premium ver. 11.95 (Dolphin Imaging & Management Solutions, Chatsworth, CA, USA) and a coordinate system was generated for tooth movement measurements ( Fig. 2A). The horizontal plane was defined as the midpoint of the incisal edge of the upper right central incisor (U1) and the mesiobuccal (MB) cusps of the bilateral U6. The plane perpendicular to the horizontal plane and passing through the midpalatal suture  The twenty-eight landmarks/points for measurement of tooth movement: 1 midpoints of the incisal edge of the maxillary central incisors; 2 the cusp tips of the maxillary canines; 3 the buccal cusp tips of the maxillary first premolars; 4 the buccal cusp tips of the maxillary second premolars; 5 the mesiobuccal cusp tips of the maxillary first molars; 6 the distobuccal cusp tips of the maxillary first molars; 7 the mesiopalatal cusp tips of the maxillary first molars; 8 midpoints of the incisal edge of the mandibular central incisors; 9 the cusp tips of the mandibular canines; 10 the buccal cusp tips of the mandibular first and 11 second premolars; and the 12 mesiobuccal, 13 buccal, and 14 mesiolingual cusps of the mandibular first molars. (C) Three-dimensional coordinate system for measurement of change in mandible position. (D) The ten anatomic landmarks of the mandible: 15 pogonion; 16 menton; 17 gonion; and the 18 uppermost, 19 most lateral, and 20 foremost points of the bilateral condylar heads. was defined as the sagittal plane. The plane perpendicular to both horizontal and sagittal planes was obtained as the coronal plane. Twenty-eight landmarks of the upper and lower dentitions were identified (Fig. 2B). A second coordinate system was established for the measurements of mandible position (Fig. 2C). The Frankfurt horizontal plane was defined as the horizontal plane. The plane passing through the nasion and the basion and perpendicular to the horizontal plane was defined as the sagittal plane. The coronal plane was perpendicular to the two aforementioned planes. Ten anatomic landmarks of the mandible were identified (Fig. 2D). The coordinate values of the aforementioned landmarks were then output for subsequent data calculation.
The changes in the coordinate systems of the landmarks on the upper and lower dentitions indicated the threedimensional movement of corresponding teeth. The difference between the virtual posttreatment model simulated by ClinCheckâ and T1 was defined as the predicted tooth movement. The difference between T2 and T1 was defined as the achieved tooth movement. The percentage of treatment accuracy was defined as the (amount achieved)/(amount predicted)x100%. The changes of the coordinates of the mandible from T1 to T2 represented changes of the mandibular position during treatment. Additional measurements included the overjet, overbite, curve of Spee, and cephalometric variables obtained from CBCT-derived lateral cephalograms such as ANB angle, mandibular plane angle, U1-SN angle, and L1-MP angle.
The same observer identified all thirty-eight landmarks again two weeks later and comparisons were analyzed with   the intraclass correlation coefficients (ICCs), which were excellent for most landmarks (ranging from 0.921 to 1.000) and good for the x-value of the MB cusp of the right U6 (0.881), the z-value of the DB cusp of the left U6 (0.870), and the x-value of the buccal cusp of the right L6 (0.804). The ICCs were exceptionally excellent for the uppermost and foremost landmarks of the condylar heads (0.996e1.000). Data were analyzed using SPSS 25.0 (IBM Corp., Armonk, NY, USA). The differences between the predicted and achieved amounts of tooth movement and the changes of cephalometric values, overjet, overbite, and the coordinates of the mandibular landmarks from T1 to T2 were evaluated using Wilcoxon signed rank tests. Those who had achieved normal overjet (the horizontal distance from the most labial side of the lower central incisor to the corresponding upper central incisor was between 1 and 3 mm) were defined as good responders, otherwise the bad responders. 16 The ManneWhitney U test was used to compare the good-and bad-responding groups. The relationships between overjet correction and the aforestated variables were accessed using the Pearson's correlation coefficient test. The significance level was set at P-value < 0.05.

Results
Only seven patients met the inclusion criteria ( Fig. 3 and Table 1). After treatment, U1-SN angle significantly decreased and L1-MP angle significantly increased. The differences of achieved upper tooth movement from prediction and the percentage of treatment accuracy are shown in Table 2A and Fig. 4A. The treatment accuracies for maxillary intercanine, inter-1st-premolar, inter-2ndpremolar, and inter-1st-molar widths were 93.4%, 86.0%, 91.2%, 85.2%, respectively. The predicted upper central incisor movement was to intrude 0.35 AE 1.36 mm. However, it extruded 0.75 AE 1.51 mm. The actual amount of retraction/distalization was significantly less than planned. The accuracies of retraction of U1 and distalization of the MB cusp, DB cusp, and MP cusp of U6 were 50%, 46.5%, 56.5%, and 37.2%, respectively. The differences of achieved lower tooth movement from prediction and the percentage of treatment accuracy are shown in Table 2A and Fig. 4B. The treatment accuracies for mandibular intercanine, inter-1st-premolar, inter-2nd-premolar, and inter-1st-molar widths were      To evaluate the factors that might have influenced the effectiveness of treatment, the patients were further divided into the good-or bad-responding groups for overjet correction. The two groups showed comparable cephalometric characteristics before treatment. Although statistically insignificant, the bad-responders tended to have more increase of the ANB and SN-MP (Table 3A). Both groups were planned to intrude L1. However, the good-responders exhibited 1.25 AE 0.54 mm of L1 intrusion (75.2% accuracy), whereas the bad-responders exhibited extrusion of 0.12 AE 0.78 mm (Table 3B and Fig. 5A). The good-responders showed better vertical control of the U6 DB cusp and the L6 ML cusp. The bad-responders had apparently less U6 distalization, U1 retraction, and L11 proclination than planned and more distalization of the L6; while the good-responders showed mesialization of the L6 ML cusp (Table 3B and Fig. 5B). With respect to the mandibular position, the goodresponders showed a significant forward movement while the bad-responders showed a backward movement of the uppermost point of the condylar head (Table 3C and Fig. 5C).
Since unilateral Class II cases were also included in this study, bilateral Class II elastic wear and sequential distalization for the Class II side but not for the Class I side were planned. Based on the amount of U6 distalization planned in ClinCheckâ, the data of the maxillary tooth Above 0-line (þ): more dental extrusion/retraction/distalization than predicted. Below 0-line (À): more dental intrusion/proclination/mesialization than predicted. For (C), mandible upward/forward movement: þ; downward/backward: -. Abbreviation: U1, the upper central incisor; U6MB, the mesiobuccal cusp of the upper first molar; U6DB, the distobuccal cusp of the upper first molar; U6P, the mesiopalatal cusp of the upper first molar; L1, the lower central incisor; L6MB, the mesiobuccal cusp of the lower first molar; L6B, the buccal cusp of the lower first molar; L6ML, the mesiolingual cusp of the lower first molar; Pg, pogonion; Me, menton; Go, gonion; Sup, the uppermost point of the condyle; Lat, the most lateral point of the condyle; Ant, the foremost point of the condyle; T1, pretreatment; T2, posttreatment. movement in the anteroposterior direction was further divided into two groups: the intended-to-change and the intended-not-to-change groups (Table 3D). Although the intended-to-change group had planned a greater amount of U6 distalization, the actually achieved amount of U6 distalization was not significantly different between the two groups. The achieved amount of U6 distalization of the intended-to-change group was significantly less than originally planned, with treatment accuracy ranging from only 31.1%e40.1%.
To delineate which factors might have affected the correction of overjet, Pearson's correlation coefficient test was performed ( Table 4). The variables that had reached statistical significance include overjet at T1, the predicted change of inter-U6-width, the actual change of inter-U6width, the vertical change of U6 DB cusp, and the actual anteroposterior movement of L1.

Discussion
Previous Invisalignâ studies have mostly adopted methods with certain errors or garnered results that could not be compared with ClinCheckâ simulation. In this study, we are the first to analyze the treatment outcomes of Invisalignâ by using digital models-integrated maxillofacial CBCT. Accurate registration of the two image-modalities is mandatory. The digital models may be integrated into the maxillofacial CBCT with minimal error using the surfacebased registration method. 17 Voxel-based method was used for skeletal superimposition because of the higher efficiency, elimination of segmentation errors in 3D surface models, and greater ease of assessing inner structures that allows the superimposed structures to be viewed in multiplanar slices. 18,19 The average overjet decreased insignificantly from 4.53 AE 1.52 mm to 2.81 AE 1.1 mm after treatment ( Table  1). The largest overjet in our patients was 7.1 mm and the molar relationship was half-cusp Class II. Therefore, the results of our study only represent the efficacy of the nonextraction treatment for mild to moderate Class II malocclusion. Invisalignâ treatment typically required additional aligners for Class II malocclusion. 9,13 All of the patients in this study were subsequently prescribed with additional aligners, indicating that completing the first series of aligners alone was insufficient to achieve the treatment goals. On the intended-to-change side, the treatment accuracy of U6 distalization ranged from only 31.1%e40.1% for the individual cusps, which was significantly less than originally planned. In comparison with the intended-not-tochange side, the actual amount of U6 distalization was not different between both sides. Since the intended-tochange side had received sequential distalization in ClinCheckâ simulation, our results show that the efficacy of sequential distalization may be questionable. In our study, we superimposed on the stable bony structure and the results showed less molar distalization and accuracy compared with previous studies.
The mandible position may be affected by the vertical and horizontal vectors of the Class II elastics indirectly via extrusion of lower posterior teeth or directly via posturing forward (condylar distraction). In our study, 3D  15,20 However, as previously mentioned in the Introduction section, Ravera et al. seemed to have more distally and superiorly positioned their posttreatment tracing during cephalometric superimposition. 15 While it seemed illogical that Caruso et al. showed a decrease of ANB angle but unchanged vertical skeletal measurements (such as SN-GoGn angle and NeMe) and a decrease of the SN-PP angle in their adult patients after treatment. 20 Therefore, possible cephalometric superimpositional errors in these studies might have skewed the results.
Orthodontists often judge Class II treatment effectiveness based on the correction of overjet. 21 In this study, the good-responders of overjet correction showed significantly more retraction of U1, intrusion of U6 DB cusp and L1, proclination of L1, and more anterior movement of the uppermost point of condylar head (condylar distraction). Pearson's correlation coefficient test showed that the larger the pretreatment overjet, the greater amount of predicted and achieved arch expansion at U6, the more intrusion of the U6 DB cusp, and the more proclinication of L1 would favor greater amount of overjet correction. Since the efficacy of molar distalization in this study was not satisfactory, its correlation with the amount of overjet correction was low. Both the good-and bad-responders showed approximately 1 mm more extrusion of U1 than planned, possibly due to effects of Class II elastics; while the L1 of bad-responders was also significantly more extruded than planned and than that of the goodresponders. Consequently, anterior bite deepening/interference might have also caused mandible to rotate more backward and downward in the bad-responding group. Planning overcorrection of upper/lower incisor intrusion in ClinCheckâ and using skeletal anchorage to facilitate anterior intrusion and total arch distalization should be considered in future when indicated.
The insufficient sample size was the greatest limitation of this study. All cases were treated by a single experienced orthodontist, who has held lectures for Align Technology and is the Black Diamond Invisalignâ Provider and advisor of Invisalignâ Academic Advisory Board. We believe that the results of this study objectively represent the standard results of non-extraction adult Class II treatment with Invisalignâ and Class II elastics. Despite that, after screening all the 2017e2018 patients, only seven patients met the inclusion criteria. Due to the small sample size of this study, we considered this a pilot study and estimated the smallest sample size required for future studies. The main parameter of interest was the difference between the predicted and achieved distalization of the U6. Power analysis indicated that at least 21 samples (11 patients) were required to Table 3D Differences of the anteroposterior movement of teeth between the intended-to-change and the intended-not-to-change groups.
Intended-to-change (greater than 1 mm distalization planned; N Z 9) Intended-not-to-change (less than 1 mm distalization planned; N

Declaration of competing interest
The authors declare no conflict of interest. Although Dr. S-J Tsai has held lectures and conferences for Align Technology in the past 10 years and is the Black Diamond Invisalignâ Provider and advisor of Invisalignâ Academic Advisory Board, this study was conducted without any support (financial or technical) from Align Technology. Dr. S-J Tsai was also not involved in the study design and analysis of the data.