Accuracy of Mandibular Dentition Distalisation With Invisalign in Class III Malocclusion: A Pilot Study Using CBCT Superimposition

ABSTRACT

Objective

By integrating digital models with cone beam computed tomography (CBCT) images and registration on stable hard tissue regions for superimposition, we aimed to enable a more precise and detailed analysis of Invisalign treatment on Class III malocclusion.

Materials and Methods

Digital models of 12 Class III adults at pretreatment (T1) and posttreatment (T2) were integrated with maxillofacial CBCT images. The T1 and T2 CBCT images were superimposed using voxel‐based registration of stable cranial base structures to assess the three‐dimensional movement of the maxillary teeth and positional changes of the mandible. Mandibular tooth movement was evaluated by superimposition of the mandibular CBCT images, registered on the symphysis and mandibular body. The virtual planning model created by ClinCheck was superimposed based on its position relative to the T1 digital model.

Results

The median accuracy of distal movement for the mandibular first molar cusps ranged from 26.72% to 33.87%. With miniscrew anchorage, the accuracy ranged from 39.28% to 44.66%. Actual distal movement averaged 0.62 ± 0.82 mm to 0.80 ± 0.89 mm with Class III elastics, and 2.02 ± 1.71 mm to 2.29 ± 1.53 mm with miniscrews. The maxillary incisors significantly proclined more with Class III elastic traction. No significant positional changes in mandibular anatomical landmarks were observed during treatment with miniscrew anchorage, whereas the use of Class III elastics led to significant positional changes in the condyle head.

Conclusion

Invisalign treatment may not reach the expected efficacy in mandibular dentition distalisation, especially when skeletal anchorage is absent.

1. Introduction

Class III adults with severe skeletal discrepancies require orthognathic surgery, while milder cases are typically managed with camouflage treatment. Non‐extraction camouflage treatments often involve distalising mandibular teeth using dental or skeletal anchorage. In less severe cases, clear aligners combined with Class III elastics have been shown to effectively correct the malocclusion [1, 2]. However, compared to Class I and II cases, there are significantly fewer studies on the efficacy of clear aligners for Class III malocclusions. A 2023 systematic review by Padmanabhan et al. analysed five studies (3 case reports, 2 retrospective studies) and concluded that clear aligners can achieve 2 to 3 mm of mandibular molar distalisation in Class III malocclusion [3].

Invisalign utilises ClinCheck software to design dental movements. Studies indicate that while Invisalign provides better control in non‐extraction cases, it encounters difficulties with buccolingual inclination, occlusal contacts, rotation, root control and vertical extrusion, but excels in distalisation and arch expansion [4, 5, 6]. Evaluating Invisalign efficacy presents challenges in model superimposition, especially in reference point/area selection. For example, Kravitz et al. [7] and Simon et al. [8] registered models on ‘untreated’ teeth. In reality, without absolute anchorage, it is unlikely that any teeth remain truly unaffected. Grünheid et al. [9] and Haouili et al. [10] developed custom processes using best‐fit registration but lacked transparency in their algorithms. Proposals to use soft tissue reference points like the palatal vault are limited to maxillary models only [11, 12]. Recent advancements in cone beam computed tomography (CBCT) have improved image superimposition. Ghoneima et al. [13] used the anterior cranial base, while Koerich et al. [14] found local anatomical areas reliable. Lin et al. introduced a digital model‐CBCT‐integrated process that combined voxel‐ and surface‐based registrations to more accurately assess dental movements and mandibular changes in Class II adults treated with Invisalign [15].

Among the Class III studies reviewed by Padmanabhan et al. [3], four used cephalometric superimposition, which can introduce distortions and inaccuracies due to limitations in two‐dimensional imaging. Only one retrospective study employed CBCT [16], but true CBCT superimposition was not used, as three‐dimensional images were converted to two‐dimensional views and distances were measured from a reference line. El Hayeck et al. emphasised that linear measurements could vary significantly when CBCT images are axially rotated and converted into two‐dimensional [17]. Given the limited research on Invisalign for Class III malocclusions compared to Class I and II, and the frequent reliance on less reliable lateral cephalometric analysis, this study aimed to address these gaps. By integrating digital models with CBCT images and using stable hard tissue regions for superimposition [15], it enabled a more precise evaluation of Invisalign treatment efficacy in Class III cases.

A single‐center, retrospective pilot study was chosen to validate the superimposition methodology, assess variability, and generate preliminary effect‐size estimates to guide future prospective investigations. Specifically, the primary objective was to assess the magnitude and accuracy of mandibular first molar distalisation, while secondary objectives included evaluation of condylar positional changes, occlusal outcomes, and discrepancies between planned and achieved tooth movements. Primary hypothesis of this study is Invisalign treatment combined with Class III elastics can achieve clinically meaningful mandibular molar distalisation (approximately 2–3 mm) in adult Class III patients when evaluated using three‐dimensional CBCT–digital model superimposition; secondary hypotheses are the use of Class III elastics is associated with measurable condylar positional changes, detectable via CBCT superimposition and differences exist between planned tooth movements (ClinCheck) and achieved movements, particularly in buccolingual inclination and vertical control. Our null hypotheses are that Invisalign treatment with Class III elastics does not produce significant mandibular molar distalisation in adult Class III patients, that there are no significant skeletal or condylar positional changes associated with Class III elastic use, and that there is no significant difference between planned and achieved tooth movements.

2. Materials and Methods

2.1. Study Subjects

Ethical approval was granted by the research ethics committee. Inclusion criteria were Class III molar relationship, age over 18, no extractions or space closure, planned mandibular molar distalisation, completed first Invisalign series, and available pre‐ and post‐treatment digital models and CBCT scans. Exclusion criteria were severe skeletal discrepancy, TMJ disorders, advanced periodontal disease, medications affecting tooth movement, and significant tooth abnormalities.

12 adult Class III patients met the inclusion criteria and were included in the analysis. Three patients were treated with mandibular miniscrew anchorage (mean age: 23.8 ± 4.39 years; follow up: 16.6 ± 5.25 months), and nine patients were treated with Class III elastics (mean age: 30.2 ± 7.68 years; follow up: 15.5 ± 5.42 months). All patients completed the first series of Invisalign aligners and had complete pre‐treatment (T1) and post–first series (T2) digital models and CBCT records available for analysis. Because of the limited sample size—particularly in the miniscrew group—between‐group comparisons were considered exploratory and descriptive in nature.

2.2. Digital Model and CBCT Data Collection

A schematic overview of the workflow for integrating digital models and CBCT scans is provided below (Table A1). Digital models and CBCT images were collected at two time points: before Invisalign treatment (T1), and after the initial aligner series (T2). Digital models, scanned with iTero Element and exported from ClinCheck, were saved in stereolithography (STL) format. CBCT scans were exported in Digital Imaging and Communications in Medicine (DICOM) format.

2.3. CBCT Superimposition

The T1 CBCT image was imported into Amira 3D Pro (Thermo Fisher Scientific, Ver. 2022.1) for 3D orientation and superimposition. A coordinate system was established to track movement along the X‐axis (horizontal), Y‐axis (anteroposterior) and Z‐axis (vertical). The T1 image was aligned using the Frankfort Horizontal plane, with the midsagittal plane passing through the nasion and basion, and the coronal plane originating at basion. For post‐treatment assessment, the T2 CBCT image was superimposed on T1 using voxel‐based registration, aligned to stable hard tissue regions such as the cranial base, orbits and zygomatic bones (Figure 1A,B).

FIGURE 1.

Superimposition of the digital model‐integrated cone beam computed tomography (CBCT) images and the dentitions. (A) Superimposition of the pre‐treatment (T1, gray) and post‐treatment (T2, beige) maxillofacial CBCT images by registration on the stable skeletal structures including the anterior cranial base, the orbits, and zygomatic regions; (B) Cross‐sectional view in the sagittal plane of superimposed CBCT images; (C) Incorporation of the T1 maxillary digital model (yellow) onto the T1 CBCT image; (D) Incorporation of the T2 maxillary digital model (red) onto the T2 CBCT image; (E) Transferring the maxillary ClinCheck virtual planning model (green, V) into the coordinate system by retaining its relationship with the T1 digital model; (F) The T1, T2, and virtual planning model V positioning within the same coordinate system by maintaining the voxel‐based registrations of the anterior cranial base structures in (A) and (B); (G) Segmentation of the T1 mandible (yellow) and T2 mandible (red) while maintaining the voxel‐based registrations of the anterior cranial base structures in (A) and (B); (H) Superimposition of the T1 and T2 mandibles by registration on the stable skeletal structures including the symphysis and the mandibular body; (I) Incorporation of the T1 mandibular digital model (yellow) onto the T1 CBCT image; (J) Incorporation of the T2 mandibular digital model (red) onto the T2 CBCT image; (K) Transferring the mandibular ClinCheck virtual planning model (green, V) into the coordinate system by retaining its relationship with the T1 digital model; (L) The T1, T2, and virtual planning model V positioning within the same coordinate system by maintaining the voxel‐based registrations of the symphysis and mandibular body in (H).

2.4. Integration of Digital Models and CBCT Images

Maxillary digital models at T1 and T2 were imported into Amira as STL files. Each crown was aligned with the corresponding dental arch on T1 and T2 CBCT images using surface‐based registration. ClinCheck model (green) was referred to as the virtual planning model (V) and was superimposed on T1 (yellow). All maxillary dentitions (T1, T2: red and V) were placed in the same coordinate system (Figure 1C–F). The V model represents the digitally planned final tooth positions generated by Invisalign software and was first aligned to the T1 maxillary digital model using surface‐based registration. This step assumes relative stability of the maxillary skeletal base, as no maxillary extractions, orthopaedic interventions, or orthognathic surgery were performed. Once aligned, the V model was imported into the same CBCT‐derived coordinate system as the T1 and T2 datasets, allowing direct three‐dimensional comparison between predicted (V–T1) and achieved (T2–T1) tooth movements. The pre‐ and post‐treatment mandibular images, including the condyles, were segmented from T1 (yellow) and T2 (red) CBCT to assess mandibular positional changes, while maintaining voxel‐based registration of the cranial base (Figure 1G). To analyse changes in the mandibular arch, the T2 CBCT was superimposed on T1 using voxel‐based registration, registered on the symphysis and mandibular body (Figure 1H). The mandibular digital models, T1 (yellow) and T2 (red), were integrated with the CBCT images, with the virtual model (green) aligned in the same coordinate system (Figure 1I–L).

2.5. Landmark Identification

Twenty‐eight dental landmarks were identified, including midpoints of the central incisors, cusp tips of the canines, buccal cusps of the premolars, and various cusps of the first molar, as previously described [15]. The mandibular surface model was segmented from CBCT images, with 10 anatomical landmarks (pogonion, menton, gonion left and right and key condylar points) extracted for analysis [15]. CBCT‐generated lateral cephalometric images were imported into Amira for cephalometric analysis. Additional data collected included age at treatment onset, duration of aligner use, and measurements of overjet, overbite, curve of Spee, space analysis and molar axis angles.

2.6. Statistical Analysis

Landmarks were re‐identified on the T1 models and T1 mandibular bone surface after 2 weeks, intra‐observer reliability measured by epeated landmark identification demonstrated excellent intra‐observer reliability, with intraclass correlation coefficient (ICC) values exceeding 0.99 for all dental and skeletal landmarks (Tables A2a, A2b, A2c). This indicated high reproducibility of the landmarking and three‐dimensional measurement procedures.

The Wilcoxon Signed Rank test compared cephalometric measurements, overjet, overbite, curve of Spee, space analysis and molar axis angles between T1 and T2. Landmark coordinate comparisons were made among T2 and T1 (achieved), V and T1 (predicted) and T2 and V (difference) across the horizontal, midsagittal and coronal planes, along with differences in mandibular bone surface landmarks between T1 and T2. Treatment accuracy (efficacy), defined as (achieved/predicted) × 100% or (T2‐T1)/(V‐T1) × 100%, was presented using both mean and median values, taking into account the potential impact of the denominator's size. Relative accuracy (%) was primarily interpreted for tooth movements with predicted displacements > 0.5 mm. For teeth planned as anchorage units with minimal programmed movement, emphasis was placed on absolute discrepancies (mm) and directional trends rather than percentage accuracy. Patients were divided into two groups based on miniscrew use, with the Mann–Whitney U test assessing intergroup differences. A p‐value of < 0.05 was deemed statistically significant.

2.7. Post Hoc Sample Size Estimation

Given the small sample size (n = 12; Miniscrew, n = 3), intergroup comparisons are exploratory, and results should be interpreted cautiously. To provide context for statistical power, a post hoc sample size calculation was performed based on the primary outcome variable: the absolute difference between predicted and achieved mandibular first molar distalisation. Using the observed standard deviation and a clinically meaningful difference of 1.5 mm, it was estimated that 41 bilateral Class III cases would be required to achieve 80% power with α = 0.05 for detecting statistically significant differences between treatment groups. This highlights that the present pilot study is underpowered for robust intergroup comparisons and primarily serves as a feasibility and hypothesis‐generating investigation.

3. Results

3.1. Patient Composition and Cephalometric Overview

Between January 2018 and June 2022, 12 of 1638 patients met the inclusion criteria, all presenting with bilateral Class III molar relationships (Figure 2). The mean pre‐treatment ANB angle was −1.67 ± 3.37 degrees. From T1 to T2, statistically significant changes were observed in levelling of the curve of Spee, relief of maxillary and mandibular crowding, and an increase in the L6‐MP angle, indicating distal tipping of the mandibular first molar crown. A comprehensive cephalometric summary is provided in Table A3.

FIGURE 2.

Sample selection flow chart.

3.2. Maxillary Dental Movements: Predicted vs. Achieved

In the transverse dimension, achieved maxillary expansion was significantly less than predicted at the inter‐second‐premolar and inter‐first‐molar widths, indicating incomplete posterior expansion (−1.08 ± 1.34 mm and −1.34 ± 1.74 mm, with median accuracy of 65.02% and 59.32%, respectively). In the anteroposterior dimension, the maxillary dentition—including central incisors (−1.04 ± 0.68 mm), canines (−0.60 ± 1.58 mm), first premolars (−0.53 ± 1.46 mm), second premolars (−0.62 ± 1.48 mm) and distobuccal cusp of the first molar (−0.56 ± 1.46 mm)—demonstrated significantly more mesial positioning than predicted, reflecting anchorage loss during distalisation mechanics. Median accuracy values varied widely from −0.10% to 69.72%, underscoring inconsistent predictability of posterior anchorage with aligner‐based Class III mechanics. In the vertical direction, only the maxillary central incisor showed a significant discrepancy, with greater intrusion than predicted. Key trends are illustrated in Figure 3A, with full quantitative data available in Table A4.

FIGURE 3.

Distribution of the difference between achieved and predicted tooth movements of (A) maxillary dentition and (B) mandibular dentition and (C) changes in mandible position.

3.3. Mandibular Dental Movements: Predicted Versus Achieved

All mandibular teeth exhibited significantly less distalisation than planned, presenting instead with mesial positioning relative to predictions. This was observed across central incisors (−2.66 ± 2.01 mm, 18.64%), canines (−2.39 ± 1.87 mm, 10.78%), first premolars (−2.30 ± 1.54 mm, 14.22%), second premolars (−2.36 ± 1.56 mm, 19.92%) and first molars, with mesiobuccal cusp (−2.24 ± 1.57 mm, 30.45%), distobuccal cusp (−2.23 ± 1.53 mm, 33.87%) and mesiolingual cusp (−2.17 ± 1.59 mm, 26.72%), confirming limited efficiency of mandibular distalisation with aligner‐based mechanics alone. Among mandibular teeth, the first molar cusps demonstrated the highest median accuracy values, though still below 50%. In the vertical dimension, mandibular central incisors showed significantly less extrusion than predicted [−1.00 ± 1.68 mm (−58.10%)]. These findings are summarised in Figure 3B, with detailed values reported in Table A5.

3.4. Condylar and Mandibular Skeletal Changes

From T1 to T2, the foremost point of the condyle moved significantly forward (−0.57 ± 1.13 mm), while the most lateral point showed a small but significant downward displacement (−0.15 ± 0.85 mm). These positional changes suggest adaptive mandibular or temporomandibular joint responses associated with Class III elastic wear. Detailed coordinate changes are reported in Table A6 and illustrated in Figure 3C.

3.5. Comparison Between Miniscrew and Class III Elastics Groups

3.5.1. Grouping, Anchorage Protocols and Biomechanics

The 12 patients were divided into the Miniscrew group (n = 3) and Class III Elastics group (n = 9).

Miniscrew group: Temporary anchorage devices were placed in the mandibular buccal shelf region, posterior to the second molars, at the level of attached gingiva. Miniscrews (approximately 2.0 mm diameter and 10–12 mm length) were inserted prior to or at the initiation of mandibular distalisation staging. Elastics were worn from the miniscrews to the mandibular canines, generating a primarily distal force vector with minimal vertical component.

Class III Elastics group: Conventional Class III elastics were worn from the maxillary first molars to the mandibular canines, producing a distal force on the mandibular dentition accompanied by a vertical component that tended to intrude maxillary incisors and extrude posterior teeth.

In both groups, aligner staging followed a two‐phase design: (1) sequential distalisation of the mandibular molars, followed by (2) simultaneous staging of the remaining mandibular dentition. However, the presence of skeletal anchorage in the Miniscrew group altered force distribution and anchorage demand, contributing to different dental and vertical responses between groups.

Baseline characteristics were comparable between groups at T1, except for a larger SN–OP angle in the Miniscrew group, which persisted at T2. In the Class III Elastics group, significant changes from T1 to T2 included a reduced curve of Spee depth and decreased maxillary and mandibular arch length discrepancies (Table 1).

TABLE 1.

Differences between miniscrew anchorage and Class III elastics at T1 and T2.

Miniscrew (n = 3)				Class III Elastics (n = 9)
Age at T1	23.8 ± 4.39			30.2 ± 7.68
T2‐T1 (Months)	16.6 ± 5.25			15.5 ± 5.42
	T1	T2	p	T1	T2	p
SNA	77.33 ± 2.49	77.33 ± 2.49	1	83.22 ± 5.20	83.22 ± 5.20	1
SNB	79.33 ± 0.94	79.00 ± 0.82	0.7902	84.78 ± 6.01	84.33 ± 5.60	0.8137
ANB	−2.00 ± 2.83	−1.67 ± 2.36	0.7898	−1.56 ± 3.53	−1.11 ± 3.48	1
SN‐FH	11.67 ± 2.25	11.67 ± 2.25	1	7.94 ± 3.75	7.94 ± 3.75	1
SN‐OP	23.67 ± 0.62#	24.33 ± 1.43#	0.4524	14.89 ± 5.25#	12.89 ± 6.43#	0.8248
SN‐MP	38.17 ± 3.42	38.83 ± 3.12	0.7565	31.06 ± 5.82	31.50 ± 6.04	1
SN‐PP	13.50 ± 1.40	13.50 ± 1.40	1	9.81 ± 4.91	9.81 ± 4.91	1
PFH/AFH	61.55 ± 3.70	61.40 ± 3.71	0.8252	65.39 ± 5.13	65.16 ± 5.20	1
Wits	−12.41 ± 3.92	−12.16 ± 2.03	0.3314	−8.96 ± 5.53	−6.83 ± 4.32	1
SN‐U1	103.38 ± 4.33	100.82 ± 3.46	1	111.31 ± 10.16	112.53 ± 7.84	0.5066
MP‐L1	84.67 ± 3.86	86.83 ± 4.09	0.9647	87.50 ± 8.06	87.94 ± 6.64	0.5066
Overjet	−1.27 ± 0.43	−0.93 ± 0.63	0.0519	−0.86 ± 2.56	1.32 ± 1.44	0.5066
Overbite	0.45 ± 0.61	−0.30 ± 1.14	0.7239	1.99 ± 2.53	1.00 ± 1.06	0.5066
Curve of spee	2.15 ± 0.63	1.52 ± 0.47	0.3827	2.38 ± 0.62	1.58 ± 0.53	0.0133*
Upper space analysis	−3.58 ± 0.05	−0.97 ± 1.93	0.25	−3.37 ± 3.42	−0.96 ± 0.94	0.0195*
Lower space analysis	−3.49 ± 1.35	−1.1 ± 0.76	0.25	−3.2 ± 2.67	−1.11 ± 1.3	0.0195*
U6‐PP	97.19 ± 8.22	98.56 ± 7.27	0.5	91.34 ± 7.96	90.51 ± 7.79	0.4961
L6‐MP	93.44 ± 8.22	95.92 ± 9.69	0.25	98.87 ± 4.54	100.57 ± 4.39	0.1289

Abbreviations: ANB, the angle formed by the anatomic landmarks A point to nasion to B point; L6‐MP, the angle formed between the mandibular first molar axis and the mandibular plane (an increase indicates distal tipping of the crown); MP‐L1, the angle formed between the mandibular central incisor axis and the mandibular plane; PFH/AFH, the ratio of posterior facial height to anterior facial height; SNA, the angle formed by the anatomic landmarks sella to nasion to A point; SNB, the angle formed by the anatomic landmarks sella to nasion to B point; SN‐FH, the angle formed between the sella‐nasion line and the Frankfort horizontal plane; SN‐MP, the angle between the sella‐nasion line and the mandibular plane (gonion‐gnathion); SN‐PP, the angle formed between the sella‐nasion line and the palatal plane; SN‐OP, the angle formed between the sella‐nasion line and the occlusal plane; T1, pretreatment; T2, posttreatment (after initial set/series of clear aligners); U1‐SN, the angle formed between the maxillary central incisor axis and the sella‐nasion line; U6‐PP, the angle formed between the maxillary first molar axis and the palatal plane (an increase indicates distal tipping of the crown).

^*Statistically significant difference between T1 and T2, p < 0.05.

^# Statistically significant difference between the Miniscrew and the Class III Elastics groups p < 0.05.

3.5.2. Maxillary Changes by Group

In the Class III Elastics group, posterior maxillary expansion was significantly less than predicted, and maxillary central incisors and second premolars were positioned more mesially than planned. Maxillary central incisors also demonstrated significantly greater intrusion; inter‐second‐premolar and inter‐first‐molar widths were significantly less than predicted with median accuracies of 52.48% and 42.86%. The maxillary central incisors and second premolars were positioned more mesially than predicted (−1.22 ± 1.85 mm and −0.66 ± 1.65 mm), and the maxillary central incisors were significantly more intruded (0.61 ± 0.76 mm). Maxillary central incisors also demonstrated significantly greater intrusion. Compared with the Miniscrew group, the Class III Elastics group achieved significantly less inter‐first‐molar width and exhibited different vertical incisor responses (Table A7, Figure 4A). The combination of incisor intrusion and minimal molar extrusion contributed to a tendency toward reduction of the SN–OP angle.

FIGURE 4.

Comparison of the difference between achieved and predicted tooth movements in (A) maxillary dentition, (B) mandibular dentition and (C) changes in mandible position in the Miniscrew and Class III Elastics groups.

3.5.3. Mandibular Dental Changes by Group

Both groups exhibited significantly less mandibular distalisation than predicted. However, the Miniscrew group demonstrated higher median accuracy values for mandibular molar distalisation (14.49% for the mandibular central incisors to 44.66% for the mesiobuccal cusp of the first molar) than the Class III Elastics group (6.22% for the canines to 33.87% for the distobuccal cusp of the first molar), consistent with improved anchorage control. The Miniscrew group also had significantly greater planned distalisation of the mandibular first molar. Vertically, the Class III Elastics group showed greater‐than‐predicted intrusion of mandibular incisors and canines, whereas the Miniscrew group exhibited less intrusion than predicted for premolars and molars, indicating superior vertical control with skeletal anchorage (Table A8, Figure 4B).

3.5.4. Condylar Changes by Group

Significant condylar displacement was observed only in the Class III Elastics group, with forward and downward movement of key condylar landmarks (lateral point moving downward: −0.49 ± 1.03 mm and foremost point moving forward: −0.52 ± 0.84 mm). Between‐group comparisons revealed opposite vertical condylar trends: upward movement in the Miniscrew group (0.34 ± 0.45 mm) versus downward movement in the Class III Elastics group (−0.25 ± 0.52 mm) (Table A9, Figure 4C).

4. Discussion

This study evaluated the clinical effectiveness and predictability of Invisalign treatment in 12 adult patients with Class III malocclusion. Although the average horizontal overbite improved from −0.96 ± 2.24 mm to 0.76 ± 1.62 mm and the vertical overbite decreased from 1.61 ± 2.31 mm to 0.67 ± 1.22 mm, the final horizontal overbite did not reach the ideal 1–3 mm range defined by the American Board of Orthodontics discrepancy index [18]. These findings highlight that, while Invisalign can achieve meaningful occlusal improvement in adult Class III patients, complete realisation of the planned treatment objectives remains challenging. Achieving 100% of prescribed movements with Invisalign aligners is uncommon and frequently necessitates refinement. Arqub et al. [19] found that 73.8% to 100% of patients needed two or more additional series depending on case complexity, underscoring the clinical expectation that refinement is an integral component of Invisalign treatment rather than an exception.

Compared with prior reports summarised in Padmanabhan et al.'s systematic review [3], the present study demonstrates substantially lower predictability of mandibular molar distalisation, particularly when evaluated using true CBCT regional superimposition. Among the reviewed studies, only Wu et al. employed CBCT imaging; however, their measurements were referenced to a vertical plane rather than stable mandibular structures, which may have incorporated mandibular positional changes and yaw during treatment [16]. Wu et al. reported 71% crown efficacy and 47% root efficacy for mandibular first molar distalisation without skeletal anchorage or Class III elastics, with the distobuccal cusp showing 1.85 ± 1.09 mm of distal movement and a distal tipping of 1.62°. In contrast, Rota et al. found approximately 1.16 mm of distal crown movement accompanied by mesial root tipping, suggesting distal tipping rather than bodily movement [20]. By using digital model–integrated CBCT with regional superimposition registered on the symphysis and mandibular body, the present study minimised confounding effects from mandibular positional changes and provides a more conservative and clinically realistic estimate of distalisation efficacy. Median accuracies for mandibular first molar distalisation were only 30.45%, 33.87% and 26.72% at the mesiobuccal, distobuccal and mesiolingual cusps, respectively, with distal tipping of approximately 1.9°, indicating that mandibular molar distalisation is consistently overestimated in ClinCheck simulations.

Further subgroup analysis reinforced the clinical relevance of this discrepancy. In the Miniscrew group, approximately 2 mm of distalisation was achieved for a planned 5 mm movement, corresponding to median accuracies of 39.28% to 44.66%. In contrast, the Class III Elastics group achieved < 1 mm of distalisation for a planned 2.5 mm movement, with median accuracies ranging from 26.72% to 33.87%. These findings suggest that Invisalign without skeletal anchorage is unlikely to produce clinically meaningful mandibular molar distalisation in adult Class III patients, while the use of miniscrews improves predictability but does not fully overcome the biomechanical limitations of aligner‐based distalisation. From a clinical perspective, these results indicate that overcorrection should be planned, refinement should be anticipated and adjunctive mechanics—including skeletal anchorage or partial fixed appliances—should be considered when mandibular distalisation is a key treatment objective.

When planned mandibular distalisation was not achieved, compensatory dentoalveolar changes were observed. Notably, the Class III Elastics group exhibited significant maxillary incisor proclination and intrusion, despite the maxillary incisors being planned as relatively stable units [15] These compensatory movements likely contributed to the observed improvement in overjet but may compromise torque control, periodontal limits and long‐term stability if not carefully monitored. In contrast, such changes were not observed in the Miniscrew group, suggesting that improved anchorage control may reduce unwanted reciprocal effects. Clinically, this finding underscores the limitation of using Class III elastics with aligners as a primary camouflage strategy and supports the use of skeletal anchorage when attempting to minimise maxillary incisor compensation. The evaluation of condylar position provides additional insight into the skeletal effects of aligner‐based Class III correction in adults. In the Miniscrew group, no significant changes in mandibular anatomic landmarks or condylar position were observed, suggesting a stable mandibular position throughout treatment. In contrast, the Class III Elastics group demonstrated significant forward and downward displacement of the condylar head, accompanied by trends toward downward and backward movement of pogonion and menton, as well as decreases in SNB and increases in SN‐MP. These findings indicate a tendency toward clockwise mandibular rotation, likely mediated by vertical dental changes rather than true skeletal advancement. Although these condylar movements do not appear to represent a clinically harmful pattern, they highlight the potential for elastics to induce mandibular positional changes in adult patients, reinforcing the need for cautious case selection and close monitoring [21, 22].

The primary limitation of this study is the small sample size, which restricts the generalisability of the findings. Nonetheless, as a pilot study using rigorous CBCT superimposition techniques, it provides clinically meaningful insights into the predictability of Invisalign for Class III correction. Based on the observed discrepancies between predicted and achieved mandibular molar distalisation, a power analysis indicated that a minimum of 82 M (41 patients with bilateral Class III molar relationships) would be required for a sufficiently powered future study.

5. Conclusions

Considering the constraints of this research, the following conclusions can be drawn.

1. Mandibular first molar distalisation using Invisalign with Class III elastics showed median accuracies of 30.45%, 33.87% and 26.72% at the mesiobuccal, distobuccal and mesiolingual cusps, respectively. In contrast, miniscrews achieved higher accuracies of 44.66%, 43.09% and 39.28% at the corresponding cusps.

2. With skeletal anchorage, the mandibular first molar achieved approximately 2 mm of distalisation for a planned 5 mm movement with skeletal anchorage, versus < 1 mm from a planned 2.5 mm movement when Class III elastics were used.

3. The use of Class III elastics during Invisalign treatment resulted in significant maxillary incisor proclination and condylar head movement. In contrast, miniscrews‐assisted mandibular distalisation did not produce notable positional changes in the maxillary incisors or condyle.

6. Clinical Implications

The findings of this study have several important implications for clinical decision‐making when using Invisalign in adult Class III patients. First, mandibular molar distalisation is consistently overestimated in ClinCheck, particularly when Class III elastics are used without skeletal anchorage. Clinicians should therefore plan distalisation conservatively, incorporate deliberate overcorrection, and anticipate the need for multiple refinement stages. Second, Invisalign without skeletal anchorage appears insufficient as a standalone modality for achieving clinically meaningful mandibular molar distalisation in moderate Class III camouflage cases. In such patients, miniscrews, partial fixed appliances, or hybrid treatment approaches should be considered to improve predictability and reduce reliance on dentoalveolar compensation. Third, the frequent occurrence of compensatory maxillary incisor proclination and intrusion in cases treated with Class III elastics highlights the need for careful torque control and periodontal risk assessment, particularly in patients with thin labial alveolar bone. Finally, while Class III elastics may induce mandibular positional and condylar changes, these effects appear primarily dental and rotational in nature; nonetheless, they warrant close monitoring in adult patients. Collectively, these findings support the use of Invisalign as an adjunctive tool rather than a primary modality for Class III correction when substantial mandibular distalisation is required.

Author Contributions

All authors made substantial contributions to the study's design, data acquisition, analysis, or interpretation; participated in drafting or critically revising the manuscript; and gave final approval for the submitted version. All authors have reviewed and approved the final version of the manuscript. Additional contributions from each author are outlined below: H.‐Y.W. contributed to the active discussion of experimental design, collected the data and made a substantial contribution to the revision of the manuscript. J.‐S.S. drafted the manuscript and assisted with study conceptualisation. C.‐Y.K. collected the data and conducted the experimental procedures. S.‐J.T. and B.‐W.S. collected the data and assisted with the data analysis. C.‐H.C. contributed to the active discussion of experimental design and assisted with the data analysis. J.F.L. executed the majority of the data analysis. J.Z.‐C.C. drafted the manuscript, supervised the study, assisted with study conceptualisation and made a substantial contribution to the revision of the manuscript.

Funding

The authors have nothing to report.

Disclosure

A statement of the location where the work was performed: All works were performed at the National Taiwan University and the National Taiwan University Hospital (Taipei City, Taiwan).

Ethics Statement

For the execution of the study, authorisation was requested from the Research Ethics Committee, National Taiwan University Hospital, Taipei, Taiwan, ROC with the approval code of NTUH‐REC No.: 202108032RIND.

Consent

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A.

TABLE A1.

Workflow.

Step‐1. Data acquisition Digital models scanned with iTero Element and exported from ClinCheck in STL format at pre‐treatment (T1) and post‐treatment (T2) CBCT scans at T1 and T2 exported in DICOM format

Step‐2. CBCT orientation and superimposition T1 CBCT oriented using Frankfort Horizontal plane; midsagittal plane passing through nasion and basion; coronal plane originating at basion T2 CBCT superimposed on T1 using voxel‐based registration: ○ Maxillary superimposition: cranial base, orbits, zygomatic bones ○ Mandibular superimposition: symphysis and mandibular body

Step‐3. Digital model integration Crowns from T1 and T2 aligned to their respective CBCT arches using surface‐based registration ClinCheck virtual model (V) superimposed on T1 to compare predicted vs. achieved movements All models placed in a single 3D coordinate system (X = transverse, Y = anteroposterior, Z = vertical)

Step‐4. Segmentation and landmark identification Mandibular bone and condyles segmented from CBCT images Dental landmarks (n = 28): midpoints of central incisors, cusp tips of canines, premolars, first molar cusps Mandibular skeletal landmarks (n = 10): pogonion, menton, left/right gonion, key condylar points Lateral cephalometric images derived from CBCT for supplemental analysis

Step‐5. Measurement and analysis Achieved movements: T2–T1 Predicted movements: V–T1 Absolute movement magnitudes (mm) prioritised for small predicted movements; accuracy (%) defined as (T2–T1)/(V–T1) × 100%, interpreted with caution when predicted movement < 0.5 mm

TABLE A2a.

Intra‐observer reliability for maxillary dental measurements.

Tooth position	Horizontal direction (X value)		Anterior–posterior direction (Y value)		Vertical direction (Z value)
	ICC	p	ICC	p	ICC	p
Right maxillary central incisor	0.997	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Left maxillary central incisor	0.998	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Right maxillary canine	0.997	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Left maxillary canine	0.996	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Right maxillary first premolar	0.999	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Left maxillary first premolar	0.996	< 0.001*	1.000	< 0.001	1.000	< 0.001*
Right maxillary second premolar	0.997	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Left maxillary second premolar	0.997	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Right maxillary first molar mesiobuccal cusp	0.997	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Right maxillary first molar distobuccal cusp	0.998	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Right maxillary first molar mesiopalatal cusp	0.998	< 0.001*	0.999	< 0.001*	1.000	< 0.001
Left maxillary first molar mesiobuccal cusp	0.997	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Left maxillary first molar distobuccal cusp	0.997	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Left maxillary first molar mesiopalatal cusp	0.995	< 0.001*	1.000	< 0.001*	1.000	< 0.001*

Note: N = 12.

Abbreviation: ICC, intraclass correlation coefficient.

^* p < 0.05.

TABLE A2b.

Intra‐observer reliability for mandibular dental measurements.

Tooth position	Horizontal direction (X value)		Anterior–posterior direction (Y value)		Vertical direction (Z value)
	ICC	p	ICC	p	ICC	p
Left mandibular central incisor	0.998	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Right mandibular central incisor	0.998	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Left mandibular canine	0.998	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Right mandibular canine	0.998	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Left mandibular first premolar	0.997	< 0.001	1.000	< 0.001*	1.000	< 0.001*
Right mandibular first premolar	0.998	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Left mandibular second premolar	0.998	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Right mandibular second premolar	0.997	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Left mandibular first molar mesiobuccal cusp	0.999	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Left mandibular first molar distobuccal cusp	0.999	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Left mandibular first molar mesiolingual cusp	0.998	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Right mandibular first molar mesiobuccal cusp	0.990	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Right mandibular first molar distobuccal cusp	0.996	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
Right mandibular first molar mesiolingual cusp	0.998	< 0.001*	0.997	< 0.001*	1.000	< 0.001*

Note: N = 12.

Abbreviation: ICC, intraclass correlation coefficient.

^* p < 0.05.

TABLE A2c.

Intra‐observer reliability for mandibular skeletal measurements.

	Horizontal direction (X value)		Anterior–posterior direction (Y value)		Vertical direction (Z value)
	ICC	p	ICC	p	ICC	p
Pogonion	0.997	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
Menton	0.999	< 0.001*	0.999	< 0.001	1.000	< 0.001*
Right gonion	0.999	< 0.001*	0.999	< 0.001*	0.998	< 0.001*
Left gonion	0.999	< 0.001*	1.000	< 0.001*	1.000	< 0.001*
The uppermost point of right condylar head	0.999	< 0.001*	0.999	< 0.001*	1.000	< 0.001*
The most lateral point of right condylar head	1.000	< 0.001*	0.999	< 0.001*	0.999	< 0.001*
The foremost point of right condylar head	0.998	< 0.001*	0.999	< 0.001*	0.997	< 0.001*
The uppermost point of left condylar head	0.998	< 0.001*	0.997	< 0.001*	1.000	< 0.001*
The most lateral point of left condylar head	0.999	< 0.001*	0.998	< 0.001*	1.000	< 0.001*
The foremost point of left condylar head	0.998	< 0.001*	0.999	< 0.001*	0.999	< 0.001*

Note: N = 12.

Abbreviation: ICC, intraclass correlation coefficient.

^* p < 0.05.

TABLE A3.

Pretreatment (T1) and posttreatment (T2) lateral cephalometric analysis.

Age at T1 (years)	28.6 ± 7.53
T2–T1 (months)	15.7 ± 5.4

	T1	T2	p
SNA	81.75 ± 5.32	81.75 ± 5.32	1
SNB	83.42 ± 5.74	83.00 ± 5.39	0.7943
ANB	(−1.67) ± 3.37	(−1.25) ± 3.24	0.7711
SN‐FH	8.88 ± 3.80	8.88 ± 3.80	1
SN‐OP	17.08 ± 5.93	15.75 ± 7.49	0.7073
SN‐MP	32.83 ± 6.15	33.33 ± 6.32	0.817
SN‐PP	10.73 ± 4.60	10.73 ± 4.60	1
PFH/AFH	64.43 ± 5.09	64.22 ± 5.14	0.7949
Wits	(−9.82) ± 5.39	(−8.16) ± 4.51	0.4883
SN‐U1	109.33 ± 9.69	109.60 ± 8.65	1
MP‐L1	86.79 ± 7.34	87.67 ± 6.12	0.7948
Overjet	(−0.96) ± 2.24	0.76 ± 1.62	0.0566
Overbite	1.61 ± 2.31	0.67 ± 1.22	0.6033
Curve of spee	2.21 ± 0.61	1.54 ± 0.44	0.0042*
Upper space analysis	(−3.42) ± 2.92	(−0.97) ± 1.15	0.0024*
Lower space analysis	(−3.27) ± 2.35	(−1.11) ± 1.16	0.0034*
U6‐PP	92.8 ± 8.08	92.52 ± 8.19	0.7646
L6‐MP	97.51 ± 5.77	99.41 ± 5.96	0.0342*

Abbreviations: ANB, the angle formed by the anatomic landmarks A point to nasion to B point; L6‐MP, the angle formed between the mandibular first molar axis to the mandibular plane; MP‐L1, the angle formed between the mandibular central incisor axis to the mandibular plane; PFH/AFH; the ratio of posterior facial height to anterior facial height; SNA, the angle formed by the anatomic landmarks sella to nasion to A point; SNB, the angle formed by the anatomic landmarks sella to nasion to B point; SN‐FH, the angle formed between the sella‐nasion line and the Frankfort horizontal plane; SN‐MP, the angle between the sella‐nasion line and the mandibular plane (gonion‐gnathion); SN‐OP, the angle formed between the sella‐nasion line and the occlusal plane; SN‐PP, the angle formed between the sella‐nasion line and the palatal plane; T1, pretreatment; T2, posttreatment (after initial set/series of clear aligners); U1‐SN, the angle formed between the maxillary central incisor axis to the sella‐nasion line; U6‐PP, the angle formed between the maxillary first molar axis to the palatal plane.

^*Statistically significant difference between T1 and T2: p < 0.05, N = 12.

TABLE A4.

Differences between the predicted and achieved tooth movements of the maxillary dentition.

	Predicted (mm)	Achieved (mm)	Difference (mm)	Accuracy (%)				p
				Mean	First quartile	Median	Third quartile
Horizontal direction (n = 12)
Intercanine width of maxillary arch	0.82 ± 1.4	0.74 ± 1.06	−0.08 ± 0.68	73.10% ± 56.32%	44.12%	81.69%	108.68%	0.4697
Interpremolar width of maxillary first premolars	3.30 ± 2.42	2.58 ± 2.33	−0.72 ± 1.16	88.77% ± 90.49%	51.02%	76.11%	114.44%	0.0923
Interpremolar width of maxillary second premolars	3.49 ± 2.51	2.41 ± 2.04	−1.08 ± 1.34	50.06% ± 58.03%	33.48%	65.02%	88.60%	0.0269*
Intermolar width of maxillary first molars	3.04 ± 1.87	1.7 ± 2.00	−1.34 ± 1.74	111.36% ± 218.10%	20.63%	59.32%	107.96%	0.0342*
Anteroposterior direction (n = 24)
Maxillary central incisor	−0.08 ± 1.59	−1.12 ± 2.50	−1.04 ± 0.68	68.99% ± 2456.37%	−72.75%	69.72%	225.49%	0.0051*
Maxillary canine	−0.03 ± 1.21	−0.62 ± 1.33	−0.60 ± 1.58	−478.82% ± 2542.91%	−75.89%	−0.10%	101.37%	0.0338*
Maxillary first premolar	−0.01 ± 1.07	−0.63 ± 1.22	−0.53 ± 1.46	52.46% ± 327.78%	−27.18%	43.77%	159.30%	0.0396*
Maxillary second premolar	0.18 ± 0.98	−0.44 ± 1.17	−0.62 ± 1.48	−103.58% ± 1345.35%	−38.04%	23.85%	123.19%	0.0205*
Mesiobuccal cusp of maxillary first molar	0.18 ± 1.06	−0.34 ± 1.28	−0.51 ± 1.49	150.06% ± 1630.92%	−146.64%	−1.40%	119.91%	0.0864
Distobuccal cusp of maxillary first molar	0.15 ± 0.82	−0.42 ± 1.29	−0.56 ± 1.46	−118.62% ± 1508.67%	−114.66%	7.19%	188.86%	0.0366*
Mesiopalatal cusp of maxillary first molar	−0.18 ± 1.04	−0.62 ± 1.06	−0.43 ± 1.21	−1400.77% ± 7058.84%	−13.90%	56.76%	203.66%	0.0661
Vertical direction (n = 24)
Maxillary central incisor	0.51 ± 1.70	0.95 ± 1.56	0.44 ± 0.74	920.47% ± 4385.11%	33.75%	33.75%	99.57%	0.0078*
Maxillary canine	0.01 ± 1.19	0.24 ± 1.02	0.23 ± 0.83	−79.01% ± 426.38%	43.58%	43.58%	85.40%	0.1948
Maxillary first premolar	0.67 ± 1.30	0.52 ± 1.22	−0.15 ± 1.24	−85.53% ± 626.16%	50.06%	50.06%	114.39%	0.9559
Maxillary second premolar	0.24 ± 1.04	0.03 ± 0.9	−0.21 ± 1.35	−163.86% ± 527.12%	1.56%	1.56%	71.37%	0.7187
Mesiobuccal cusp of maxillary first molar	0.07 ± 0.98	−0.19 ± 1.11	−0.26 ± 1.56	−738.33% ± 2930.96%	−29.99%	−29.99%	68.48%	0.6775
Distobuccal cusp of maxillary first molar	0.30 ± 0.80	−0.19 ± 1.21	−0.49 ± 1.48	59.27% ± 225.28%	5.90%	5.90%	174.87%	0.1661
Mesiopalatal cusp of maxillary first molar	0.25 ± 0.94	−0.33 ± 0.93	−0.58 ± 1.21	109.20% ± 485.57%	−23.42%	−23.42%	90.43%	0.118

Note: Arch expansion, incisor retraction/M distalisation, tooth intrusion: +arch constriction, incisor proclination/M mesialisation, tooth extrusion: −. Difference = achieved – predicted. Accuracy = (achieved/predicted) ×100%.

Abbreviation: n, number.

^* p < 0.05.

TABLE A5.

Differences between the predicted and achieved tooth movements of the mandibular dentition.

	Predicted (mm)	Achieved (mm)	Difference (mm)	Accuracy (%)				p
				Mean	First quartile	Median	Third quartile
Horizontal direction (n = 12)
Intercanine width of mandibular arch	0.21 ± 2.26	0.28 ± 1.90	0.07 ± 0.74	72.36% ± 53.65%	62.87%	75.90%	94.61%	1
Interpremolar width of mandibular first premolars	2.69 ± 2.79	2.38 ± 2.01	−0.31 ± 1.14	82.93% ± 160.13%	60.84%	81.76%	100.44%	0.5693
Interpremolar width of mandibular second premolars	3.81 ± 3.62	2.64 ± 2.42	−1.16 ± 1.58	94.02% ± 130.40%	51.29%	67.50%	99.13%	0.0771
Intermolar width of mandibular first molars	1.95 ± 3.28	1.57 ± 2.14	−0.38 ± 1.73	−57.45% ± 244.87%	−18.48%	15.68%	69.80%	0.791
Anteroposterior Direction (n = 24)
Mandibular central incisor	2.70 ± 2.04	0.04 ± 0.84	−2.66 ± 2.01	80.41% ± 179.57%	2.76%	18.64%	49.02%	< 0.0001*
Mandibular canine	2.82 ± 1.93	0.43 ± 0.95	−2.39 ± 1.87	−103.88% ± 386.79%	−8.87%	10.78%	50.40%	< 0.0001*
Mandibular first premolar	2.74 ± 1.73	0.44 ± 0.98	−2.30 ± 1.54	4.17% ± 79.56%	−13.07%	14.22%	50.04%	< 0.0001*
Mandibular second premolar	3.14 ± 2.02	0.78 ± 1.29	−2.36 ± 1.56	13.56% ± 89.15%	0.05%	19.92%	42.56%	< 0.0001*
Mesiobuccal cusp of mandibular first molar	3.39 ± 1.97	1.15 ± 1.31	−2.24 ± 1.57	30.98% ± 42.84%	12.36%	30.45%	47.58%	< 0.0001*
Distobuccal cusp of mandibular first molar	3.35 ± 1.95	1.12 ± 1.19	−2.23 ± 1.53	29.35% ± 47.51%	11.84%	33.87%	55.53%	< 0.0001*
Mesiolingual cusp of mandibular first molar	3.14 ± 1.91	0.97 ± 1.27	−2.17 ± 1.59	102.70% ± 409.51%	7.87%	26.72%	61.19%	< 0.0001*
Vertical direction (n = 24)
Mandibular central incisor	0.42 ± 1.79	−0.58 ± 1.15	−1.00 ± 1.68	−843.70% ± 3876.84%	−144.83%	−58.10%	−17.17%	0.0096*
Mandibular canine	−0.16 ± 2.04	−0.72 ± 1.35	−0.56 ± 1.65	477.81% ± 1882.15%	−36.66%	36.83%	165.88%	0.1111
Mandibular first premolar	−0.88 ± 1.51	−0.72 ± 0.90	0.16 ± 1.47	282.51% ± 1587.06%	−35.62%	48.69%	100.20%	0.698
Mandibular second premolar	−1.47 ± 1.44	−0.92 ± 0.75	0.54 ± 1.48	90.31% ± 352.01%	−3.23%	57.25%	145.00%	0.2497
Mesiobuccal cusp of mandibular first molar	−1.14 ± 1.30	−0.55 ± 0.64	0.60 ± 1.41	37.02% ± 167.89%	−18.06%	30.19%	123.68%	0.1849
Distobuccal cusp of mandibular first molar	−0.93 ± 1.31	−0.26 ± 0.66	0.66 ± 1.46	−11.03% ± 221.66%	−9.35%	22.03%	93.78%	0.1487
Mesiolingual cusp of mandibular first molar	−0.98 ± 1.17	−0.60 ± 0.89	0.39 ± 1.35	116.25% ± 328.01%	−6.25%	33.04%	126.01%	0.3277

Note: Arch expansion, incisor retraction/M distalisation, tooth extrusion: + arch constriction, incisor proclination/M mesialisation, tooth intrusion: −. Difference = achieved – predicted. Accuracy = (achieved/predicted) ×100%.

Abbreviation: n, number.

^* p < 0.05.

TABLE A6.

The positional changes of the mandibular landmarks during treatment.

	Anteroposterior direction (mm)	p	Vertical direction (mm)	p
Pogonion (n = 12)	0.40 ± 1.67	0.5693	−0.44 ± 1.55	0.5186
Menton (n = 12)	0.19 ± 1.92	0.9097	−0.37 ± 1.52	0.6772
Gonion (n = 24)	0.27 ± 1.81	0.8032	0.05 ± 1.47	0.9119
The uppermost point of condylar head (n = 24)	−0.40 ± 0.98	0.1948	−0.13 ± 0.86	0.4354
The most lateral point of condylar head (n = 24)	−0.21 ± 1.07	0.746	−0.15 ± 0.85	0.0418*
The foremost point of condylar head (n = 24)	−0.57 ± 1.13	0.0354*	−0.12 ± 0.71	0.7238

Note: Upwardβ/backward movement: +. Downward/forward movement: −.

Abbreviation: n, number.

^* p < 0.05.

TABLE A7.

Differences between the miniscrew and the Class III elastics groups: Maxillary tooth movement.

		Predicted (mm)	Achieved (mm)	Difference (mm)	Accuracy (%)				p
					Mean	First quartile	Median	Third quartile
Horizontal direction
Miniscrew (n = 3)	Intercanine width of maxillary arch	2.09 ± 0.35	1.93 ± 0.77	−0.17 ± 0.52	89.77% ± 27.41%	79.66%	108.29%	109.15%	1
	Interpremolar width of maxillary first premolars	4.98 ± 1.34	5.04 ± 2.24	0.06 ± 1.02	97.44% ± 20.66%	87.28%	105.47%	111.61%	1
	Interpremolar width of maxillary second premolars	4.22 ± 0.28	4.22 ± 0.99	0.00 ± 0.78	99.14% ± 17.82%	88.51%	100.22%	110.31%	1
	Intermolar width of maxillary first molars	3.51 ± 1.73	4.10 ± 1.27#	0.59 ± 0.48#	126.48% ± 19.95%	117.05%	135.24%	140.28%	0.5
Class III Elastics (n = 9)	Intercanine width of maxillary arch	0.40 ± 1.44	0.35 ± 0.91	−0.05 ± 0.75	67.55% ± 62.78%	23.38%	80.38%	86.34%	0.4258
	Interpremolar width of maxillary first premolars	2.74 ± 2.56	1.76 ± 1.87	−0.97 ± 1.16	85.89% ± 105.17%	38.19%	67.37%	113.34%	0.0742
	Interpremolar width of maxillary second premolars	3.24 ± 2.97	1.81 ± 2.06	−1.44 ± 1.37	33.70% ± 57.50%	21.40%	52.48%	71.03%	0.0195*
	Intermolar width of maxillary first molars	2.88 ± 1.99	0.90 ± 1.63#	−1.98 ± 1.63#	106.32% ± 255.22%	18.31%	42.86%	63.39%	0.0117*
Anteroposterior direction
Miniscrew (n = 6)	Maxillary central incisor	0.72 ± 1.05	0.23 ± 0.93	−0.49 ± 0.90	210.44% ± 283.46%	−5.85%	130.55%	247.52%	0.4375
	Maxillary canine	−0.23 ± 0.90	−0.67 ± 0.96	−0.44 ± 0.89	73.19% ± 199.74%	−65.80%	−19.30%	115.90%	0.3125
	Maxillary first premolar	−0.39 ± 0.65	−0.76 ± 0.66	−0.36 ± 0.67	−82.46% ± 356.27%	−15.11%	22.38%	119.23%	0.3125
	Maxillary second premolar	−0.13 ± 1.04	−0.62 ± 0.76	−0.49 ± 0.79	61.52% ± 94.73%	16.19%	30.23%	81.79%	0.4375
	Mesiobuccal cusp of maxillary first molar	0.51 ± 1.31	0.03 ± 0.90	−0.48 ± 0.94	489.68% ± 748.27%	35.65%	78.58%	553.69%	0.3125
	Distobuccal cusp of maxillary first molar	0.60 ± 0.89	0.11 ± 0.65	−0.49 ± 0.69	70.54% ± 103.18%	−2.41%	71.99%	160.22%	0.4375
	Mesiopalatal cusp of maxillary first molar	−0.16 ± 1.06	−0.89 ± 0.69	−0.73 ± 0.75	161.68% ± 208.97%	−6.02%	89.85%	273.52%	0.1563
Class III Elastics (n = 18)	Maxillary central incisor	−0.35 ± 1.65	−1.58 ± 2.69	−1.22 ± 1.85	21.84% ± 2850.53%	−245.55%	69.72%	222.11%	0.0104*
	Maxillary canine	0.04 ± 1.29	−0.61 ± 1.43	−0.65 ± 1.75	−662.82% ± 2931.07%	−109.43%	−0.10%	78.38%	0.0814
	Maxillary first premolar	0.00 ± 1.16	−0.59 ± 1.35	−0.59 ± 1.63	97.44% ± 303.30%	−41.72%	43.77%	182.77%	0.0814
	Maxillary second premolar	0.28 ± 0.94	−0.38 ± 1.27	−0.66 ± 1.65	−158.61% ± 1559.74%	−40.95%	19.89%	142.23%	0.0432*
	Mesiobuccal cusp of maxillary first molar	0.06 ± 0.93	−0.46 ± 1.36	−0.53 ± 1.63	36.86% ± 1829.43%	−160.44%	−56.08%	29.85%	0.1674
	Distobuccal cusp of maxillary first molar	−0.01 ± 0.74	−0.59 ± 1.39	−0.59 ± 1.64	−181.68% ± 1748.95%	−169.26%	−2.90%	369.71%	0.1084
	Mesiopalatal cusp of maxillary first molar	−0.19 ± 1.03	−0.52 ± 1.15	−0.33 ± 1.32	−1921.58% ± 8139.36%	−7.96%	45.32%	162.48%	0.2645
Vertical direction
Miniscrew (n = 6)	Maxillary central incisor	0.06 ± 0.47	−0.02 ± 0.27#	−0.08 ± 0.34#	−6.68% ± 82.34%	−24.29%	30.45%	48.17%	0.6875
	Maxillary canine	0.15 ± 0.90	0.03 ± 0.52	−0.12 ± 0.70	24.54% ± 95.13%	10.78%	36.55%	46.14%	1
	Maxillary first premolar	1.01 ± 0.71	0.59 ± 0.65	−0.42 ± 0.84	72.26% ± 83.33%	41.82%	65.97%	132.59%	0.4375
	Maxillary second premolar	0.58 ± 0.94	0.21 ± 0.73	−0.37 ± 1.25	−31.01% ± 222.42%	−70.24%	−0.91%	51.85%	0.6875
	Mesiobuccal cusp of maxillary first molar	0.39 ± 0.84	−0.05 ± 0.79	−0.43 ± 1.25	−2930.13% ± 5128.58%	−2592.60%	−103.00%	5.12%	0.5625
	Distobuccal cusp of maxillary first molar	0.68 ± 0.69	−0.03 ± 0.94	−0.71 ± 1.25	134.33% ± 206.45%	−23.91%	89.92%	255.74%	0.3125
	Mesiopalatal cusp of maxillary first molar	0.36 ± 0.75	−0.20 ± 0.58	−0.56 ± 0.85	−57.27% ± 137.28%	−131.73%	−62.33%	62.61%	0.3125
Class III Elastics (n = 18)	Maxillary central incisor	0.66 ± 1.92	1.27 ± 1.68#	0.61 ± 0.76#	1229.52% ± 5060.54%	−4.61%	37.13%	114.31%	0.0056*
	Maxillary canine	−0.04 ± 1.27	0.31 ± 1.13	0.35 ± 0.83	−113.53% ± 487.57%	29.47%	51.01%	88.34%	0.1084
	Maxillary first premolar	0.56 ± 1.42	0.50 ± 1.22	−0.07 ± 1.34	−138.13% ± 718.54%	−202.84%	44.56%	95.54%	0.7337
	Maxillary second premolar	0.13 ± 1.04	−0.03 ± 0.94	−0.15 ± 1.38	−208.14% ± 591.74%	−243.83%	1.56%	72.03%	0.9323
	Mesiobuccal cusp of maxillary first molar	−0.04 ± 1.00	−0.24 ± 1.19	−0.20 ± 1.64	−7.73% ± 280.43%	−98.46%	−0.82%	77.47%	0.865
	Distobuccal cusp of maxillary first molar	0.18 ± 0.80	−0.24 ± 1.28	−0.42 ± 1.54	34.25% ± 225.76%	−119.25%	−20.40%	118.57%	0.3465
	Mesiopalatal cusp of maxillary first molar	0.21 ± 0.99	−0.37 ± 1.02	−0.59 ± 1.65	164.68% ± 547.09%	−108.51%	−23.42%	355.29%	0.2837

Note: Arch expansion, incisor retraction/M distalisation, tooth intrusion: +. Arch constriction, incisor proclination/M mesialisation, tooth extrusion: difference = achieved – predicted. Accuracy = (achieved/predicted) ×100%.

Abbreviation: n, number.

^*Statistically significant difference between Achieved versus Predicted values: p < 0.05.

^# Statistically significant difference between Miniscrew versus Class III Elastic groups: p < 0.05.

TABLE A8.

Differences between the miniscrew and the Class III elastics groups: mandibular tooth movement.

		Predicted (mm)	Achieved (mm)	Difference (mm)	Accuracy (%)				p
					Mean	First quartile	Median	Third quartile
Horizontal direction
Miniscrew (n = 3)	Intercanine width of mandibular arch	1.40 ± 2.12	1.30 ± 2.00	−0.10 ± 0.12	84.74% ± 12.84%	80.05%	90.00%	92.05%	0.5
	Interpremolar width of mandibular first premolars	4.27 ± 1.15#	3.28 ± 1.89	−0.99 ± 0.77	69.77% ± 35.52%	57.21%	85.31%	90.09%	0.25
	Interpremolar width of mandibular second premolars	1.83 ± 1.83#	1.32 ± 1.01	−0.51 ± 1.10	169.49% ± 224.94%	40.11%	59.61%	243.93%	0.75
	Intermolar width of mandibular first molars	−0.53 ± 0.83#	−0.36 ± 0.41	0.17 ± 1.21	−54.26% ± 104.46%	−84.88%	5.12%	6.05%	1
Class III Elastics (n = 9)	Intercanine width of mandibular arch	−0.18 ± 2.29	−0.06 ± 1.85	0.12 ± 0.88	68.24% ± 63.66%	50.58%	68.76%	96.11%	0.8203
	Interpremolar width of mandibular first premolars	2.16 ± 3.11	2.08 ± 2.07	−0.08 ± 1.21	87.32% ± 191.53%	62.97%	80.57%	117.11%	1
	Interpremolar width of mandibular second premolars	4.47 ± 4.01	3.09 ± 2.71	−1.38 ± 1.73	68.86% ± 40.86%	51.76%	73.46%	98.13%	0.1289
	Intermolar width of mandibular first molars	2.77 ± 3.54	2.22 ± 2.21	−0.56 ± 1.92	−58.51% ± 290.14%	−17.37%	25.76%	75.53%	0.7344
Anteroposterior direction
Miniscrew (n = 6)	Mandibular central incisor	3.55 ± 1.17	0.55 ± 0.39	−3.00 ± 1.25	17.99% ± 16.65%	4.85%	14.49%	25.27%	0.0313*
	Mandibular canine	3.83 ± 1.19	0.89 ± 1.00	−2.94 ± 1.14	20.66% ± 26.71%	−2.30%	18.82%	44.09%	0.0313*
	Mandibular first premolar	3.70 ± 1.47	1.05 ± 1.25	−2.65 ± 1.05	17.95% ± 42.06%	−17.46%	33.23%	52.19%	0.0313*
	Mandibular second premolar	4.86 ± 2.18	1.85 ± 1.82	−3.01 ± 1.61	26.38% ± 44.61%	12.59%	32.38%	61.51%	0.0313*
	Mesiobuccal cusp of mandibular first molar	5.13 ± 1.41#	2.29 ± 1.53	−2.83 ± 1.51	42.56% ± 28.43%	19.82%	44.66%	66.05%	0.0313*
	Distobuccal cusp of mandibular first molar	5.08 ± 1.71#	2.10 ± 1.40	−2.98 ± 1.62	39.92% ± 23.29%	19.60%	43.09%	59.06%	0.0313*
	Mesiolingual cusp of mandibular first molar	4.85 ± 1.48#	2.02 ± 1.71	−2.84 ± 1.58	36.61% ± 35.53%	12.37%	39.28%	61.54%	0.0313*
Class III Elastics (n = 18)	Mandibular central incisor	2.42 ± 2.18	−0.13 ± 0.88	−2.55 ± 2.20	101.22% ± 202.94%	0.78%	19.29%	80.22%	< 0.0001*
	Mandibular canine	2.49 ± 2.01	0.28 ± 0.89	−2.21 ± 2.03	−145.39% ± 438.62%	−13.88%	6.22%	46.02%	0.0004*
	Mandibular first premolar	2.42 ± 1.69	0.24 ± 0.77	−2.18 ± 1.66	−0.42% ± 88.68%	−12.68%	10.74%	33.91%	< 0.0001*
	Mandibular second premolar	2.57 ± 1.60	0.43 ± 0.77	−2.14 ± 1.48	9.29% ± 99.85%	−5.99%	17.99%	34.19%	< 0.0001*
	Mesiobuccal cusp of mandibular first molar	2.81 ± 1.78#	0.77 ± 0.96	−2.04 ± 1.54	27.12% ± 46.51%	12.34%	30.45%	39.62%	< 0.0001*
	Distobuccal cusp of mandibular first molar	2.77 ± 1.66#	0.80 ± 0.89	−1.98 ± 1.41	25.82% ± 53.00%	11.39%	33.87%	42.78%	< 0.0001*
	Mesiolingual cusp of mandibular first molar	2.57 ± 1.67#	0.62 ± 0.82	−1.95 ± 1.53	124.73% ± 470.43%	3.36%	26.72%	46.19%	< 0.0001*
Vertical direction
Miniscrew (n = 6)	Mandibular central incisor	−0.10 ± 0.75	0.26 ± 0.73#	0.36 ± 1.38	−211.30% ± 227.58%	−277.20%	−111.49%	−54.54%	0.5625
	Mandibular canine	−0.87 ± 0.91	−0.32 ± 1.00	0.56 ± 1.52	266.95% ± 428.13%	19.19%	166.15%	207.72%	0.6875
	Mandibular first premolar	−1.73 ± 0.79#	−0.31 ± 1.00	1.42 ± 1.39#	5.73% ± 115.23%	−24.23%	12.04%	58.16%	0.0938
	Mandibular second premolar	−2.49 ± 0.91#	−0.61 ± 0.96	1.88 ± 1.60#	36.33% ± 64.37%	−11.43%	26.59%	59.71%	0.0625
	Mesiobuccal cusp of mandibular first molar	−1.85 ± 0.82	−0.11 ± 0.80	1.74 ± 1.14#	9.00% ± 88.88%	−10.29%	24.87%	30.60%	0.0625
	Distobuccal cusp of mandibular first molar	−1.45 ± 0.92	0.29 ± 0.81	1.73 ± 1.14#	−82.46% ± 263.70%	−25.19%	9.11%	24.60%	0.0625
	Mesiolingual cusp of mandibular first molar	−1.26 ± 0.47	0.19 ± 0.46#	1.45 ± 0.77#	−1.03% ± 67.81%	−47.03%	−10.09%	5.84%	0.0625
Class III Elastics (n = 18)	Mandibular central incisor	0.59 ± 1.99	−0.86 ± 1.12#	−1.45 ± 1.52	−1054.50% ± 4455.08%	−83.90%	−51.75%	−6.24%	0.0016*
	Mandibular canine	0.07 ± 2.25	−0.86 ± 1.43	−0.93 ± 1.51	548.10% ± 2157.00%	−41.88%	29.57%	122.09%	0.0237*
	Mandibular first premolar	−0.60 ± 1.58#	−0.86 ± 0.83	−0.26 ± 1.24#	374.77% ± 1822.25%	−50.05%	55.83%	128.87%	0.3927
	Mandibular second premolar	−1.12 ± 1.42#	−1.02 ± 0.63	0.10 ± 1.13#	108.31% ± 403.44%	41.24%	79.44%	190.51%	0.766
	Mesiobuccal cusp of mandibular first molar	−0.91 ± 1.35	−0.70 ± 0.49	0.22 ± 1.28#	46.37% ± 187.19%	−11.27%	51.44%	133.19%	0.8317
	Distobuccal cusp of mandibular first molar	−0.75 ± 1.37	−0.45 ± 0.47	0.31 ± 1.37#	12.78% ± 209.59%	0.73%	46.27%	132.78%	0.9661
	Mesiolingual cusp of mandibular first molar	−0.89 ± 1.31	−0.86 ± 0.84#	0.03 ± 1.31#	155.35% ± 368.87%	5.81%	75.02%	153.32%	1

Note: Arch expansion, incisor retraction/M distalisation, tooth extrusion: +. Arch constriction, incisor proclination/M mesialisation, tooth intrusion: −. Difference = achieved – predicted. Accuracy = (achieved/predicted) ×100%.

Abbreviation: n, number.

^*Statistically significant difference between Achieved versus Predicted values: p < 0.05.

^# Statistically significant difference between Miniscrew versus Class III Elastic groups: p < 0.05.

TABLE A9.

Differences between the miniscrew and the Class III elastics groups: mandibular positional changes during treatment.

	Anteroposterior direction (mm)	p	Vertical direction (mm)		p
Miniscrew	Pogonion (n = 3)	1.26 ± 1.94	0.5	−1.29 ± 0.47	0.25
	Menton (n = 3)	1.20 ± 1.94	0.75	−1.22 ± 1.02	0.5
	Gonion (n = 6)	1.50 ± 2.61	0.3125	0.39 ± 2.07	0.6875
	The uppermost point of condylar head (n = 6)	−0.28 ± 0.66	0.3125	0.34 ± 0.45#	0.3125
	The most lateral point of condylar head (n = 6)	−0.09 ± 1.19	1	0.11 ± 0.63	1
	The foremost point of condylar head (n = 6)	−0.73 ± 1.73	0.8125	0.06 ± 0.77	1
Class III Elastics	Pogonion (n = 9)	0.11 ± 1.45	1	−0.16 ± 1.68	0.8203
	Menton (n = 9)	−0.14 ± 1.79	0.8203	−0.08 ± 1.55	0.8203
	Gonion (n = 18)	1.50 ± 2.61	0.6095	1.50 ± 2.61	0.766
	The uppermost point of condylar head (n = 18)	−0.43 ± 1.06	0.4951	−0.25 ± 0.52#	0.0898
	The most lateral point of condylar head (n = 18)	−0.26 ± 1.03	0.5509	−0.49 ± 1.03	0.0139*
	The foremost point of condylar head (n = 18)	−0.52 ± 0.84	0.0237*	−0.16 ± 0.85	0.6095

Note: Upward/backward movement: +; downward/forward movement: −.

Abbreviation: n, number.

^*Statistically significant difference between pretreatment versus posttreatment (after initial set/series of clear aligners) values, p < 0.05.

^# Statistically significant difference between Miniscrew versus Class III Elastic groups, p < 0.05.

Data Availability Statement

The datasets used and/or analysed in the current study are available from the corresponding author on reasonable request.