Introduction
The study aimed to determine the center of rotation and the type of orthodontic tooth movement (OTM) of the mandibular central incisors (Cis) and lateral incisors (Lis), and the efficacy of achieving planned labiolingual incisor inclination changes after nonextraction space closure (NESC) with the Invisalign (Align Technology, Santa Clara, Calif) appliance.
Methods
Digital study models of initial, planned, and achieved treatment outcomes were obtained from the Invisalign treatment planning facility, ClinCheck. Vectors analogous to the long axes of the incisors were generated using Geomagic Control X (version 2022.0: 3D Systems, Cary, NC) metrology software. Intersecting vectors represented the incisors’ center of rotation, whereas measurement of the vectors to a reference y-plane enabled determination of incisor labiolingual inclination.
Results
A total of 166 mandibular incisors from 42 patients satisfied the inclusion criteria. The achieved mean (standard deviation) OTMs were 41.4% (23.6) of those planned. Translation was the least successful OTM, with 7.6% of Cis and 8.3% of Lis translating as planned. Planned retroclination resulted in overexpression of 151% for CIs and 165% for Lis. The accuracy of planned proclination was low, with only 16.7% of CIs and 25.8% of Lis proclining as planned, whereas the remainder retroclined instead.
Conclusions
Less than half of the planned OTM for the mandibular incisors during NESC was achieved. Planned retroclination was overexpressed, and most of planned proclination resulted in retroclination. Clinicians should consider these findings when planning NESC treatment with the Invisalign appliance.
Highlights
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Mandibular incisor orthodontic tooth movement (OTM) assessed after initial aligner series.
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Determining the center of rotation enabled the identification of planned and achieved OTM.
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Less than half the planned OTM for mandibular incisors in nonextraction space closure achieved.
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Planned retroclination overexpressed and planned proclination underexpressed.
Clear aligner therapy (CAT) is commonly used in orthodontic practice, with the Invisalign (Align Technology, Santa Clara, Calif) appliance reportedly being the most prescribed by orthodontists globally. ,,, Align Technology uses ClinCheck, a cloud-based treatment planning interface, which enables communication between the company and the treating clinician and facilitates customized treatment planning and visualization of the planned outcome. On approval of the treatment plan by the clinician, a series of aligners is provided to the patient by the treating clinician. The purpose of CAT was to treat minor irregularities when first introduced, but developments in material and digital technology have resulted in claims that more challenging malocclusions can now be effectively treated using aligners. ,,
However, the findings from multiple investigations ,,,,, have suggested that Invisalign may not achieve treatment outcomes planned before the commencement of treatment. In 2009, Kravitz et al conducted one of the first prospective studies and concluded that Invisalign had a 41% accuracy in achieving planned anterior tooth movement. To improve force delivery and aligner fit, SmartForce features were introduced by Align Technology. Features included a new material—SmartTrack, power ridges, and composite resin attachments of specified predesigned shapes and sizes, bonded to the teeth. However, a follow-up prospective study incorporating these features indicated that the mean efficacy of Invisalign in achieving planned orthodontic tooth movements (OTM) was approximately 50%.
To predictably move a tooth with orthodontic mechanotherapy, a force must be applied at an appropriate location in the desired direction and magnitude. The center of resistance (Cres) is defined as the point at which the force application results in pure translation without tipping or rotation. , If a tooth was unrestrained in space, the Cres would align with the tooth’s center of mass or gravity. , However, teeth are restrained by the periodontal ligament. , A center of rotation (Crot) has been identified as the location around which an object rotates while being displaced. In relation to tooth movement, it refers to the location in which a tooth has been rotated, based on its initial and final positions. Thus, it applies not only to the long axis of the tooth but also when viewed from the occlusal or incisal aspect. , Identifying a tooth’s Crot can determine various tooth movements, such as pure tipping or uncontrolled tipping (PT), controlled tipping (CT), torque (TQ), and translation (TN). , In PT, the Crot rotational aspect is closer to the Cres. , In CT, the Crot is closer to the root apex. , TQ has been defined as the labiolingual or buccolingual inclination of the long axis of the crown. TQ has also been described as a shear-based moment that causes rotation. This means that during TQ movement, the Crot is displaced incisally, and the root apex is moved more than the crown.
Several studies have assessed the accuracy of achieving the planned OTM with CAT. ,, However, the evaluation of specific malocclusion characteristics, such as crowding and spacing, is limited. Gaddam et al evaluated TQ changes in maxillary and mandibular incisors in patients with between <4 mm of spacing and <6 mm of crowding. They concluded that planned labial crown TQ was underexpressed, and the planned lingual crown TQ was overexpressed. Jiang et al investigated the accuracy of attaining the planned OTM in a crowded dentition with conservative space-gaining measures such as proclination, expansion, and interproximal enamel reduction (IPR). They concluded that PT was more accurate, and that the least accurate OTM was the achievement of the planned TQ.
Evidence regarding the efficacy of achieving the planned labiolingual inclination incisor change in extraction and NESC patients is limited. A recent investigation indicated that planned maxillary incisor retroclination overexpressed by 169% for central incisors (Cis) and 126% for lateral incisors (Lis). The study also emphasized that the planned incisor proclination was underexpressed. The investigation showed that only 10.7% of maxillary Cis and 43.5% of Lis proclined as planned. Furthermore, the incisors that proclined as planned did so with an efficacy of 24.7% for Cis and 68.1% for Lis. This compared with the Chan et al investigation, in which a 59.0% accuracy in achieving the planned mandibular incisor proclination during planned mandibular incisor extraction space closure was recorded.
Evidence from 4 investigations ,,, suggested that during mandibular incisor extraction space closure, an additional series of aligners may be required to achieve the ideal root position. Currently, there is little evidence regarding the accuracy of CAT in achieving the planned OTM change in a mandibular spaced dentition, with nonextraction space closure (NESC) being a treatment goal. A recent study concerning maxillary incisors demonstrated differences between planned and achieved OTMs during NESC. However, considering that the cortical bone in the mandible differs from that in the maxilla, similar assumptions cannot be made about NESC of incisors in the mandible.
The primary aim of this study was to determine the Crot of the mandibular incisors after wear of an initial series of clear aligners, with a treatment goal of NESC. By identifying the Crot, different types of planned OTM, and the accuracy in achieving planned tooth movements after wear of a series of aligners can be elicited. The secondary aim was to determine the efficacy of achieving the planned labiolingual incisor inclination change with respect to retroclination and proclination, irrespective of the type of OTM planned. The null hypotheses are that there are no differences between the type of OTM planned and achieved, and between the planned and achieved labiolingual inclination changes of the mandibular incisors after treatment of NESC with an initial series of aligners.
Material and Methods
The University of Adelaide Human Research Ethics Committee approved the project. Data for this study were obtained from the Australasian Aligner Research Database. The database contained >16,500 relevant records of patients who underwent treatment with the Invisalign appliance at the commencement of this study. Treatment was provided by 17 orthodontists, experienced in the use of aligners. All orthodontists are obliged to provide all patients whom they have treated with aligner therapy—there is no cherry-picking. An en masse staging protocol was used for all patients, with no use of alternative patterns such as frogging or W-staging.
All patients consented to the use of their data for research purposes before starting their orthodontic treatment. The inclusion criteria were (1) patients who started their treatment with the Invisalign appliance after the introduction of the SmartTrack aligner material by Align Technology in 2013, (2) patients aged ≥18 years with a permanent dentition, (3) mandibular spaced dentition: any visible interdental space between the contact points mesial to the first molar was defined as spaced, (4) patients without signs of active periodontal disease as evaluated during the initial assessment and with panoramic radiographs (5) availability of digital models representing the initial (T0) occlusion, planned (T1) treatment outcome and achieved (T2) treatment outcome after wear of the initial series of Invisalign aligners, (6) successful superimposition of digital models, (7) mandibular incisors without restorations or changes in the shape or size of the crown during orthodontic treatment, (8) patients without space-gaining measures such as extractions and IPR conducted in addition to their CAT, (9) completion of wear of the initial series of aligners as planned by the treating practitioner, (10) a 1-week wear protocol, and (11) patients who demonstrated compliance with aligner wear and adhered to the treatment protocol as prescribed by the treating clinician.
Exclusion criteria included: (1) insufficient records, (2) patients with craniofacial syndromes, along with medications or health issues that might influence tooth movement, and (3) patients undergoing combined orthodontic and orthognathic surgery treatment.
The methodology used in this study was adapted from a corresponding study related to the maxillary arch. The sample size was calculated from a previous similar investigation, which established that a minimum of 15 patients was necessary to achieve a power of 0.8 at an α level of 0.05. Three-dimensional (3D) stereolithographic files of the patients’ mandibular dentition digital models at 3 timepoints (T0, T1, and T2) ( Fig 1 , A- C ) were exported from ClinCheck into the Geomagic Control X metrology software platform (version 2022.0: 3D Systems, Cary, NC). T2 corresponded to the achieved outcome after wear of the initial prescribed series of aligners. The T0 and T1 ( Fig 2 , A ) models were superimposed to analyze the planned changes in the position of the mandibular incisors, and similarly, the T0 and T2 ( Fig 2 , B ) models were superimposed to analyze the achieved changes. The superimpositon of the T0, T1 and T2 models is shown for illustration ( Fig 2 , C ). To superimpose, the automated best-fit alignment between the measured model technique, with a maximum iteration ratio of 50 and an 80% sampling ratio, was used. This corresponded to the superimposition protocol adopted in similar research. ,
Three-dimensional stereolithographic files of the patients’ mandibular dentition digital models at 3 timepoints: A , T0 (initial); B , T1 (planned treatment); C , T2 (achieved treatment).
A , T0-T1 superimposition; B , T0-T2 superimposition; C , T0-T1-T2 superimposition.
Moreover, 3D vectors, analogous to the long axes of the Ci and Li of each quadrant, were obtained using the flood selection tool ( Fig 3 , A – C ). The type of OTM was identified by determining the Crot. , To analyze the planned and achieved OTM, the intersection of the T0 and T1 incisor vectors ( Fig 4 , A ) represented the Crot of the planned OTM. Similarly, the intersection of the T0 and T2 incisor vectors ( Fig 4 , B ) established the Crot of the achieved OTM. The crown and root length of the mandibular incisors was standardized as 21 mm. The Cres was identified to be situated at two-thirds of the distance from the incisal edge. The linear distances from the incisor edge to the respective vector intersections of T0 − T1 and T0 − T2 were generated. The OTM TQ has been reported purely as a labiolingual inclination change. However, equivalent variation in inclination in the sagittal plane can also occur during OTMs, such as CT or PT. Therefore, in this study, the TQ was classified under OTM and established based on Crot, and labiolingual inclination change was presented in the form of retroclination and proclination, irrespective of the planned OTM.
A , T0 3D vector; B , T1 vector; C , T2 3D vector. The flood selection tool extracts the tooth shape and autogenerates the long axis of the selected mandibular incisor.
A , Intersection of T0 ( blue ) vector and T1 ( green ) vector; B , Intersection of T0 ( blue ) vector and T2 ( yellow ) vector. Purple, Cres; black , Crot.
All data were recorded on an Excel spreadsheet (version 16.0: Microsoft, Redmond, Wash). For calculation purposes, the relative position of the intersection was mapped to the Cres of the incisor, and the type of OTM was determined according to the classification established by Smith et al ( Fig 5 ).
Type of tooth movement as determined by Smith et al. The distance of Crot from Cres in millimeters. Red , TN (−30< Crot >30). Green , TQ, (6< Crot ≤30). Gray , PT (−3< Crot ≤6). Blue , CT (−30≤ Crot <−3).
To determine the incisors’ inclination measurement, the vectors to the y-axis Cartesian coordinate system represented the incisor’s angle at T0, T1, and T2 ( Fig 6 , A – C ).
A , T0 incisor angle; B , T1 incisor inclination change; C, T2 incisor inclination change. Blue , y-plane; orange , initial, planned, and achieved incisor inclinations.
To quantify spacing, a plane was created that corresponded to the maximum convexity of the (potential) interproximal contact point on either side of the space ( Fig 7 ). All spaces mesial to the first mandibular molar were measured using the Geomagic Control X software. The linear distance between the interdental planes was calculated for each interproximal space, and these measurements were added to produce the total space for each of the T0, T1, and T2 models.
Analysis of space in the mandibular arch. The distance between each plane was calculated and added to determine the total space located mesial to the first molars on the right and left in the mandibular arch.
The percentage accuracy of the achieved OTM was calculated using the formula: (achieved/planned) × 100. , The difference between the planned and achieved inclination change was computed by subtracting the planned outcome from the achieved outcome. The achieved OTM was reported in terms of accuracy, whereas the labiolingual change was reported as efficacy.
Statistical analysis
Statistical analysis was performed using SPSS (version 29, IBM, Armonk, NY) and Microsoft Excel. The level of significance was set at P <0.05. Descriptive statistics were calculated for patient age, sex, and the prescribed number of aligners.
The Kolmogorov-Smirnov test was used to assess the normality of data distribution regarding age, sex, prescribed number of aligners, planned and achieved inclination change, and Crot. All data were normally distributed except for the Ci planned lingual root TQ and achieved TN for Li. Normally distributed data were assessed using paired sample t tests, and nonnormally distributed data were evaluated via the Wilcoxon test. An independent t test was employed to assess for significant differences in age and the prescribed number of aligners between sexes.
Intrarater reliability was measured by repeating 10 randomly selected patients’ records 2 weeks after the initial evaluation. For interrater reliability, the data were measured by a clinician experienced in the use of Geomagic Control X software in orthodontic research.
The software algorithm generated all angular measurements, so interrater and intrarater reliability were in absolute agreement. The software has a measurement tolerance of ± 0.1 mm for linear measurements and ±0.0° for angular measurements. For analyzing the space between the dentition, the 2-way mixed-effect model indicated excellent intrarater reliability (intraclass correlation coefficient, 0.97 [95% confidence interval, 0.95-0.98]). Similarly, the interrater reliability was also excellent (intraclass correlation coefficient from the 2-way mixed-effect model 0.97 [95% confidence interval, 0.96-0.98]).
Results
A total of 44 patients met the selection criteria. Because 2 models could not be superimposed, they were excluded, resulting in the assessment of the digital study models of 42 patients. One patient presented with 2 developmentally absent mandibular Ci, meaning that 82 Cis and 84 Lis were evaluated.
Table I indicates that most patients were female with a mean age of 41 (standard deviation [SD], 15.1) years. Table II provides a summary of planned and achieved OTM. Tables II-V show significant differences between most of the planned and achieved OTM after wear of the initial series of aligners. TQ was further divided into labial root torque (LRT) and lingual root torque (LinRT), with Table IV presenting LRT and LiRT OTM data for Cis and Lis. Of the planned Ci OTM, PT was the most accurate, with 63.6% accuracy. It was also the most frequently achieved OTM, accounting for 45.1% of all planned OTM.
Table I
Demographic characteristics for age and number of aligners (n = 42)
| Characteristics | Male | Female | t | 95% confidence interval | P value |
|---|---|---|---|---|---|
| Age (y) | 29.4 (6.4) | 41.0 (15.1) | −2.8 | −19.7 to −3.4 | 0.006 |
| Aligner number (n) | 37.4 (17.7) | 39.1 (18.4) | −0.2 | −13.3 to 9.9 | 0.760 |
Note. Values are presented as mean ± SD, unless specified otherwise.
Table II
OTM planned and achieved (n = 166)
| Planned mandible | Achieved | |||
|---|---|---|---|---|
| PT | CT | TQ | TN | |
| Cis | ||||
| PT (22) | 14 (63.6) | 6 (27.2) | 2 (9.0) | 0 (0.0) |
| CT (20) | 10 (50.0) | 10 (50.0) | 0 (0.0) | 0 (0.0) |
| TQ (27) | 10 (37.0) | 8 (29.6) | 9 (33.3) | 0 (0.0) |
| TN (13) | 3 (23.0) | 8 (61.5) | 1 (7.6) | 1 (7.6) |
| Total (82) | 37 (45.1) | 32 (39.0) | 12 (14.6) | 1 (1.2) |
| Lis | ||||
| PT (28) | 14 (50.0) | 12 (42.8) | 1 (3.5) | 1 (3.5) |
| CT (18) | 4 (22.2) | 13 (72.2) | 1 (5.5) | 0 (0.0) |
| TQ (26) | 8 (30.7) | 6 (23.0) | 12 (46.1) | 0 (0.0) |
| TN (12) | 5 (41.6) | 5 (41.6) | 1 (8.3) | 1 (8.3) |
| Total (84) | 31 (36.9) | 36 (42.8) | 15 (17.8) | 2 (2.3) |
Note. Values are presented as number (percentage).
Ci, central incisor; Li, lateral incsior; PT, pure tipping; CT, controlled tipping; TQ, torque; TN, translation.
Table III
The mean accuracy in achieving the planned OTM
| OTM | PT | CT | TQ | TN | Mean (SD) |
|---|---|---|---|---|---|
| Cis | 63.6 | 50.0 | 33.3 | 7.6 | 38.6 (24.1) |
| Lis | 50.0 | 72.2 | 46.1 | 8.3 | 44.1 (26.5) |
| Total mean | 56.8 | 61.1 | 39.7 | 7.9 | 41.4 (23.6) |
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