Introduction
The objective of this study was to evaluate the forces and moments exerted by orthodontic aligners on 3 different displaced maxillary teeth and their adjacent supporting teeth.
Methods
An in vitro orthodontic simulator was used to measure the forces and moments of a 0.75-mm thick glycol-modified polyethylene terephthalate material for 3 maxillary teeth: central incisor, canine, and second premolar. Forces and moments were recorded for tested teeth displaced lingually one by one for 0.20 mm. Repeated measures of multivariate analysis of variance was used to assess the outcome.
Results
The mean buccolingual force applied on a displaced canine (2.25 ± 0.38 N) was significantly ( P <0.001) more than the central incisor (1.49 ± 0.18 N) and second premolar (1.50 ± 0.16 N). The mean moment (that tends to tip the teeth buccally) exerted on a canine (−20.11 ± 5.27 Nmm) was significantly more ( P <0.001) than the central incisor (−8.42 ± 1.67 Nmm) and second premolar (−11.45 ± 1.29 Nmm). The forces and moments acting on teeth adjacent to the displaced tooth were clinically significant and acted in opposing directions to those on the displaced tooth.
Conclusions
The results of this study highlighted that for the same amount of displacement on a given tooth, the forces and moments imposed by the orthodontic aligner depend on location around the arch. These findings highlight the need to further study aligner mechanics around the dental arch and optimize aligner design to impose desired mechanical loads to avoid detrimental effects during orthodontic tooth movement.
Highlights
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Biomechanics of orthodontic aligners are studied in vitro.
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Maxillary central incisor, canine, and second premolar movements were considered.
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Forces and moments were measured for displaced and adjacent teeth.
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The position of the displaced tooth around the arch was found to be of significance.
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Forces and moments acting on adjacent teeth were found to be clinically significant.
Clear thermoplastic appliances have been used in dentistry as retainers, temporomandibular joint splints, bleaching trays, surgical splints, and aligners for orthodontic tooth movement. Orthodontic aligners are designed to move teeth to a desirable position through incremental movements with a series of aligners. When engaged, the slight offset of the aligner from the engaged teeth and the material resiliency impose forces and moments on teeth which results in their movement toward the desired position. It is imperative to evaluate forces and moments exerted by orthodontic aligners as the magnitude and direction of the applied forces and moments directly contribute to physiological and predictable tooth movement compared with detrimental effects such as tissue necrosis and unpredicted tooth movement.
A limited number of studies have investigated the forces and moments produced by aligners. Barbagallo et al, using an in vivo pressure film approach, evaluated that the initial force for buccal tipping of premolar was 5.12 N when the appliance was activated by 0.5 mm in 8 patients. An in vitro study by Kohda et al demonstrated that forces exerted by aligners for bodily tooth movement of the central incisor is dependent on the type of material (Hardcast material applied significantly lower force than Duran and Erkodur [which were not significantly different from each other]), material thickness (thicker material [0.75 mm or 0.8 mm] produced significantly greater force than those fabricated from thinner material [0.4 mm or 0.5 mm]) and the amount of activation (1.0-mm activation produced significantly lower force than those with 0.5-mm activation). Several in vitro studies by Hahn et al have quantitatively investigated forces delivered to maxillary central incisor for derotation, tipping, torquing by 1.0-mm thick Ideal Clear, Erkodur, and Biolon materials. The forces exerted by the Biolon material was much greater than those of the other materials.
The available literature has assessed the effect of thermoplastic material choice, thickness, and amount of activation on single tooth models; however, the forces and moment systems imposed on different types of teeth (eg, incisors, canines, premolars, and molars) has yet to be explored. Incisors, canines, premolars, and molars have different anatomy of the crown, both in terms of shape and length. As a result, it could reasonably be suggested that different surface areas may be engaged by the aligner, and the contact mechanics between the aligner and the tooth may vary with different types of teeth. It is anticipated that the varying tooth/aligner engagement between teeth can alter aligner material deformation that could result in a difference in applied orthodontic forces and moments. There is a curvature in the arch form that could further influence the deformation of the engaged aligner and possibly affect the forces and moments on the basis of the location of the teeth in the arch. Beyond the proposed variations in mechanics based on tooth geometry and location, recent reviews have also pointed out the less predictable nature of tooth movement when using orthodontic aligners. Such factors point to a need to study the biomechanics of clear orthodontic aligner therapy. Therefore, the objective of this in vitro study was to assess the forces and moments exerted on a central incisor, canine, and second premolar teeth around the arch using a clinically representative glycol-modified polyethylene terephthalate thermoplastic aligner material.
Material and methods
An in vitro electro-mechanical orthodontic simulator (OSIM) was used to quantify the forces and moments generated around a simulated maxillary arch. A comprehensive description of the OSIM is provided in previous studies. , Briefly, anatomic teeth were generated digitally using Linek’s tooth carving manual. The root portion of these anatomic teeth were reduced as cylindrical posts below cementoenamel junction to adapt and fix them on OSIM. Later, digital anatomic teeth were 3-dimensional (3D) printed using stainless steel. OSIM has horizontal and vertical micrometers that were used to move teeth in buccolingual (toward and away from the cheek) and occlusogingival (vertical) directions, respectively, to develop a symmetrical maxillary arch ( Fig 1 ). The load cells (Nano17 by ATI industrial automation), capable of measuring forces and moments in 3D, were located at a distance from the teeth for OSIM. Load cell measurements were transformed to an approximated center of resistance of teeth by using a Faro arm (Faro, Lake Mary, Fla) coordinate measurement machine and subsequent Jacobian transformation matrices. The center of resistance for single- and multi-rooted teeth was approximated from the literature , as used in previous studies, , and represent the theoretical central point of support provided by the bone and periodontal ligament structures surrounding the tooth root.
A digital scan of the OSIM was obtained using a Lythos intraoral scanner (Ormco, Orange, Calif) which was used to generate a plastic 3D print of the arch. The maxillary arch printed model had slight undercuts that were filled with wax and further replicated by using polysiloxane impression material to make the stone cast of high strength dental stone for aligner fabrication. Taglus material is a US Food and Drug Administration-approved glycol-modified polyethylene terephthalate material and was selected as a representative material for this study. Sheets of 0.75 mm thickness Taglus material were randomly selected from the packet for each test. An aligner was formed through the thermoforming process with a Biostar machine (Scheu Dental, Iserlohn, Germany) using the manufacturer-specified process. As suggested by the manufacturer, a code 113 was used on the Biostar machine, which automatically set the pressure of more than 5 bar and heating time of 25 seconds ( Fig 2 ).
Once an aligner was formed, it was stored for approximately 24 hours in dry conditions in the retainer box in an airtight bag before being inserted onto the OSIM. All aligners (n = 30) were inserted using an anteroposterior path of insertion in which the aligner was first inserted on the anterior teeth followed by posterior teeth by putting pressure on the molar teeth. Teeth were moved with the horizontal and vertical micrometers to obtain a position for the teeth such that forces and moments in the buccolingual and occlusogingival directions on all maxillary teeth were less than 0.10 N and 5 Nmm, respectively. There are 4 types of teeth in the human oral cavity such as the incisor, canine, premolar, and molar. During orthodontic tooth movement, incisor, canine, and premolar are frequently moved, and molars are used as anchor teeth. Therefore, for this study, central incisor, canine, and second premolar were translated individually by 0.20 mm in the lingual direction and taken back to their original position. After each tooth movement, the aligner was made passive before beginning the next test. This was done so that there were no clinically relevant forces and moments acting on the system from the previous tooth movement before the start of the next tooth movement ( Fig 3 ). Initial forces and moments in the XYZ direction were recorded for the tested teeth and adjacent teeth at 0.20 mm of displacement. The variables buccolingual force (Fy) and moment (tend to tip tooth crown buccally and lingually) (Mx) on the tested teeth were the primary outcome measures. The sign conventions for forces and moments of interest in this study are provided in Table I . Each trial was completed at 37°C to mimic the oral temperature using a heating chamber. Furthermore, to account for any variations in aligner engagement, each aligner was tested 3 times for each tooth movement and averaged.
| Forces and moments sense | Buccolingual (Fy) | Occlusogingival (Fz) | Third-order moment (Mx) |
|---|---|---|---|
| Positive sense of forces or moments | Buccal-directed Fy | Occlusal-directed Fz | Mx causing buccal root tip |
Statistical analysis
Repeated measures of multivariate analysis of variance (MANOVA) were used to assess if there was a significant mean difference in the Fy and Mx exerted on 3 teeth when the Fy and Mx were considered jointly. Statistical analysis was performed by applying repeated measured MANOVA on the 2 response variables, Fy (Newton) and Mx (Nmm), and a predictor variable, type of teeth (incisor, canine, and second premolar). Repeated measures of MANOVA were robust to violations of multivariate normality for this study as the groups were of equal size.
As the multivariate test based on Wilks’ lambda rejected the null hypothesis, it was followed by repeated measures of analysis of variance on each of the primary outcomes. A statistical significance was set at 0.05. A clinically significant difference was set at force levels of more than 0.10 N and moment of more than 5 Nmm. Statistical analysis was conducted using SPSS software (version 24.0; IBM, Armonk, NY).
Results
All forces and moments data were reported at the center of resistance for each tooth. Box plots showed the distribution of data for Fy ( Fig 4 ) and Mx ( Fig 5 ). The multivariate test based on Wilks’ lambda Λ = 0.004 and P < 0.001 indicated that there were significant differences among the central incisor, canine, and second premolar when the 2 outcome variables (Fy and Mx) were considered jointly. The initial mean buccal force acting on the central incisor was 1.49 ± 0.18 N ( Fig 6 ), canine 2.25 ± 0.38 N ( Fig 7 ), and second premolar 1.50 ± 0.16 N ( Fig 8 ). Pairwise comparison with Bonferroni correction showed that there was a statistically and clinically significant mean difference in Fy between the canine and central incisor (mean difference, 0.76 N; P <0.001; 95% confidence interval [CI], 0.56-0.96) and between the canine and second premolar (mean difference, 0.75 N, P <0.001; 95% CI, 0.54-0.95). There was no significant difference in the Fy exerted on the central incisor and second premolar ( Table II ).
