Are aligners capable of inducing palatal bodily translation or palatal root torque of upper central incisors? A biomechanical in vitro study

In the last two decades, aligners have been widely used as a therapeutic tool for correcting tooth malpositions [1‐3]. After shape-driven orthodontic tooth movement was introduced by Kesling in 1945 [4] and thermoforming of transparent foils was developed, aligners were used to treat mild tooth malpositions mostly in the anterior segment by tipping or derotation [5, 6]. Improvements in aligner techniques have allowed more complex tooth movements and have expanded the therapeutic indications of aligners [6‐8].

Some of the most challenging movements for aligners are bodily tooth movements or root torque as they depend on controlled root movement [9‐13]. To improve treatment outcomes and overcome underlying biomechanical problems during these challenging tasks, specific aligner modifications have been recommended [9, 14, 15]. These modifications were described by Sheridan et al. [16‐18] and included composite bumps adhesively attached to the crowns or local aligner reinforcements made by indentations in the tooth model to intensify local force application [9, 14, 15]. These pressure areas have been integrated into the commercial Invisalign® system as power ridges™ [14, 15, 19]. A local pressure area can be pressed either directly into the aligner with a special plier or through a recess in the digital tooth model [20]. From a biomechanical perspective, these aligner modifications apply a relatively high local contact force on the tooth, thereby increasing the force vector in the direction of movement and generating the force couple required for controlled root movement [9]. However, these effects may be rather complex because the tooth makes contact with the aligner at multiple points and these contacts change during ongoing tooth movement [11, 15].

Whether aligners can induce controlled root movements for bodily tooth translation or true root torque remains controversial [5, 21]. Importantly, studies have not consistently distinguished between bodily tooth movement and crown tipping, or between incisor inclination changes caused by crown tipping and predominant root torque. In orthodontics, the term “torque” originates from treatment with multibracket appliances, because controlled root movement to change a tooth’s inclination is usually generated by torsion of the arch wire around its longitudinal axis [22‐24]. Consequently, a force couple (i.e., a moment) is created in the bracket slot, which (in combination with an appropriate force component) may generate root torque [22‐24]. It has to be noted that, independent of the appliance used, true root torque is a predominant root movement, while the center of the tooth crown remains more or less in its original vestibulo-oral position. In contrast, dominating crown movements are related to controlled or uncontrolled tooth tipping [25].

This study addresses the following three questions on aligner treatment: (1) can aligners induce bodily movement or root torque of incisors in a labio-palatal direction? (2) Do aligner modifications affect the efficacy of bodily tooth movement or torque control of incisors? And (3) which modifications are most effective at controlling root torque or translational tooth movement of incisors?

To answer these questions, we first carried out a systematic review according to the PRISMA guidelines. We searched the literature in the following electronic databases: PubMed, Science Direct, Cochrane Central Register of Controlled Clinical Trials, IEEE Explorer, and the NLM Catalog in the NCBI databases. The electronic search and an additional manual search yielded 521 articles. After excluding non-relevant articles, six studies remained for qualitative analysis, two of which were experimental in-vitro studies [9, 15] and four of which were in-vivo studies in patients (clinical trials) [12, 13, 15, 26].

Based on the results of this systematic review, we concluded the following:

Based on these conclusions, our biomechanical in vitro study aimed to examine the effect of three different modification geometries and different aligner foil thicknesses on the 3D F/M system exerted on an upper central incisor. These pressure regions were implemented in polyethylene terephthalate glycol (PET-G) aligners in the labio-cervical crown region of tooth 11. This allowed us to systematically explore the ability of such aligners to induce a palatally directed bodily movement or even palatal root torque of upper central incisors.

Without modifications, 0.75-mm-thick aligners showed negligible Fy and Mx magnitudes with tooth 11 in the neutral position (Table 1). Furthermore, experimental palatal translation of tooth 11 induced an increasing labially directed force (+ Fy) when modifications were absent. This showed that aligners do not meet the requirements for bodily movement of tooth 11 in the palatal direction or palatal root torque of tooth 11 without modifications.

Figure 3 shows individual Fy and Mx curves for 0.75-mm-thick aligners with 1.5-mm deep capsular modifications (which are representative of all aligner variants with modifications). These modified aligners induced relatively high palatally directed forces (i.e., negative Fy magnitudes) on tooth 11 in the neutral position. The Fy magnitudes for these modified aligners were approx. − 10 N, and the positive Mx values were approx. + 35 Nmm, corresponding to a reclining effect on tooth 11 (which is actually the opposite rotational direction compared to palatal root torque). As palatal displacement of tooth 11 increased, both the positive Mx and negative Fy values decreased towards the zero line. Importantly, the Fy magnitudes were still negative (approx. − 5 N) at the displacement at which Mx curves crossed the zero line from positive to negative values. Consequently, at this displacement, F/M values begin to fulfill the requirements for bodily movement and palatal root torque of tooth 11 (i.e., the palTR-start). Mx and Fy curves showed a nearly linear interrelation with increasing palatal displacement of tooth 11, and this observation was representative for all test aligners.

The palTR-start displacements for all investigated modification geometries, modification depths, and aligner thicknesses are presented in Table 1 and Fig. 4a and b. All aligner variants with digitally designed or manually indented modifications achieved the palTR at a certain palatal displacement of tooth 11. Generally, we observed that both the modification depth and the aligner foil thickness significantly influenced the palTR-start values (linear mixed-effect models, p < 0.01).

The linear models for 0.75-mm aligners with crescent and capsular modifications revealed that a 1-mm increase in the modification depth was related to a ca. 0.10-mm increase in palTR-start displacement. Boxplots for this variable (Fig. 4a) showed that, for 0.5-mm deep modifications, the palTR started at very small displacements of ≤ 0.03 mm for all shapes. For 0.75-mm aligners with 1.5-mm deep modifications, the palTR started significantly later (Wilcoxon–Mann–Whitney tests, p < 0.05), at displacements between 0.09 and 0.12 mm. By increasing the digital modification depth to 2.0 mm, crescent and capsular modifications showed palTR-start displacements of 0.14 mm and 0.15 mm, respectively. In contrast, the palTR-start values for 2-mm deep double-spherical digital modifications decreased to 0.06 mm. The palTR-start displacements of 0.75-mm aligners with 1.0-mm deep manually indented double-spherical and capsular modifications were 0.12 mm and 0.14 mm, respectively.

Linear mixed-effect models of all three modifications revealed a significant interrelation between aligner thickness and palTR-start displacements; for 1.5-mm deep modifications, the palTR started 0.007 mm earlier per 0.1-mm increase in foil thickness (p < 0.01). However, boxplots showed that this trend and the differences between the modifications were not consistent (Fig. 4b).

The relationships between modification depth and the palatally directed forces (− Fy) are illustrated as boxplots in Fig. 5a. The − Fy magnitudes increased significantly with increasing digital modification depth with tooth 11 in the neutral position and at palTR-start (linear mixed-effect models, p < 0.01). Every 1-mm increase in the depth of crescent, double-spherical, and capsular modifications increased the − Fy magnitudes in the neutral position by − 7.32 N, − 3.55 N, and − 8.10 N and at palTR-start by − 2.99 N, − 2.42 N, and − 2.53 N, respectively. These estimates explain why − Fy magnitudes for ≥ 1.5-mm deep crescent and capsular modifications tended to be higher than those for double-spherical modifications (Wilcoxon–Mann–Whitney tests, p < 0.01 for the majority of pairwise comparisons). With tooth 11 in the neutral position, aligners with 0.5-mm deep modifications induced relatively small − Fy magnitudes with median values ranging between − 1.05 and − 2.27 N (Table 1); these values dropped to < 0.85 N once tooth 11 was displaced to the palTR-start. In comparison, aligners with ≥ 1.5-mm deep digital modifications had significantly greater median − Fy magnitudes (Wilcoxon–Mann–Whitney tests, p < 0.05), ranging from − 6.61 to − 11.85 N in the neutral position and from − 3.26 to − 5.35 N at the palTR-start (Table 1). In contrast to the positive correlation observed between − Fy magnitudes and the modification depth (Fig. 5a), aligners with 2.0-mm deep digital double-spherical modifications had lower − Fy magnitudes with tooth 11 in the neutral position than aligners with 1.5-mm deep double-spherical modifications did (Wilcoxon–Mann–Whitney tests, p < 0.01). Furthermore, an increase in the depth of digital crescent and capsular modifications from 1.5 to 2.0 mm did not significantly increase − Fy magnitudes at the palTR-start (Wilcoxon–Mann–Whitney tests, p > 0.05). The − Fy magnitudes of the two manual modifications were within the range of those for the digital 1.5-mm and 2.0-mm deep modifications (Fig. 5a).

The relationship between foil thickness and negative Fy magnitudes is shown in Fig. 5b and Table 2. Boxplots showed that the − Fy magnitudes increased significantly with foil thickness with tooth 11 in the neutral position and at the palTR-start (linear mixed-effect models, p < 0.01). This influence was greater for crescent and capsular modifications than for double-spherical modifications (Wilcoxon–Mann–Whitney tests, p < 0.01). Accordingly, with tooth 11 in the neutral position, the increases in − Fy magnitudes per 0.1-mm foil thickness were − 1.57 N for crescent modifications, − 1.54 N for capsular modifications, and only − 0.80 N for double-spherical modifications. At the palTR-start, the increases in − Fy magnitudes per 0.1-mm foil thickness were − 0.97 N for crescent modifications, − 1.03 N for capsular modifications, and − 0.76 N for double-spherical modifications. Accordingly, boxplots indicated higher − Fy magnitudes for aligners with crescent and capsular modifications than for aligners with double-spherical modifications (Wilcoxon–Mann–Whitney tests, p < 0.01); for instance, with tooth 11 in the neutral position, − Fy magnitudes for 0.75-mm aligners were − 9.80 N with crescent modifications, − 9.54 N with capsular modifications, and − 8.66 N with double-spherical modifications. These differences were even greater for 1.0-mm aligners, with − Fy magnitudes of − 15.41 N with crescent modifications, − 15.32 N with capsular modifications, and − 9.84 N with double-spherical modifications (Table 2).

One of the main goals in patients with class II and class II division 2 malocclusions is the correction of the anterior and/or retroclined position of the maxillary frontal segment. This correction requires palatal bodily movement of maxillary incisors and/or palatal root torque. To induce palatal bodily movement, a palatally directed force (− Fy) with sufficient magnitude is required together with a moment (− Mx) to counteract the palatal tipping effect of the force. To induce palatal root torque, the magnitude of − Mx has to be further increased [9, 11, 25, 28]. A clear definition of the orthodontic term “torque” is important here. For instance, “palatal root torque” describes a pure or at least predominant root movement in the palatal direction with the tooth crown retaining its original vestibulo-oral position. This movement consists of two components: (1) a rotational component in the sagittal direction, which changes the tooth’s inclination by palatal root and labial crown movement, and (2) a palatally directed translational component, which compensates the rotational labial crown displacement. Based on these clear definitions, previous studies have shown that aligners have limited ability to induce true palatal root torque or palatal bodily movement of incisors. In this study, we have shown (in agreement with previous work [9, 11, 29]) that unmodified aligners cannot generate the F/M components needed for palatal incisor root torque or bodily movement. A potential solution—which was originally described by Sheridan et al. [16‐18] and has been implemented in the Invisalign® system as power ridges™—is to introduce pressure areas into the aligner in the labio-cervical regions of corresponding incisors. These pressure areas can be created either digitally as a recess in the model or manually by indenting the aligner with pliers. In this study, we used both methods and investigated how different modification geometries, modification depths, and foil thicknesses affected the F/M system exerted on an upper central incisor.

The main finding of this biomechanical in vitro study was that modified aligners can generate the F/M components required for palatal bodily movement of maxillary incisors or even palatal root torque in vitro. This may be explained by strong contact at the aligner-tooth interface, which is generated by the labio-cervical pressure area of the aligner seated on the model without any setup displacement of tooth 11. The corresponding palatally directed contact force (reaching nearly − 10 N for 0.75-mm aligners with 1.5-mm deep modifications) acts cervical to the center of resistance of the tooth and generates a high positive Mx component (Fig. 6a) that tips the crown in the palatal direction (which is actually not desired). Experimental palatal movement of tooth 11 showed that negative Fy and positive Mx magnitudes decrease linearly towards the zero line (Fig. 3) during the corresponding initial clinical tooth movement. This is explained by successively reduced bending of the aligner at its labio-cervical region. The Mx values decreased because the − Fy decreased (which also reduced the palatal tipping, positive Mx moment) and because an additional moment was generated with opposite polarity (− Mx). This additional moment component was related to a successively stronger aligner-tooth contact at the palato-incisal region of tooth 11 generating a labially directed contact force; this contact occurred once the play of the tooth within the aligner was eliminated. Hence, two contact forces with opposite directions acted on different vertical levels of the tooth, building a force couple that corresponded to the additional negative Mx moment mentioned before (Fig. 6b and c). As shown in Fig. 3, the polarity of total Mx values changed after a very small initial palatal tooth displacement (i.e., palTR-start) ranging between 0.09 and 0.12 mm for 0.75-mm aligners with 1.5-mm deep modifications (Tables 1 and 2). Importantly, Fy values at the palTR-start were still negative enough (i.e., approx. − 5 N for 0.75-mm aligners with 1.5-mm deep modifications) to induce sufficient palatal translation of the tooth. Consequently, the incisor received both a sufficient palatally directed force (− Fy) and palatal root torquing moment (− Mx). It has to be noted that the reported Fy and Mx magnitudes are specific for the tested aligner types which also includes the height of the aligners in the cervical region. Future studies may investigate whether aligners with reduced cervical height have similar capabilities for generating moment magnitudes required for palatal root torque of incisors.

We also investigated which pressure-area geometries, modification depths, and foil thicknesses are optimal for generating palatal bodily translation or palatal root torque of an upper central incisor. This involved comparing the palatal displacement of the incisor at the palTR-start and the magnitude of the palatally directed force (Fy) at this displacement. Here, an important question is which force magnitude is needed for palatal bodily movement of a maxillary central incisor. Values of 0.5 ± 0.2 N have been reported as adequate [28, 30]. However, aligners start to reduce force magnitudes within a few hours to residual values of ca. 10–20% after 1 week [31]. In this respect, a force range between 2.5 and 5 N may be more appropriate. Additionally, in vivo application of aligners is confronted with a force decay due to the presence of PDL which is, however, difficult to quantify.

Our results showed that capsular and crescent modification geometries are equally able to generate high − Fy magnitudes and that both generate higher − Fy magnitudes than double-spherical modifications do. This difference was more pronounced with deeper modifications and thicker aligners, which may be explained by an incomplete thermoforming process—the smaller the negative forms of the two half-spheres and the deeper their penetration into the model, the more difficult it is for thicker foils to completely adapt to the model’s negative modification forms. Another reason might be the enclosure of air in the modification shapes during the thermoforming process, which might be more pronounced in smaller and deeper modifications. These limitations of the thermoforming process might also explain why − Fy magnitudes of 1.0-mm deep manual indentations in the thermoformed aligner were even higher than those of 1.5-mm deep digital modifications (with corresponding shape) and not smaller, as expected based on the correlation we observed between modification depth and − Fy magnitude. Accordingly, we conclude that manual modifications of aligners using pliers can also generate the F/M components required for palatal root torque.

Our results show that a modification depth of 1.5 mm is appropriate for aligners to induce palatal root torque. The − Fy magnitudes at lower depths (0.5 mm) were too small, whereas higher depths (2.0 mm) did not consistently increase the − Fy magnitudes at the palTR-start. Furthermore, 2.0-mm deep modifications increased undesired palatal tipping of the crown by around 0.05 mm until the palTR started.

Although thinner aligners (0.4 mm and 0.5 mm) fulfilled the requirements for palatal root torque, their − Fy magnitudes at the palTR-start were too small. Thicker aligners were within the appropriate range of − 2.5 to − 5 N because Fy values were − 4 N and − 5 N for 0.625-mm and 0.75-mm-thick aligners with 1.5-mm deep crescent or capsular modifications, respectively. The palTR started 0.05 mm earlier with 0.75-mm-thick aligners, so we recommend using this foil thickness for palatal root torque of upper central incisors. This recommendation, however, applies to thermoformed aligners which usually experience a considerable, non-uniform reduction of the original foil thickness during the thermoforming process [32]; hence, a direct transfer of the results to 3D-printed aligners requires caution.

Our data show that modified aligners with a sole labio-cervical pressure region and appropriate − Fy magnitudes have an offset of ca. 0.1 mm until the palTR starts. This offset may be eliminated in clinical therapy by an initial palatal movement of the crown, consisting of a dominant palatal tipping component (in the first phase) or a dominant bodily movement (closer to the palTR-start). This palatal tipping is suboptimal during correction of retroclined incisors because the root needs additional uprighting to compensate for the initial palatal tipping. Correction could be optimized by eliminating (or reducing) the initial play between the tooth to be torqued and the aligner, e.g., by adding a pressure region in the palato-incisal crown region (as in the Invisalign® system) or by suitable crown preinclination in the setup model. These alternatives and the effects of different material types are currently being investigated in follow-up experiments.

There are some limitations to this in vitro experimental study which should be considered when interpreting the quantitative results of this study. The initial movement from the neutral position of the tooth to the start of palTR was simulated as a translational movement, which is only true shortly before the palTR-start. A more realistic initial movement, considering the successive transition from palatal tipping to palatal translation (which would be very complex to realize experimentally), may result in an earlier start because the palatal tipping component would eliminate the tooth-aligner play in the palato-incisal region earlier. Another limitation is that the reported M/F magnitudes and palTR-start values were affected by the anisotropic mechanical behavior of the periodontal ligament (which could not have been simulated) [33, 34], and this influenced the initial tooth movement and contact between the tooth and aligner. Results may also have been affected by the viscoelastic aligner material behavior, which is influenced by multiple variables that are difficult to quantify [35]. Although the measurement setup was configured and optimized to achieve the maximum possible mechanical stiffness, a certain residual mechanical compliance could not be avoided, which may have influenced the palTR-start values we observed. Furthermore, our experiments simulated and investigated an isolated movement of one (measurement) tooth. In the clinical situation, however, several (if not all) teeth are simultaneously moved, which implies mutual influences on the F/M systems applied to adjacent individual teeth. This exemplifies the complexity of clinical mechanical loading of individual teeth with aligners, which is similar to complex load application of multibracket appliances. Despite these limitations, we would like to emphasize that in vitro studies are valuable for investigating fundamental research questions and for comparing different materials and modifications with maximum control. Moreover, establishing orientation values for design variables in vitro (such as the modification geometries and depths investigated here) is necessary for further testing and evaluation in patients.

Modified PET-G aligners with integrated pressure regions in the labio-cervical region of an upper central incisor crown may generate sufficient palatally directed force and palatal root torque for palatal bodily movement or root torque of these teeth.

Our results suggest that 0.75-mm PET-G aligners designed with 1.5-mm deep crescent or capsular modifications achieve appropriate contact force magnitudes and a relatively early palTR-start. This seems particularly important for in-office aligner fabrication because concrete information on how aligner modifications have to be designed is either unknown or not publicly available.

Further in vitro studies are needed to minimize or eliminate the offset range before the palTR starts (e.g., by implementing additional palatal pressure points) and to compare the performance of single-layer and multilayer aligner materials. Once the design and materials have been optimized, clinical trials are needed to test the performance of these aligners.