Force decay of polyethylene terephthalate glycol aligner materials during simulation of typical clinical loading/unloading scenarios

Interest in aligners as an alternative treatment for correction of tooth malpositions and malocclusions continues to grow. The main concept of aligner therapy is based on incremental correction of a tooth’s malposition, with each increment corresponding to a single setup model on which an aligner or a set of aligners is fabricated. Aligners generate tooth movement that results from the discrepancy between the actual tooth position and the programmed tooth position on the setup model. This discrepancy causes local deformation of the aligner and generates contact forces between the aligner and teeth [4‐7, 9, 13, 15‐17]. Since the introduction of the principle of aligner therapy by Kesling, different materials and concepts have been developed [19]. With regard to the setup increment sizes and material thicknesses used, two fundamentally different approaches are applied. The first approach is based on very small setup increments (range 0.1–0.2 mm) and uses identical aligners for the same movement increment; e.g., Invisalign® system (Align Technology, Santa Clara, CA, USA). The second approach is based on larger movement increments (range 0.5–1.0 mm) and uses a sequence of aligners of ascending thickness within each increment.

The forces and moments applied to individual teeth by aligners are affected by several material-dependent variables such as the initial stiffness of the aligner and the behavior of the aligner material during its period of intraoral application (usually 1–2 weeks) [8, 20]. Several experimental studies have used multi-axial sensors to investigate the force–moment systems delivered by aligners on central incisors or canines depending on the kind of movement (i.e., tipping, derotation, and bodily movement) [4‐7, 15‐17]. These studies generally indicated that the recommended combinations of setup increments and material thicknesses produce force and moment magnitudes significantly in excess of those considered sufficient for orthodontic tooth movement [22]. Such overloading of the periodontal ligament (PDL) is known to increase the risk of orthodontically induced irreversible root resorption [22]. It is important to note, however, that the force–moment systems generated by aligners during clinical application are subject to a certain deterioration related to the physiological mobility of the tooth within the PDL, orthodontic tooth movement, and the stress relaxation properties of aligner materials [4, 20].

Several studies have investigated this third aspect by using three-point-bending tests and flat polyethylene terephthalate glycol (PET-G) or thermoplastic polyurethane (TPU) specimens to evaluate the effect of different durations of constant loading on the mechanical properties of aligners [10, 18, 21]. In two of these studies, specimens were only loaded for 30–180 min, which is unrepresentative of the typical long use periods for aligners of up to 2 weeks [10, 18]. Nevertheless, the results showed that the initially determined stresses decreased by approximately 22.9% after 30 min of constant loading, and by 44.5% after 180 min [10]. Other studies were performed for longer constant loading periods of up to 24 h, and residual forces of 56 and 38% were observed for PET‑G specimens after 8 h and 24 h of constant loading, respectively [21]. Similar patterns were reported for the TPU specimens with residual forces of 59.5 and 45.5% for the 8‑ and 24-hour loading periods, respectively [21]. Based on these results, it was concluded that the forces applied by PET‑G aligners reduce substantially during the first 8 h of loading and then reach a plateau. It must be noted, however, that the constant loading pattern applied in these previous studies did not account for the fact that aligners are not worn by the patient constantly, but are usually inserted and removed several times throughout the day [25]. The specific intraoral application schedule of a patient, in turn, might affect the force delivery of the aligner material and, therefore, the force–moment systems applied to individual teeth during aligner therapy. The aim of this study was to evaluate the effect of different loading/unloading intervals on the mechanical properties of thermoformed PET‑G aligner materials in a simulated intraoral environment during a 1-week observation period. We hypothesized that longer loading cycles would result in greater stress relaxation and larger reductions in force than shorter loading cycles.

During the typical intraoral application period for an aligner of 7–10 days, aligner materials are exposed to saliva and are constantly loaded due to the discrepancy between the “programmed” tooth position on the setup model and the actual tooth position. Many studies have investigated the effect of loading on aligner materials for short periods of up to 24 h [10, 21, 24]. Only one has studied how different deflection ranges affect the stress relaxation of thermoformed aligners over a longer period, examining 1.0-mm-thick aligners under constant loading for 14 days [20]. The results indicated rapid stress relaxation within the first 8 h, followed by a lower rate of reduction until a plateau-like level was reached after the fourth or fifth day. These studies provided important insights into time-dependent force delivery under constant material loading. However, they did not address the fact that aligners are not worn constantly, but are usually inserted and removed several times throughout the day. This loading and unloading schedule is, to a certain extent, repeated daily and exhibits inter-individual variability depending on the patient’s lifestyle and treatment compliance. By examining different loading/unloading modes, we aimed to simulate different clinically representative scenarios in order to clarify their effect on the forces exerted by aligners on individual teeth. The PET‑G specimens tested in our study clearly showed the largest force decay (i.e., stress relaxation) during the first loading period, followed by smaller reductions until a near-constant residual force value was reached. This is in accordance with previous studies in which constant loading of thermoplastic film specimens also yielded a very high rate of force reduction during the first 8 h of constant loading [20, 21]. The inclusion of loading and unloading periods in the study protocol revealed that, irrespective of the specific loading/unloading mode, PET‑G specimens exhibit a certain force-recovery pattern after unloaded periods, which is most prominent in the first loading cycle and then decreases progressively during subsequent cycles (Fig. 6b). Such long-term and load-dependent force–deflection behavior is mainly due to the viscoelastic behavior of PET‑G aligner materials. More specifically, such materials exhibit both elastic and time-dependent viscous properties when subjected to load. This behavior has been mathematically explained by means of the standard linear solid model, which consists of springs and pistons representing both the elastic and viscous properties, respectively [23]. The viscous characteristics are manifested in the time-dependent plastic deformation of the tested specimens (Fig. 7; Table 3). The specific plastic deformation values are clearly not only time-dependent, but also depend on the effective deflection range (d_eff), which can be calculated by subtracting play due to plastic deformation (d_pd) from the predefined thickness-dependent deflection (d_thick; Eq. 1).

The reduction of effective deflection after loading described by Eq. 1 is important for the interpretation of our results. For example, the 0.5-mm specimens were initially deflected by 0.15 mm, creating a local stress of approximately 14.41 MPa [8]. After the first loading/unloading cycle, plastic deformation was 0.13 mm. This means that during the second loading/unloading cycle, the 0.5-mm specimens were effectively deflected by only 0.02 mm, resulting in stress values of only 1.92 MPa. Such stress reduction from cycle to cycle explains the plateau-like behavior of both the deflection force and plastic deformation. Our measurements indicate that the reduction in PET‑G material stiffness was much smaller, as illustrated by the flatness of the lines in Fig. 8. The somewhat unsystematic fluctuations in stiffness after a clear initial reduction may be explained by the subsequent, small effective deflections (d_eff) ranging between 0.01 and 0.06 mm, which also resulted in fewer points to apply a linear fit to the terminal curve portions.

In vitro studies performed with similar aligner materials thermoformed on dentition models indicated very large initial forces for different types of tooth movement, with values exceeding the forces required for the types of movement investigated [4‐7, 12, 14, 16, 17]. With regard to the actual load magnitudes applied during clinical therapy, however, two main factors must be considered, both of which reduce the forces and moments applied to individual teeth: (i) the elasticity of the PDL, which initially reduces the effective discrepancy between the tooth’s position on the setup model and that in the aligner, and (ii) the stress relaxation phenomenon observed in the current study. The latter can also be expected, although with a different extent, for other aligner materials due to the viscoelasticity of the polymers used [21]. In mathematical terms, forces applied by aligner materials to individual teeth can be deduced from the effective discrepancy x(t) between the actual tooth position and the programmed position (z_setup) after subtracting the time-dependent initial tooth movement (tm_i) and the time-dependent plastic deformation of the aligner (d_pd). This discrepancy can be calculated as follows:

In turn, the effective forces F(t) can be calculated as follows:where x(t) is the effective discrepancy and k(t) is the stiffness of the aligner.

From a clinical point of view, these factors might explain why the amount of root resorption observed after treatment with PET‑G aligners is slightly larger than that for light orthodontic forces [1]. However, it should be noted that aligners fabricated from less stiff or multi-layered aligner materials might induce less external root resorption when compared to orthodontic treatment with fixed appliances [11].

The residual forces at the end of the observation period differed among the three loading/unloading modes. Specifically, residual forces for the 12 h/12 h loading/unloading mode were significantly larger than those for the 23 h/1 h loading mode (Mann–Whitney U test, p < 0.05; Table 2). This difference is probably related to (i) longer loading times and, in turn, more plastic deformation of the aligner material, and (ii) shorter unloading periods, reducing the length of time for material recovery. Therefore, our initial hypothesis was accepted, indicating that longer loading cycles will result in greater stress relaxation and larger initial force reductions than shorter loading cycles. Although equal stresses were applied to the different specimen thicknesses, the effect was thickness-dependent, with the largest normalized residual forces recorded for the 0.75-mm specimens (Mann–Whitney U test, p < 0.01).

This in vitro study considered the effect of body temperature and water immersion on the force delivery of PET‑G specimens. Further studies, however, should be performed on the newly developed multilayered aligner materials (e.g., SmartTrack, Align Technology, Santa Clara, CA, USA; Zendura™ FLX, Bay Materials LLC, Fermont USA or CA-Pro, Scheu Dental GmbH, Iserlohn, Germany), due to their potentially different behavior in the intraoral environment and different stress relaxation patterns [2, 3, 26].

It is important to note that flat probes do not replicate the geometry of a real aligner. However, in vitro measurements with flat specimens not only enable simpler mechanical testing but also easier interpretation of the test results; this is because they limit the number of influencing factors, e.g., the complex geometry of aligners thermoformed on dentition models. A general limitation of investigating flat material specimens is that the measured force magnitudes cannot be directly compared with those found in clinical application due to the complex effect of the geometry of the three-dimensional dental arch. Therefore, we included only the normalized force changes and normalized plastic deformation for the further analysis of the measured data instead of the raw force values. Nonetheless, further studies are required to investigate how such geometry affects force decay, stiffness change, and plastic deformation. Moreover, according to our power analysis the selected sample size (n = 3) was sufficient to statistically evaluate the differences of the force reduction after the first loading cycle for the different thicknesses and loading/unloading modes. Along the further loading cycles, a higher sample size (n = 17) would have been required to evaluate the difference between the different loading/unloading modes. However, due to the variability and overlapping of the force reduction values we considered these differences as clinically irrelevant, omitting the need to include further samples.

During long-term loading of aligner materials, plastic deformation of up to 83% should be expected without affecting material stiffness. The highest force reduction could already be observed after the first loading interval. Moreover, we found that the longest investigated simulated intraoral application period of 23 h per day induced the largest decay in force, with residual forces after one week of a mere 5% of those initially applied. The observed force reduction, in addition to the constantly decreasing discrepancy between the programmed tooth position in the aligner and the actual tooth position, will attenuate the initially applied excessive forces observed in previous in vitro studies.