In Vitro Comparison of Direct Attachment Shape and Size on the Orthodontic Forces and Moments Generated by Thermoplastic Aligners During Expansion

ABSTRACT

Objective

To evaluate the effects of varying direct attachment shape and size on the forces and moments generated by thermoplastic aligners during simulated expansion.

Materials and Methods

An in vitro orthodontic force tester (OFT) was used to measure the forces and moments from a typodont where the buccal teeth were translated lingually 0.2 mm to simulate expansion. Hemi‐ellipsoid and rectangular attachments with either 0.5 or 1.0 mm thickness were added on upper right first premolar (UR4), second premolar (UR5) and first molar (UR6). Analysis of variance (ANOVA) was used to determine two‐way interactions among the factors on the outcomes.

Results

The interactions between group and tooth were significant for all outcomes (p < 0.001). The greatest buccal forces (Fy) were observed with 1 mm rectangular attachment on the UR4 (0.78 ± 0.29 N), with 1 mm hemi‐ellipsoid attachment on UR5 (0.28 ± 0.21 N) and with 0.5 mm rectangular attachment on UR6 (1.71 ± 0.18 N). The greatest buccolingual moments (Mx) were obtained with 1 mm rectangular attachment on UR4 (5.61 ± 1.43 Nmm), without any attachments on UR5 (3.33 ± 1.73 Nmm) and with 1 mm hemi‐ellipsoid attachment on UR6 (4.18 ± 4.31).

Conclusion

Direct attachment shape and size had a significant effect on the orthodontic forces and moments generated by thermoplastic aligners during simulated expansion. Although loads varied significantly by tooth morphology and its location in the arch, best forces and moments for expansion were obtained with 1 mm rectangular attachments on UR4s, 1 mm hemi‐ellipsoid attachments on UR5s and 0.5 mm rectangular attachments on UR6s.

1. Introduction

Clear aligner therapy (CAT) has become increasingly prevalent in orthodontics today. The clear plastic provides an aesthetic alternative to traditional metal brackets for patients [1, 2]. These computer‐generated aligners have been employed in the treatment of hundreds of thousands of malocclusions, with their removability helps minimise interference with eating and maintaining proper oral hygiene [3]. Applications have expanded outside orthodontic tooth movement, including use for retention, temporomandibular joint and surgical splints, and bleaching trays [4, 5, 6, 7]. Align Technology has contended that patients with dentoalveolar‐constricted arches relapse following fixed appliance treatment, mild‐to‐moderate crowding and spacing qualify as candidates for CAT [3]. When the aligner material engages teeth and bonded attachments, the slight discrepancy between the two exerts forces and moments allowing planned tooth movement towards its desired location [2, 8, 9]. Evaluation of these orthodontic forces and moments is essential as their direction and magnitude determine predictable, physiologic tooth movement [2, 9].

Clinically, the efficiency of certain movements has been previously investigated [10, 11, 12, 13, 14]. Kravitz et al. [10] found a mean accuracy of 41% in 37 patients treated with Invisalign therapy when comparing the predicted tooth position to the superimposed actual position. There was a difference in accuracy among the various movements with extrusion being the most difficult (29.6%) and lingual constriction being the most reliable (47.1%). Pre‐ and post‐treatment changes have also been investigated [12, 13, 14]. When comparing transverse changes with CAT, researchers observed less actual expansion than was planned [12, 13, 14]. Arch width increases were more effective in the mandible than the maxilla and in the premolar area than in the second molar and canine regions. Most of the transversal change was attributed to buccolingual tipping [12, 13, 14].

Previous research has demonstrated the limitations of clear aligners in complex movements, like extrusion and derotation, achieved by conventional fixed appliances [10, 15]. Overcoming such restrictions requires the use of auxiliaries, like composite resin attachments, to improve aligner retention and increase the biomechanical possibilities to allow more complex force systems on the teeth [15, 16, 17]. Some researchers have concluded that without the controlled force and moments provided by well‐defined attachments, undesired orthodontic tooth movement can result [16, 17, 18]. However, limited research has been conducted on how attachments can alter forces and moments generated by aligners during these movements [19, 20, 21, 22]. This includes studies observing in vitro orthodontic loads under various movements such as rotation, extrusion, intrusion, tipping and translation [19, 20, 21, 22, 23, 24, 25]. A finite element analysis by Hong et al. conducted on bodily movement of a lower central incisor found that an overhanging attachment, closest to the centre of resistance, effectively reduced crown tipping [18]. Another simulation study evaluated the distribution of force ranges for varying shapes in retraction of anterior teeth. Authors found that an ellipsoid shape had the most evenly distributed force levels [26]. Cai et al. used biomechanical principles to design the most optimal attachment based on specified moment‐to‐force ratios for translation. Authors employed multiple biomechanical theorems including the theorem of force system, Varignon theorem and the theorem of force translation to construct a pyramidal attachment design for optimally translating a canine lingually [17]. Kaur et al. evaluated in vitro expansion forces on a central incisor, canine and second premolar without any attachments. Investigators observed significantly increased forces and tipping moments on the canine versus the other evaluated teeth [2].

The initial load system, or moment‐to‐force ratios, produced by an attachment can determine whether that particular design can assist in orthodontic treatment [18]. Forces and moments during expansion have been examined, but without attachments, leaving the possibility for tipping movement rather than true buccolingual translation [2]. To our knowledge, no previous study has evaluated the effects of varying direct attachment shape and size on the forces and moments exerted on targeted teeth by thermoplastic aligners during simulated expansion. The purpose of this in vitro study is to find the optimum shape and size of direct attachments needed for bodily movement of the teeth during simulated expansion. We hypothesise that altering direct attachment shape and size will have an effect on the buccal force and tipping moment during simulated expansion.

2. Materials and Methods

2.1. Fabrication

To create the digital maxillary typodont, a maxillofacial Cone Beam Computerised Tomography (CBCT) scan was processed by Mimics software v.17.0 (Materialise, Leuven, Belgium) to construct a 3D model via segmentation, with cubic voxels defined by grayscale values representing bone density. The split mask tool was used to isolate the maxilla by removing the mandible from the segmented model. Since only the crowns of the teeth were needed for installation on the force tester system, the teeth were separated from their bones and roots. Each tooth was then individually separated from the whole model and 3D printed (Form 3B; Formlabs Inc., Somerville, Mass). This separation allowed for precise adjustments in the position of each tooth, including rotation and displacement, to create constrictions and mismatches between the teeth and the aligner. Digitally assembled typodonts were printed, and 0.76‐mm‐thick clear aligners (Great Lakes Dental Technologies, Tonawanda, NY) were thermoformed with Biostar (Scheu Dental, Iserlohn, Germany) according to manufacturer‐specified instructions. The aligners were then stored in dry conditions until inserted into the dentoform within 3 days of fabrication.

2.2. Group Allocation

As a result of a 2 (shape) × 2 (size) factorial design, four different typodonts were created. Typodonts 1 and 2 had 0.5‐ and 1‐mm‐thick hemi‐ellipsoid attachments on upper right first premolar (UR4), second premolar (UR5) and first molar (UR6). Typodonts 3 and 4 had 0.5‐ and 1‐mm‐thick rectangular attachments on the same teeth. A typodont without any attachments but still constricted (No attachment) and another typodont with no attachments and no constriction (Control) served as controls. Hemi‐ellipsoid attachments were 3 mm wide and 2 mm tall, while rectangular attachments were 3 mm wide by 1 mm tall.

2.3. Data Collection

An orthodontic force tester (OFT) was used to precisely measure the 3D loads applied to each tooth (Figure 1A,B). The OFT features 14 load cell sites designed to capture the 3D forces and moments for all 14 teeth within an arch. The load cells are stationary, while each tooth is held in its clinical position using an adaptor, which is connected into the corresponding load cell. The location of the tooth with respect to the load cell can be digitally adjusted to ensure precise positioning. Both the teeth and adaptors were 3D printed using dental resin material and Laser‐Powered Stereolithography (SLA) technology. In this experiment, two models were created to simulate the pre‐ and post‐treatment tooth positions. The pre‐treatment model was used to assemble the teeth on the OFT simulating the clinical condition. The post‐treatment model was used to fabricate aligners, simulating the intended treatment outcome. The pre‐treatment model was created by translating the bilateral upper premolars and first molars in the segmented model 0.20 mm palatally, which allowed them to receive buccal forces from the aligners. These aligners were designed based on the ideal post‐treatment buccal position, allowing for an accurate representation of the treatment forces exerted on the teeth. This setup aimed to assess the forces generated by the aligners and their effectiveness in guiding tooth movement towards the intended treatment outcome [27]. The loads on each tooth were measured using Nano17 load cells (ATIndustrial Automation, Apex, NC), which are capable of detecting forces and moments in three dimensions. After the segmented typodont was assembled to the pre‐treatment condition, the load cells were zeroed. Then, aligners were positioned using an anteroposterior path of insertion by a single investigator for each trial. The load cell readings corresponded to the load applied by the aligner on each associated tooth. The load cells simultaneously measured force and moment components expressed in their own coordinate systems using a data acquisition software. Readings were recorded for 10 s after insertion, and the last five values were averaged. Each aligner was tested twice. Each tooth had its own local coordinate system with origins at the central fossa of the premolars or molars (Figure 1C). The x‐axis was defined as the mesio‐distal direction with positive values being mesial. The y‐axis was defined as the buccolingual direction with positive values being buccal. Finally, the z‐axis was defined as the occluso‐gingival direction with positive values being occlusal. The load in the load cell coordinate system was then transformed to the corresponding tooth's local system as previously described [28].

FIGURE 1.

(A) Occlusal view of the Orthodontic Force Tester (OFT). (B) Lateral view of the OFT. (C) Digital setup of the experimental model with the defined local coordinate system for upper right first premolar (UR4), second premolar (UR5) and first molar (UR6).

2.4. Power Analysis

Means and standard deviations (SD) of the differences that can be detected with a sample size of 5% and 80% power are given in Table S1. Calculations are based on a two‐sided 5% significance level, two‐sample t‐test and standard deviations.

2.5. Statistical Analysis

The forces and moments were summarised (mean, SD, median, first and third quartiles, minimum and maximum) for each of the attachment shapes and size combinations for each of the teeth. The effects of the attachment shape and size on the forces and moments were analysed using two‐way ANOVAs, separately for each tooth. A two‐sided 5% significance level was used for all tests.

3. Results

The descriptive statistics including mean, SD, and minimum and maximum of the forces in the buccolingual direction (Fy) and buccal root tipping moments (Mx) were given in Table 1. The distributions of the Fy values combined and for each individual tooth are shown with box and whisker plots in Figure 2. The greatest Fy in the desired buccal direction was observed with 1 mm rectangular attachment on the UR4 (0.78 ± 0.29 N), with 1 mm hemi‐ellipsoid attachment on UR5 (0.28 ± 0.21 N) and with 0.5 mm rectangular attachment on UR6 (1.71 ± 0.18 N).

TABLE 1.

Descriptive statistics including mean, standard deviation (SD), minimum (Min) and maximum (Max) for the generated forces (Fy) and moments (Mx) in the buccolingual direction.

	Fy (N)				Mx (Nmm)
	Mean	SD	Min	Max	Mean	SD	Min	Max
First premolar
Control	0.06	0.11	−0.16	0.19	3.73	0.96	1.89	5.37
No attachment	−0.3	0.21	−0.54	0.17	3.18	0.95	2.17	5.07
0.5 mm Hemi‐ellipsoid	−2.19	0.18	−2.6	−1.99	−28.6	3.65	−36.66	−24.6
1 mm Hemi‐ellipsoid	−1.29	0.2	−1.58	−0.9	−4.37	1.75	−7.24	−2.2
0.5 mm Rectangular	−0.42	0.28	−0.89	−0.05	4.48	1.53	2.26	7.85
1 mm Rectangular	0.78	0.29	0.27	1.13	5.61	1.43	2.97	7.65
Second premolar
Control	−1.17	0.13	−1.37	−1.01	−3.76	0.78	−4.42	−1.99
No attachment	−1.68	0.25	−2.19	−1.27	3.33	1.73	−0.77	5.45
0.5 mm Hemi‐ellipsoid	−0.71	0.24	−1.12	−0.4	−8.09	1.36	−9.81	−5.79
1 mm Hemi‐ellipsoid	0.28	0.21	0.01	0.76	0.47	1.38	−2.18	2.6
0.5 mm Rectangular	−1.9	0.21	−2.24	−1.63	2	2.4	−1.73	6.98
1 mm Rectangular	−1.22	0.22	−1.54	−0.87	2.95	1.67	1.17	6.73
First molar
Control	0.37	0.11	0.18	0.5	2.4	0.7	1.3	3.69
No attachment	1.28	0.21	0.92	1.53	4.14	0.91	2.47	4.88
0.5 mm Hemi‐ellipsoid	0.12	0.13	−0.05	0.4	3.26	3.81	−1.36	10.73
1 mm Hemi‐ellipsoid	−0.62	0.19	−0.82	−0.23	4.18	4.31	0.52	13.46
0.5 mm Rectangular	1.71	0.18	1.5	2.16	2.09	0.65	0.76	2.82
1 mm Rectangular	−2.3	0.14	−2.51	−2.04	0.34	3.43	−4.77	4.37

FIGURE 2.

Box and whisker plot depicting the distribution of the buccolingual forces (Fy). (A) Combined, (B) On the upper right first premolar (UR4), (C) The upper right first premolar (UR5) and (D) The upper right first molar (UR6).

The distributions of the Mx values combined and for each individual tooth are shown with box and whisker plots in Figure 3. The greatest Mx values in the desired direction were obtained with 1 mm rectangular attachment on UR4 (5.61 ± 1.43 Nmm), without any attachments on UR5 (3.33 ± 1.73 Nmm) and with 1 mm hemi‐ellipsoid attachment on UR6 (4.18 ± 4.31). However, the optimal Mx should be coupled with the Fy in the desired direction (buccal). Therefore, the optimal Fy and Mx combination was obtained with 1 mm rectangular attachment on UR4, 1 mm hemi‐ellipsoid attachment on UR5 and 0.5 mm rectangular attachment on UR6.

FIGURE 3.

Box and whisker plot depicting the distribution of the buccolingual moments (Mx). (A) Combined, (B) On the upper right first premolar (UR4), (C) The upper right first premolar (UR5) and (D) The upper right first molar (UR6).

The results of the two‐way ANOVA for Fy are given in Table 2. The interaction between group and tooth was significant for all outcomes (p < 0.001). 1 mm rectangular attachment on UR4 yielded significantly higher Fy values than 0.5 and 1 mm hemi‐ellipsoid and 0.5 mm rectangular attachments (p = 0.000). For UR5, 1 mm hemi‐ellipsoid attachment produced significantly higher Fy values than 0.5 mm hemi‐ellipsoid and rectangular attachments, as well as 1 mm rectangular attachment (p = 0.000). For UR6, 0.5 mm rectangular attachment revealed significantly higher Fy values than 0.5 and 1.0 mm hemi‐ellipsoid, and 1 mm rectangular attachments (p = 0.000).

TABLE 2.

Comparison of the forces in buccolingual direction (Fy) between groups by analysis of variance (ANOVA).

Group comparison	Difference	SE	p
First premolar
Control > No attachment	0.36	0.08	0.000
Control < 1 mm Rectangular	−0.72	0.10	0.000
Control > 0.5 mm Rectangular	0.48	0.09	0.000
Control > 1 mm Hemi‐ellipsoid	1.35	0.07	0.000
Control > 0.5 mm Hemi‐ellipsoid	2.25	0.07	0.000
No attachment < 1 mm Rectangular	−1.08	0.11	0.000
No attachment and 0.5 mm Rectangular	0.11	0.11	0.317
No attachment > 1 mm Hemi‐ellipsoid	0.98	0.09	0.000
No attachment > 0.5 mm Hemi‐ellipsoid	1.88	0.09	0.000
1 mm Rectangular > 0.5 mm Rectangular	1.19	0.13	0.000
1 mm Rectangular > 1 mm Hemi‐ellipsoid	2.06	0.11	0.000
1 mm Rectangular > 0.5 mm Hemi‐ellipsoid	2.96	0.11	0.000
0.5 mm Rectangular > 1 mm Hemi‐ellipsoid	0.87	0.11	0.000
0.5 mm Rectangular > 0.5 mm Hemi‐ellipsoid	1.77	0.10	0.000
1 mm Hemi‐ellipsoid > 0.5 mm Hemi‐ellipsoid	0.90	0.09	0.000
Second premolar
Control > No attachment	0.51	0.09	0.000
Control and 1 mm Rectangular	0.05	0.08	0.538
Control > 0.5 mm Rectangular	0.73	0.08	0.000
Control < 1 mm Hemi‐ellipsoid	−1.45	0.08	0.000
Control < 0.5 mm Hemi‐ellipsoid	−0.45	0.09	0.000
No attachment < 1 mm Rectangular	−0.46	0.10	0.000
No attachment > 0.5 mm Rectangular	0.22	0.10	0.044
No attachment < 1 mm Hemi‐ellipsoid	−1.96	0.10	0.000
No attachment < 0.5 mm Hemi‐ellipsoid	−0.96	0.11	0.000
1 mm Rectangular > 0.5 mm Rectangular	0.68	0.09	0.000
1 mm Rectangular < 1 mm Hemi‐ellipsoid	−1.50	0.10	0.000
1 mm Rectangular < 0.5 mm Hemi‐ellipsoid	−0.50	0.10	0.000
0.5 mm Rectangular < 1 mm Hemi‐ellipsoid	−2.18	0.09	0.000
0.5 mm Rectangular < 0.5 mm Hemi‐ellipsoid	−1.18	0.10	0.000
1 mm Hemi‐ellipsoid > 0.5 mm Hemi‐ellipsoid	0.99	0.10	0.000
First molar
Control < No attachment	−0.91	0.08	0.000
Control > 1 mm Rectangular	2.67	0.06	0.000
Control < 0.5 mm Rectangular	−1.34	0.07	0.000
Control > 1 mm Hemi‐ellipsoid	0.99	0.07	0.000
Control > 0.5 mm Hemi‐ellipsoid	0.25	0.05	0.000
No attachment > 1 mm Rectangular	3.58	0.08	0.000
No attachment < 0.5 mm Rectangular	−0.43	0.09	0.000
No attachment > 1 mm Hemi‐ellipsoid	1.90	0.09	0.000
No attachment > 0.5 mm Hemi‐ellipsoid	1.16	0.08	0.000
1 mm Rectangular < 0.5 mm Rectangular	−4.01	0.07	0.000
1 mm Rectangular < 1 mm Hemi‐ellipsoid	−1.68	0.07	0.000
1 mm Rectangular < 0.5 mm Hemi‐ellipsoid	−2.42	0.06	0.000
0.5 mm Rectangular > 1 mm Hemi‐ellipsoid	2.33	0.08	0.000
0.5 mm Rectangular > 0.5 mm Hemi‐ellipsoid	1.59	0.07	0.000
1 mm Hemi‐ellipsoid < 0.5 mm Hemi‐ellipsoid	−0.74	0.07	0.000

Abbreviations: ns, non‐significant; SE, standard error.

The results of the two‐way ANOVA for Mx are given in Table 3. The interaction between group and tooth was significant for all outcomes (p < 0.001). Rectangular attachments on UR4 and UR5 yielded significantly higher Mx values than the hemi‐ellipsoid attachments (p = 0.000). No statistically significant difference was noted between 0.5 and 1.0 mm rectangular attachments (p = 0.101). For UR6, most of the comparisons between the groups did not yield statistically significant differences (p < 0.05). However, 1 mm hemi‐ellipsoid attachment yielded significantly higher Mx values than the 1 mm rectangular ones (p = 0.042).

TABLE 3.

Comparison of the moments in buccolingual direction (Mx) between groups by analysis of variance (ANOVA).

Group comparison	Difference	SE	p
First premolar
Control and No attachment	0.55	0.44	0.226
Control < 1 mm Rectangular	−1.88	0.54	0.003
Control and 0.5 mm Rectangular	−0.75	0.57	0.208
Control > 1 mm Hemi‐ellipsoid	8.10	0.64	0.000
Control > 0.5 mm Hemi‐ellipsoid	32.33	1.19	0.000
No attachment < 1 mm Rectangular	−2.43	0.54	0.000
No attachment < 0.5 mm Rectangular	−1.30	0.57	0.038
No attachment > 1 mm Hemi‐ellipsoid	7.55	0.64	0.000
No attachment > 0.5 mm Hemi‐ellipsoid	31.78	1.19	0.000
1 mm Rectangular and 0.5 mm Rectangular	1.13	0.65	0.101
1 mm Rectangular > 1 mm Hemi‐ellipsoid	9.98	0.71	0.000
1 mm Rectangular > 0.5 mm Hemi‐ellipsoid	34.21	1.23	0.000
0.5 mm Rectangular > 1 mm Hemi‐ellipsoid	8.85	0.74	0.000
0.5 mm Rectangular > 0.5 mm Hemi‐ellipsoid	33.08	1.25	0.000
1 mm Hemi‐ellipsoid > 0.5 mm Hemi‐ellipsoid	24.23	1.28	0.000
Second premolar
Control < No attachment	−7.09	0.59	0.000
Control < 1 mm Rectangular	−6.71	0.58	0.000
Control < 0.5 mm Rectangular	−5.76	0.79	0.000
Control < 1 mm Hemi‐ellipsoid	−4.24	0.49	0.000
Control > 0.5 mm Hemi‐ellipsoid	4.33	0.49	0.000
No attachment and 1 mm Rectangular	0.38	0.76	0.629
No attachment and 0.5 mm Rectangular	1.33	0.93	0.172
No attachment > 1 mm Hemi‐ellipsoid	2.85	0.70	0.001
No attachment > 0.5 mm Hemi‐ellipsoid	11.42	0.69	0.000
1 mm Rectangular and 0.5 mm Rectangular	0.96	0.92	0.316
1 mm Rectangular > 1 mm Hemi‐ellipsoid	2.48	0.69	0.002
1 mm Rectangular > 0.5 mm Hemi‐ellipsoid	11.04	0.69	0.000
0.5 mm Rectangular and 1 mm Hemi‐ellipsoid	1.52	0.87	0.102
0.5 mm Rectangular > 0.5 mm Hemi‐ellipsoid	10.09	0.87	0.000
1 mm Hemi‐ellipsoid > 0.5 mm Hemi‐ellipsoid	8.57	0.61	0.000
First molar
Control < No attachment	−1.74	0.38	0.000
Control and 1 mm Rectangular	2.06	1.10	0.092
Control and 0.5 mm Rectangular	0.31	0.31	0.320
Control and 1 mm Hemi‐ellipsoid	−1.77	1.39	0.232
Control and 0.5 mm Hemi‐ellipsoid	−0.86	1.23	0.501
No attachment > 1 mm Rectangular	3.80	1.12	0.007
No attachment > 0.5 mm Rectangular	2.05	0.36	0.000
No attachment and 1 mm Hemi‐ellipsoid	−0.03	1.40	0.982
No attachment and 0.5 mm Hemi‐ellipsoid	0.89	1.24	0.492
1 mm Rectangular and 0.5 mm Rectangular	−1.75	1.10	0.144
1 mm Rectangular < 1 mm Hemi‐ellipsoid	−3.83	1.74	0.042
1 mm Rectangular and 0.5 mm Hemi‐ellipsoid	−2.91	1.62	0.088
0.5 mm Rectangular and 1 mm Hemi‐ellipsoid	−2.09	1.39	0.165
0.5 mm Rectangular and 0.5 mm Hemi‐ellipsoid	−1.17	1.22	0.362
1 mm Hemi‐ellipsoid and 0.5 mm Hemi‐ellipsoid	0.92	1.82	0.621

Abbreviation: SE, standard error.

4. Discussion

The primary reasons for including direct attachments in CAT were to provide retention for the aligners and create an additional surface to exert forces, thereby generating a desired moment [1]. Despite their crucial role in contemporary CAT, the biomechanical basis for specific attachment designs remains poorly understood. According to Cai et al. [17], the most critical factor in determining an effective attachment is the direction of the active surface, which they optimised based on the required moment‐to‐force ratio. Invisalign introduced an optimised expansion attachment, featuring a horizontal dome‐shaped design, in their eighth‐generation system [29]. This design includes a flat surface facing the gingiva to provide extrusive forces that counteract tipping. However, the hemi‐ellipsoid design examined in this study did not fall within the ideal range. In a finite element analysis study [26], researchers compared forces produced by rectangular, ellipsoid and pyramidal attachments during anterior retraction and found that the differences were not significant; however, the ellipsoid design exhibited the most evenly distributed forces. Interestingly, another finite element analysis study focused on extrusion found that an ellipsoid‐shaped attachment produced the highest undesired moments [30]. These findings indicate that the effects of attachment shape on the forces and moments generated by clear aligners are highly variable and depend on the specific type of desired tooth movement. Therefore, there is a pressing clinical and scientific need for further research to identify the most optimal attachment shape for specific orthodontic tooth movements.

The size of the attachment also plays a significant role. Smaller, lower‐profile attachments are generally preferred for their more aesthetic appearance. Ahmad et al. [31] assessed the effect of increasing attachment size while mesialising the lateral incisor, canine, first premolar and second molar. The investigators found that a 0.5 mm increase in the attachment's length, width and thickness led to an increase in force, moment and moment‐to‐force ratio, with the most substantial changes observed when the thickness was increased. Similarly, our results showed that doubling the size of the attachments significantly increased the forces and moments generated.

The forces and moments observed in this study varied significantly depending on the tooth. Previous research has demonstrated this phenomenon, suggesting that such variation could be attributed not only to differences in tooth anatomy but also to the tooth's location along the curved arch [2]. This variation can also be seen in the differing retentiveness of aligners. Takara et al. [32] evaluated the gripping forces of aligners around the arch and found that the highest retentiveness occurred near the incisors and anterior teeth, while the lowest retentiveness was observed in the posterior region, particularly lingual to the molars.

Although there is no universal consensus on the optimal range of forces required for bodily tooth movement, the forces observed in this study across the investigated teeth fell within the previously reported range (0.68–1.18 N) [33, 34]. A systematic review by Theodorou et al. [33, 34], which included two randomised controlled trials and ten split‐mouth studies, assessed the ideal force range for orthodontic tooth movement. Their qualitative analysis revealed that forces between 50 and 250 cN resulted in comparable rates of tooth movement, while forces greater than 250 cN produced a higher rate of movement but also increased negative side effects. Another study reported buccal force values of 2.25 ± 0.38 N at the canine and 1.50 ± 0.16 N at the second premolar when investigating forces exerted on lingually constricted teeth by clear aligners [35]. According to Proffit, the optimal moment‐to‐force ratio for translation is 8–10. With the ideal force for buccal translation being approximately 1 N, a necessary counter buccal root torque moment would be 8–10 Nmm [33]. In this study, certain combinations of attachment shapes and sizes produced force and moment levels closest to the desired ranges for the teeth investigated. Overall, the best forces and moments for expansion were achieved with 1 mm rectangular attachments on UR4s, 1 mm hemi‐ellipsoid attachments on UR5s and 0.5 mm rectangular attachments on UR6s. Some lower Fy and Mx values observed across certain attachment–tooth combinations could be attributed to the degree of mismatch investigated. Previous studies have indicated that the ideal discrepancy between the aligner and tooth for optimal force delivery is 0.2–0.5 mm per aligner, while another study evaluating optimised attachments for posterior expansion required at least 0.5 mm of prescribed expansion [27, 29].

It is important to consider the effects on adjacent teeth when using clear aligners. In this study, each tooth was constricted by 0.2 mm, with the resulting buccal forces creating a counterlingual force on the adjacent teeth. A recent study found that when single teeth were constricted, the adjacent teeth experienced clinically significant forces in the opposite direction [27, 29]. Another in vitro study [2], which evaluated the extrusion of an upper central incisor, observed unplanned forces affecting the upper lateral incisor. Thus, undesired forces from the expansion of adjacent teeth may interfere with the prescribed buccal forces exerted by the clear aligner.

It is important to consider the clinical significance of our findings. While the differences in outcomes between different attachment designs are statistically significant, they may not always lead to clinically significant differences in patient outcomes. Therefore, these findings should be interpreted with caution in a clinical context, and further studies are needed to explore the clinical relevance of these statistically significant differences.

The limitations of this study are related to both the conditions of the oral environment and potential operator inconsistency, which are critical for the clinical applicability of these findings. First, the experimental models were based on an ideal typodont without root structures, periodontal ligaments, bonded attachments or other oral environmental factors. Future research could include patient models with root structures, thermoform aligners incorporating gingival tissue or thermocycling to simulate oral temperatures. Additionally, the storage time of the aligners varied slightly, which could have affected the results across trials. Most clinical aligner prescriptions address multiple orthodontic movements rather than isolated expansion, so future studies could investigate compounded movements. Furthermore, only the initial load was measured, which does not account for aligner deformation after repeated use in clear aligner therapy for orthodontic tooth movement. Additional research could examine the load degradation observed with the repeated removal and replacement of aligners. Another limitation of this study is the potential presence of residual forces in the system, resulting from zeroing the load cells after the aligner was inserted without moving the teeth to a truly passive position. Although the load cells registered zero after this adjustment, residual forces may have remained within the system due to initial aligner deformation. Consequently, the measured forces during tooth movement could reflect not only the forces generated by the movement itself but also changes in these residual forces, such as relaxation or additional deformation from the initial state. This introduces some uncertainty regarding the exact contribution of the tooth movement to the overall force measurements. However, we believe the findings remain valuable and relevant, as they align with previous studies that have demonstrated the inherent forces within aligner systems, even in passive configurations [36]. Future studies should aim to move the teeth to a truly passive position prior to zeroing the load cells, ensuring that any subsequent measurements are solely due to target tooth movement, thus providing more accurate and reliable force data. Other factors, such as aligner material, aligner thickness and the number of attachment combinations, were also limited in this study. Future research could evaluate the effects of altering the aligner material and thickness, as well as exploring additional attachment shapes, sizes and locations. Finally, all aligner fabrication was performed manually. Variation in the results occurred among the five aligners tested, not between trials, suggesting that differences could be attributed to the manual fabrication and trimming of the aligners.

5. Conclusions

Based on the results, we conclude that the shape and size of direct attachments have a statistically significant effect on the orthodontic forces and moments generated by thermoplastic aligners during expansion. Certain attachment designs, such as the 1 mm rectangular attachments on UR4s, 1 mm hemi‐ellipsoid attachments on UR5s and 0.5 mm rectangular attachments on UR6s, were found to produce best force/moment couples for the bodily expansion of posterior teeth.

Author Contributions

Megann Lear: conceptualisation, methodology, investigation, data curation, writing – original draft, writing – review and editing. Amin Akbari: conceptualisation, methodology, formal analysis, investigation, data curation, writing – review and editing. Olivia Robertson: investigation, data curation, writing – review and editing. Janine Magura: conceptualisation, methodology, investigation, data curation, writing – review and editing. Alexandra Bojrab: conceptualisation, methodology, investigation, data curation, writing – review and editing. George Eckert: formal analysis, writing – review and editing. Jie Chen: conceptualisation, methodology, investigation, resources, writing – review and editing. Richard Scott Conley: conceptualisation, methodology, investigation, writing – review and editing. Hakan Turkkahraman: conceptualisation, methodology, investigation, data curation, writing – original draft, writing – review and editing, supervision, project administration.

Ethics Statement

Ethical review and approval were not required for this study, as it did not involve human participants, human data or animal subjects.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Data S1.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request. The data are not publicly available due to privacy or ethical restrictions.