Anchorage consumption of the posterior teeth under different extraction patterns in bimaxillary dentition using clear aligner: a finite element study

doi:10.21203/rs.3.rs-4665593/v1

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Anchorage consumption of the posterior teeth under different extraction patterns in bimaxillary dentition using clear aligner: a finite element study

https://doi.org/10.21203/rs.3.rs-4665593/v1

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Background: Extracting the premolars is an effective strategy for patients with bimaxillary dentoalveolar protrusion. Clear aligners (CAs) close the extraction spaces through shortening the length of aligners. The contraction force generated by the terminal of aligners makes the posterior teeth tip mesially, which is known as the roller coaster effect. This phenomenon is even worse in the second premolar extraction cases. Posterior anchorage preparation is commonly used to protect the angulation of molars, taking the form of presetting distal tipping value. However, the distal tipping design aggravates the anchorage consumption of anterior teeth simultaneously. This study aimed to explore the relatively suitable distal tipping value of posterior teeth when the first or the second premolars were extracted in bimaxillary dentition using CAs, further providing guidance for anchorage preparation design in clinical practice.

Methods: Two bimaxillary finite element models (FEMs) with different extraction patterns were established to simulate the anterior en-masse retraction process of the CAs. In Model 1, the upper and lower first premolars were extracted, while in Model 2, the second premolars were extracted. Finite element analysis (FEA) methods were utilized to analyze the tipping angle of anchorage consumption and anchorage provided teeth.

Results: Inter-group comparison revealed that the anterior teeth exhibited a greater lingual inclination and the posterior teeth exhibited a slighter mesial tipping tendency in Model 1 in response to the same tooth site. Intra-group comparison revealed that the closer to the extraction space, the greater the tilt, and the distal tipping tendency of the first premolar was more evident than the mesial tipping tendency of the first molar in Model 2. Compared between the bimaxillary dentition, the mesial tipping tendency of each tooth was more evident in maxilla. As for the posterior segments, the total mesial tipping tendency of maxillary posterior segments was heavier in Model 2, while regarding the mandibular posterior segments, it was heavier in Model 1. In addition, the highest hydrostatic stress of the periodontal ligament(PDL) was concentrated on the cervical and apical parts directly adjacent to the extraction spaces, and it exhibited relatively uniform distribution in Model 1 .

Conclusions: During clear aligner treatment (CAT), the posterior teeth showed the same mesial tipping direction but to different degree when the first or the second premolars were extracted. Presetting the anchorage preparation design for the posterior teeth is necessary to alleviate the roller coaster effect, especially in the second premolar extraction cases. The anchorage consumption attributed to anatomical structure counteracts the effect of the number of anchorage provided units to a certain extent, so larger anchorage preparation value should be proposed for the maxillary posterior teeth.

Clear aligners

Anchorage preparation

Tooth extraction patterns

Bimaxillary dentition

Biomechanics

Bimaxillary dentoalveolar protrusion patients often turn to orthodontist complaining about unsatisfied appearance and easily injured incisors[1]. To improve the lateral profile, extracting the premolar is recommended. Whether to extract the first or the second premolar should consider a combination of factors, including arch crowding, lateral profile protrusion, vertical dimension, and endodontic diseases[2-6].

During the retraction process, the anterior and posterior segments move in opposite directions[7]. The number of teeth in front of and behind the denture vacuoles represent different anchorage consumption units and anchorage provided units, which plays a great role in anchorage management. It’s crucial to use all the premolar extraction space for anterior retraction without undesired mesial movement of the molars[8]. In other words, the maximum anchorage management design is the key to achieve the ideal lateral profile and occlusal relationship.

Clear aligner treatment (CAT) is gaining popularity due to its improved aesthetic value and comfort. By virtue of its reliability and validity[9], CAT is also suitable for the malocclusion with complex mechanical principles[10], such as premolar extraction cases. However, clear aligners (CAs) close the extraction spaces through shortening the length of aligners. The contraction force generated by the terminal of aligners makes the posterior teeth tip mesially, especially when the second premolar is selected[11]. This phenomenon is known as the roller coaster effect.

Enhancing the anchorage management through overcorrection is the cornerstone to deal with this side effect. Previous studies adopted multiple strategies to reinforce the anchorage management of the anterior teeth. For instance, adding intrusive activation for the incisors, designing power ridge with a specific height[11-13]. Apart from this, in order to compensate the delayed tooth movement with the aligners, optimization of posterior anchorage management should be strengthened simultaneously, taking the form of presetting distal tipping for the posterior teeth before retraction process[9]. To date, although there is consensus relating to posterior anchorage preparation in premolar extraction cases, the specific value under different extraction patterns is still controversial[9, 14-16].

Clinical observation finds that the roller coaster effect is more serious in the maxillary dentition. Liu et al. demonstrated that the bimaxillary dentition exhibited the same tipping direction although the upper posterior dentition experienced greater levels of tipping when retracting the anterior teeth[17]. To our knowledge, the density of the maxilla and mandible is of inconformity[18]. Base on this, a hypothesize is raised that posterior anchorage design varies in maxillary and mandibular dentition owing to the anatomical structure.

Finite element analysis (FEA) is an effective discretized numerical computation technology that simulates the in vivo situation by controlling a number of experimental conditions, including finite elements, nodes, and degrees of freedom[19]. Over recent years, FEA has been widely used in the orthodontic biomedical field to investigate the initial displacement and stress distribution following the application of force[12, 20].

This is the first study to construct the bimaxillary models with different parameters of maxilla and mandible, exploring the difference of posterior anchorage consumption under two extraction patterns. FEA is conducted on the assumption of the maximum anchorage management. Furthermore, we elucidate the potential biomechanical effects of premolar extraction cases when applying CAs. Finally, we aim to derive relatively specific anchorage preparation value and provide guidance for clinical orthodontic treatment.

Original 3D model design

To construct a standard bimaxillary model, cone-beam computed tomography (CBCT) data (HiRes3D-Plus; Largev, Beijing, China) were derived from a healthy volunteer with well-aligned dentition and normal axial inclination of the bimaxillary anterior teeth. Each CBCT had a thickness of 0.15 mm, resulting in a total of 640 horizontal slices. The volunteer willingly participated in this experiment and provided written informed consent. This study was approved by the Ethics Committee of The Air Force Medical University (IRB Reference: KQ-YJ-2024-012).

The CBCT data were imported into Mimics software (version 20; Materialise Software, Leuven, Belgium). Then, by applying the threshold procedure, we generated mask layers for the bimaxillary dentition, jaws, and temporomandibular joint (TMJ). Next, we used GEOMAGIC Studio 2014 software (3D Systems, Rock Hill, North Carolina) to optimize the original 3-dimension(3D) models and organize the surface structure. Then NX 1911 software (Siemens, Nuremberg, Germany) was utilized to construct a basic model of the periodontal ligament (PDL), bone cortex and cancellous, and attachments. We extended the outer surface of the tooth roots by 0.25 mm to generate a preliminary model for the PDL, which incorporated linear elasticity, a uniform thickness and homogeneity. Although the width of the PDL varied among locations and individuals, the realistic PDL geometry shifted the center of resistance (CRes) towards the alveolar margin by 2.3% for the linear material models only, so the hypothesis of uniform thickness was valid[21]. The elastic modulus of the mandibular PDL was set to twice that of the maxillary PDL in order to reflect the difference between arches[22]. The jaws were also shifted inwards by 1.3 mm; then, Boolean subtraction operation instructions were used to build cortical and cancellous bone. This study adopted the attachment design which had been proved to have high efficacy in root control movement[23], with vertical rectangular attachments (2×3×1 mm) set for the canines and premolars while horizontal rectangular attachments (3×2×1 mm)set for the molars for aligner retention. The bimaxillary crowns and attachments were extended outwards by 0.5 mm to simulate a 0.5 mm-thick CA membrane. Figure 1 shows the geometry of the components in the two models. All components were imported into ANSYS Workbench 2019 software (Ansys, Canonsburg, Pa) to build 3D finite element models and perform FEA.

Material property

The models consisted of 3D 10-node tetrahedrons. The structures were set as linear, elastic, isotropic, and homogenous (Table 1), as previously reported[24]. The density of the maxillary and mandibular cancellous was of inconformity, and the mechanical response was significantly influenced by the assumed elastic properties of bone[18]. The elastic modulus of Class III bone, which consisted of trabeculae that were tightly arranged, was approximately six-fold higher than that of Class IV bone, which had sparsely arranged trabeculae. Based on this, we pioneered the concept of setting the elastic modulus of the mandibular cancellous as 6-fold higher than that of the maxilla[25].

Boundary and contact condition

With regards to the boundary condition, we set the lower edge of the mandible as the lower boundary and the upper edge of the maxilla as the upper boundary. Bonding contact was set on the interfaces of the cortex to the cortical bone, the cortical bone to the PDL, the PDL to the tooth, and the tooth to the attachment. Adjacent teeth were given a small amount of frictionless sliding on the contact surfaces. With a friction coefficient of 0.2, the contact interfaces between the aligner and the tooth crown surface and attachments made it possible to move the teeth and retain the appliance[26]. The interaction between the bimaxillary dentition was neglected.

Configuration setting and experimental design

Two different extraction groups were established(Fig. 1). Model 1 simulated the extraction of the upper and lower first premolars (4/4), while Model 2 simulated the extraction of the upper and lower second premolars (5/5). The torque of the maxillary central incisors was 110° (U1-SN=110°) and the torque of the mandibular central incisors was 100° (L1-MP=100°).

In both models, the anterior teeth were set with a sagittal inward step of 0.25 mm to simulate one step retraction. We assumed that the anterior torque would recover to normal through 60 orthodontic steps; in other words, the upper anterior torque reduced to 105° (U1-SN=105°) and the lower anterior torque reduced to 95° (L1-MP=95°).

Loading method

FEA was used to investigate the initial force systems during OTM under static loading. To simulate the clinical situation that treating patients with bimaxillary dentoalveolar protrusion, the bimaxillary incisors were set to be retracted in a sagittal manner by 0.25 mm and the canines were shifted distally by 0.25 mm, thus deforming the anterior region of the CAs. The finite element models were assembled using the discrete numerical method, and the number of elements and nodes for each model was shown in Table 2. The displacement tendency, rotation angle of teeth and hydrostatic stress of PDL was output by the ANSYS software[27].

Reference coordinate system

Two separate coordinate systems were established to investigate the OTM of a single tooth and the entire dentition. The global coordinate system was defined for the whole dentition(Fig. 2a). The X-axis represented the coronal plane with positive values denoting the left side and negative values denoting the right side. The Y-axis represented the sagittal plane, with positive values denoting the posterior side and negative values denoting the anterior side. The Z-axis represents the vertical plane with positive values denoting the superior side and negative values denoting the inferior side. The origin of the local coordination system lay in the center of mass for each tooth, and was defined as follows: the x-axis (positive and negative values denoted mesial and distal, respectively), the y-axis (positive and negative values denoted lingual and buccal, respectively), and the apex of the maxillary dentition and the incisor and occlusal of the mandibular dentition signified positive orientation on the z-axis(Fig. 2b).

Calculation and analysis

The displacement direction, rotation angle of the anterior and posterior teeth, also the hydrostatic stress distribution of the PDL were addressed to evaluate the anchorage consumption of bimaxillary dentition under different extraction patterns.

With the same en-masse anterior retraction set, we identified differences between the two models in terms of anterior torque, posterior angulation, and PDL hydrostatic stress.

The effect of tooth extraction patterns on the rotation angle of the anterior teeth in the sagittal direction

In both models, the anterior segments exhibited similar lingual inclination tendency (Fig.3). With regards to the anterior teeth in front of the extraction space as an anchorage consumption unit, the central incisors exhibited the lowest lingual inclination tendency while the canines exhibited the most severe distal tipping tendency.

Compared between the two models, the inclination/ tipping tendency was more notable in Model 1, and the inter-group difference was the most obvious for the upper and lower central incisors. With regard to the upper dentition, the lingual inclination angle in Model 1 was 0.11722° for the central incisor and 0.22835° for the lateral incisor; these values were compared to 0.04417° for the central incisor and 0.15897° for the lateral incisor in Model 2. The canine was distal-titled with the same tendency (Model 1: 0.2966°; Model 2: 0.24231°). The lingual inclination angle and sagittal movement value of the maxillary central incisor in Model 1 was more than 2-fold higher than that of Model 2 (Table 3).

The effect of tooth extraction patterns on the angulation angle of the posterior teeth in the sagittal direction

As the anchorage provided unit, the posterior dentition behind the extraction spaces underwent mesial tipping on the X-axis, buccal torque on the Y-axis, and intrusion on the Z-axis, in both two models. The total deformation in Model 1 was larger than that in Model 2; this was because the anchorage provided unit in Model 1 consisted of three teeth while that of Model 2 only consisted of two teeth (Fig. 4).

By superimposing the bimaxillary dentition of the two models on the rotation center of each tooth, we firstly performed an inter-group comparison (Fig. 5a). The mesial tipping tendency of the posterior teeth in Model 2 was more pronounced than that of Model 1 in response to the same sites. For the maxillary dentition, the first molar in Model 2 tipped mesially by 0.26716°; this was over 1.4-fold larger than that in Model 1 (0.18883°). For the mandibular dentition, the first molar in Model 2 tipped mesially by 0.15957°; this was over 1.7-fold larger than that in Model 1 (0.092706°)(Fig. 5b). These data suggested that the anchorage consumption for each posterior tooth was more remarkable when the second premolars were extracted (Fig. 6).

Next, we performed intra-group comparisons. In Model 1, the second premolars and the molars tipped mesially; the closer to the extraction spaces, the greater the tendency for tipping. As the extraction spaces were located in the middle of the posterior segments in Model 2, the first premolars showed a distal tipping tendency when the molars tipped mesially. As shown in Table 4, the first premolars in Model 2 exhibited the most severe tipping tendency while the second molars in Model 1 exhibited the least.

The differences of anchorage consumption between the maxillary and mandibular dentition

The bimaxillary dentition exhibited the same tipping tendency but to a different extent (Fig. 5b). The tipping tendency of maxillary teeth was more obvious than the mandibular teeth according to the local coordinate system. With regard to the anterior teeth, this phenomenon was the most predominant in the central incisors of Model 1 with a lingual inclination of 0.11722° for the upper central incisor; this was 3-fold higher than that of the lower central incisor (0.033484°).

The same tendency could be found for the posterior segments. In Model 1, the upper second premolar, first molar, and second molar tipped mesially by 0.28587°, 0.18883°, and 0.14662°, almost 1.63-, 2.04-, 2.34-fold higher than that of the same site in the mandible, respectively. In Model 2, the upper first molar and the second molar tipped mesially by 0.26716° and 0.20102°, almost 1.67- and 1.88-fold higher than that of the same site in the mandible, respectively. The most visible difference was detected for the second molar in Model 1.

As for the maxillary posterior segments, the total mesial tipping tendency was heavier in Model 2, while regarding the mandibular posterior segments, it was heavier in Model 1.

PDL hydrostatic stress in the anterior and posterior segments

As shown in Figure 7, the PDL hydrostatic stress was more evenly distributed in Model 1, and the closer to the extraction spaces, the greater the tipping tendency, furthermore the higher PDL hydrostatic stress.

In Model 1, the highest compressive stress was concentrated on the distal cervical region and the mesial apex of the canines (maxillary: -0.11163MPa; mandibular: -0.16239MPa). The highest tensile stress was detected in the mesial cervical region and distal apex of the canines (maxillary: 0.11358MPa; mandibular: 0.14067MPa).

The PDL hydrostatic stress in Model 2 exhibited relatively higher values of compressive and tensile stress. The highest compressive stress was concentrated on the distal cervical region and the mesial apex of the maxillary first premolar ((maxillary: -0.11172MPa; mandibular: -0.13101MPa). The highest tensile stress was detected in the mesial cervical region and the distal apex of the first premolar (maxillary: 0.081092MPa; mandibular: 0.13307MPa).

Compared between the upper and lower jaws, the PDL hydrostatic stress was higher in the maxilla for the posterior segments.

Extracting the premolars is a widely used strategy for bimaxillary dentoalveolar protrusion patients during orthodontic treatment. The extraction spaces are expected to relieve crowding, reduce protrusion of the anterior teeth and improve the lateral profile as much as possible[8, 28]. So the maximum anchorage design is needed.

FEA does well in estimating the initial displacement tendency and stress distribution of organism structures. Without the influence of confounding factor in clinical observation studies, FEA is regarded as a reliable method for investigating orthodontic biomechanics[29]. But it’s hard to specify the anchorage type involved in the retraction process because FEA reveals only the instantaneous effect. Innovatively, we observed the initial tipping tendency and took it as anchorage consumption. In premolar extraction cases with the maximum posterior anchorage management design, the finial anchorage preparation value only need to be multiplied according to personalized orthodontic steps.

CAT has clear advantages in terms of aesthetics and comfort[30]. Attachments, anchorage design and materials are three basic principles of CAT. However, there remains a large distance between the predicted and achieved OTM, especially in premolar extraction cases[9, 31, 32]. Clinical observation finds that without additional anchorage management design, CAT is more prone to the roller coaster effect than fixed orthodontic treatment due to the lower rigidity and stress relaxation property, further emphasizing the importance of anchorage management using CAs.

Miniscrews are widely used as temporary anchorage devices (TADs), which provide strong anchorage management[17]. However, CAs close the extraction spaces by shortening the denture vacuoles, the tooth movement always falls behind the CAs. TADs only cannot match the actual OTM with the appliance exactly, the roller coaster effect will still happen[33]. Deriving from the modern Tweed-Merrifield sequential directional force treatment philosophy, anchorage preparation concept is gradually emerging in CAT[34]. Some believed that compared to the straight wire appliance, aligners displayed better sagittal control due to the lingual component[35]. Jim Vaden et al. drew the conclusion that 15° tip-back for the mandibular second molar displayed the best vertical control and most en-masse mesial movement using CAs combined with class II elastics[35]. However, Cheng et al. reported that severe mesial tipping tendency of the posterior teeth occurred notwithstanding the power ridge was added as anterior torque compensation during the retraction process[13]. Therefore, it is necessary to strengthen the posterior anchorage management.

Based on questions raised by the existing literature, we focused particularly on the posterior anchorage design in premolar extraction cases. Our findings revealed that teeth in the posterior segments underwent mesial tipping tendency in two models. In Model 1, the second premolar is adjacent to the extraction space and it’s angulation is crucial to the anchorage protection. The tendency for mesial tipping was ranked as follows: second premolar > the first molar > the second molar, thus indicating that the closer to the extraction spaces, the more pronounced the tipping tendency, highlighting the need for an anti-tipping design. In Model 2, all of the posterior teeth showed a tendency for tipping towards the extraction spaces, and this tendency was more obvious in the second premolar than in the molars. The first premolar and the first molar were almost adjacent to the extraction spaces; however, the anchorage value for the first premolar was smaller than that of the first molar according to the area of the PDL; therefore, a greater level of tipping tendency occurred under reciprocal force.

Assuming that the anterior retraction process was completed in 60 orthodontic steps, anti-tipping design for each posterior tooth was shown in Figure 8a. Previous studies have concentrated on the anchorage management of the first molar. Align Technology proposed the G6 protocol which focused on premolar extraction cases; the core concept of this protocol relies upon overcorrection. If the anterior overbite is deeper than 2 mm, 4° of mesial angulation will be activated for the molars’ root. Dai et al. reported that a distal tipping angle of 6.6° should be planned for the maxillary first molars in order to achieve bodily retraction[9]. In another study, Feng et al. suggested that a distal tilt of 8.7° should be designed for the upper first molars to prevent mesial tipping[14]. Another study prescribed overcorrection (distal tipping) for the first molars by 2.9° to counter the anchorage consumption. However, the first molars experienced greater mesial movement (by 2.2 mm) with a great level of mesial tipping (5.4°)[32]. Based on the exact anchorage consumption amount, we believe the results will be of significant clinical guidance meaning.

Up to now, there is no literature available on the potential biomechanical effects of CAs under the circumstance of anchorage preparation design. This process involves two systems of forces (Fig. 8b). Firstly, the posterior segments achieve anchorage preparation through the distal deformation of CAs. As the posterior teeth receive the backwards force, a forward counter-force to the posterior appliance is produced. Due to the entire structure of the appliance, the anterior part receives the transmitted counter-force and exerts labial force on the anterior teeth. Secondly, as the CAs contract, the dentition receives the force in the direction of the extraction space. Since the CAs only wrap the crown, the force generated by CAs can only create minimal counter-moments in labio-palatal directions[36]. Therefore, the anterior teeth receive a clockwise force while the posterior teeth receive a counterclockwise force in the maxillary dentition. In contrast, the anterior teeth receive a counterclockwise force and the posterior teeth receive a clockwise force in the mandibular dentition; this makes the teeth move in an oblique manner rather than a bodily manner. With regards to the posterior segments, the two forces remain in conflict, and the anchorage preparation force takes the responsibility to strengthen the posterior anchorage. With regards to the anterior segments, the appliance contraction force opposes the transmitted counter-force. In order to improve lateral profile, the extraction space should be used to retract the anterior teeth as much as possible, that means the posterior teeth should be designed as the maximum anchorage. This requires that the anchorage preparation be used to offset the posterior appliance contraction force, thus exerting a contraction force on the anterior appliance.

Heavier roller coaster effect has always been observed in the second premolar extraction cases using CAs. Under the reciprocal anchorage system, the anchorage consumption is related to the ratio of the posterior vs anterior units. According to this research, the posterior anchorage consumption was more severe when the second premolar was extracted, which was in agreement with clinical observation. Three factors may be responsible for the difference in anchorage value between the two extraction patterns. Firstly, as the ratio of the posterior vs anterior units is smaller when the second premolar is extracted, greater levels of posterior anchorage consumption will occur[7]. Secondly, when estimated by Jepsen's root-area ratio, the PDL’s area ratio of the anchorage provided teeth and the anchorage consumption teeth in Model 1 is 1.67; this compared to 0.98 in Model 2 (both for the maxillary dentition); thus, the posterior segments in Model 1 exhibit stronger anti-tipping ability. Thirdly, the second premolar extraction spaces are bound by a molar and a premolar, whereas the first premolar extraction spaces are bound by a premolar and a canine, thus suggesting that the moment-to-force ratio applied to teeth by an aligner produces more tipping in the molars because the disparity between premolars and molars was more obvious[37]. These findings indicate that more posterior anchorage preparation should be designed in the second premolar extraction cases for better anchorage management.

In addition, the selection of premolar extraction patterns can be influenced by the arch crowding degree, lateral protrusion profile and vertical dimension[2-6]. Shaweesh AI. noted that the mesiodistal diameter of the first premolar was larger than that of the second premolar, thus providing a larger space for decongestion[6]. Another study reported that the 4/4, 4/5 and 5/5 groups had mean incisor retractions of 4.2 mm, 3.7 mm and 2.3 mm, respectively[38]. A previous study of mandibular dentition found that the average mandibular reciprocal relative anchorage consumption was 25% or 40% for extraction of the first or second premolar respectively in CAT[7]. These data suggest that extraction of the first premolar is a superior choice in cases that require the greatest improvement in lateral protrusion profile.

Enhancing the anchorage management of molars is not only a prerequisite to establish the desirable occlusion, but also a guarantee against deterioration of the vertical dimension profile. The TMJ is a hinge joint with the disc-condylar complex as its axis. Theoretically, due to Christensen's phenomenon, the mesial movement of anchorage molars will reduce the vertical dimension[39]. As the mesial movement amount of the posterior tooth is larger in second premolar extraction cases, the anterior facial height will exhibit greater reduction[38, 40]. That’s one of the reasons that caution must be paid to low-angled patients with premolar extracted. In contrast, several studies have failed to identify wedge effect[2, 3]. They believed that the amount of anchorage consumption might play a greater role in the vertical dimension than the location of premolar extractions[3]. Further highlights the importance of anchorage preparation. As described above, the clinical indication of two different extraction patterns are summarized in Figure 9.

The anatomical structure and number of anchorage provided units contribute to the differences between the bimaxillary dentition. Although the maxillary posterior segment in Model 1 was composed of three teeth, the total mesial-distal movement tendency(X- axis) was still heavier in Model 2 (Fig. 4). The mesial tipping angle of the maxillary posterior teeth in Model 2 was approximately 1.4-fold larger than that of Model 1; this compared to 1.7-fold in the mandible. These results confirmed that the anchorage consumption attributed to anatomical structure concealed the effect of the number of anchorage provided units, at least to a certain extent.

This study demonstrated that the tipping tendency of each maxillary tooth was 1.6–2-fold higher than that of the mandibular. And the farther away from the extraction space, the greater the divergence. This can be interpreted by following reasons(Fig. 5b). Firstly, there are differences in the anatomical structure of the maxilla and mandible, the mean bone mineral density for the mandible is twice that of the anterior maxilla. The maxilla is composed of a thin bone cortex and slender trabeculae, while the mandible is made up of a thicker bone cortex and stouter trabeculae[41]. During the OMT, resorption of the alveolar bone occurs in front while reconstruction occurs behind. A maxilla with a lower density is more prone to resorption and reconstruction; therefore, it is easier for the maxillary posterior teeth to tilt mesially than the mandibular posterior teeth; thus, the anchorage consumption is more pronounced in the maxilla. Secondly, the variation in tooth size should be taken into consideration. The central incisors of the mandibular are the smallest teeth among the whole dentition while the lower dentition exhibits a larger difference in anterior-posterior anchorage than the upper dentition[17, 32]. Thirdly, according to Andrews' six keys to normal occlusion, the maxillary molars tip mesially by 5° and the mandibular molars tip mesially by 2°; this means that the initial physiological angulation prior to orthodontics makes the maxillary posterior teeth more sensitive to lose anchorage control. Finally, we need to consider the target torque of the maxillary and mandibular anterior teeth(maxillary central incisor: +7°; mandibular central incisor: -1°). That means the lower anterior teeth can accept a greater degree of lingual inclination, while the upper anterior teeth cannot. In conclusion, a much higher anchorage demand is required by the maxilla posterior segments. But then again, the bone density is different in the anterior and posterior region of maxilla and mandible, which may influence the posterior anchorage value[41]. The realism of FEA study need to be addressed by adjusting the materials parameters in deeply research.

It is important that we highlight the fact that the roller coaster effect is not absolutely unfavorable; the selection of indications needs to be taken into account when designing the anchorage preparation. The lingual inclination of the incisors can make up for patients with a mild open-bite when retracting the anterior teeth[33].

There are some limitations to this study that need to be taken into account. FEA cannot completely simulate the real situation in vivo. Although we try to simulate the real elastic modulus of the maxilla, mandible and PDL, it’s impossible to completely reappear the physiological situation. For instance, the bone density is different in the anterior and posterior region of maxilla and mandible, which may influence the actual anchorage consumption[41]. The realism of FEA study need to be addressed by adjusting the material parameters in deeply research. Under the present circumstances, the anchorage preparation value during CAT need individualized revision based on the clinical situation.

In this study, we used FEA to evaluate the movement tendency of anterior and posterior teeth in two models.

Under different extraction patterns, the posterior teeth showed the same mesial tipping direction but to different degree using CAs. In order to alleviate the roller coaster effect, it’s necessary to preset the anchorage preparation design for the posterior teeth.
With the same anterior retraction step, the posterior anchorage consumption was significantly higher in the second premolar extraction cases. And the first premolars require the greatest anti-tipping design, followed by the first molars; the second molars require the smallest anti-tipping design. When considering extraction of the first premolars, the closer to the extraction spaces, the greater the anchorage preparation value is required for the posterior teeth.
The anchorage consumption was larger in the maxilla than the mandible for the same tooth sites. The anchorage consumption attributed to anatomical structure counteracts the effect of the number of anchorage teeth. When adopting CAT in premolar extraction cases, the anchorage preparation design should be enhanced for the maxillary posterior teeth.
From a clinical point-of-view, it is important to select the extraction pattern based on the desired movement ratio of the anterior and posterior teeth. If there is desire to improve the lateral profile protrusion by the greatest amount, then the first premolar is the superior choice.

CAT: Clear aligner treatment; OTM: Orthodontic tooth movement; FEA: Finite element analysis; CA: Clear aligner; CBCT: Cone-beam computed tomography; TMJ: Temporomandibular joint; 3D: Three-dimensional; PDL: periodontal ligament; CRes: Center of resistance; TAD: Temporary anchorage device.

Human Ethics and Consent to Participate declarations

This study was approved by the Ethics Committee of The Air Force Medical University (IRB Reference: KQ-YJ-2024-012). Written informed consent was obtained from the participant.

All methods were performed in accordance with the Declaration of Helsinki.

Consent for publication

Not applicable.

Availability of data and materials

The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.

Competing interests

The authors declare that they have no competing interests.

Funding

This study was supported by the National Clinical Research Center for Oral Diseases（LCA202202, LCB202202); Key Research and Development Program of Shaanxi Province (2021SF-050, 2022SF-227); the CSA Clinical Research Fund (CSA-02022-01); College Science and Technology Innovation Plan of Shanxi Education Department (2021L242); New Technologies and New Business of School of Stomatology, Air Force Medical University Fund (LX2022-401); China Oral Health Foundation (A2023-013).

Authors’ contributions

Ruyue Qiang: Contributed to conceptualization, methodology, formal analysis, preparing original draft. Jie Gao: Contributed to validation and resources, critically revised manuscript. Yanqi Wang: Contributed to validation and visualization. Wei Wang: Contributed to building models and data acquisition. Zuolin Jin and Yanning Ma: Contributed to conceptualization, funding acquisition, formal analysis, review and editing. All the authors read and approved the final manuscript.

Acknowledgements

The authors would like to express their gratitude to EditSprings (https://www.editsprings.cn ) for the expert linguistic services provided.

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Table 1. Material properties

		Young’ s modulus, E (MPa)	Poisson’ s ratio
Tooth		1.96×10⁴	0.3
PDL	Maxilla	6.9×10^-1	0.45
	Mandible	1.38
Cortical bone		1.47×10⁴	0.3
Cancellous bone	Maxilla	2.31×10²	0.3
	Mandible	1.47×10³
CA		5.28×10²	0.36
Attachments		1.25×10⁴	0.36
Cartilage		7.9×10^-1	0.49
Disc		44.1	0.4

PDL, periodontal ligament; CA, clear aligner.

Table 2. Nodes and elements

	Model 1	Model 2
Nodes	1050593	1056660
Elements	582229	585413

Table 3. Sagittal movement value of the anterior tooth crown on the Y axis

		Central incisor	Lateral incisor	Canine
Model 1	Maxilla	3.6823L	6.2846L	-10.034D
Model 1	Mandible	0.71106L	5.0576L	-7.8499D
Model 2	Maxilla	1.3844L	4.3772L	-8.1857D
Model 2	Mandible	0.6694L	3.1218L	-6.1769D

+values indicate lingual or mesial movement of the tooth crown (× 10⁻²mm); − values indicate buccal or distal movement of the tooth crown (× 10⁻²mm). The direction is also marked after the value. B, buccal movement; L, lingual movement; M, mesial movement; D, distal movement.

Table 4. Mesial/ distal movement value of the posterior tooth crown on the X axis

		The 1^st premolar	The 2^nd premolar	The 1^st molar	The 2^nd molar
Model 1	Maxilla	-	6.6624M	4.5316M	3.4879M
Model 1	Mandible	-	4.4759M	2.2422M	1.4731M
Model 2	Maxilla	-9.064D	-	6.2605M	4.7905M
Model 2	Mandible	-6.8226D	-	3.808M	2.5315M

+values indicate mesial movement of the tooth crown (× 10⁻²mm); − values indicate distal movement of the tooth crown (× 10⁻²mm). The direction is also marked after the value. M, mesial movement; D, distal movement.

No competing interests reported.

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Anchorage consumption of the posterior teeth under different extraction patterns in bimaxillary dentition using clear aligner: a finite element study

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