Evaluation of dental and skeletal effects of the asymmetric rapid maxillary expansion appliance: A three-dimensional finite element study

Abstract

BACKGROUND:

Transverse maxillary deficiency is one of the most common skeletal anomalies. The incidence of posterior crossbite caused by maxillary deficiency is between 2.7% and 23.3%. Unilateral posterior crossbite is more common than bilateral crossbite. The most common treatment for skeletal posterior crossbite is rapid maxillary expansion (RME), in which the base of the maxillary bone is expanded by separating the midpalatal suture.

OBJECTIVE:

This study compares the biomechanical effects of three different RME appliances, especially the effects on the midline, and evaluates the usability of the modified asymmetric RME (ARME) appliance for treating unilateral crossbites.

METHODS:

Three scenarios were created with skull models using three different appliances: (1) conventional-bonded RME appliance; (2) full-cap splint RME appliance, with all teeth covered with acrylic; and (3) ARME, with all teeth on the right side and premolars and molars on the left side covered with acrylic. The finite element method was used to assess stress levels and displacements in all models after applying a 5-mm horizontal displacement to the RME screw.

RESULTS:

The lateral transverse movement of the first molars was greater with the conventional RME appliance than with the full-cap splint RME appliance. The lateral transverse movement of the first molar was greater on the left than on the right side with the ARME. The lateral transverse movement of the central incisors was greater with the full-cap splint RME appliance than with the conventional RME appliance. The lateral transverse movement of the central incisor was greater on the right than on the left side with the ARME.

CONCLUSION:

Asymmetrical RME appliance increases unilateral expansion compared to other appliances. Therefore, it should be used in cases of unilateral posterior crossbite. This appliance can also successfully treat posterior crossbite with upper midline deviation, since it corrects the shifted midline.

Keywords

Asymmetrical RME appliance finite element method rapid maxillary expansion

1. Introduction

Transverse maxillary deficiency is one of the most common craniofacial disorders. Factors such as mouth breathing, early occlusal contacts and genetics play a role in the aetiology of maxillary deficiency [1]. Posterior crossbite is the most common clinical presentation of maxillary deficiency. Several studies have shown that the prevalence of posterior crossbite is between 2.7% and 23.7% [2, 3, 4, 5]. The prevalence of unilateral crossbites is reportedly higher than that of bilateral crossbites [6]. In unilateral crossbite cases, mandibular growth is restricted, and the ramus height is relatively shortened on the crossbite side. Therefore, condylar, mandibular and facial asymmetry are observed in unilateral crossbite patients [1].

The most common treatment for unilateral or bilateral skeletal posterior crossbite is rapid maxillary expansion (RME) [3]. RME has been used as an effective treatment since Angell first demonstrated it in 1860 [7]. During RME, high forces applied to the maxillary basal bone and other adjacent skeletal bones separate the midpalatal suture, and alveolar processes move laterally with the maxilla in young individuals [8]. It is recommended that appliances and biomechanics that create a unilateral effect should be used in unilateral crossbite treatment [3]. When unilateral crossbite is corrected with an RME appliance, buccal non-occlusion occurs on the non-crossbite side due to the bilateral force exerted by the RME appliance. This side effect can be prevented with reverse crossbite elastics on the non-crossbite side [3]. Elastics require patient cooperation and might extrude the involved teeth due to their vertical force component. This extrusion effect is undesirable in vertically growing patients [9].

Different appliances have been used to treat unilateral crossbites. Ileri and Basciftci [10] achieved unilateral expansion with an asymmetric RME (ARME) appliance with an occlusal index extending to the mandible. Toroglu et al. [9] achieved unilateral expansion with the asymmetric maxillary expansion appliance they designed by modifying the quad helix. Alcan et al. [11] used a modified RME appliance to correct the upper midline shift, which provided asymmetric expansion and could be used to treat unilateral crossbites.

The finite element method (FEM) is used to calculate stress and loads in complex structures and is widely adopted in biomechanics and studies on the behavior of biological structures [12]. This method is based on dividing a complex difficult-to-analyze structure into smaller simpler structures called elements [13]. It involves three steps: pre-processing, processing and post-processing [14]. The latter are assigned properties (e.g. elasticity modulus and Poisson’s ratio) that describe physical behavior under an external load (e.g. mastication and orthodontic forces) or after a positional modification [15]. The different directed applied forces and stresses that develop can be calculated with FEM. This experimental method requires a resource with anatomical records and modifications in computer-aided design software to build geometrically superior and accurate models [16]. Computational methods have been used to understand the oral biomechanics of complex structures such as the stomatognathic system. It is possible to anticipate and visualise tissue responses to orthodontic mechanics applied with FEM by observing stress areas created from applied orthodontic mechanics [17].

Few studies have used FEM to examine the skeletal and dental effects of modified RME appliances. Accordingly, this study evaluated the effects of three different RME appliances with FEM. Our study aimed to evaluate the ARME appliance’s effectiveness and compare it with other appliances.

2. Methods

The geometry of a dry skull without the mandible and teeth was digitally reconstructed based on computed tomography (CT) images. The CT data were obtained using an Iluma cone-beam CT (IMTEC Co., Hatfield, PA, USA) with 120 kvp and 3.8 mA for 40 s in Digital Imaging and Communications in Medicine (Arlington, VA, USA) format. It consisted of 601 sections with a thickness of 0.2 mm and was transferred into 3D-DOCTOR (Able Software Corp., Lexington, MA, USA) software for modelling. A 3D finite element model was prepared with an Intel Xeon computer (CPU 3.30 GHz, 14 GB RAM; Intel Co., Santa Clara, CA, USA). VRMesh Studio (VirtualGrid Inc., Bellevue City, WA, USA) and Algor Fempro (ALGOR, Inc., Pittsburgh, PA, USA) software were used for analysis.

Cortical bone, cancellous bone, maxillary sinuses and teeth were modelled according to their anatomy (Fig. 1a and b). The modelled periodontal ligament had a thickness of 0.2 mm, and the midpalatal suture had a thickness of 0.5 mm. FEA was performed by a professional company (AyTasarım, Florida, USA) using models obtained from cadaveres which are open for public use by the World Health Organization.

Figure 1.

Skull model: (a) frontal view and (b) occlusal view.

Figure 2.

Occlusal view of skull models with appliances: (a) model 1, (b) model 2 and (c) model 3.

The appliance’s screw part was modelled using 3D-scanned images of the RME screw (Forestadent, Germany), which can be opened by up to 10 mm with a one-quarter turn equal to 0.2 mm (Fig. 2). Three different models were created by designing the RME appliance’s acrylic part in three different ways. In model 1, premolars and molars were symmetrically covered with acrylic (Fig. 2a). In model 2, all teeth were symmetrically covered with acrylic (Fig. 2b). In model 3, all teeth on the right side and premolars and molars on the left side were covered with acrylic (Fig. 2c). The surface of the teeth and the acrylic’s inner surface were bonded to simulate the bonding of the appliance to teeth in clinical conditions.

The 3D models were converted to solid models in the form of bricks and tetrahedra elements in Algor Fempro software. The model used elements with 10 nodes as much as possible. Elements with fewer nodes were used when elements with 10 did not provide sufficient detail. All models were assumed to be linear, homogeneous and isotropic materials (Table 1). Young’s modules and Poisson’s ratio were obtained from the literature and entered into the software (Table 2) [18, 19, 20, 21]. The skull model was fixed from the supraorbital region and the posterior plane (Fig. 3). Symmetry was assumed to reduce the complexity of the finite element models and node numbers. The simulations were applied to the model’s left side and projected onto the right side. A 2.5-mm displacement in opposite directions was applied to the RME screw, making a total displacement of 5 mm.

Table 1

The number of elements and nodes in the models

	Model 1	Model 2	Model 3
Number of elements	698256	733202	722645
Number of nodes	160140	184256	188446

Table 2

Young’s modulus and Poisson’s ratio of the structures used in this study

	Young’s modulus (Mpa)	Poisson’s ratio
Cortical bone	13700	0.3
Spongious bone	7900	0.3
Teeth	20000	0.3
Periodontal ligament (PDL)	0.68	0.49
Suture	0.68	0.47
RME screw (stainless steel)	200000	0.29
Acrylic (polimethyl methacrilate)	1800	0.35

Figure 3.

Frontal, lateral and posterior view of the boundary conditions of the finite element model.

Table 3

Displacements of model 1 and model 2

	Model 1						Model 2
	X (mm)		Y (mm)		Z (mm)		X (mm)		Y (mm)		Z (mm)
Central incisor crown		0.18		0.08	$-$	0.17		0.58	$-$	0.05	$-$	0.25
Central incisor root		0.04	$-$	0.04	$-$	0.15	$-$	0.04		0.02	$-$	0.27
1st molar crown		0.81	$-$	0.16		0.23		0.66	$-$	0.16		0.16
1st molar root	$-$	0.03		0.06		0.15		0.002		0.05		0.13
FMS		0		0		0		0		0		0
ZMS		0.025	$-$	0.005		0.017		0.026	$-$	0.004		0.018
MPS		0.077	$-$	0.002	$-$	0.041		0.085	$-$	0.005	$-$	0.045
LNW		0.024	$-$	0.004	$-$	0.010		0.026	$-$	0.004	$-$	0.010
Point A		0.050	$-$	0.004	$-$	0.043		0.065	$-$	0.005	$-$	0.046
ANS		0.006	$-$	0.001	$-$	0.046		0.007	$-$	0.001	$-$	0.048
PNS		0.031	$-$	0.006	$-$	0.035		0.036	$-$	0.007	$-$	0.035
Medial pterygoid plate		0.022	$-$	0.005	$-$	0.005		0.023	$-$	0.006	$-$	0.008
Lateral pterygoid plate		0.013	$-$	0.003	$-$	0.003		0.016	$-$	0.003	$-$	0.006

FMS: Frontomaxillary suture, ZMS: Zygomaticomaxillary suture, MPS: Midpalatal suture, LNW: İnferior of lateral nasal Wall, ANS: Anterior nasal spine, PNS: Posterior nasal spine.

Table 4

Displacements of model 3

	Right						Left
	X (mm)		Y (mm)		Z (mm)		X (mm)		Y (mm)		Z (mm)
Central incisor crown		0.52	$-$	0.01	$-$	0.24		0.14		0.06	$-$	0.16
Central incisor root	$-$	0.08		0.01	$-$	0.25		0.03	$-$	0.05	$-$	0.14
First molar crown		0.69	$-$	0.19		0.20		0.85	$-$	0.18		0.24
First molar root		0.01		0.04		0.17	$-$	0.03		0.06		0.17
FMS		0		0		0		0		0		0
ZMS		0.025	$-$	0.005		0.017		0.025	$-$	0.005		0.016
MPS		0.095	$-$	0.008	$-$	0.046		0.074	$-$	0.005	$-$	0.044
LNW		0.025	$-$	0.004	$-$	0.010		0.025	$-$	0.004	$-$	0.010
Point A		0.062	$-$	0.006	$-$	0.046		0.055	$-$	0.005	$-$	0.045
ANS		0.006	$-$	0.002	$-$	0.048		0.006	$-$	0.002	$-$	0.048
PNS		0.032	$-$	0.019	$-$	0.034		0.032	$-$	0.019	$-$	0.034
Medial pterygoid plate		0.022	$-$	0.007	$-$	0.008		0.022	$-$	0.007	$-$	0.008
Lateral pterygoid plate		0.012	$-$	0.004	$-$	0.005		0.012	$-$	0.004	$-$	0.005

FMS: Frontomaxillary suture, ZMS: Zygomaticomaxillary suture, MPS: Midpalatal suture, LNW: İnferior of lateral nasal Wall, ANS: Anterior nasal spine, PNS: Posterior nasal spine.

Figure 4.

Total displacements: (a) model 1, (b) model 2 and (c) model 3.

Figure 5.

Von Mises stress distribution: (a) model 1, (b) model 2 and (c) model 3.

Table 5

von Mises stress distribution in all three models

	Model 1 Von Mises (MPa)	Model 2 Von Mises (MPa)	Model 3 (R) Von Mises (MPa)	Model 3 (L) Von Mises (MPa)
Central incisor crown	1.34	1.49	1.57	1.29
Central incisor root	3.06	13.46	11.57	3.13
First molar crown	7.43	15.82	12.26	7.98
First molar root	5.89	4.59	4.72	6.13
FMS	0.82	0.88	0.81	0.81
ZMS	29.72	32.69	33.52	32.7
MPS	0.43	1.1	1.8	0.81
LNW	12.04	18.84	17.91	15.95
Point A	0.58	0.42	0.042	0.42
ANS	25.23	30.70	29.65	28.11
PNS	0.1	0.1	0.2	0.2
Medial pterygoid plate	0.19	0.16	0.14	0.14
Lateral pterygoid plate	0.32	0.34	0.30	0.31

FMS: Frontomaxillary suture, ZMS: Zygomaticomaxillary suture, MPS: Midpalatal suture, LNW: İnferior of lateral nasal Wall, ANS: Anterior nasal spine, PNS: Posterior nasal spine.

3. Results

The displacements for models 1 and 2 are shown in Table 3 and Fig. 4. The displacement for model 3 is shown in Table 4 and Fig. 4. The models 1, 2, and 3 von Mises stresses are shown in Table 5 and Fig. 5. Positive changes indicated lateral, posterior and superior displacements – positive x-axis value: lateral movement; negative x-axis value: medial movement; positive y-axis value: posterior movement; negative y-axis value: anterior movement; positive z-axis value: superior movement; and negative z-axis value: inferior movement.

Displacement in the Transverse Plane ( $x$ -axis)

A wedge-shaped opening was formed in all three models. Midpalatal suture expansion was lower in model 1 (0.15 mm) than in models 2 (0.17 mm) and 3 (0.17 mm). The greatest lateral movement among the determined skeletal points was observed at point A. The maximum lateral movement at point A was observed in model 2 (0.065 mm). Point A showed greater lateral movement on the right (0.062 mm) than on the left (0.055 mm) in model 3.

The greatest expansion between the central incisors was observed in model 2 (1.16 mm), followed by model 3 (0.66 mm) and model 1 (0.36 mm). The right central incisor (0.52 mm) showed approximately four times the lateral movement of the left (0.14 mm) in model 3. The central incisor’s root moved laterally in model 1 but medially in model 2. In model 3, the right central incisor’s root moved medially, but the left central incisor’ root moved laterally. The lateral movement of the first molars was greater in model 1 than in model 2. The lateral movement was greater for the left first molar than the right in model 3. The first molar’s root moved medially in model 1 but laterally in model 2. In model 3, the right first molar’s root moved laterally, but the left first molar’s root moved medially.

Displacement in the Sagittal Plane ( $y$ -axis)

There was minimal sagittal movement in all skeletal points in all three models. However, anterior movement occurred in other skeletal points, except the nasion point. The greatest anterior movement was observed in the posterior alveolar crests. Point A moved more anteriorly on the right ( $-$ 0.006) than on the left ( $-$ 0.005) in model 3, but all other points moved right and left equally.

In all three models, posterior movement occurred in the incisor crowns that were not covered by acrylic; anterior movement occurred for all other incisor crowns. The first molars’ crowns moved anteriorly, but their roots moved posteriorly.

Displacement in the Vertical Plane ( $z$ -axis)

In all three models, medial structures such as point A and the anterior nasal spine (ANS) moved inferiorly. In contrast, lateral structures such as posterior alveolar crests and the zygomaticomaxillary suture moved superiorly. The right zygomaticomaxillary suture (0.017 mm) moved more superiorly than the left zygomaticomaxillary suture (0.016 mm). Point A moved more inferiorly on the right ( $-$ 0.046 mm) than on the left ( $-$ 0.045 mm) in model 3. In all three models, the central incisors moved inferiorly and the first molars moved superiorly.

Von Mises Stress Distribution

The highest von Mises stress occurred inferior to the zygomaticomaxillary suture in all three models. Less stress occurred in model 1 (29.72 MPa) than in models 2 (32.69 MPa) and 3 (33.52 MPa, 32.70 MPa). More stress occurred on the right (33.52 MPa) than on the left (32.70 MPa) in model 3. Moreover, more stress occurred for the first molars’ buccal alveolar crest (28.87 MPa) in model 1 than in model 2 (25.85 MPa). More stress occurred on the left (29.42 MPa) than on the right (26.09 MPa) in model 3.

For the orbital’s lateral wall, the highest stress occurred in model 2 (5.77 MPa) and the least stress occurred on the left in model 3 (5.19 MPa). More stress occurred on the right (5.42 MPa) than on the left (5.19 MPa) in model 3. The greatest width of the palate’s intense-stress area was found in model 3, followed by models 2 and 1. All three models showed low von Mises stresses at nasion, posterior nasal spine (PNS) and point A.

Von Mises stresses on the central incisor’s crown and root were higher in model 2 than in model 1. Von Mises stresses on the right central incisor’s crown and root were higher than the left in model 3. Differences in von Mises stresses were more pronounced in roots than in crowns. Von Mises stress on the first molar crown was greater in model 1 than in model 2; in model 3, it was greater on the right first molar crown compared with the left. Von Mises stress on the first molars’ root was higher in model 1 than in model 2; in model 3, it was greater on the left first molars’ root compared with the right.

4. Discussion

Posterior crossbite is usually treated with RME. Many expansion appliances and their modifications have been investigated since Angell first used a screw-on expansion appliance [22]. Many appliances have been designed to treat unilateral crossbites [9, 10, 23]. This study examined three different RME appliances. The first appliance was the conventional-bonded RME, the second was the full-cap splint RME appliance used by Ulusoy et al. [1] and the third was the ARME appliance used by Alcan et al. [11]. Due to the frequent use of conventional RME appliances (acrylic type) in the orthodontics literature and clinical practice, this kind of expansion appliance was preferred in this study.

This study used CT data consisting of 601 sections with 0.2-mm intervals. Therefore, this study aimed to reflect the geometry more realistically than previous studies, which had wider cross sections [27, 28, 30]. The accuracy of FEM results is affected by node numbers and the number and type of elements. More elements should be used to ensure the results are reliable [24]. This study used at least 698,256 elements and 160,140 nodes in model construction, which is more than previous studies [8, 25, 26, 27, 28]. Furthermore, this study used 10-node tetrahedral elements, which is similar to many previous studies [27, 28, 29].

RME uses many appliances, such as Hyrax, Haas and miniscrew-assisted rapid palatal expansion [30]. Previous studies evaluated the effects of many different RME appliances using FEM [18, 28, 29, 31]. Ulusoy et al. [1] used a full-cap splint RME appliance to evaluate the effects of surgical-assisted RME with FEM. However, few studies have used the full-cap splint RME appliance and compared it with the traditional RME appliance.

Alcan et al. [11] used a modified ARME appliance in posterior crossbite cases with midline deviation. They reported that the midline was improved through the transseptal fibres during the retention period with ARME [11]. In this study, the central incisor moved 0.52 mm laterally on the right and 0.14 mm on the left with the ARME appliance. Unlike Alcan et al. [11], we found that this appliance achieved midline correction through the transseptal fibres during the retention period and the asymmetrical expansion during the expansion period.

When transversal displacements were evaluated, the inferior structures expanded more than the superior structures, and the anterior structures expanded more than the posterior structures in all three models, which is consistent with previous studies reporting wedge-shaped expansion [26, 28].

The expansion in the midpalatal suture’s anterior tip was lower in model 1 (0.15 mm) compared with the other two models (0.17 mm). Sucu et al. [31] used a displacement of 5 mm and reported a 2.21-mm suture expansion. They also open modelled craniofacial sutures other than the midpalatal. Therefore, they reported a greater midpalatal suture expansion than the present study. However, Trojan et al. [32] reported suture expansion of $<$ 10% of applied displacement; they open modelled the midpalatal suture but closed modelled the other craniofacial sutures [32]. Therefore, their results are similar to this study.

Some previous studies have reported that the maxilla moves forward and down due to RME [18, 28]. Similarly, the maxilla moved down and forward in this study. The greater downward movement of the ANS than the PNS in all three models indicated that the maxilla rotates clockwise.

In this study, the palatal cusps of the posterior teeth moved in the inferior direction and the buccal cusps in the superior direction. This result showed buccal teeth tipping, which is consistent with previous studies [33, 34]. More buccal tipping occurred in model 1 than in model 2. In addition, more buccal tipping occurred on the left than on the right side in model 3.

The lateral movement of the central incisors was greater in model 2 than in model 1. In addition, the lateral movement was greater on the right than on the left side in model 3. This advantage provides midline correction. Alcan et al. reported that a modified RME appliance and unilateral bracket placement after RME had similar effects on midline correction [11]. Our results indicate that, when an equal amount of expansion is applied, the ARME appliance is more effective than the others in correcting the midline. This is because it shifted the midline not only during the retention period but also during the expansion period.

İleri and Basciftci [10] used an ARME appliance, i.e. a splint type (tooth and tissue-borne) appliance with a locking mechanism on the non-crossbite side, to treat unilateral crossbites. Unilateral crossbite was successfully treated without buccal non-occlusion on the non-crossbite side because this mechanism extends to the mandible. They also found that some expansion occurred on the non-crossbite side [10]. Similarly, while expansion was observed on both sides in model 3 in this study, the expansion in posterior teeth was greater on the right side than on the left. Therefore, the ARME appliance reduced buccal non-occlusion risk in treating unilateral crossbites. Clinical studies should further evaluate its success in treating unilateral crossbites.

4.1 Limitations

CT data were used to construct a finite element model that accurately reflects real morphology. However, it was assumed that all model structures have isotropic material properties, which is inconsistent with real-life conditions. Most FEM studies have used this assumption, since anisotropic data are unavailable. In addition, our results are only valid for patients with comparable craniofacial structures, since the reported stresses and displacement are based on a model generated from a CT scan of a cadaver.

5. Conclusions

The full-cap splint RME appliance provided greater midpalatal suture expansion than the conventional RME appliance. The full-cap splint RME appliance is preferred over the conventional RME appliance when greater skeletal effects are required.

The full-cap splint RME appliance provided greater incisor expansions but lower molar expansions than the conventional RME appliance. The full-cap splint RME appliance is preferred over the conventional RME appliance when greater expansion is required in anterior than posterior teeth.

Greater central incisor expansion occurred on the full acrylic side than on the other side with the ARME appliance. This appliance can successfully treat posterior crossbites with upper midline deviation.

When treating unilateral crossbites with the ARME appliance, buccal non-occlusion on the non-crossbite side can be prevented by providing greater expansion on the other side.

However, these suggestions need support from future clinical studies.

Ethics statement

Ethical approval was not required.

Informed consent

Informed consent was not required.

Author contributions

MK, BG and BB equally contributed to this work and were involved in methodology, investigation, validation, software, data curation and original-draft preparation; MK, BG and BB were involved in conceptualisation, writing, editing and supervision. All authors read and approved the final manuscript.

Funding

The study was supported by Karadeniz Technical University Scientific Research Projects.

Footnotes

Acknowledgments

The authors have no acknowledgements.

Conflict of interest

None to report.

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Evaluation of dental and skeletal effects of the asymmetric rapid maxillary expansion appliance: A three-dimensional finite element study

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSION:

Keywords

1. Introduction

2. Methods

Displacement in the Transverse Plane ( x -axis)

Displacement in the Sagittal Plane ( y -axis)

Displacement in the Vertical Plane ( z -axis)

Von Mises Stress Distribution

4. Discussion

4.1 Limitations

5. Conclusions

Ethics statement

Informed consent

Author contributions

Funding

Footnotes

Acknowledgments

Conflict of interest

References

Displacement in the Transverse Plane ( $x$ -axis)

Displacement in the Sagittal Plane ( $y$ -axis)

Displacement in the Vertical Plane ( $z$ -axis)