FEM methodology was chosen for this study because it is a precise mathematical process, which could test the mechanical quality of three MARME models. These devices were chosen because of their different advantages. Model A was designed to perform RME in cases of severe atresia . Model B was chosen because it has already shown satisfactory results in clinical studies [19, 20, 21]. Model C was chosen because it has open rings for insertion of mini-implants, which is advantageous in situations of mini-implant loss (it is possible to reposition another mini-implant with a different angulation from the original installation) [10, 22].
Regarding the stress distribution found in the supporting tooth region, high stress intensity up to 489,199 gf/mm2 was found in general (Fig. 5, Table 6). In the lateral (Fig. 6a, Video 1) and vestibular views (Video 4), the maximum stress region observed in model A was in the distal portion of the tooth that received the band. Models B and C (Fig. 6c, b) presented extremely high forces (category 5—maximum principal stress 489.199 gf/mm2) in the mesial, buccal, and distal faces. Jain et al. 2017  concluded that excessive force on the supporting teeth is closely related to the side effect of tooth tipping. Clinically, a high incidence of tooth tipping (90.1%)  after RME was reported with a model similar to that of model B [23, 24]. Another clinical study found increased tooth inclination in the right and left upper molars of 2.77° and 2.03°, respectively . Hence, it could conceivably be hypothesized that model A has a minor side effect of tipping of teeth. However, as the periodontal tissue was not included in the evaluation, the amount of stress on the supporting teeth cannot suggest reliable clinical implications.
All evaluated models presented tensions in the infraorbital region. Model C (Figs. 5c and 6c) presented the lowest distribution of these stresses (6626 gf/mm2), while model B (Figs. 5b and 6b) presented low and medium stress (ranging from 3.076 to 9726 gf/mm2) and a relatively non-diffused distribution. Model A presented well-distributed tensions (S3), varying from low to medium stress intensities (from 3.076 to 9726 gf/mm2—Figs. 5a and 6a). This corroborates previous studies on MARME [16, 21]. As it is a region with important nerves, more clinical studies are necessary to assess whether there are any side effects in this region.
Models B (maximum principal stress of 6626) and C (from 6.626 to 9.726 gf/mm2) showed an external stress distribution pattern (Fig. 5b, c), corresponding to the buccal alveolar bone surface, with a better stress distribution in model B (S2). Reportedly, RME conventional treatment can change buccal bone thickness [7, 7]. This corroborates with a previously published FEM study of MARME . In a clinical study, Moon et al.  reported a reduction in the buccal cortical thickness of the alveolar bone of 0.67 ± 0.44 mm on the right upper molars and 0.48 ± 0.48 mm on the left upper molars. Similar results were demonstrated by Lim et al. . Furthermore, Ngan et al.  observed a 39% reduction in buccal cortical thickness after the use of a model similar to model B in their clinical study. In the present study, model A presented more internal tension in the maxillary bones and an S3 distribution in the buccal region (Fig. 26a; Video 27). This distribution included the internal portion of the bone, but greater intensity of stress was observed in the nasal bone and lateral lamina of the pterygoid process. Future clinical studies are necessary to evaluate the clinical consequences of these results.
Nasal, frontonasal, and internal sutures received tensions of up to 9.726 gf/mm2 in models B and C (Fig. 5b, c). Similar results were observed previously with the same magnitude of transverse force application . Model B showed a better force distribution (Table 6). Model C showed the same stress levels as model B but showed a low distribution of stress. Model A showed up to 14.2760 gf/mm2 of stress with S3 distribution category. Song et al.  observed similar results in their clinical study and showed that frontonasal and frontomaxillary sutures underwent major changes after RME, which were more desirable than the changes found in the sutures involved with the zygomatic bone. Furthermore, another clinical study showed a significant increase in the cross-sectional dimension of the nasal cavity (in the premolar and molar region) and a consequent improvement in nasal respiratory flow . Therefore, changes in this region are desirable. It is speculated that model A has better effects on the patient's respiratory flow. Longitudinal clinical studies will be necessary to evaluate these changes.
Considering the three models in occlusal view, the region of the medial lamina of the sphenoid process with the wing of the vomer was the location where the models were similar, both in maximum stress and distribution (489,199 gf/mm2). In a previous prospective clinical study, changes were observed in the sphenoid process with the use of a model similar to model B . According to the author, more clinical studies should evaluate RME alterations in this region because of the presence of important vessels and nerves.
The expander bodies of the three models have different sagittal distances between the mini-implants. The higher distance of model A allows a position with a greater amount of bone thickness in the anterior region while keeping the posterior mini-implants in a more posterior position (higher resistance region during RME) . Model A fits into a larger portion of the maxilla, which suggests better stress distribution in the palate and the region of the mini-implants.
MacGinnis et al.  found high stress around the mini-implants of a model similar to model B, without a wide palatal distribution. These findings are alarming because high-intensity forces with no stress distribution can bend or fracture the mini-implants. Additionally, with this weak tension distribution, the opening of the midpalatal suture may not occur .
Lack of tension or distribution in the lateral lamina of the pterygoid process area may result in the failure of RME . The images suggest that model A had a better effect on this area, both in amount of force and quality of the distribution, when compared to model B and even greater effect, when compared to that of model C. Model A showed the best stress distribution pattern in the maxillary bone, nasal region, as well as in the mini-implant insertion region.
Another interesting advantage of model A is that, owing to the height adjustment of the rings, it is possible to place the body screw expander with wider screw sizes. In this way, treatment possibilities are extended with the use of this device.
MARME in adults is a relevant and current topic for orthodontics. Previous evidence already shows that this is a promising method, which should be accurately indicated. Thus, more clinical research is needed to clarify the influence of differences in installation sites, distance from the expander body to the palate, appliance design, and activation protocols.