Monofocal orthodontic mechanics focusing on molar intrusion have been preferentially used to correct open-bite malocclusions characterized by greater deviations in skeletal components to minimize their effects on facial appearance and allow the achievement of incisor overlap.^1-5 However, skeletal open-bite malocclusions may require a certain degree of incisor extrusion to increase incisor crown exposure and rebuild the smile arc, which is often flattened in such cases.⁶ In contrast, monofocal orthodontic mechanics focusing on incisor extrusion can produce a gummy smile, especially when a large amount of anterior extrusion is required to close the open-bite. In addition, the extrusion techniques used for open-bite correction are inefficient in controlling the molar vertical position, allowing for an increase in facial height.^2,7-10

Multifocal mechanics does not focus on a specific regional change and can produce a set of beneficial changes for open-bite correction, which generally include posterior teeth uprighting, occlusal plane rotation, posterior teeth intrusion, and anterior teeth extrusion and retroclination (e.g., multiloop edgewise archwire mechanics, accentuated and reversed curve, angulated posterior accessories, and clear aligners).^2,11-15 However, multifocal mechanics depend on patient compliance with removable devices and cannot be adjusted for varying degrees of intrusion/extrusion according to patient requirements. To address these limitations, multifocal dual action vertical intra-arch technique (DAVIT)^16,17 mechanics was introduced. This technique allows for open-bite correction using similar or differential degrees of posterior intrusion and anterior extrusion according to the patient’s needs, without requiring compliance with removable devices, such as vertical elastics or aligners.

Although multifocal DAVIT mechanics have proven to be an efficient nonsurgical alternative for open-bite correction,^16,17 its dentoalveolar effects are still poorly understood and have not been systematically evaluated. Thus, this study aimed to evaluate the amount and pattern of tooth displacement, as well as the periodontal ligament stresses generated by the DAVIT device, using finite element analysis.

This study was approved by the Institutional Review Board of the Faculty of Dentistry, Federal University of Rio Grande do Sul under registration number 6.198.447. Written informed consent was obtained from all participants. A digital model of the maxillary region was created using Rhinoceros 7.0 SR8 Software (McNeel North America, Seattle, WA, USA). The maxillary geometry was obtained from a database at the Information Technology Center (ITC), Campinas, Brazil. This virtual model was created using the BioCAD protocol, which was developed using computer-aided design (CAD) software to generate a model extracted from the interpolation of multiple tomographies while maintaining universal anatomical landmarks.^18-20

This three-dimensional (3D) maxillary model considers the trabecular bone surrounded by a 2 mm maxillary cortical bone. The alveolar bone and teeth were modeled from the second molar to the central incisor, with a cortical bone thickness of 2 mm in the palatal alveolar bone and reduced from 2 mm to 1 mm from the upper part of the alveolar bone to the nasal floor of the buccal alveolar bone. The periodontal ligament was modeled with a linear thickness of 0.3 mm.²¹ As boundary conditions were defined, the model fixation region was assigned to the nodes on the nasal cavity floor as null displacement in all directions and presented in red (Figure 1). The boundary symmetry condition is presented in white (Figure 1) and simulates the reactions of an opposite face with the same forces and configuration on both sides of the anatomy.

A finite element model was generated using HyperMesh 2022 (Altair Engineering Inc., Detroit, MI, USA). Each structure (cortical bone, trabecular bone, periodontal ligament, tooth, bracket, orthodontic wire, cantilever, and cross-tubes) was differentiated and generated in the form of a solid body. Material attributes were entered into each solid body. The Young’s modulus (modulus of elasticity) and Poisson’s coefficient of each material involved in the study were necessary for correct material discrimination,^21-24 since the study involved linear and isotropic analyses. The properties of the materials used in this study are listed in Table 1. All materials used in the finite element analysis were assumed to be homogeneous, isotropic, and linearly elastic. The numbers of finite element analysis elements and nodes in the DAVIT model were 1.678.781 and 346.393, respectively.

In clinical settings, a skeletally anchored DAVIT device is used to produce vertical forces for the correction of vertical malocclusions.^16,17 Activation of the DAVIT device for open-bite correction involves raising the posterior power arm and lowering the anterior power arm. DAVIT wire activation occurs at the bending between the vertical wire segment and the horizontal power arms. The posterior power arm of the DAVIT was apically bent to produce an intrusive force of approximately 300 g in the posterior cross-tubes (Figure 2). The anterior power arm was occlusally bent to produce an extrusive force of approximately 150 g in the anterior cross-tubes (Figure 2). Subsequently, the anterior and posterior power arms are moved to the cross-tube level and fixed to transfer the tension induced by the DAVIT wire deflection to the fixed appliance and teeth (Figure 2).

All orthodontic accessories and devices were drawn from high-resolution photographs and modeled using a revolution tool in Rhinoceros 3D software, using a 0.022 × 0.028-inch slot size and a stainless-steel wire measuring 0.018 × 0.025-inch as a reference (Figure 2). The same software was used to draw the DAVIT appliance using a 0.017 × 0.025-inch titanium-molybdenum alloy wire as a reference (Figure 2). Two steps were performed to evaluate the 3D displacement of the maxillary teeth caused by the action of the DAVIT device on the vertical tubes. One consisted of activating the molar portion and the other consisted of activating the canine portion of the orthodontic device to simulate its clinical manipulation (Figure 2). The intrusion and extrusion forces acting on the posterior and anterior cross-tubes are produced by the reaction to the tension applied to the DAVIT device power arms, with the mini-implant anchorage serving as a fixed point. Using a linear static simulation, the models were analyzed for the displacement of molars, premolars, canines, and incisors in 3D, and the maximum principal stress induced in the periodontal ligament. The total 3D displacement of the teeth was expressed in millimeters (mm); warm colors represented high displacement, whereas cold colors represented low displacement. Teeth displacement was evaluated separately along the x (cervico-occlusal), y (bucco-lingual), and z (mesio-distal) axes. Positive and negative values indicate tooth displacements in opposite directions. The stress was recorded in Mpa, with red color indicating maximum tensile stress and dark blue color indicating maximum compressive stress.

The greatest total displacement occurred between the first and second molars and between the canine and lateral incisor, which are adjacent to the posterior and anterior cross-tubes, where the intrusion and extrusion forces are directly loaded (Figures 2 and 3). In contrast, the first premolar and the mesial portion of the second premolar had the smallest total displacement, indicating that this was a displacement-neutral zone due to a fulcrum area, which can be especially observed in the distal portion of the first premolar in the buccal view (Figure 3 and Table 2).

The evaluation of tooth displacement in each plane showed that the vertical displacement in the z-axis occurred in opposite directions when the anterior and posterior dental arch segments were compared (Figure 4A and Table 2). The incisors and canine were extruded such that the lateral incisor, canine, and central incisor were the most and least extruded anterior teeth, respectively (Figure 4A, Table 2, and Supplementary Video 1). The intrusion was concentrated in the posterior segment of the arch and progressively increased from the second premolar to the second molar (Figure 4A, Table 2, and Supplementary Video 1). The vertical displacement of the first premolar was close to zero, indicating that this area represented a neutral transition zone between the posterior intrusion and anterior extrusion (Figure 4A, Table 2, and Supplementary Video 1). The fulcrum of rotation of the occlusal plane is located in this transition area and is caused by the dual action of the DAVIT appliance (intrusion/extrusion). Consequently, the occlusal plane rotated clockwise. The tooth displacement amount along the z-axis was similar to that along the x-axis and significantly greater than that observed along the y-axis (Table 2).

The evaluation of the buccolingual displacement on the x-axis showed that the molars and second premolar were displaced buccally (Figure 4B, Table 2, and Supplementary Video 1). Buccal displacement was greatest on the second and first molars, decreasing towards the premolars and reversing from this point so that the canine and incisors were palatally tipped (Figure 4B, Table 2, and Supplementary Video 1). In general, the palatal cusps had greater buccal displacement than the buccal cusps, indicating buccal tipping of these teeth, with consequent maxillary arch expansion in the transverse dimension (Figure 4B). The transition area between buccal and palatal displacements was located on the first premolar, indicating that this was also a neutral zone for buccolingual displacement (Figure 4B and Table 2).

The displacement observed on the y-axis (mesiodistal) showed the smallest range when compared with the cervico-occlusal and buccolingual displacements observed on the z- and x-axes, respectively (Table 2). Greater distal displacement was observed in teeth anterior to the second premolar (Figure 4C). These teeth were more prone to distal displacement when the occlusal plane was rotated clockwise (Figure 4A, 4C, and Table 2). The mesial displacement observed in the posterior teeth was smaller than the distal movement that occurred in the anterior teeth and was more focused on the second molar (Figure 4C and Table 2). This was probably related to its greater buccal displacement (Figure 4B), as the expansion of the posterior segment of the dental arch included some mesial displacement in this area.

The analysis of periodontal ligament stress generated by the posterior intrusion and anterior extrusion forces of DAVIT showed that the greatest compressive stress (0.082 MPa) was concentrated in the molars, especially in the apexes of the buccal roots and furcation area (Figure 5). Conversely, the highest tensile stress (0.109 MPa) was observed at the apex of the canine and lateral incisors (Figure 5). The tendency for palatal tipping of the anterior teeth due to extrusion force was evidenced by the high tensile stress extending from the root apex to the palatal root surface, whereas the buccal surface showed compressive stress (Figure 5). This tensile/compressive stress distribution pattern tends to invert toward the cervical third of the root. In the posterior teeth, the buccal tipping tendency due to the intrusion force was evidenced by high tensile stress extending from the root apex to the buccal surface of the palatal root of the molars, whereas the palatal surface of this root showed compressive stress (Figure 5). This tensile/compressive stress distribution pattern tended to invert toward the cervical third of the palatal root (Figure 5). There was a tendency for tensile stress on the apical and middle thirds of the distal surface of the roots, whereas compressive stress was most often seen on the mesial surface of the roots (Figure 5). This finding is associated with the clockwise rotation of the occlusal plane and the uprighting of the posterior teeth. Overall, the premolars had the lowest degree and range of periodontal ligament stress (Figure 5), suggesting a lower force intensity and tooth movement in this area (the fulcrum area).

The total displacement analysis showed that the most significant changes in tooth position occurred in teeth adjacent to the cross-tubes (i.e., between first and second molars, and between canine and lateral incisor), where posterior intrusion and anterior extrusion forces were directly applied (Figure 3). Specifically, intrusion and extrusion tooth displacements were more intense in these adjacent teeth (Figure 4A). In contrast, the region between the first and second premolars showed the smallest tooth displacement (Figure 3). This static condition can be attributed more to its location in the fulcrum area, positioned between the intrusive and extrusive tooth displacements (occlusal plane rotation), than its greater distance from the loading points.

The posterior intrusion force applied to the cross-tubes resulted in the intrusion of the first and second molars, as expected,^16,17 in addition to buccal displacement and a small mesial shift (Figure 4).^21,25-27 In the posterior teeth, the points of greatest compressive stress were found at the apex of the buccal roots and in the molar furcation area, indicating the buccal tipping of the molars (Figure 5). This is because of the line of action of the intrusion force, which passes buccally to the center of resistance of the molar, generating a moment of rotation, compressive stresses at the apex of the buccal roots and furcation area, and tensile stresses at the apex of the palatal roots of the maxillary molars (Figure 5). These results align with the first model analyzed in the study by Kawamura et al.²⁶ To control molar buccal displacement associated with buccal mechanics for intrusion, a passive transpalatal arch, constricted archwire, and lingual crown torque can be used.²⁶ However, this side effect is not always a disadvantage, as open-bite malocclusions are commonly associated with transverse maxillary arch discrepancy due to oral habits. Thus, expansion of the maxillary arch can be beneficial, especially in adult patients where rapid palatal expansion is more difficult to achieve. However, controlling molar buccal displacement is crucial to avoid molar palatal cusp lowering and occlusal interferences.

The anterior extrusion force led to the extrusion and palatal displacement of the incisors and canine (Figure 4A and 4B). Extrusion and palatal tipping (drawbridge effect) significantly aid in open-bite correction, particularly in patients with a flattened smile arc and limited incisor crown exposure during smiling. Palatal tipping causes compressive stress on the buccal surface and tensile stress on the palatal surface of the root apical third of the anterior teeth; this stress distribution pattern is prone to inversion toward the root cervical third. These findings align with a recent study that evaluated the biomechanics of tooth movements and their respective stresses generated in the periodontal ligament using a finite element model.²⁵ Posterior intrusion combined with anterior extrusion induces occlusal plane rotation and consequent posterior teeth uprighting.^16,17 These changes are beneficial for open-bite closure, as patients with an open-bite often exhibit excessive mesial angulation of the posterior teeth.²⁸ Overall, the results of these finite element studies further support DAVIT as an effective multifocal technique for open-bite correction through a set of beneficial occlusal changes, including molar intrusion, occlusal plane rotation, molar uprighting, incisor extrusion and palatal tipping. When multiple occlusal changes occur to correct a malocclusion, efficiency gains can be expected without overloading a single component of the correction.

Apical inflammatory root resorption has various causes, with the most common being the inflammatory response caused by stress on the periodontal ligament from orthodontic tooth movement.²⁹ The posterior intrusion and anterior extrusion forces associated with the DAVIT device increased stress, mainly in the periodontal ligament of molars, canine, and lateral incisor. In addition, the teeth adjacent to the intrusion/extrusion load site showed greater tooth movement. Thus, clinicians should be aware that increased periodontal ligament stress associated with greater tooth displacement may elevate the risk of root resorption, necessitating special attention. Although intrusive forces may statistically produce a greater magnitude of apical root resorption, this difference is not considered clinically significant.³⁰

Because the mini-implant anchorage was considered a fixed point in this finite element method study, the rotational moment caused by DAVIT mechanics on the mini-implant was not evaluated. A clinical trial is currently being conducted to investigate the success rate of mini-implants exposed to these rotational loads. To minimize the loosening effect of the rotational moment, we recommend using clockwise and counterclockwise mini-implant threads on the left and right sides, respectively.^16,17

This study has some limitations as it involves simulating movements and stresses using DAVIT mechanics with the finite element method. This linear static simulation analyzed the immediate response of the teeth and periodontal ligament to the application of orthodontic forces in the short term. This finite element method study was not configured to simulate the dynamic behavior, making it impossible to analyze the progression and response of this force over an extended period. Therefore, clinical studies are needed to confirm the dentoalveolar effects of DAVIT mechanics and address the challenges posed by the action of rotational force on the mini-implant long axis.

Finite element analysis suggests that tooth displacement and periodontal stress generated by DAVIT mechanics may result from synergistic and multifocal actions on the maxillary dental arch. These actions produce a set of changes that are deemed beneficial for open-bite correction, including extrusion and palatal tipping of the anterior teeth, intrusion of the first and second molars, and occlusal plane rotation with a fulcrum in the first premolar region. However, it is important to approach these findings with caution and consider the limitations of this computer simulation.