Editorial Type:
Article Category: Research Article
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Online Publication Date: 10 Jun 2021

Finite element simulations of the effects of an extraoral device, RAMPA, on anterosuperior protraction of the maxilla and comparison with gHu-1 intraoral device

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Page Range: 804 – 814
DOI: 10.2319/020521-106.1
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ABSTRACT

Objectives

To investigate the effects of an extraoral device, right-angle maxillary protraction appliance (RAMPA), combined with a semi-rapid maxillary expansion intraoral device (gHu-1) on the anterosuperior protraction of maxillary bone.

Materials and Methods

The finite element (FE) model included craniofacial bones and all sutures. The linear assumption was assumed for the FE simulations and the material properties of bones and sutures. The gHu-1 was simulated under screw activations equal to Δx = 0.25 and 0.5 mm in the lateral direction with and without RAMPA under a set of external forces {F1 = 2.94, F2 = 1.47, F3 = 4.44} N.

Results

Displacement contours, nodal displacements of 12 landmarks, and von Mises stresses were compared. Combining RAMPA and gHu-1 (with Δx = 0.25 mm) resulted in changes in the displacement of the front part of the maxilla near the mid-palatal suture from (0.02, −0.1, −0.02) mm to (0.02, 0.3, 0.8) mm. For gHu-1 with Δx = 0.5 mm, the displacement of the same part changed from (0.04, −0.04, −0.2) mm to (0.04, 0.3, 0) mm. Similar trends were found in other locations.

Conclusions

The findings are in agreement with the previous cephalometric clinical data of an 8-year-old patient and prove the positive effects of RAMPA on the anterosuperior protraction of the maxilla when it is combined with the intraoral device gHu-1. In addition, RAMPA does not interfere with the lateral expansion generated by the intraoral device.

Keywords: Finite element method; Craniofacial bones; Suture; Anterosuperior displacement; RAMPA; gHu-1

INTRODUCTION

The finite element method (FEM) provides fast and reliable tools for assessing new correctional methods in orthodontics. Hence, this research used FEM to investigate the influence of a right-angle maxillary protraction appliance (RAMPA) on the anterosuperior protraction of the maxillary bone and compare it with an intraoral device, gHu-1, without RAMPA.

Thanks to FEM, many researchers have been able to analyze stress and displacement of craniofacial bones in different cases. For example, Jafari et al.1 studied stress distribution on the craniofacial complex during rapid maxillary expansion in a young female. Lee et al.2 investigated the effects of lateral expansion on various midpalatal sutures. Stress distribution and displacement of the maxilla and teeth were assessed using various bone-borne palatal expanders, Hyrax arms, micro-implants, and a surgically assisted tooth-borne expander.3–7 In addition, Mitani et al.8,9 compared the results of an finite element (FE) model and clinical observations about the protraction effect of RAMPA combined with a gHu-1 device. However, their model did not include sutures, except for the midpalatal suture (MPS).

Because of small thicknesses and complex geometries, accurate FE simulations of sutures and periodontal ligaments (PDLs) have been always challenging. Hence, many researchers have ignored or oversimplified these components. However, research has shown that sutures10,11 and PDLs12,13 have considerable effects on FE predictions. Thus, in this study, all of the sutures and PDLs were modeled so that the final FE model could capture the effects of the flexibility of these parts.

Even as an isotropic material, sutures have been reported to have a wide range of properties and thicknesses. For example, Romanyk et al.14 reported a Young's modulus of E = 500–1370 MPa with a Poisson's ratio of υ = 0.3 and 0.49, and Jasinoski and Reddy15 assumed that E = 28 MPa and υ = 0.3. Also, the thickness of MPS was assumed to be 1.72 mm14 (different from 0.25 mm16 and 0.1–0.25 mm17). In addition, PDLs have been featured with material properties such as E = 0.044–90 MPa and υ = 0.3–0.49.18

Orthotropic and anisotropic assumptions are even more complex, because they deal with directional stiffnesses.16,19,20 For example, Peterson and Dechow20 measured a wide range of thicknesses, Poisson's ratios, and Young's moduli for the skull and facial bones. They reported thicknesses ranging from t = 2.0–3.3 mm and E = 10,500–27,700 MPa.

Assuming bones and sutures to have isotropic properties has been more popular in FEM, and many scholars usually consider bones to have linear isotropic material properties. Likewise, in the present study, we used linear FE simulation and isotropic properties for all materials. Our goal was to investigate the influence of the extraoral device RAMPA combined with an intraoral device gHu-1 on the anterosuperior protraction of craniofacial bones, especially the maxilla. Four different load cases were simulated, and their results were compared.

MATERIALS AND METHODS

A three-dimensional computer-aided design (CAD) model of the skull was generated using a digitizer device (Geomagic Touch TM Graft3D Healthcare Solutions Pvt. Ltd., Chennai, India) based on 3B Scientific skull replica model 9982-1000069 (3B Scientific, Hanmurg, Germany). Later, the CAD files were modified, and the cancellous bones were generated according to the cortical bones. The thicknesses of the cancellous and cortical components were checked to be in the range of the reported values.21,22 PDLs were generated using shell structures with a thickness of 0.1 mm.18,23,24 In addition, all cranial sutures were produced in the CAD model with thicknesses ranging from 0.1 to 0.5 mm.16,17,25Figure 1 demonstrates all of the components (except sutures that can be seen in Figure 2). For the FE simulations, each of these parts had material properties that were selected according to previous research (Table 1).4,26,27

Figure 1.Figure 1.Figure 1.
Figure 1. Visual demonstration of the craniofacial components, except sutures, for the finite element method simulations: (A) Front view. (B) Cancellous and cortical bones. (C) Periodontal ligaments. (D) Teeth. Color map: dark blue, frontal bone; orange, zygomatic bone; purple, maxilla; light blue, nasal bone; copper, cancellous; red, teeth; gray, periodontal ligament.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 2.Figure 2.Figure 2.
Figure 2. Two views of element arrangement in the finite element method model (finer mesh is applied to sutures).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Table 1. Material Properties Applied to the Finite Element Method Simulations
Table 1.

The mesh for FEM simulations (Figure 2) was generated and then solved using ANSYS Workbench 17.2 (Ansys Inc., Canonsburg, Penn). To produce an acceptable element arrangement, element size was manually set for each suture part, and at least five elements were placed across the thickness of each suture. To increase the mesh quality, the “automatically controlled adaptive mesh size” option was chosen in the software. The final mesh contained 1,343,569 nodes with six degrees of freedom and 738,821 tetrahedral elements, which was greater than 419,0002 and 462,91627 tetrahedral elements. The final mesh had average values of mesh skewness, quality, and aspect ratio equal to 0.43, 0.7, and 2.53, respectively.

RAMPA is an extraoral device that should be worn by a patient (Figure 3). It is connected to an intraoral appliance (gHu-1) consisting of a set of connecting rods, an acrylic resin part, and a screw for activation (Figure 4). For real application, six forces are applied symmetrically to RAMPA by rubber bands. These include two horizontal forces and two vertical forces applied to the front part of the device. The other two forces are applied vertically to the left and right sides of RAMPA. However, because of the symmetry in the FE model, only three forces (F1 = 2.94 N, F2 = 1.44 N, and F3 = 4.4 N) were simulated (Figure 5). The magnitudes of the forces were specified from the elastic constant of the rubber band that was determined by a tensile test8 (Figure 6).

Figure 3.Figure 3.Figure 3.
Figure 3. A schematic of the right-angle maxillary protraction appliance worn by a patient: (A) front view; (B) side view.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 4.Figure 4.Figure 4.
Figure 4. Images of the gHu-1 intraoral appliance. (A) Front view (yellow arrows show the direction of activation of the device's screw); (B) side view.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 5.Figure 5.Figure 5.
Figure 5. Coordinate system, direction and position of the external forces, and boundary conditions applied to the finite element method simulations.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 6.Figure 6.Figure 6.
Figure 6. Force-distance curve of a rubber band used in real right-angle maxillary protraction appliance treatment. Data are reproduced from Mitani et al.8

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Using F1, F2, and F3, the total force, Ft, and moment, Mt, acting on RAMPA can be calculated as where

In equations 1 and 2, Ft is directed anterosuperiorly and Mt creates a rotation in the upward direction (Figure 7). In this study, the coordinate system was defined so that the X, Y, and Z axes were in the lateral, anterior, and superior directions, respectively (Figures 4 and 5).

Figure 7.Figure 7.Figure 7.
Figure 7. Resultant force and moment applied to the skull as a result of the right-angle maxillary protraction appliance.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

In addition, the activation of the screw of gHu-1 was simulated by the lateral displacement of the resin parts of gHu-1 (yellow arrows in Figure 4A) with the values of Δx = 0.25 mm and 2*Δx = 0.5 mm in different load cases. In total, four different load cases were simulated as described in Table 2.

Table 2. Name and Values of Different Load Cases Applied to the Finite Element Method Simulations
Table 2.

The boundary conditions are depicted in Figure 5. Because of the symmetry, the MPS was restricted to move only in the sagittal plane. Also, the back of the coronal suture and the foramen magnum were considered to be fixed.

RESULTS

The demonstrations of the results of the four load cases (Table 2) on craniofacial bones and also on some landmark points (Figure 8) were arranged in the following structure. First, the effects of RAMPA were investigated by comparing load cases 1*gHu-1 and R+1*gHu-1, in which the screw in the intraoral device gHu-1 was activated by Δx = 0.25 mm. For these load cases, von Mises stresses are shown in Figure 9, and the displacements in the X, Y, and Z directions are compared in Figures 10–12, respectively. Very similar comparisons were performed for load cases 2*gHu-1 and R+2*gHu-1, in which the value of the activation of the gHu-1 was doubled (2*Δx = 0.5 mm). For these load cases, von Mises stresses are shown in Figure 13, and displacements in the X, Y, and Z directions are compared in Figures 14–16, respectively. In addition, the displacement values of the landmark points (Figure 8) and teeth are listed in Tables 3–5. Finally, the displacements (in the Y and Z directions) of seven points along the MPS are plotted in Figures 17A and B, respectively.

Figure 8.Figure 8.Figure 8.
Figure 8. Landmark points on the craniofacial bones.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 9.Figure 9.Figure 9.
Figure 9. von Mises stress distribution on craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 10.Figure 10.Figure 10.
Figure 10. Displacements along the X axis on the craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 11.Figure 11.Figure 11.
Figure 11. Displacements along the Y axis on the craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 12.Figure 12.Figure 12.
Figure 12. Displacements along the Z axis on craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 13.Figure 13.Figure 13.
Figure 13. von Mises stress distribution on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 14.Figure 14.Figure 14.
Figure 14. Displacements along the X axis on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 15.Figure 15.Figure 15.
Figure 15. Displacements along the Y axis on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Figure 16.Figure 16.Figure 16.
Figure 16. Displacements along the Z axis on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

Table 3. Displacements of Landmark Points on the Midpalatal Suture
Table 3.
Table 4. Displacement of Landmark Points on Maxillofacial Bones
Table 4.
Table 5. Alveolar Bone Displacement
Table 5.
Figure 17.Figure 17.Figure 17.
Figure 17. Effects of combining the right-angle maxillary protraction appliance with gHu-1 on the anterosuperior displacement of midpalatal landmark points under different load cases: (A) along the Y axis; (B) along the Z axis.

Citation: The Angle Orthodontist 91, 6; 10.2319/020521-106.1

DISCUSSION

Analysis of the von Mises Stresses and Displacements

The von Mises stress is an important criterion in mechanical engineering since it is calculated based on all of the stress components. Hence, it is usually assumed as a yield criterion for ductile materials. Although bones are anisotropic materials with some similarities to brittle materials, von Mises is still widely used for their analysis. This is because, in many simulations including this research, bones are simulated using isotropic and linear assumptions.

Figure 9 shows that the load case R+1*gHu-1 generated a considerably different von Mises stress distribution from 1*gHu-1, especially on the frontal bone. The remarkable von Mises distribution related to R+1*gHu-1 was because of the presence of RAMPA and its three cushions on the frontal bone (parts A and B in Figure 7). Displacements in +X (Figure 10) showed that both the maximum and minimum values were changed trivially. Areas near the first and second molars had similar maximum values, whereas areas near the nasal and lacrimal bones had minimum displacements. Figure 11 demonstrates that RAMPA had a great influence on the displacement in the anterior direction. While the maximum displacement of the maxilla in the +Y direction under the load case 1*gHu-1 was 0.08 mm, it increased to 0.43 mm (537%) under R+1*gHu-1. Also, the upper part of the frontal bone showed almost no displacement in the Y direction, while the lower areas (near the nasal bone and the eye orbit) showed forward movements. Figure 12 reveals that RAMPA entirely changed the distribution of the displacements in the Z direction, especially on the maxillary bone. There, the negative displacement of maxillary bone under 1*gHu-1 (−0.05 mm) was changed to 0.07 mm for R+1*gHu-1. In addition, RAMPA increased the maximum displacement from 0.057 mm to 0.161 mm (281% increase), whereas the minimum value stayed almost constant.

The effects of doubling Δx from 0.25 to 0.5 mm are presented in Figures 13–16. Figure 13 shows that the effects of RAMPA were more noticeable on the changes of von Mises distribution on the frontal bone than other bones. Figure 14 depicts that the maximum and minimum values in both load cases happened near the nasal bone (values were only 2% different). Returning to very similar findings in Figure 10, it was seen that RAMPA had trivial interfering effects on the lateral protraction of the maxilla. Figure 15 reveals that displacements along the Y axis under 2*gHu-1 and R+2*gHu-1 were completely different. Under 2*gHu-1, the front part of MPS moved posteriorly (−0.07 mm), while the same location under R+2*gHu-1 moved anteriorly (+0.3 mm), which was the direct effect of the forward pull generated by RAMPA. Finally, Figure 16 demonstrates that load case 2*gHu-1 created vertical displacement in the range of −0.09 to −0.14 mm on the maxilla. However, under R+2*gHu-1, the maxillary moved upward (from 0.0 to 0.098 mm). RAMPA also caused a 203% increase in the maximum displacement in the Z direction.

Finally, the effects of RAMPA on the anterosuperior movement of MPS were analyzed by comparing the displacements of points A–F (Table 3; Figure 17). Figure 17 shows that, as a result of increasing Δx from 0.25 mm to 0.5 mm, MPS had a noticeable dropdown. However, this was alleviated by the use of RAMPA, especially at the location near the soft palate. These behaviors were in complete agreement with the direction of resultant forces and moments demonstrated in Figure 7. Also, it is of note that these effects of RAMPA on the anterosuperior movement of the maxilla were in agreement with the cephalometric clinical data presented by Mitani et al.8 for an 8-year-old patient.

Table 4 reveals that the lateral displacements of points G, J, K, and L were trivially affected by RAMPA; however, the anterosuperior movements depended substantially on the existence of RAMPA. For point H, the RAMPA affected the displacement in all directions; however, the relative displacements in the Y and Z directions were more profound. Also, it was seen that point I had negative displacements in the X direction when RAMPA was not combined. Nonetheless, the same point showed a positive lateral movement after RAMPA was involved.

Lastly, Table 5 shows the anterosuperior effects of RAMPA on the central and lateral incisors and canine, in which the negative values in Y and Z turned to positive values after RAMPA was combined. RAMPA also increased the positive movement of other teeth along these axes. In addition, it can be determined from this table that the lateral movements of the first and second premolars and molar teeth were trivially affected by the RAMPA but mainly affected by the gHu-1.

CONCLUSIONS

  • The displacements of the craniofacial bones indicate that the application of only the intraoral device gHu-1 for maxillary lateral expansion had negative effects on the dropdown of the midpalatal suture, especially at the posterior part.

  • It was also observed that increasing the screw activation exacerbated the downward movement of the MPS and hence the drop down of the soft palate. The combination with RAMPA had four major positive effects:

    • generating protraction in the anterior direction,

    • eliminating the downward movement of the maxilla,

    • generating superior displacement at the location of the MPS, and

    • no considerable interfering effects with the protraction of the maxilla in the lateral direction.

Copyright: © 2021 by The EH Angle Education and Research Foundation, Inc.
Figure 1.
Figure 1.

Visual demonstration of the craniofacial components, except sutures, for the finite element method simulations: (A) Front view. (B) Cancellous and cortical bones. (C) Periodontal ligaments. (D) Teeth. Color map: dark blue, frontal bone; orange, zygomatic bone; purple, maxilla; light blue, nasal bone; copper, cancellous; red, teeth; gray, periodontal ligament.

Figure 2.
Figure 2.

Two views of element arrangement in the finite element method model (finer mesh is applied to sutures).

Figure 3.
Figure 3.

A schematic of the right-angle maxillary protraction appliance worn by a patient: (A) front view; (B) side view.

Figure 4.
Figure 4.

Images of the gHu-1 intraoral appliance. (A) Front view (yellow arrows show the direction of activation of the device's screw); (B) side view.

Figure 5.
Figure 5.

Coordinate system, direction and position of the external forces, and boundary conditions applied to the finite element method simulations.

Figure 6.
Figure 6.

Force-distance curve of a rubber band used in real right-angle maxillary protraction appliance treatment. Data are reproduced from Mitani et al.8

Figure 7.
Figure 7.

Resultant force and moment applied to the skull as a result of the right-angle maxillary protraction appliance.

Figure 8.
Figure 8.

Landmark points on the craniofacial bones.

Figure 9.
Figure 9.

von Mises stress distribution on craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Figure 10.
Figure 10.

Displacements along the X axis on the craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Figure 11.
Figure 11.

Displacements along the Y axis on the craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Figure 12.
Figure 12.

Displacements along the Z axis on craniofacial bones caused by load case 1*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+1*gHu).

Figure 13.
Figure 13.

von Mises stress distribution on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Figure 14.
Figure 14.

Displacements along the X axis on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Figure 15.
Figure 15.

Displacements along the Y axis on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Figure 16.
Figure 16.

Displacements along the Z axis on the craniofacial bones caused by load case 2*gHu and its combination with the right-angle maxillary protraction appliance (load case: R+2*gHu).

Figure 17.
Figure 17.

Effects of combining the right-angle maxillary protraction appliance with gHu-1 on the anterosuperior displacement of midpalatal landmark points under different load cases: (A) along the Y axis; (B) along the Z axis.

Contributor Notes

a  Research Professor, Department of Mechanical Engineering, Sogang University, Seoul, Korea.
b  Private practice, Tokyo, Japan.
c  Professor, Department of Mechanical Engineering, Sogang University, Seoul, Korea.
d  PhD candidate, Mechanical Engineering, Guilan University, Rasht; and CEO, Isra Sanat Shar NoAfarin Engineering Co., Qazvin, Iran.
Corresponding author: Dr B. Choi, Department of Mechanical Engineering, Sogang University, Seoul, Korea (e-mail: bkchoi@sogang.ac.kr)
Received: 01 Feb 2021
Accepted: 01 Apr 2021
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