New highlights on effects of rapid palatal expansion on the skull base: a finite element analysis study

ABSTRACT Objective: The objective of this study was to evaluate the effect of the rapid palatal expansion (RPE) on the pterygoid process (PP), spheno-occipital synchondrosis (SOS) and sella turcica (ST) in the skull of a patient with transversal maxillary collapse, and identify the distribution of mechanical stresses and displacement, by finite element analysis (FEA). Methods: Cone-beam computed tomography (CBCT) was employed to examine the skull of a patient in this study. The patient was a 13-year-old boy, with Class II skeletal relationship due to transverse atresia and maxillary protrusion. The computer-aided design (CAD) geometry of skull was imported into the SimLab v. 13.1 software, to build the finite element mesh. For the simulation, a displacement of 1 mm, 3 mm and 5 mm in a transverse direction was defined at the midpalatal suture, thereby representing the RPE. For the analysis of results, maximum principal stress (MPS) and displacements were evaluated by identifying different nodes, which were represented by the points as per the areas of interest in the study. Results: In MPS, the maximum tensile stress was found at point 2 (366.50 MPa) and point 3 (271.50 Mpa). The maximum compressive stress was found at point 8 (-5.84 Mpa). The higher displacements in the transversal plane and the lateral segment were located at point 1 (2.212 mm), point 2 (0.903 mm) and point 3 (0.238 mm). Conclusions: RPE has a direct effect on PP, SOS and ST in the Class II model skeletal relationship with a transversal maxillary collapse. PP supported a higher tensile stress and displacement.


INTRODUCTION
Posterior dental crossbites and transversal maxillary collapse are often treated with rapid palatal expansion (RPE), which involves increasing the perimeter of the dental and skeletal arches and skeletal Class III treatment combined with maxillary protraction. 1,2 The main anatomical objective is to open the midpalatal suture (MPTS), which becomes harder with the age of an individual. However, there is not an absolute correlation between the ossification and the biological age. 3 In majority of adult patients with transversal maxillary collapse, for whom surgery does not remains a viable option, RPE protocols were proposed that involved more tooth than skeletal movement. 4,5 Through the application of bone anchorage via micro-implant assisted rapid palatal expansion (MARPE), the opening of the MPTS was made possible in adult patients. 6,7 The stress that can be withstand by the craniofacial structures during the RPE has been registered for both conventional approach 8,9 and MARPE. 10 Due to bone elasticity, 11 the stress generated on the craniofacial structures during RPE are correlated with age and the ossification degree from the bone sutures, especially in adult patients. Many sutures around maxillary bones are opened during RPE, but pterygopalatine suture was found to be among the ones that offered a greater resistance to MPTS. 12 However, partial success has been achieved when the sutures were even opened with the MARPE. 13 Dental Press J Orthod. 2021;26(6):e2120162 Sevillano MGC, Kemmoku DT, Noritomi PY, Fernandes LQP, Capelli Junior J, Quintão C New highlights on effects of rapid palatal expansion on the skull base: a finite element analysis study 5 There is an important anatomical relationship between the maxillary region of the skull base and the pterygoid processes (PP) of the sphenoid bone. It happens because RPE also affects the deep regions and the neurocranium and viscerocranium. The transmission of mechanical stress produced by the expander appliance during the opening of the MPTS may affect the anatomical structures directly or indirectly, 14 for example in the case of the spheno-occipital synchondrosis (SOS), 12,15,16 PP, 8,9,14 sella turcica (ST) 17 and some cranial base foramina with its vascular and nerve content. 17,18 Although there was described in the literature that human bone has the ability to adapt to the application of mechanical loads, these must be functional and cyclical, 19 which is not achieved during RPE.
The finite element analysis (FEA) allows the simulation of the system of mechanical forces that act on the human skull during the process of a conventional RPE or MARPE, and analyses the response of such mechanical loads on the neurocranium and viscerocranium. 10 Knowing that this delicate structure might be affected by heavy loads generated during the process of RPE, the knowledge of these effects presents a great importance for the monitoring and programming of the treatment of transversal maxillary collapse. Sevillano MGC, Kemmoku DT, Noritomi PY, Fernandes LQP, Capelli Junior J, Quintão C New highlights on effects of rapid palatal expansion on the skull base: a finite element analysis study 6 The present research evaluated the effect of RPE on PP, SOS and ST in the skull of a patient with transversal maxillary collapse, in order to identify the distribution of mechanical stresses and displacements at the specific points of these anatomical structures, by the FEA method.

The ethics committee of Piracicaba Dental School -State
University of Campinas approved this study (Protocol number: 056/2013).

GEOMETRY AND FINITE ELEMENT MODEL ACQUISITION
Cone-beam computed tomography (CBCT) was employed to examine the patient's skull in this study. The case used is of a 13-year-old male with Class II skeletal relationship by maxillary protrusion, transversal maxillary collapse, complete permanent dentition, posterior dental crossbite and non-ossified SOS.
The CBCT images, presenting slice thickness at the intervals of 0.25 mm, were imported in the InVesalius 3.0 software (Center for Information Technology "Renato Archer", Campinas, Brazil) and segmented through the grayscale threshold, to obtain the three-dimensional (3D) surface of maxilla and skull base (Fig 1).
The selected bone structure was converted into a 3D stereolithography (STL) surface.      The most inferior and posterior point of the medial pterygoid plate.

2
The most posterior and middle point of the medial pterygoid plate.

3
The most upper and posterior point of the medial pterygoid plate.

4
The most inferior point of the posterior surface of the sphenoid body.

5
The most inferior point of the anterior surface of the basilar part of the occipital bone. 6 The point of intersection between the S-Ba line and the anterior surface of the basilar of the occipital bone. 7 The point of intersection between the S-Ba line and the posterior surface of the sphenoid body. 8 The deepest point of the floor of the sella turcica.

9
The uppermost point of the tuberculum sellae.   Table 3).     Video 2: Analysis of displacements during rapid palatal expansion simulation. The color scale shows the high displacement areas in red color, and low displacement areas in light blue. A pattern of displacement can be clearly seen in a "V" pattern in the axial view.
a connection between the maxilla and PP. 9,14 It significantly prevents the forces to reach the skull base, thereby achieving the opening of the pterygopalatine suture, which would further imply the separation of pyramidal process of the palatine bone from PP. 25 The opening of pterygopalatine suture in adolescents and young adults is accompanied by fractures due to the strong interdigitation between bone surfaces, 26  Wolff 19 stated that, when human bone is subjected to mechanical loads, the bone structure in its internal and external constitution undergoes a remodeling as a mechanism of adaptation to these forces. A fundamental characteristic of these forces is that they are functional and cyclical, 19 such as occlusion forces.
During the RPE, some intense forces created are neither functional nor cyclical; therefore, we suggest that it is difficult to find a healthy adaptation remodeling in the compromised internal situations, especially in adults. 13 The displacement of the palatal process was simulated in almost parallel way, following the clinical responses obtained in a study in CBCTs by Cantarella et al. 13 Regardless of whether the load force was applied to the teeth or micro-implant, only the opening of the MPTS was simulated as reported protocols. 8,27 In the MPS analysis, tensile stress was found at points 1, 2 and It is important to note that tensile stress decreases at points 3 and 4, as compared with point 2, what could be related to the proximity to the SOS cartilage and its ability to absorb the forces. 29 This effect can be clearly observed by the difference in the tensile stress between points 4 and 7 (before SOS) and points 5 and 6 (after SOS). Thilander and Ingervall 29 found collagen fibres in SOS, arranged in the longitudinal direction of the clivus, which could probably mean the preparation for tensile stress distribution. It is possible to suggest that when SOS is fully ossified, the tensile stress on the base of the skull could be much higher. The tensile stresses that SOS receives were also observed in previous studies. 17,18,27 Although tensile stress reduces its value at point 3 in relation to In addition to the body, that was considered elastic and linear, it can be seen in Tables 3 and 4 that point 1 had greater displacement and less tensile stress than points 2 and 3, and point 3 had less displacement and less tensile stress than point 2.
We suggest that this result is due to the presence of cartilage and the complex geometry of the anatomical structure. 20 When the 5-mm expansion was performed, the greatest displacements were recorded in the transverse plane in PP at points 1, 2 and 3, which are consistent with the results of previous studies. 8,9,28 The same points were also displaced in the superior and posterior directions, which suggest an opening of the MPTS in "V" pattern in the axial and coronal planes. The movements recorded in the points before the SOS (points 4 and 7) and the later ones (points 5 and 6) would be related to SOS movements, as described by other studies. 15,16,18 The movements was simulated with the objective of finding significant displacements at the maximum expansion of 5 mm, and at points 8 and 9, the movement was found to be almost negligible. By observing the simulation of the Knowing that stress difference found between the skull model is based on morphology, because the geometry is fundamental to the mechanical response, 11,20 the present study has certain limitations. In order to be able to simplify and represent the biomechanical procedure, the complete skull model was assumed to be isotropic and linearly elastic. 20 Since it is important to know the different types of stresses that occur on the craniofacial structures, the MPS analysis was selected instead of the equivalent von-Mises and the minimum principal stress analysis. This also allows a qualitative and quantitative assessment of stress forces.
The bone structures were analyzed by MPS to determine the tensile (positive values) and compressive (negative values) stresses.
Although the analysis has expressed the MPS stress values, this study was not intended to determine absolute stress magnitudes, but assisted in the localization of high and low stress distribution based on PP, SOS, and ST geometry. 20 The meshes corresponding to spongy bone tissue, teeth, periodontal ligament and circummaxillary sutures were not individualized since, in this study, the beginning of the expansion simulation starts assuming that the initial resistance of these anatomical structures had already been overcome (after the initial opening of the MPTS), as described in a previous study. 8,27 Also, the application of molar and premolar forces was not simulated, but the opening of the MPTS following the protocols of previous studies. 27 to corroborate the present results. Therefore, this study does not induce to limit the use of conventional RPE or MARPE, but it seeks to know the biomechanical impact of extreme forces on the delicate craniofacial anatomical structures that could occur in adolescents patients.