Finite element analysis of stress distribution in anchor teeth in surgically assisted rapid palatal expansion

Abstract

The treatment of a transverse maxillary deficiency in skeletally mature individuals should include surgically assisted rapid palatal expansion. This study evaluated the distribution of stresses that affect the expander’s anchor teeth using finite element analysis when the osteotomy is varied. Five virtual models were built and the surgically assisted rapid palatal expansion was simulated. Results showed tension on the lingual face of the teeth and alveolar bone, and compression on the buccal side of the alveolar bone. The subtotal Le Fort I osteotomy combined with intermaxillary suture osteotomy seemed to reduce the dissipation of tensions. Therefore, subtotal Le Fort I osteotomy without a step in the zygomaticomaxillary buttress, combined with intermaxillary suture osteotomy and pterygomaxillary disjunction may be the osteotomy of choice to reduce tensions on anchor teeth, which tend to move mesiobuccally (premolar) and distobuccally (molar).

The characteristics of a transverse maxillary deficiency (TMD) are a narrow maxilla, high-arched palate, crowded and rotated teeth, and bilateral or unilateral crossbite. Treatment varies according to the degree of transverse deficiency, patient age, association with other facial deformities, and the aims of expansion. Expansion may be achieved using orthodontic or orthopaedic procedures, or combinations of surgeries and orthopaedic procedures, called surgically assisted rapid palatal expansion (SARPE).

The best results in the treatment of skeletally mature individuals have been achieved using SARPE, whereas non-surgically assisted rapid maxillary expansion (NSARPE) in these individuals has been associated with complications, such as buccal tilt and displacement of the teeth that anchor the expander.

SARPE techniques and variations have been described elsewhere, and studies have confirmed that the activation of the tooth-borne (Hyrax) or tooth-tissue-borne (Haas) expanders after osteotomies dissipates tensions responsible for the lateral movement of the maxilla and all adjacent structures, such as the teeth and the bones of the face and skull, which affects the nasal cavity, nasal septum, lateral walls and floor of the nose and nasal area, as well as the upper lip, alar base, gingiva, and facial soft tissues.

This study used finite element analysis (FEA) to evaluate the distribution of tensions in the anchor teeth of a tooth-tissue-borne expander when different types of osteotomies were simulated.

Materials and methods

Based on computed tomography (CT) scans of Brazilian adults, a computer-aided design (CAD) model of a maxilla was built using the software Rhinoceros 4.0 (McNeel North America, USA), which generated images of the major anatomical maxillary landmarks.

The geometry of this anatomical model was imported using the software FEMAP 10.1.1 (Siemens PLM Software Inc., USA) to generate a tetrahedral finite element mesh with 10 nodes in the preprocessing phase. After that, the software NEi Nastran (Noran Engineering Inc.) was used to analyze the model, and results were sent to FEMAP 10.1.1 (Siemens PLM Software Inc., USA) for post-processing.

As symmetry was assumed, the materials simulated were elastic, isotropic, linear, and homogeneous. The axes for model displacement in space were defined as x , side to side (lateral), y , front to back (horizontal), and z , top to bottom (vertical). In the areas above the osteotomies, the models were fully fixed on the z -axis. Table 1 shows the properties of the simulated materials.

Table 1
Properties of simulated materials.
Structure Young’s modulus/elasticity ( E ) (GPa) Poisson’s coefficient
Cortical bone 17.5 0.3
Tooth 20 0.3
Palatal soft tissue 0.2 0.45
Acrylic 2.4 0.3
Steel 210 0.35

Measurement unit: GPa, giga Pascal.

Five different models were built: M1, no osteotomy; M2, Le Fort I osteotomy with a step in the zygomaticomaxillary buttress; M3, Le Fort I osteotomy with a step in the zygomaticomaxillary buttress and pterygomaxillary disjunction; M4, Le Fort I osteotomy without a step; and M5, Le Fort I osteotomy with pterygomaxillary disjunction and no zygomaticomaxillary buttress step, all using a simulated Haas expander ( Fig. 1 ).

Fig. 1
(A) Model 2: Le Fort I osteotomy with a step in the zygomaticomaxillary buttress. (B) Model 3: Le Fort I osteotomy with a step in the zygomaticomaxillary buttress and pterygomaxillary disjunction. (C) Model 4: Le Fort I osteotomy without a step. (D) Model 5: Le Fort I osteotomy with pterygomaxillary disjunction and no step.

The amount of expansion was 1 mm ( Fig. 2 ) because the subject of interest was the dissipation of forces in the early stages of the expansion, and the contacts were fixed between the orthodontic bands and the teeth, the bone and soft tissue, and the expander parts. The models detached the maxilla from the nasal septum, posterior maxillary wall, and palatine bones, and no type of contact was applied to the surfaces that had osteotomies, which could move free of friction or contact, but limited to the simulated 1-mm gap. Maximum stress (MS) was determined for all five models.

Fig. 2
Models: finite element mesh and application of 1-mm displacement to the expander screw.

Results

In general, traction and compression dissipated through the anchor teeth, alveolar bone, maxillary bone, nasal floor, and pterygoid process of the sphenoid bone. On the colour maps shown in Figs. 3–7 , traction is represented by the values above zero in mega Pascal (MPa), and compression by values below zero in MPa. Table 2 shows MS values obtained in the region of the alveolar bone at the level of the first premolar and the first molar in all five models; Table 3 shows MS values in the regions of the first premolar and first molar in the five models.

Fig. 3
Maximum stress in the dental alveolus of the first premolar (A) and first molar (B) on occlusal view, and on the labial (C) and lingual (D) surfaces of the first molar and first premolar; simulation of 1-mm maxillary expansion without osteotomies (model 1).

Fig. 4
Maximum stress in the dental alveolus of the first premolar (A) and first molar (B) on occlusal view, and on the labial (C) and lingual (D) surfaces of the first molar and first premolar in model 2.

Jan 24, 2018 | Posted by in Oral and Maxillofacial Surgery | Comments Off on Finite element analysis of stress distribution in anchor teeth in surgically assisted rapid palatal expansion
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