This study was supported by the American Association of Orthodontists Foundation (AAOF) Orthodontic Faculty Development Fellowship Award (for C.L.), American Association of Orthodontists (AAO) Full-Time Faculty Fellowship Award (for C.L.), the University of Pennsylvania School of Dental Medicine Joseph and Josephine Rabinowitz Award for Excellence in Research (for C.L.), the J. Henry O&#39;Hern Jr. Pilot Grant from the Department of Orthodontics, University of Pennsylvania School of Dental Medicine (for C.L.), and the International Orthodontic Foundation Young Research Grant (for C.L.).

This study utilized a pre-existing, de-identified, pre-treatment CBCT image of a patient who had SARPE as part of the treatment plans. The study was conducted in accordance with the Declaration of Helsinki and approved by the Institutional Review Board (protocol #853608).
1. Sample acquisition and tooth segmentation
<ol>
	<li>Acquire a human CBCT image of the head in a natural head position that includes the patient&#39;s maxillary complex, including the maxillary basal bone...

Analysis of Expansion Patterns from SARPE Using Finite Element Models

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G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Complications+in+transpalatal+distraction+osteogenesis:+a+retrospective+clinical+study.">Complications in transpalatal distraction osteogenesis: a retrospective clinical study.</a> Journal of Oral and Maxillofacial Surgery. 69 (3), 899-905 (2011).</li><li>de Assis, D. S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Finite+element+analysis+of+stress+distribution+in+anchor+teeth+in+surgically+assisted+rapid+palatal+expansion.">Finite element analysis of stress distribution in anchor teeth in surgically assisted rapid palatal expansion.</a> International Journal of Oral and Maxillofacial Surgery. 42 (9), 1093-1099 (2013).</li><li>Han, U. A., Kim, Y., Park, J. U. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Three-dimensional+finite+element+analysis+of+stress+distribution+and+displacement+of+the+maxilla+following+surgically+assisted+rapid+maxillary+expansion.">Three-dimensional finite element analysis of stress distribution and displacement of the maxilla following surgically assisted rapid maxillary expansion.</a> Journal of Cranio-Maxillofacial Surgery. 37 (3), 145-154 (2009).</li><li>Lee, S. C., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effect+of+bone-borne+rapid+maxillary+expanders+with+and+without+surgical+assistance+on+the+craniofacial+structures+using+finite+element+analysis.">Effect of bone-borne rapid maxillary expanders with and without surgical assistance on the craniofacial structures using finite element analysis.</a> American Journal of Orthodontics and Dentofacial Orthopedics. 145 (5), 638-648 (2014).</li><li>M&#246;hlhenrich, S. C., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Simulation+of+three+surgical+techniques+combined+with+two+different+bone-borne+forces+for+surgically+assisted+rapid+palatal+expansion+of+the+maxillofacial+complex:+a+finite+element+analysis.">Simulation of three surgical techniques combined with two different bone-borne forces for surgically assisted rapid palatal expansion of the maxillofacial complex: a finite element analysis.</a> International Journal of Oral and Maxillofacial Surgery. 46 (10), 1306-1314 (2017).</li><li>Nowak, R., Olejnik, A., Gerber, H., Fr&#261;tczak, R., Zawi&#347;lak, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Comparison+of+tooth-+and+bone-borne+appliances+on+the+stress+distributions+and+displacement+patterns+in+the+facial+skeleton+in+surgically+assisted+rapid+maxillary+expansion-A+finite+element+analysis+(FEA)+study.">Comparison of tooth- and bone-borne appliances on the stress distributions and displacement patterns in the facial skeleton in surgically assisted rapid maxillary expansion-A finite element analysis (FEA) study.</a> Materials (Basel). 14 (5), 1152 (2021).</li><li>Shi, Y., Zhu, C. N., Xie, Z. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Displacement+and+stress+distribution+of+the+maxilla+under+different+surgical+conditions+in+three+typical+models+with+bone-borne+distraction:+a+three-dimensional+finite+element+analysis.">Displacement and stress distribution of the maxilla under different surgical conditions in three typical models with bone-borne distraction: a three-dimensional finite element analysis.</a> Journal of Orofacial Orthopedics/Fortschritte der Kieferorthopadie. 81 (6), 385-395 (2020).</li><li>Tomazi, F. H. S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Hyrax+appliance+with+tooth+anchorage+variations+in+surgically+assisted+rapid+maxillary+expansion:+a+finite+element+analysis.">The Hyrax appliance with tooth anchorage variations in surgically assisted rapid maxillary expansion: a finite element analysis.</a> Oral and Maxillofacial Surgery. , (2022).</li><li>Trivedi, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Finite+element+analysis:+A+boon+to+dentistry.">Finite element analysis: A boon to dentistry.</a> Journal of Oral Biology and Craniofacial Research. 4 (3), 200-203 (2014).</li><li>Sankar, S. G., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+comparison+of+different+osteotomy+techniques+with+and+without+pterygomaxillary+disjunction+in+surgically+assisted+maxillary+expansion+utilizing+modified+hybrid+rapid+maxillary+expansion+device+with+posterior+implants:+A+finite+element+study.">A comparison of different osteotomy techniques with and without pterygomaxillary disjunction in surgically assisted maxillary expansion utilizing modified hybrid rapid maxillary expansion device with posterior implants: A finite element study.</a> National Journal of Maxillofacial Surgery. 12 (2), 171-180 (2021).</li><li>Han, U. A., Kim, Y., Park, J. U. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Three-dimensional+finite+element+analysis+of+stress+distribution+and+displacement+of+the+maxilla+following+surgically+assisted+rapid+maxillary+expansion.">Three-dimensional finite element analysis of stress distribution and displacement of the maxilla following surgically assisted rapid maxillary expansion.</a> Journal of Craniomaxillofacial Surgery. 37 (3), 145-154 (2009).</li><li>Esen, A., Soganci, E., Dolanmaz, E., Dolanmaz, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Evaluation+of+stress+by+finite+element+analysis+of+the+midface+and+skull+base+at+the+time+of+midpalatal+osteotomy+in+models+with+or+without+pterygomaxillary+dysjunction.">Evaluation of stress by finite element analysis of the midface and skull base at the time of midpalatal osteotomy in models with or without pterygomaxillary dysjunction.</a> British Journal of Oral &amp; Maxillofacial Surgery. 56 (3), 177-181 (2018).</li><li>Huzni, S., Oktianda, F., Fonna, S., Rahiem, F., Angriani, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+use+of+frictional+and+bonded+contact+models+in+finite+element+analysis+for+internal+fixation+of+tibia+fracture.">The use of frictional and bonded contact models in finite element analysis for internal fixation of tibia fracture.</a> Frattura ed Integrit&#224; Strutturale. 61, 130-139 (2022).</li><li>Holmes, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Closing+the+gap.">Closing the gap.</a> Nature. 550 (7677), S194-S195 (2017).</li><li>Lombardo, L., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Evaluation+of+the+stiffness+characteristics+of+rapid+palatal+expander+screws.">Evaluation of the stiffness characteristics of rapid palatal expander screws.</a> Progress in Orthodontics. 17 (1), 36 (2016).</li><li>Zandi, M., Miresmaeili, A., Heidari, A., Lamei, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+necessity+of+pterygomaxillary+disjunction+in+surgically+assisted+rapid+maxillary+expansion:+A+short-term,+double-blind,+historical+controlled+clinical+trial.">The necessity of pterygomaxillary disjunction in surgically assisted rapid maxillary expansion: A short-term, double-blind, historical controlled clinical trial.</a> Journal of Cranio-Maxillofacial Surgery. 44 (9), 1181-1186 (2016).</li><li>M&#246;hlhenrich, S. 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The direction of the buccal osteotomy in SARPE can be either a horizontal cut from the nasal aperture before stepping down at the maxillary buttress area or a ramped cut from the piriform rim towards the buttress corresponding to the maxillary first molar, as described by Betts2. Either way, the osteotomy extends well below the zygomatic process of the maxilla. However, most current FEA studies on SARPE use a horizontal cut extending posteriorly at the same level as the piriform rim<sup class="xre...

Surgically assisted rapid palatal expansion (SARPE) is a commonly used technique for transversely expanding the maxillary bony structure and the dental arch in skeletally mature patients1. The surgery involves a LeFort I osteotomy, a mid-palatal corticotomy, and, optionally, the release of the pterygoid-maxillary fissure2. However, undesired expansion patterns from SARPE, such as uneven expansion between left and right hemimaxillae3 and dentoalveolar process buccal tipping/rotation4, have been reported, which could lead to failure of SARPE, and sometimes, even requiring additional surgeries for correction5. Previous studies have indicated that the variation in circum-maxillary osteotomies may play a significant role in post-SARPE expansion pattern2,3, as the collisions between the bone blocks at the Le Fort I osteotomy sites can contribute to the uneven resisting force of lateral expansion of the hemimaxillae and to the rotation of the hemimaxillae with the alveolar edges below the cut moving inwards while the dentoalveolar process expands3,4. Therefore, there is a need to investigate the effects of different osteotomy directions, especially the buccal osteotomy, on post-SARPE expansion patterns.
Several finite element analysis (FEA) models have been set up to evaluate the force distribution during SARPE. However, the amount of expansion set in these models is limited to up to 1 mm, which is far below the required clinical amount6,7,8,9,10,11,12. Inadequate expansion in FEA models can lead to erroneous predictions of post-SARPE outcomes. More specifically, the collision between the bones at the osteotomy site, as reported by Chamberland and Proffit4, may not be demonstrated if the expander is not adequately turned, which may not reflect the true clinical reality. With the limited amount of expansion built in the previous models, the outcome evaluations of these models were focused on stress analysis. However, the stress analysis of FEA in dentistry is usually conducted under static loading with the mechanical properties of materials set as isotropic and linearly elastic, which further restricts the clinical relevance of the FEA studies13.
Furthermore, most of these studies did not consider the thickness of the surgical instrument at the osteotomy site6,7,8,10,11,12, often setting friction to zero at the cuts as part of the boundary conditions. However, this setting oversimplifies the contacts between the hard and soft tissues. It may significantly impact the distribution of force and the resulting expansion pattern of the hemimaxillae.
Nevertheless, no available literature has investigated the effect of osteotomy on post-SARPE asymmetry using finite element analysis (FEA) models. All the current studies employed models with symmetrical osteotomy patterns6,7,8,9,10,11,12,14, which do not reflect the reality of clinical practice where the osteotomies may differ on each side of the skull. The lack of literature examining the effect of asymmetrical osteotomies on post-SARPE asymmetry represents a significant knowledge gap that must be addressed.
Therefore, the goal of this study is to develop a novel FEA model of SARPE that can truly mimic the clinical conditions, including the expansion amount and osteotomy gap, and investigate the expansion patterns of the hemimaxillae in all three dimensions with various designs of the osteotomy. Such an approach would provide valuable insight into the mechanics underlying post-SARPE expansion patterns and serve as a useful tool for clinicians in the planning and execution of SARPE procedures.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Ansys</td>
			<td>Ansys</td>
			<td>Version 2019</td>
			<td>Ansys is a software for finite element analysis that can solve complicated models based on differential equations. The expansion results of different buccal osteotomy angles were analyzed through this software.</td>
		</tr>
		<tr>
			<td>Geomagic Studio</td>
			<td>3D Systems</td>
			<td>Version 10</td>
			<td>Geomagic Studio is a software for reverse engineering that can generate digital models based on physical scanning points. This study built cancellous bone and periodontal ligaments through this software.</td>
		</tr>
		<tr>
			<td>Mimics</td>
			<td>Materialise</td>
			<td>Version 16</td>
			<td>Mimics is a medical 3D image-based engineering software that efficiently converts CT images to a 3D model. This study reconstructed a maxilla complex through the patient&#39;s DICOM images.</td>
		</tr>
		<tr>
			<td>SolidWorks</td>
			<td>Dassault Syst&#232;mes</td>
			<td>Version 2018</td>
			<td>SolidWorks is a computer-aided design software for designers and engineers to create 3D models. A Haas expander was designed and drawn through this software in this study.</td>
		</tr>
	</tbody>
</table>

finite element analysis model for assessing expansion patterns from surgically assisted rapid palatal expansion

Surgically assisted rapid palatal expansion (SARPE) was introduced to release bony resistance to facilitate skeletal expansion in skeletally mature patients. However, asymmetric expansion between the left and right sides has been reported in 7.52% of all SARPE patients, of which 12.90% had to undergo a second surgery for correction. The etiologies leading to asymmetric expansion remain unclear. Finite element analysis has been used to evaluate the stress associated with SARPE in the maxillofacial structures. However, as a collision of the bone at the LeFort I osteotomy sites occurs only after a certain amount of expansion, most of the existing models do not truly represent the force distribution, given that the expansion amount of these existing models rarely exceeds 1 mm. Therefore, there is a need to create a novel finite element model of SARPE that could perform a clinically required amount of expander activation for further analysis of the expansion patterns of the hemimaxillae in all three dimensions. A three-dimensional (3D) skull model from cone beam computed tomography (CBCT) was imported into Mimics and converted into mathematical entities to segment the maxillary complex, maxillary first premolars, and maxillary first molars. These structures were transferred into Geomagic for surface smoothing and cancellous bone and periodontal ligament creation. The right half of the maxillary complex was then retained and mirrored to create a perfectly symmetrical model in SolidWorks. A Haas expander was constructed and banded to the maxillary first premolars and first molars. Finite element analysis of various combinations of buccal osteotomies at different angles with 1 mm clearance was performed in Ansys. A convergence test was conducted until the desired amount of expansion on both sides (at least 6 mm in total) was achieved. This study lays the foundation for evaluating how buccal osteotomy angulation influences the expansion patterns of SARPE.

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques 

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion

SARPE is commonly used for maxillary expansion in skeletal immature patients. However, asymmetric expansion has been reported with unknown etiologies. This study aims to develop a novel FEA model of SARPE that can truly mimic the clinical conditions, and to investigate the expansion patterns of the hemi-maxilla in all three dimensions.Finite element analysis has been used in the dental and bioengineering field to allow in vitro simulation of surgeries, such as SARPE. In this study, four software were utilized to set up the FEA model and to predict expansion pattern. The most challenging part, which most previous studies link, is to simulate forces at the wound healing site across osteotomy surface.To achieve this, springs were set in our pilot study and is considered a novel design for SARPE FEA. This unified element model focused on its patient patterns, making it more realistic SARPE simulation through osteotomy gap creation and experience inclusion. It presents significant potential as the clinical tool for branding and its guiding SARPE procedures.Our interdisciplinary group will work diligently to develop cutting-edge 3D models that can provide valuable insights into personalized treatment strategies to analyze and improve orthognatic surgical technique by utilizing an engineering-assisted approach and to improve communication and collaboration between orthodontists and oral maxillofacial surgeons through engineering-assisted 3D imaging system.

The demonstration model utilized the CBCT image of a 47-year-old female with maxillary deficiency. In the generated model, the anatomic structure of the nasal cavity, the maxillary sinus, and the periodontal ligament space for the expander anchored teeth (first premolar and first molar) are preserved (Figure 1).
To simulate the surgical procedure accurately, the nasal septum, lateral walls of the nasal cavity, and pterygomaxillary fissure were separated from the m...

Watch this Scientific Journal Video about Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques at JoVE.com

A set of novel finite element models of surgically assisted rapid palatal expansion (SARPE) that could perform a clinically required amount of expander activation with various angles of buccal osteotomy was created for further analysis of the expansion patterns of the hemimaxillae in all three dimensions.

Surgically assisted rapid palatal expansion (SARPE) was introduced to release bony resistance to facilitate skeletal expansion in skeletally mature ...

finite-element-analysis-model-for-assessing-expansion-patterns-from