|Year : 2021 | Volume
| Issue : 5 | Page : 415-422
Applications of finite element analysis in dentistry: A review
Shruti Shivakumar1, Vishal Shrishail Kudagi2, Priyanka Talwade1
1 Department of Pedodontics and Preventive Dentistry, JSS Dental College and Hospital, JSS AHER, Mysore, Karnataka, India
2 Department of Orthodontics, JSS Dental College and Hospital, JSS AHER, Mysore, Karnataka, India
|Date of Submission||21-Jan-2021|
|Date of Decision||21-May-2021|
|Date of Acceptance||01-Jun-2021|
|Date of Web Publication||11-Oct-2021|
Dr. Vishal Shrishail Kudagi
Department of Orthodontics, JSS Dental College and Hospital, JSS AHER, Mysore 570 015, Karnataka.
Source of Support: None, Conflict of Interest: None
Aim: This review highlights the fundamentals of finite element analysis (FEA) and its applications in various fields in dentistry. FEA is a computer-based numerical technique for calculating the strength and behavior of structures. It can be used to calculate deflection, stress, vibration, buckling behavior, and many other phenomena. Established knowledge regarding applications and limitations of FEA which are published are discussed in detail which can aid in identifying the caveats in research. Materials and Methods: Various literature sources were selected through a search of PubMed, Scopus, Web of Sciences, Google Scholar, and other electronic databases and were subjected to intense scrutiny under the search title “Finite Element Analysis in Dentistry.” We identified and reviewed most relevant and recent work mostly indexed in Scopus and PubMed. Results: A simple search on Google Scholar resulted in 144,000 scientific articles and 17,200 articles since 2017. Most of the articles were related to the application of FEA in implant dentistry. Forty-four such articles were included in this review. Conclusion: Based on our literature search, we came to the conclusion that applications of Finite Element Analysis in Dentistry are myriad and this technology is constantly upgrading. This review will provide an update on the current state of scientific knowledge in this field that encompasses all areas of dentistry. We also emphasise the need for further research in this area.
Keywords: Computer Simulation, Dental Material, Dentistry, Finite Element Analysis, Material Science
|How to cite this article:|
Shivakumar S, Kudagi VS, Talwade P. Applications of finite element analysis in dentistry: A review. J Int Oral Health 2021;13:415-22
|How to cite this URL:|
Shivakumar S, Kudagi VS, Talwade P. Applications of finite element analysis in dentistry: A review. J Int Oral Health [serial online] 2021 [cited 2023 Mar 27];13:415-22. Available from: https://www.jioh.org/text.asp?2021/13/5/415/327861
| Introduction|| |
A new era in dentistry has dawned with the advent of various innovations in technology like nano-science technology and other bio-engineering technologies whose applications in the field of dentistry is expanding exponentially.
The merging of biological sciences and engineering sciences through various technological developments has led to the precise understanding of the nature and properties of human tissues as well as different materials and techniques used in dentistry at a microbiological and ultrastructural level. One such development in the field of engineering is Finite element method (FEM) or Finite element analysis (FEA) which has become a very important research tool in dentistry to understand the behavior of various material and techniques.
The FEA method was developed in 1956. In the initial years of its conception, it was primarily used in aerospace engineering. Gradually, owing to this technique’s versatility and the ability to simulate complex geometries and obtain speedy results, it made its way into medical fields especially dentistry. It was first used in dentistry in the 1970s as a substitute for photoelasticity tests.
The development in computers and availability of powerful microcomputers has brought this method within the reach of students and engineers. FEA is used in all fields of dentistry especially in implant dentistry.
Though there have been many review articles on FEA, the field still seems a big mystery to many dentists due to complex mathematical and engineering terminologies used. Digital world is changing and upgrading every second and any topic relating to this area needs to be updated constantly to keep up with the current research trends. So, the aim of this review is to update and simplify the concepts of FEA and make it more understandable from a dentist’s perspective. This article also aims to address its various applications in dentistry and its limitations.
This review gives an insight into FEA which has totally overshadowed other experimental analysis due to its ability to model even the most complex of geometries with its immensely flexible and adaptable nature.
| Materials and Methods|| |
Records were identified by searching through databases of PubMed, Scopus, Web of Sciences, Embase, and Google scholar.
A random search on google scholar by “Finite Element Analysis in Dentistry” showed 149,000 articles till the year 2021 (April). Customized search showed 17,700 articles since 2017 to 2021.
English language articles with completed texts were included. Further refinement for latest relevant articles published 2017 onwards was executed.
A search was also done in Scopus database under the same key words which revealed 540 relevant primary documents which were indexed in Scopus from the year 1974 to 2021 and 27 secondary documents which are not indexed in Scopus. Also, the Scopus search showed various patents relating to the key words (726). Most of these studies and reviews were published under the engineering subject area accounting to 320 articles. And surprisingly, the second in the list were the ones listed under the subject area of dentistry with 168 documents. These were followed by material sciences, computer sciences and medicine subject areas. Literature search in PubMed database showed 4237 articles from 1973 to 2021 of which 20 articles were systematic reviews, 109 articles were narrative reviews and 5 articles were meta-analysis. Our literature search concluded in April 2021, after which we identified and reviewed the most updated and relevant articles for a narrative discussion. The total number of articles finalized and referred for this narrative review is 44 with most of the articles being indexed in Scopus and PubMed. The types of articles included were published reviews and original research articles.
The aim of this narrative review was to consolidate findings on applications of “Finite Element Analysis in Dentistry” and to clarify current understanding of the area in a simplified manner. Due to the relative lack of publications on the subject matter, the authors chose to include all relevant studies conducted as recently as 2021 to as early as 1973.
| Results|| |
The process of deciding the inclusion criteria is explained using a flow chart [Figure 1]. This process resulted in 44 scientific articles which were included in the final step. As per the requirements for a narrative review, the articles were perused and analyzed to investigate the rationale for utilizing FEA as an efficient tool in different areas of dentistry. We also extracted information regarding the limitations of FEM. The screened articles were assessed independently by two separate authors to prevent bias.
| Discussion|| |
What is FEA?
In FEA, the behavior of a particular physical system is mathematically simulated. A continuous structure is divided into different elements, which maintain the properties of the original structure. Each of these elements is described by differential equations and solved using mathematical models selected according to the data under investigation.
Such a structural analysis allows the determination of stress and strain resulting from external force, pressure, thermal change, and other factors. Since it is impossible to quantify the stress and strain in human tissues in response to an external force, this method is extremely useful for assessing the mechanical aspects of biomaterials in human tissues that is very challenging to study directly on human subjects owing to ethical considerations in conducting the research., The results obtained can then be studied using visualization software within the FEA environment to view a variety of parameters, and to fully identify implications of the analysis.
2D and 3D modeling are the types of analysis used. Although 2D modeling is very user friendly which requires simple computers, it has a major drawback of its inability to provide accurate results. They also do not take plastic deformity into consideration. 3D analysis has its precision as a major advantage. However, it requires advanced computer set up which has a higher processor.
Steps involved in FEA method
Any engineering problem can be deduced by using one of the three methods which consists of numerical, experimental, or analytical. FEA is categorized under numerical method for studying designs which consists of a simulated computer model of a structure that undergoes a required command and is evaluated for specific results.
The basic steps involved in FEA include pre-processing, processing, or solution and post-processing. In the pre-processing step, data are obtained by CAD (computer-aided designing) or CT to construct a 2D or 3D model [Figure 2] followed by meshing [Figure 3] and [Figure 4], and boundary conditions [Figure 5]. In the processing or solution step, calculations are done using appropriate computer software which executes matrix formulations, inversion, multiplications, and finally derives at the solution. This solution or the conclusive design is further verified and refined as per requirement in the post-processing step.
FEA uses a “mesh” [Figure 3] which is a grid consisting of a complex system of points (nodes) and elements. Through various programs this mesh is made to hold specific material and structural properties [listed in [Table 1]]. These properties determine the reactions of the structure to different loading conditions. The most important aspect of the analysis is assigning appropriate material properties to the FEM model for precise simulation of the behavior of the object evaluated. Stress and strain distribution in an object is highly influenced by the material properties which can be simulated in FEA as anisotropic, orthotropic, isotropic, and transversely isotropic. The properties remain alike in all direction. Therefore, only two independent material constants of Young’s modulus and Poisson’s ratio exist in an isotropic material.
The mesh basically behaves like a spider web. Each node or point connects a mesh element to adjacent nodes. The rationale is to compute at limited or finite number of points and to build the results for the complete domain (surface or volume). But as all living components are continuous and have infinite degree of freedom (dofs) it is an unattainable task to infer a problem in this particular format which necessitates the reduction of degree of freedom (dofs) from infinite to finite, wherein the applicability of FEM comes into action. FEM reduces the dofs from infinite to finite with the help of meshing (nodes and elements).
The boundary conditions in FEA models basically represent the load imposed on the structures under study and the area of the model which is restrained [Figure 5]. To ensure an equilibrated solution, zero constraints must be placed on some boundaries. To prevent overlapping of the stress and strain associated with reaction forces the constraints should be placed on nodes that are distant from the area of interest.
Software used in FEA method:,
The various softwares used in FEA are:
Abaqus Explicit - SIMULIA by Dassault Systèmes, France.
Ansys by Ansys Inc., Canonsburg, Pennsylvania, USA.
Femfat, Magna international, Canada.
Hypermesh, Altair Engineering, USA.
Ls – dyna, Ansys Inc., Canonsburg, Pennsylvania, USA.
Madymo, TASS International, Helmond, The Netherlands.
Magmasoft, Magma Gieberetechnologie, Aechen, Germany.
Nastran, MSC California, USA.
Star-CD, CD Adaptico, Millville, USA.
Tosca, Tricentis, Vienna, Austria.
Uni-Graphics, Siemens PLM, Plano, Texas, USA, etc.
Applications of FEA method in different aspects of dentistry and research
Its versatility and ease of operation has made it effective in all spheres of engineering like aeronautical, automobile, biomedical, and electrical engineering. Application of FEA method is most commendable in crash testing procedures in automobile industries., In the recent years, it has shown overwhelming efficiency and exactitude in its applications in dentistry.
Applications of FEA method in orthodontics
FEA has been an aid in describing form changes in biological structures (morphometrics), especially in the area of craniofacial growth and development. Therefore, it is a very important tool in craniofacial research. FEA is helpful to assess the effect of using different mini-screw materials by comparing stress levels generated by each of them. It also aids in assessing different angulations of insertion for different stress levels and analyzing the biomechanical effect of abutment on stability of mini-screws., FEA aids in the investigation of orthodontic biomechanics and tooth movement. There have been several studies in which the 3D orthodontic force measurements and lingual orthodontic system have been evaluated using FEA. It is a pre-requisite assessment tool in studying growth modulation and myo-functional therapy and analyzing different mechanical aspects in orthodontic treatment and planning.,,
Applications in operative dentistry and endodontics
A recent study by Correia and Andrade investigated the influence of bulk-fill restoration on polymerization shrinkage stress and marginal gap formation in class 5 restorations. This study evaluated the influence of Class V cavity extension and restorative material on the marginal gap formation, before and after aging, and the theoretical polymerization shrinkage stress distribution in a tooth restoration. FEM was used to investigate the hypothesis. Therefore, it aids to optimize the design of dental restorations and to determine the strength and effectiveness of different restorative material.
FEA can also be applied in analyzing stress and strain relations in restoring teeth using posts and cores. For example, effects of posts on dentin stress distribution and stress analysis of tooth restored with post and core can be evaluated using FEA method and to analyze stress distribution in tooth with cavity preparation and biomechanical preparation during root canal treatment.,
Applications in periodontics
FEA guides in efficient analysis of stresses produced in the periodontal ligament under different orthodontic forces and loading conditions and to conduct in-vitro and in-vivo natural frequency analysis of periodontal conditions in an innovative approach. Deformation and recovery cycle in the periodontal ligament can also be studied in an accurate way. A research was conducted to assess the stress concentration in simulated periodontal alveolar bone containing healthy teeth with and without attachment loss using FEM and concluded that attachment loss increases stress concentration in the surrounding bone suggesting a partly explanation regarding bone resorption risk for teeth with periodontal attachment loss. Also, it is an efficient tool in skeletal tissue engineering.
Applications in prosthodontics
The applications of FEA in the specialty of prosthodontics are myriad from designing prosthesis and crowns. FEA is utilized to study stress distribution in supporting structures of tooth in relation to different designs of fixed and removable prosthesis. FEA is also used to analyze material behavior, material failures, and successes in various types of prosthetic rehabilitations.,
Applications in implant dentistry
The use of dental implants has enabled the fabrication of highly functional and esthetic restorations and improved the predictability of treatment. The importance and application of FEA in implant dentistry is paramount which can also be considered essential. In implant dentistry, commonly used materials in FEA studies can be classified as either implant, peri-implant bone (cortical and cancellous bone), or restoration. FEA method allows application of simulated forces at specific points in the system and stress analysis in the peri-implant region and surrounding structures. The nature of response of the bone tissue to an implant that may act as a foreign insert has been an area of interest since its popularity in dental clinics. However, long-term effects of such stresses are not studied adequately. A clear scientific understanding based on intense research can help reduce untoward stress effects on the surrounding bony structures. One of the paramount causes for implant failure is the stress shielding effect which is the bone remodeling induced by the change of normal biological stresses. Using finite element method and innovative designing, the stress- shielding effects can be reduced.,, Reddy and Sundaram systematically reviewed the applications of finite element model in implant dentistry in 2019. Their review concurred the knowledge about FEA outcomes that can give detailed structure of the bone around the implant and that of the implant that is being simulated behavior of the material, boundary, and loading conditions, interface between bone and implant, convergence test and validation.
Applications in pedodontics and preventive dentistry
FEA can be employed in pediatric and preventive dentistry as well, especially to study traumatic injuries in orofacial structures and to study human head impact simulations., A recent study investigated the use of mouth guards on biomechanical response of an ankylosed maxillary central incisors during traumatic impact using FEA. Finite element models can also be applied in cleft lip and palate area. Parveen and Reddy studied the nature of stress and displacement on craniofacial system during treatment of unilateral cleft lip and palate model. The protraction therapy was studied with different forces and directions. Their findings were interesting with one observation being that asymmetric displacement was higher in dental structures than skeletal and more on the non-cleft side. FEM can also be used to analyze the outcomes of different treatment modalities in cleft lip and palate repair. A study assessed the 3D morphologic changes in the craniofacial component in cleft clip and palate repair using naso-alveolar molding technique pre-surgically.
Applications in the management of temporomandibular joint disorders and Bruxism
Temporomandibular joint anatomy can be assessed using FEM and CBCT. TMDs have a multifactorial etiology, bruxism and trauma being one of them. But the relation between bruxism and TMD remains a confusion. FEM finds its application in its ability to quantify bruxism and also investigate the stress and strain relationships surrounding the temporomandibular joint area. Scientists are also aiming to determine the stress distributions in the mandible, teeth, and PDL during clenching, grinding, and chewing with different sized boluses, also when dental implants are incorporated at different positions of the mandible. FEM is also used to study the outcomes of TMJ replacement therapy., Mandibular advancement devices used in the management of sleep apnea can be evaluated using FEM. A study using FEM and simulated maxilla and mandible were able to emphasis the ability of splints, which acts as a stress dissipator in the management of bruxism.
Reddy et al. and Srirekha et al. have outlined the advantages and limitations in a simplified manner.,
Advantages of FEM
Minimizes the need for animal studies and unethical human trials.
The technique is not invasive.
It enables the visualization of superimposed structures.
Analysis of material properties of craniofacial structures and their geometries is easier.
Direction and magnitude of the force applied can be located precisely.
Theoretical measurement of stress points is possible.
Unaltered physical properties of the evaluated materials.
Repetition of the test can be done multiple times
Both static and dynamic analyses can be executed.
The technique is time efficient.
Limitations of FEM
This method is technique sensitive.
The researcher needs to have an in-depth understanding in material sciences.
Errors in inputs, statistics, and result interpretation can lead to incorrect output.
Need to be computer savvy.
Certain expectations are bound to be accepted. Hence, outcomes will be determined by people associated in the study.
FEM is not time-dependent. Biological dynamics of a living component cannot be modeled with precision as it is difficult to take factors like time and other exposures the structure is subjected to take into account.
Requirement for large data input for the mesh used in terms of nodal connectivity and other parameters depending on the problem.
| Conclusion|| |
With rapid improvements and developments of computer technology, the FEA has become a powerful technique in dental research because of its versatility in calculating stress distributions within complex structures. It is also a great assessment tool in research investigations where animal and human models cannot be deployed due to ethical consideration. Knowledge of the fundamental principles, method, applications and drawbacks of FEM, the dentist will be in a better position to study the results of FEM and apply the same to clinical cases.
Thus, it is a beneficent, efficient, and essential tool to evaluate the influence of model parameter variations once a basic model is correctly defined. Further research should focus in analyzing stress distributions under dynamic loading conditions of mastication, which would better mimic the actual clinical situation. One of the authors of this review, Kudagi, conducted a three-dimensional finite element study in 2017 to evaluate the efficacy of transpalatal arch as an anchorage reinforcement unit during orthodontic space closure and we as a team are intending to conduct research in future in different areas of dentistry utilizing this time tested tool of FEA.
We are grateful for the support provided by JSS academy of Higher Education and Research (JSSAHER), Mysore, India.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
Ethical policy and Institutional Review board statement
Patient declaration of consent
Data availability statement
We confirm that the data supporting the review article are available within the article and also provided in the references which are available in Google Scholar, Scopus, and PubMed databases.
| References|| |
Tang G, Galluzzi M, Zhang B, Shen YL, Stadler FJ. Biomechanical heterogeneity of living cells: Comparison between atomic force microscopy and finite element simulation. Langmuir 2019;35:7578-87.
Thresher RW, Saito GE. The stress analysis of human teeth. J Biomech 1973;6:443-9.
Marcián P, Wolff J, Horáčková L, Kaiser J, Zikmund T, Borák L. Micro finite element analysis of dental implants under different loading conditions. Comput Biol Med 2018;96:157-65.
Boccaccio A, Uva AE, Fiorentino M, Monno G, Ballini A, Desiate A. Optimal load for bone tissue scaffolds with an assigned geometry. Int J Med Sci 2018;15:16-22.
Szucs A, Bujtár P, Sándor GK, Barabás J. Finite element analysis of the human mandible to assess the effect of removing an impacted third molar. J Can Dent Assoc 2010;76:a72.
Gokhale N, Deshpande S, Bedekar B, Thite A. Practical Finite Element Analysis. 1st ed. Pune: Finite to Infinite; 2008.
Tajima K, Nikaido T, Inoue G, Ikeda M, Tagami J. Effects of coating root dentin surfaces with adhesive materials. Dent Mater J 2009;28:578-86.
Srirekha A, Bashetty K. Infinite to finite: An overview of finite element analysis. Indian J Dent Res 2010;21:425-32.
] [Full text]
Kul E, Korkmaz İH. Effect of different design of abutment and implant on stress distribution in 2 implants and peripheral bone: A finite element analysis study. J Prosthet Dent2021:S0022-3913(20)30736-8. doi: 10.1016/j.prosdent.2020.09.058.
Romanyk DL, Vafaeian B, Addison O, Adeeb S. The use of finite element analysis in dentistry and orthodontics: Critical points for model development and interpreting results. Semin Orthod 2020;26:162-73.
Zadi ZH, Bidhendi AJ, Shariati A, Pae EK. A clinically friendly viscoelastic finite element analysis model of the mandible with Herbst appliance. Am J Orthod Dentofacial Orthop 2020. https://doi.org/10.1016/j.ajodo.2020.04.017
Gupta M, Madhok K, Kulshrestha R, Chain S, Kaur H, Yadav A. Determination of stress distribution on periodontal ligament and alveolar bone by various tooth movements–A 3D FEM study. J Oral Biol Craniofac Re 2020;10:758-63.
Malde O, Libby J, Moazen M. An overview of modelling craniosynostosis using the finite element method. Mol Syndromol 2019;10:74-82.
Takeshita S, Sasaki A, Tanne K, Publico AS, Moss ML. The nature of human craniofacial growth studied with finite element analytical approach. Clin Orthod Res 2001;4:148-60.
Mascarenhas R, Parveen S, Shenoy BS, Kumar GS, Ramaiah VV. Infinite applications of finite element method. J Indian Orthod Soc 2018;52(4_suppl2):142-50.
Sugii MM, Barreto BCF, Francisco Vieira-Júnior W, Simone KRI, Bacchi A, Caldas RA. Extruded upper first molar intrusion: Comparison between unilateral and bilateral miniscrew anchorage. Dental Press J Orthod 2018;23:63-70.
Jain V, Shyagali TR, Kambalyal P, Rajpara Y, Doshi J. Comparison and evaluation of stresses generated by rapid maxillary expansion and the implant-supported rapid maxillary expansion on the craniofacial structures using finite element method of stress analysis. Prog Orthod 2017;18:3.
Kushwah A, Kumar M, Goyal M, Premsagar S, Rani S, Sharma S. Analysis of stress distribution in lingual orthodontics system for effective en-masse retraction using various combinations of lever arm and mini-implants: A finite element method study. Am J Orthod Dentofacial Orthop 2020;158:e161-72.
Singh JR, Kambalyal P, Jain M, Khandelwal P. Revolution in orthodontics: Finite element analysis. J Int Soc Prev Community Dent 2016;6:110-4.
Cattaneo PM, Cornelis MA. Orthodontic tooth movement studied by finite element analysis: An update. What can we learn from these simulations? Curr Osteoporos Rep2021;19:175-81.
Huiskes R, Chao EY. A survey of finite element analysis in orthopedic biomechanics: The first decade. J Biomech 1983;16:385-409.
Correia A, Andrade MR, Tribst J, Borges A, Caneppele T. Influence of bulk-fill restoration on polymerization shrinkage stress and marginal gap formation in class V restorations. Oper Dent 2020;45:E207-16.
Ausiello P, Ciaramella S, De Benedictis A, Lanzotti A, Tribst JP, Watts DC. The use of different adhesive filling material and mass combinations to restore class II cavities under loading and shrinkage effects: A 3D-FEA. Comput Method Biomech Biomed Eng2020:1-11.
Zhang Y, Liu Y, She Y, Liang Y, Xu F, Fang C. The effect of endodontic access cavities on fracture resistance of first maxillary molar using the extended finite element method. J Endod 2019;45:316-21.
Corsentino G, Pedullà E, Castelli L, Liguori M, Spicciarelli V, Martignoni M, et al
. Influence of access cavity preparation and remaining tooth substance on fracture strength of endodontically treated teeth. J Endod 2018;44:1416-21.
Reddy RT, Vandana KL. Effect of hyperfunctional occlusal loads on periodontium: A three-dimensional finite element analysis. J Indian Soc Periodontol 2018;22:395-400.
] [Full text]
da Rocha MC, da Rocha DM, Tribst JPM, Borges ALS, Alvim-Pereira F. Reduced periodontal support for lower central incisor - A 3D finite element analysis of compressive stress in the periodontium. J Int Acad Periodontol 2021;23:65-71.
Hendrikson WJ, van Blitterswijk CA, Rouwkema J, Moroni L. The use of finite element analyses to design and fabricate three-dimensional scaffolds for skeletal tissue engineering. Front Bioeng Biotechnol 2017;5:30.
Schmid A, Strasser T, Rosentritt M. Finite element analysis of occlusal interferences in dental prosthetics caused by occlusal adjustment. Int J Prosthodont 2021. doi:10.11609/ijp.7178.
Coelho C, Calamote C, Pinto AC, Esteves JL, Ramos A, Escuin T, et al
. Comparison of CAD-CAM and traditional chairside processing of 4-unit interim prostheses with and without cantilevers: Mechanics, fracture behavior, and finite element analysis. J Prosthet Dent 2021;125:543.e1-10.
Markose J, Suresh S, Eshwar S, Rekha K, Jain V, Manvi S. Comparison of platform switched and sloping shoulder implants on stress reduction in various bone densities: Finite element analysis. J Contemp Dent Pract 2017;18:510-5.
Küçükkurt S, Alpaslan G, Kurt A. Biomechanical comparison of sinus floor elevation and alternative treatment methods for dental implant placement. Comput Method Biomech Biomed Engin 2017;20:284-93.
Yashwant AV, Dilip S, Krishnaraj R, Ravi K. Does change in thread shape influence the pull out strength of mini implants? An in vitro study. J Clin Diagn Res 2017;11:ZC17-20.
Reddy MS, Sundram R, Abdemagyd HA. Application of finite element model in implant dentistry: A systematic review. J Pharm Bioallied Sci 2019;11:85.
Madhukar A, Ostoja-Starzewski M. Finite element methods in human head impact simulations: A review. Ann Biomed Eng 2019;47:1832-54.
Diac MM, Oprea RC, Iov T, Damian SI, Knieling A, Iliescu AI. Finite elements models of the head in craniocerebral trauma–review. Brain 2020;11:08-21.
Borges ALS, Dal Piva AMO, Concílio LRDS, Paes-Junior TJA, Tribst JPM. Mouthguard use effect on the biomechanical response of an ankylosed maxillary central incisor during a traumatic impact: A 3-dimensional finite element analysis. Life (Basel) 2020;10:294.
Parveen S, Husain A, Gosla Reddy S, Mascarenhas R, Shenoy S. Three-dimensional finite element analysis of initial displacement and stress on the craniofacial structures of unilateral cleft lip and palate model during protraction therapy with variable forces and directions. Comput Method Biomech Biomed Engin 2020:1-7.
Huang H, Luo X, Cheng X, Zhang Z, Ma G, Shi B, et al
. Recapitulation of unilateral cleft lip nasal deformity on normal nasal structure: A finite element model analysis. J Craniofac Surg 2018;29:2220-5.
Sagl B, Schmid-Schwap M, Piehslinger E, Kundi M, Stavness I. A dynamic jaw model with a finite-element temporomandibular joint. Front Physiol 2019;10:1156.
Bekcioglu B, Bulut E, Bas B. The effects of unilateral alloplastic temporomandibular joint replacement on the opposite-side natural joint: A finite-element analysis. J Oral Maxillofac Surg 2017;75:2316-22.
Caragiuli M, Mandolini M, Landi D, Bruno G, De Stefani A, Gracco A, et al
. A finite element analysis for evaluating mandibular advancement devices. J Biomech 2021;119:110298.
Oliveros-López LG, Castillo-de-Oyagüe R, Serrera-Figallo MÁ, Martínez-González ÁJ, Pérez-Velasco A, Torres-Lagares D, et al
. Bone loss in bruxist patients wearing dental implant prostheses: A finite element analysis. Metals (Basel) 2020;10:1132.
Kudagi V, Vijay N, Kumar HK, Shetty K. Efficacy of transpalatal arch as an anchorage reinforcing unit during orthodontic space closure: A three-dimensional finite element study. APOS Trends Orthod 2017;7:94. [Full text]
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]