medalphabetМедицинский алфавитMedical alphabet2078-56312949-2807ООО «Альфмед»10.33667/2078-5631-2023-1-18-23medalphabet-3002Research ArticleСтатьиПрименение метода конечно-элементного анализа при разработке новых систем дентальных имплантатов. Обзор литературыApplication of the finite element analysis in the development of new dental implant systems. Literature reviewhttps://orcid.org/0000-0002-6183-2586СергеевЮ. А.SergeevYu. A.

Юрий Андреевич Сергеев, заочный аспирант

кафедра стоматологии общей практики и детской стоматологии

Ставрополь

Yuriy Andreevich Sergeev, Postgraduate Student

Department of General Practice and Pediatric Dentistry

Stavropol

serg_yuriy@mail.ruhttps://orcid.org/0000-0002-6352-6750ДолгалевА. А.DolgalevA. A.

Александр Александрович Долгалев, д. м. н., профессор, начальник центра

кафедра стоматологии общей практики и детской стоматологии

центр инноваций и трансфера технологий научно-инновационного объединения

Ставрополь

Alexander Alexandrovich Dolgalev, MD, Head of the Center, Professor

Center for Innovation and Technology Transfer

Department of General Practice Dentistry and Pediatric Dentistry

Stavropol

dolgalev@dolgalev.proЧониашвилиД. З.ChoniashviliD. Z.

Давид Зурабович Чониашвили, к. м. н., доцент, декан

медицинский факультет

кафедра терапевтической, хирургической и детской стоматологии с курсом имплантология, реконструктивная хирургия полости рта, детская ЧЛХ

Владикавказ

David Zurabovich Choniashvili, Candidate of Medical Sciences, Associate Professor, Dean

Medical Faculty

Department of Therapeutic, Surgical and Pediatric Dentistry with courses inImplantology, Reconstructive Oral Surgery, Pediatric maxillofacial surgery

Vladikavkaz

davidchoniashvili@mail.ruhttps://orcid.org/0000-0002-0316-5957АванисянВ. М.AvanisyanV. M.

Вазген Михайлович Аванисян, ординатор 1 года обучения

кафедра терапевтической стоматологии

Ставрополь

Vazgen Mikhailovich Avanisyan, 1-st year resident

Department of Therapeutic Dentistry

Stavropol

avanvaz@yandex.ruФГБОУ ВО «Ставропольский государственный медицинский университет» Министерства здравоохранения РФРоссияStavropol State Medical University of the Ministry of Health of the Russian FederationRussian FederationФГБОУ ВО «Северо-Осетинский государственный университет имени Коста Левановича Хетагурова» (СОГУ)РоссияFederal State Budgetary Educational Institution of Higher Professional Education «Kosta Khetagurov North Ossetian State University» (NOSU)Russian Federation20231703202311Стоматология (1)1823Copyright © Сергеев Ю.А., Долгалев А.А., Чониашвили Д.З., Аванисян В.М., 20232023Сергеев Ю.А., Долгалев А.А., Чониашвили Д.З., Аванисян В.М.Sergeev Y.A., Dolgalev A.A., Choniashvili D.Z., Avanisyan V.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.med-alphabet.com/jour/article/view/3002

   Введение. Разработка новых дентальных имплантатов в условиях бурно развивающейся отечественной промышленности позволяет найти альтернативные возможности при лечении клинически сложных ситуаций, подобрать необходимое индивидуальное решение при проведении операции дентальной имплантации, а соответственно выполнить операцию безошибочно и достичь желаемых результатов. Однако разработка дентального имплантата является сложным многоступенчатым процессом, в связи с чем необходимо досконально изучить как характеристики материала, из которого изготавливается имплантат, так и его биофизические особенности до момента его интеграции в костную ткань.   Цель работы: по данным литературных источников оценить возможности и особенности применения метода конечных элементов при разработке новых систем дентальных имплантатов.   Материал и методы. Был проведен поиск в отечественных электронных библиотеках e-library, «КиберЛенинка», а также PubMed, Medline, Web of Science и Google Scholar по следующим ключевым словам: дентальный имплантат, конечно-элементный анализ, математическая модель. Было отобрано и проанализировано 66 работ.   Результаты. Метод конечных элементов является точным методом анализа разрабатываемого имплантата, однако имеет определенные ограничения, так как в конечно-элементной сетке граница раздела имплантата и кости представляет собой непрерывную связь. Отсутствие микродвижения на границе имплантата и кости во время нагрузки, в действительности, отличается от реальной клинической ситуации. Ожидаемая 100 % остеоинтеграция на основании 3D-моделирования не может быть идеальным вариантом и никогда не соответствует реальности в клинической ситуации. Однако использование метода конечных элементов позволяет протестировать одиночные нагрузки и углы наклона, что в клинической ситуации проявляется крайне редко.

   Introduction. The development of new dental implants in the context of the booming domestic industry makes it possible to find alternative options in the treatment of clinically difficult situations, to select the necessary individual solution during dental implant surgery, and consequently, to perform the surgery in an error-free manner and achieve the desired results. The development of a dental implant is a multistep process, and the characteristics of the implant material and its biophysical characteristics must be studied in detail until the implant is integrated into the bone tissue.   The aim of the study: to estimate the opportunities and prospects of applying the finite elements method by developing the new systems of dental implants according to the literature data.   Material and methods. A search was carried out in the national digital libraries e-library, CyberLeninka, as well as PubMed, Medline, Web of Science and Google Scholar using the following keywords: dental implant, finite-element analysis, mathematical model. Sixty-nine papers were selected and analysed.   Results. The finite element method is an accurate method to analyse the implant being developed, but it has certain limits, because in the finite element mesh, the implant-bone interface is a continuous relationship. The absence of micro-movement at the implant-bone interface during loading is different from the actual clinical situation. The expected 100 % osseointegration based on 3D-modelling can’t be an ideal option and never corresponds to the reality in the clinical situation. However, the use of the finite element method makes it possible to test single loads and inclination angles, which in the clinical situation is very rare.

биосовместимостьостеоинтеграциябиомеханикадентальный имплантатконечно-элементный анализматематическая модельbiocompatibilityosseointegrationbiomechanicsdental implantfinite element analysismathematical modelReferencesAnanth H.; Kundapur V.; Mohammed H.; Anand M.; Amarnath G.; Mankar S. A review on biomaterials in dental implantology. Int. J. Biomed. Sci. 2015, 11, 113.Ananth H.; Kundapur V.; Mohammed H.; Anand M.; Amarnath G.; Mankar S. A review on biomaterials in dental implantology. Int. J. Biomed. Sci. 2015, 11, 113.Kawahara et al. // Image synthesis with deep convolutional generative adversarial networks for material decomposition in dual-energy CT from a kilovoltage CT / Comput. Biol. Med.(2021).Kawahara et al. // Image synthesis with deep convolutional generative adversarial networks for material decomposition in dual-energy CT from a kilovoltage CT / Comput. Biol. Med.(2021).Marcián P. et al. // Micro finite element analysis of dental implants under different loading conditions / Comput. Biol. Med.(2018).Marcián P. et al. // Micro finite element analysis of dental implants under different loading conditions / Comput. Biol. Med.(2018).Chang P.-K.; Chen Y.-C.; Huang C.-C.; Lu W.-H.; Chen Y.-C.; Tsai H.-H. Distribution of micromotion in implants and alveolar bone with different thread profiles in immediate loading: A finite element study. Int. J. Oral Maxillofac. Implant. 2012, 27, e96–e101.Chang P.-K.; Chen Y.-C.; Huang C.-C.; Lu W.-H.; Chen Y.-C.; Tsai H.-H. Distribution of micromotion in implants and alveolar bone with different thread profiles in immediate loading: A finite element study. Int. J. Oral Maxillofac. Implant. 2012, 27, e96–e101.Dos Santos, M. C. L. G.; Campos, M. I. G.; Line, S. R. P. Early dental implant failure: A review of the literature. Braz. J. Oral Sci. 2002, 1, 103–111.Dos Santos, M. C. L. G.; Campos, M. I. G.; Line, S. R. P. Early dental implant failure: A review of the literature. Braz. J. Oral Sci. 2002, 1, 103–111.Han et al. // Continuous functionally graded porous titanium scaffolds manufactured by selective laser melting for bone implants / J. Mech. Behav. Biomed. Mater. (2018)Han et al. // Continuous functionally graded porous titanium scaffolds manufactured by selective laser melting for bone implants / J. Mech. Behav. Biomed. Mater. (2018)Himmlova, L.; Dostalova, T.; Kacovsky, A.; Konvickova, S. Influence of implant length and diameter on stress distribution: A finite element analysis. J. Prosthet. Dent. 2004, 91, 20–25Himmlova, L.; Dostalova, T.; Kacovsky, A.; Konvickova, S. Influence of implant length and diameter on stress distribution: A finite element analysis. J. Prosthet. Dent. 2004, 91, 20–25Jafari et al. // A comparative study of bone remodeling around hydroxyapatite-coated and novel radial functionally graded dental implants using finite element simulation/Med. Eng. Phys.(2022)Jafari et al. // A comparative study of bone remodeling around hydroxyapatite-coated and novel radial functionally graded dental implants using finite element simulation/Med. Eng. Phys.(2022)Kang, X.; Li, Y.; Wang, Y.; Zhang, Y.; Yu, D.; Peng, Y. Relationships of Stresses on Alveolar Bone and Abutment of Dental Implant from Various Bite Forces by Three-Dimensional Finite Element Analysis. Biomed Res. Int. 2020, 2020, 7539628.Kang, X.; Li, Y.; Wang, Y.; Zhang, Y.; Yu, D.; Peng, Y. Relationships of Stresses on Alveolar Bone and Abutment of Dental Implant from Various Bite Forces by Three-Dimensional Finite Element Analysis. Biomed Res. Int. 2020, 2020, 7539628.Schwitalla, A.; Abou-Emara, M.; Spintig, T.; Lackmann, J.; Müller, W. Finite element analysis of the biomechanical effects of PEEK dental implants on the peri-implant bone. J. Biomech. 2015, 48, 1–7.Schwitalla, A.; Abou-Emara, M.; Spintig, T.; Lackmann, J.; Müller, W. Finite element analysis of the biomechanical effects of PEEK dental implants on the peri-implant bone. J. Biomech. 2015, 48, 1–7.Bozkaya, D.; Muftu, S.; Muftu, A. Evaluation of load transfer characteristics of five different implants in compact bone at different load levels by finite elements analysis. J. Prosthet. Dent. 2004, 92, 523–530.Bozkaya, D.; Muftu, S.; Muftu, A. Evaluation of load transfer characteristics of five different implants in compact bone at different load levels by finite elements analysis. J. Prosthet. Dent. 2004, 92, 523–530.Cozzolino et al. // Implant-to-bone force transmission: a pilot study for in vivo strain gauge measurement technique / J. Mech. Behav. Biomed. Mater.(2019).Cozzolino et al. // Implant-to-bone force transmission: a pilot study for in vivo strain gauge measurement technique / J. Mech. Behav. Biomed. Mater.(2019).Dutta et al. // Design of porous titanium scaffold for complete mandibular reconstruction: the influence of pore architecture parameters / Comput. Biol. Med. (2019).Dutta et al. // Design of porous titanium scaffold for complete mandibular reconstruction: the influence of pore architecture parameters / Comput. Biol. Med. (2019).Li et al. // 3D porous Ti6Al4V-beta-tricalcium phosphate scaffolds directly fabricated by additive manufacturing / Acta Biomater. (2021).Li et al. // 3D porous Ti6Al4V-beta-tricalcium phosphate scaffolds directly fabricated by additive manufacturing / Acta Biomater. (2021).Sato et al. // The effects of bone remodeling on biomechanical behavior in a patient with an implant-supported overdenture / Comput. Biol. Med.(2021)Sato et al. // The effects of bone remodeling on biomechanical behavior in a patient with an implant-supported overdenture / Comput. Biol. Med.(2021)Wang Juncheng & Yang Sefei. (2017). Risk factors affecting osseointegration of implants: (eds.) Proceedings of the 8th Academic Conference of the General Stomatology Committee of the Chinese Stomatological Association (pp. 338).Wang Juncheng & Yang Sefei. (2017). Risk factors affecting osseointegration of implants: (eds.) Proceedings of the 8th Academic Conference of the General Stomatology Committee of the Chinese Stomatological Association (pp. 338).Cynthia S. Petrie D. D. S., M. S. and John L. Williams Ph. D. Shape optimization of dental implant designs under oblique loading using the p‐version finite element method [J]. Journal of Prosthodontics, 2002, 11 (4): 333-334.Cynthia S. Petrie D. D. S., M. S. and John L. Williams Ph. D. Shape optimization of dental implant designs under oblique loading using the p‐version finite element method [J]. Journal of Prosthodontics, 2002, 11 (4): 333-334.Ghaziani A. O. et al. // The effect of functionally graded materials on bone remodeling around osseointegrated trans-femoral prostheses / J. Mech. Behav. Biomed. Mater.(2021).Ghaziani A. O. et al. // The effect of functionally graded materials on bone remodeling around osseointegrated trans-femoral prostheses / J. Mech. Behav. Biomed. Mater.(2021).Günther F. et al. // Design procedure for triply periodic minimal surface based biomimetic scaffolds / J. Mech. Behav. Biomed. Mater.(2022).Günther F. et al. // Design procedure for triply periodic minimal surface based biomimetic scaffolds / J. Mech. Behav. Biomed. Mater.(2022).Verri, F. R.; de Souza Batista, V. E.; Santiago, J. F., Jr.; de Faria Almeida, D. A.; Pellizzer, E. P. Effect of crown-to-implant ratio on peri-implant stress: A finite element analysis. Mater. Sci. Eng. P. 2014, 45, 234–240.Verri, F. R.; de Souza Batista, V. E.; Santiago, J. F., Jr.; de Faria Almeida, D. A.; Pellizzer, E. P. Effect of crown-to-implant ratio on peri-implant stress: A finite element analysis. Mater. Sci. Eng. P. 2014, 45, 234–240.Wu, S.-W.; Lee, C.-C.; Fu, P.-Y.; Lin, S.-C. The effects of flute shape and thread profile on the insertion torque and primary stability of dental implants. Med. Eng. Phys. 2012, 34, 797–805.Wu, S.-W.; Lee, C.-C.; Fu, P.-Y.; Lin, S.-C. The effects of flute shape and thread profile on the insertion torque and primary stability of dental implants. Med. Eng. Phys. 2012, 34, 797–805.Li et al.//Early osteointegration evaluation of porous Ti6Al4V scaffolds designed based on triply periodic minimal surface models/J. Orthop. Transl.(2019)Li et al.//Early osteointegration evaluation of porous Ti6Al4V scaffolds designed based on triply periodic minimal surface models/J. Orthop. Transl.(2019)Mehboob et al.//Finite element modelling and characterization of 3D cellular microstructures for the design of a cementless biomimetic porous hip stem / Mater. Des. (2018).Mehboob et al.//Finite element modelling and characterization of 3D cellular microstructures for the design of a cementless biomimetic porous hip stem / Mater. Des. (2018).Salou et al. // Enhanced osseointegration of titanium implants with nanostructured surfaces: an experimental study in rabbits/Acta Biomater. (2015).Salou et al. // Enhanced osseointegration of titanium implants with nanostructured surfaces: an experimental study in rabbits/Acta Biomater. (2015).Shim, H. W.; Yang, B.-E. Long-term cumulative survival and mechanical complications of single-tooth Ankylos Implants: Focus on the abutment neck fractures. J. Adv. Prosthodont. 2015, 7, 423–430.Shim, H. W.; Yang, B.-E. Long-term cumulative survival and mechanical complications of single-tooth Ankylos Implants: Focus on the abutment neck fractures. J. Adv. Prosthodont. 2015, 7, 423–430.Azcarate-Velázquez et al. // Influence of bone quality on the mechanical interaction between implant and bone: a finite element analysis / J. Dent.(2019).Azcarate-Velázquez et al. // Influence of bone quality on the mechanical interaction between implant and bone: a finite element analysis / J. Dent.(2019).Kasani R. et al.//Stress distribution of overdenture using odd number implants – a Finite Element Study/J. Mech. Behav. Biomed. Mater.(2019).Kasani R. et al.//Stress distribution of overdenture using odd number implants – a Finite Element Study/J. Mech. Behav. Biomed. Mater.(2019).Peyroteo M. M. A. et al. // A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method / Comput. Biol. Med.(2021).Peyroteo M. M. A. et al. // A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method / Comput. Biol. Med.(2021).Piccinini et al. // Numerical prediction of peri-implant bone adaptation: comparison of mechanical stimuli and sensitivity to modeling parameters / Med. Eng. Phys.(2016).Piccinini et al. // Numerical prediction of peri-implant bone adaptation: comparison of mechanical stimuli and sensitivity to modeling parameters / Med. Eng. Phys.(2016).Негматова Д. У. Современные подходы к решению биомеханических проблем дентальной имплантологии / Д. У. Негматова, М. К. Камариддинзода // Вопросы науки и образования. – № 7 (53). – 2019. – С. 227–234.Negmatova D. U., Kamariddinzoda M. K. // Modern approaches for solving biomechanical problems of dental implantology / Problems of science and education. – 2019. – Vol. 7 (53). – Pp. 227–234.Cheong V. S. et al. // Bone remodelling in the mouse tibia is spatio-temporally modulated by oestrogen deficiency and external mechanical loading: a combined in vivo / in silico study / Acta Biomater. (2020).Cheong V. S. et al. // Bone remodelling in the mouse tibia is spatio-temporally modulated by oestrogen deficiency and external mechanical loading: a combined in vivo / in silico study / Acta Biomater. (2020).Tyrovola J. B. (2015). The «Mechanostat Theory» of Frost and the OPG/RANKL / RANK System. Journal of cellular biochemistry, 116 (12), 2724–2729. doi: 10.1002/jcb.25265.Tyrovola J. B. (2015). The «Mechanostat Theory» of Frost and the OPG/RANKL / RANK System. Journal of cellular biochemistry, 116 (12), 2724–2729. doi: 10.1002/jcb.25265.Gubaua J. E. et al. // Techniques for mitigating the checkerboard formation: application in bone remodeling simulations / Med. Eng. Phys.(2022).Gubaua J. E. et al. // Techniques for mitigating the checkerboard formation: application in bone remodeling simulations / Med. Eng. Phys.(2022).Santiago Junior, J. F.; Pellizzer, E. P.; Verri, F. R.; de Carvalho, P. S. Stress analysis in bone tissue around single implants with different diameters and veneering materials: A 3-D finite element study. Mater. Sci. Eng. C Mater. Biol. Appl. 2013, 33, 4700–4714.Santiago Junior, J. F.; Pellizzer, E. P.; Verri, F. R.; de Carvalho, P. S. Stress analysis in bone tissue around single implants with different diameters and veneering materials: A 3-D finite element study. Mater. Sci. Eng. C Mater. Biol. Appl. 2013, 33, 4700–4714.Yao Y. et al.//A personalized 3D-printed plate for tibiotalocalcaneal arthrodesis: design, fabrication, biomechanical evaluation and postoperative assessment / Comput. Biol. Med.(2021).Yao Y. et al.//A personalized 3D-printed plate for tibiotalocalcaneal arthrodesis: design, fabrication, biomechanical evaluation and postoperative assessment / Comput. Biol. Med.(2021).Zheng et al. // Bone remodeling following mandibular reconstruction using fibula free flap / J. Biomech.(2022).Zheng et al. // Bone remodeling following mandibular reconstruction using fibula free flap / J. Biomech.(2022).Alzahrani F. S. et al. // Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data / J. Therm. Biol. (2019).Alzahrani F. S. et al. // Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data / J. Therm. Biol. (2019).Chakraborty et al. // Finite element and experimental analysis to select patient’s bone condition specific porous dental implant, fabricated using additive manufacturing/Comput. Biol. Med.(2020).Chakraborty et al. // Finite element and experimental analysis to select patient’s bone condition specific porous dental implant, fabricated using additive manufacturing/Comput. Biol. Med.(2020).Zanichelli, A., Colpo, A., Friedrich, L., Iturrioz, I., Carpinteri, A., & Vantadori, S. (2021). A Novel Implementation of the LDEM in the Ansys LS-DYNA Finite Element Code. Materials (Basel, Switzerland), 14 (24), 7792. doi: 10.3390/ma14247792Zanichelli, A., Colpo, A., Friedrich, L., Iturrioz, I., Carpinteri, A., & Vantadori, S. (2021). A Novel Implementation of the LDEM in the Ansys LS-DYNA Finite Element Code. Materials (Basel, Switzerland), 14 (24), 7792. doi: 10.3390/ma14247792Bulaqi, H. A.; Mashhadi, M. M.; Safari, H.; Samandari, M. M.; Geramipanah, F. Effect of increased crown height on stress distribution in short dental implant components and their surrounding bone: A finite element analysis. J. Prosthet. Dent. 2015, 113, 548–557.Bulaqi, H. A.; Mashhadi, M. M.; Safari, H.; Samandari, M. M.; Geramipanah, F. Effect of increased crown height on stress distribution in short dental implant components and their surrounding bone: A finite element analysis. J. Prosthet. Dent. 2015, 113, 548–557.Kong, L.; Liu, B.; Li, D.; Song, Y.; Zhang, A.; Dang, F.; Qin, X.; Yang, J. Comparative study of 12 thread shapes of dental implant designs: A three-dimensional finite element analysis. World J. Model. Simul. 2006, 2, 134–140.Kong, L.; Liu, B.; Li, D.; Song, Y.; Zhang, A.; Dang, F.; Qin, X.; Yang, J. Comparative study of 12 thread shapes of dental implant designs: A three-dimensional finite element analysis. World J. Model. Simul. 2006, 2, 134–140.Kong, L.; Zhao, Y.; Hu, K.; Li, D.; Zhou, H.; Wu, Z.; Liu, B. Selection of the implant thread pitch for optimal biomechanical properties: A three-dimensional finite element analysis. Adv. Eng. Softw. 2009, 40, 474–478.Kong, L.; Zhao, Y.; Hu, K.; Li, D.; Zhou, H.; Wu, Z.; Liu, B. Selection of the implant thread pitch for optimal biomechanical properties: A three-dimensional finite element analysis. Adv. Eng. Softw. 2009, 40, 474–478.Koolstra, J. H.; van Eijden, T. M. Combined finite-element and rigid-body analysis of human jaw joint dynamics. J. Biomech. 2005, 38, 2431–2439.Koolstra, J. H.; van Eijden, T. M. Combined finite-element and rigid-body analysis of human jaw joint dynamics. J. Biomech. 2005, 38, 2431–2439.Korioth, T. W.; Hannam, A. G. Mandibular forces during simulated tooth clenching. J. Orofac. Pain 1994, 8, 179–189.Korioth, T. W.; Hannam, A. G. Mandibular forces during simulated tooth clenching. J. Orofac. Pain 1994, 8, 179–189.Su, K.-C.; Chang, C.-H.; Chuang, S.-F.; Ng, E. Y.-K. Biomechanical evaluation of endodontic post-restored teeth – finite element analysis. J. Mech. Med. Biol. 2013, 13, 1350012.Su, K.-C.; Chang, C.-H.; Chuang, S.-F.; Ng, E. Y.-K. Biomechanical evaluation of endodontic post-restored teeth – finite element analysis. J. Mech. Med. Biol. 2013, 13, 1350012.El-Anwar, M. I.; El-Zawahry, M. M. A three dimensional finite element study on dental implant design. J. Genet. Eng. Biotechnol. 2011, 9, 77–82.El-Anwar, M. I.; El-Zawahry, M. M. A three dimensional finite element study on dental implant design. J. Genet. Eng. Biotechnol. 2011, 9, 77–82.Van Staden, R. C.; Guan, H.; Loo, Y. C. Application of the finite element method in dental implant research. Comput. Methods Biomech. Biomed. Eng. 2006, 9, 257–270.Van Staden, R. C.; Guan, H.; Loo, Y. C. Application of the finite element method in dental implant research. Comput. Methods Biomech. Biomed. Eng. 2006, 9, 257–270.Chieruzzi, M.; Pagano, S.; Cianetti, S.; Lombardo, G.; Kenny, J. M.; Torre, L. Effect of fibre posts, bone losses and fibre content on the biomechanical behaviour of endodontically treated teeth: 3D-finite element analysis. Mater. Sci. Eng. C Mater. Biol. Appl. 2017, 74, 334–346.Chieruzzi, M.; Pagano, S.; Cianetti, S.; Lombardo, G.; Kenny, J. M.; Torre, L. Effect of fibre posts, bone losses and fibre content on the biomechanical behaviour of endodontically treated teeth: 3D-finite element analysis. Mater. Sci. Eng. C Mater. Biol. Appl. 2017, 74, 334–346.Hijazi, L.; Hejazi, W.; Darwich, M. A.; Darwich, K. Finite element analysis of stress distribution on the mandible and condylar fracture osteosynthesis during various clenching tasks. J. Oral. Maxillofac. Surg. 2016, 20, 359–367.Hijazi, L.; Hejazi, W.; Darwich, M. A.; Darwich, K. Finite element analysis of stress distribution on the mandible and condylar fracture osteosynthesis during various clenching tasks. J. Oral. Maxillofac. Surg. 2016, 20, 359–367.Baggi, L.; Cappelloni, I.; Di Girolamo, M.; Maceri, F.; Vairo, G. The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: A three-dimensional finite element analysis. J. Prosthet. Dent. 2008, 100, 422–431.Baggi, L.; Cappelloni, I.; Di Girolamo, M.; Maceri, F.; Vairo, G. The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: A three-dimensional finite element analysis. J. Prosthet. Dent. 2008, 100, 422–431.Luo, E. D.; Rong, Q.; Chen, Q. Finite-element design and optimization of a three-dimensional tetrahedral porous titanium scaffold for the reconstruction of mandibular defects. Med. Eng. Phys. 2017, 47, 176–183.Luo, E. D.; Rong, Q.; Chen, Q. Finite-element design and optimization of a three-dimensional tetrahedral porous titanium scaffold for the reconstruction of mandibular defects. Med. Eng. Phys. 2017, 47, 176–183.Su, K.-C.; Chang, C.-H.; Chuang, S.-F.; Ng, E.Y.-K. Biomechanical evaluation of endodontic post-restored teeth—finite element analysis. J. Mech. Med. Biol. 2013, 13, 1350012.Su, K.-C.; Chang, C.-H.; Chuang, S.-F.; Ng, E.Y.-K. Biomechanical evaluation of endodontic post-restored teeth—finite element analysis. J. Mech. Med. Biol. 2013, 13, 1350012.Jo, J.-Y.; Yang, D.-S.; Huh, J.-B.; Heo, J.-C.; Yun, M.-J.; Jeong, C.-M. Influence of abutment materials on the implant-abutment joint stability in internal conical connection type implant systems. J. Adv. Prosthodont. 2014, 6, 491–497.Jo, J.-Y.; Yang, D.-S.; Huh, J.-B.; Heo, J.-C.; Yun, M.-J.; Jeong, C.-M. Influence of abutment materials on the implant-abutment joint stability in internal conical connection type implant systems. J. Adv. Prosthodont. 2014, 6, 491–497.Amid, R.; Ebrahimi, N.; Kadkhodazadeh, M.; Mirakhori, M.; Mehrinejad, P.; Nematzadeh, F.; Dehnavi, F. Clinical evaluation of a new device to measure maximum bite force. Dentist. Case. Rep. 2018, 2, 26–29.Amid, R.; Ebrahimi, N.; Kadkhodazadeh, M.; Mirakhori, M.; Mehrinejad, P.; Nematzadeh, F.; Dehnavi, F. Clinical evaluation of a new device to measure maximum bite force. Dentist. Case. Rep. 2018, 2, 26–29.Ashley, E. T.; Covington, L. L.; Bishop, B. G.; Breault, L. G. Ailing and failing endosseous dental implants: A literature review. J. Contemp. Dent. Pract. 2003, 4, 35–50.Ashley, E. T.; Covington, L. L.; Bishop, B. G.; Breault, L. G. Ailing and failing endosseous dental implants: A literature review. J. Contemp. Dent. Pract. 2003, 4, 35–50.Li, T.; Hu, K.; Cheng, L.; Ding, Y.; Ding, Y.; Shao, J.; Kong, L. Optimum selection of the dental implant diameter and length in the posterior mandible with poor bone quality–A 3D finite element analysis. Appl. Math. Model. 2011, 35, 446–456.Li, T.; Hu, K.; Cheng, L.; Ding, Y.; Ding, Y.; Shao, J.; Kong, L. Optimum selection of the dental implant diameter and length in the posterior mandible with poor bone quality–A 3D finite element analysis. Appl. Math. Model. 2011, 35, 446–456.Мураев А. А. Сравнительный анализ биомеханики при различных узлах сопряжения имплантата и абатмента на основании данных трехмерного конечно-элементного моделирования / А. А. Мураев [и др.] // Стоматология. – 2019. – Т. 98. – № 1. – С. 11–16. DOI: 10.17116/stomat20199801111.Muraev A. A., Ivanov S. Y., Leonov S. V. [et al.] // Comparative analysis of biomechanics at different implant-abutment interface nodes based on three-dimensional finite element modelling data / Dentistry. – 2019. – Vol. 98. – № 1. – Pp. 11–16. DOI: 10.17116/stomat20199801111.Chang, Y.-H.; Chan, M.-Y.; Hsu, J.-T.; Hsiao, H.-Y.; Su, K.-C. Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following Bilateral Sagittal Split Osteotomy Treatment for Mandibular Deficiency. Appl. Bionics Biomech. 2019, 2019, 4989013.Chang, Y.-H.; Chan, M.-Y.; Hsu, J.-T.; Hsiao, H.-Y.; Su, K.-C. Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following Bilateral Sagittal Split Osteotomy Treatment for Mandibular Deficiency. Appl. Bionics Biomech. 2019, 2019, 4989013.Ryu, H.-S.; Namgung, C.; Lee, J.-H.; Lim, Y.-J. The influence of thread geometry on implant osseointegration under immediate loading: A literature review. J. Adv. Prosthodont. 2014, 6, 547–554.Ryu, H.-S.; Namgung, C.; Lee, J.-H.; Lim, Y.-J. The influence of thread geometry on implant osseointegration under immediate loading: A literature review. J. Adv. Prosthodont. 2014, 6, 547–554.Hansson, S. A conical implant–abutment interface at the level of the marginal bone improves the distribution of stresses in the supporting bone: An axisymmetric finite element analysis. Clin. Oral Implant. Res. 2003, 14, 286–293.Hansson, S. A conical implant–abutment interface at the level of the marginal bone improves the distribution of stresses in the supporting bone: An axisymmetric finite element analysis. Clin. Oral Implant. Res. 2003, 14, 286–293.Huang, H.-L.; Hsu, J.-T.; Fuh, L.-J.; Tu, M.-G.; Ko, C.-C.; Shen, Y.-W. Bone stress and interfacial sliding analysis of implant designs on an immediately loaded maxillary implant: A non-linear finite element study. J. Dent. 2008, 36, 409–417.Huang, H.-L.; Hsu, J.-T.; Fuh, L.-J.; Tu, M.-G.; Ko, C.-C.; Shen, Y.-W. Bone stress and interfacial sliding analysis of implant designs on an immediately loaded maxillary implant: A non-linear finite element study. J. Dent. 2008, 36, 409–417.Marcián, P.; Borák, L.; Valášek, J.; Kaiser, J.; Florian, Z.; Wolff, J. Finite element analysis of dental implant loading on atrophic and non-atrophic cancellous and cortical mandibular bone–a feasibility study. J. Biomech. 2014, 47, 3830–3836.Marcián, P.; Borák, L.; Valášek, J.; Kaiser, J.; Florian, Z.; Wolff, J. Finite element analysis of dental implant loading on atrophic and non-atrophic cancellous and cortical mandibular bone–a feasibility study. J. Biomech. 2014, 47, 3830–3836.Савранский Ф. З. Использование метода математического моделирования напряженно- деформированного состояния костной ткани при дентальной имплантации (литературный обзор) / Ф. З. Савранский [и др.] // Современная ортопедическая стоматология. – 2018. – № 30. – С. 30–33.Savransky F. Z., Grishin P. O., Kushnir E. N. [et al.] // Using the method of mathematical modelling of the stress-strain state of bone tissue in dental implantation (literature review) / Modern Prosthodontics. – 2018. – № 30. – Pp.Huang, H.-L.; Su, K.-C.; Fuh, L.-J.; Chen, M. Y.; Wu, J.; Tsai, M.-T.; Hsu, J.-T. Biomechanical analysis of a temporomandibular joint condylar prosthesis during various clenching tasks. J. Cranio-MaxilloFac. Surg. 2015, 43, 1194–1201.Huang, H.-L.; Su, K.-C.; Fuh, L.-J.; Chen, M. Y.; Wu, J.; Tsai, M.-T.; Hsu, J.-T. Biomechanical analysis of a temporomandibular joint condylar prosthesis during various clenching tasks. J. Cranio-MaxilloFac. Surg. 2015, 43, 1194–1201.Van Eijden, T. Three-dimensional analyses of human bite-force magnitude and moment. Arch. Oral Biol. 1991, 36, 535–539.Van Eijden, T. Three-dimensional analyses of human bite-force magnitude and moment. Arch. Oral Biol. 1991, 36, 535–539.Merdji et al.//Stress distribution in dental prosthesis under an occlusal combined dynamic loading/Mater. Des.(2012)Merdji et al.//Stress distribution in dental prosthesis under an occlusal combined dynamic loading/Mater. Des.(2012)30–33.

The authors declare that there are no conflicts of interest present.