MATHEMATICAL MODELLING IN THE APPLICATION OF ORTHOPAEDIC STRUCTURES SUPPORTED BY DENTAL IMPLANTS
Abstract and keywords
Abstract (English):
The article is devoted to topical issues of improving the durability and functional reliability of orthopaedic structures based on dental implants. The authors justify the significance of the research topic, which is determined by the need for accurate prediction of the biomechanical behaviour of implant systems, including the influence of the type of implant and abutment connection, the fixation method, and the angle of the implant. The relevance of this research is confirmed by the active introduction of mathematical modelling methods, in particular the finite element method (FEM), which allows analysing the distribution of loads and stresses in bone tissue and prosthesis components. However, the aspects of the influence of various connection configurations (external, internal, conical) and fixation methods (cemented, screw) on the long-term stability of orthopaedic structures remain insufficiently studied. The study conducted a systematic analysis of domestic and foreign scientific publications from the PubMed, Medline, Cochrane, eLIBRARY, and CyberLeninka databases devoted to mathematical modelling in orthopaedic dentistry. A set of methods was used, including comparative analysis, data summarisation, assessment of result reliability, and critical analysis of clinical studies. The results of the study showed that internal and conical connections are more resistant to micromobility and stress concentration than external ones; screw fixation provides better stability under high loads, while cemented fixation requires further study in the long-term; the angle of the implant significantly affects the distribution of stresses in bone tissue. Conclusion. Despite advances in mathematical modelling, there is still a need to standardise analysis methods and conduct additional studies to optimise the parameters of implant systems. The data obtained can be used to improve the accuracy of orthopaedic treatment planning and reduce the risk of complications.

Keywords:
implant-abutment connection, fixation screw, biomechanics, mathematical modelling, finite element method, prosthetic design
References

1. Büyük F.N., Savran E., Karpat F. Review on finite element analysis of dental implants. Journal of Dental Implant Research. 2022;41(3):50–63. http://dx.doi.org/10.54527/jdir.2022.41.3.50

2. Lemos C.A.A., Verri F.R., Noritomi P.Y., Kemmoku D.T., Souza Batista V.E. de, Cruz R.S. et al. Effect of bone quality and bone loss level around internal and external connection implants: A finite element analysis study. The Journal of Prosthetic Dentistry. 2021;125(1): 137.e1-137.e10. https://doi.org/10.1016/j.prosdent.2020.06.029

3. Adatia N.D., Bayne S.C., Cooper L.F., Thompson J.Y. Fracture Resistance of Yttria-Stabilized Zirconia Dental Implant Abutments. Journal of Prosthodontics. 2009;18(1):17–22. https://doi.org/10.1111/j.1532-849x.2008.00378.x

4. Al-Thobity A.M. Titanium Base Abutments in Implant Prosthodontics: A Literature Review. European Journal of Dentistry. 2021;16(01):49–55. https://doi.org/10.1055/s-0041-1735423

5. Camps-Font O., Rubianes-Porta L., Valmaseda-Castellón E., Jung R.E., Gay-Escoda C., Figueiredo R. Comparison of external, internal flat-to-flat, and conical implant abutment connections for implant-supported prostheses: A systematic review and network meta-analysis of randomized clinical trials. The Journal of Prosthetic Dentistry. 2023;30(3):327-340. https://www.thejpd.org/article/S0022-3913(21)00529-1/fulltext

6. Rubianes-Porta L., Traver-Méndez V., Ghiorghiu R., Piera-Auguet J., Subirà-Pifarré C., Figueiredo R. et al. Impact of implant-abutment connection design on biological and mechanical outcomes in posterior single-tooth restorations: A randomized clinical trial. The Journal of Prosthetic Dentistry. Published online July 14, 2025. Online ahead of print. https://doi.org/10.1016/j.prosdent.2025.06.022

7. Derksen W., Joda T., Chantler J., Fehmer V., Gallucci G.O., Gierthmuehlen P.C. et al. Group 2 ITI Consensus Report: Technological developments in implant prosthetics. Clinical oral implants research. 2023;34(S26):104–111. https://doi.org/10.1111/clr.14148

8. Falcinelli C., Valente F., Vasta M., Traini T. Finite element analysis in implant dentistry: State of the art and future directions. Dental Materials. 2023;39(6):539–556. https://doi.org/10.1016/j.dental.2023.04.002

9. María Prados-Privado, Ivorra C., Martínez-Martínez C., Gehrke S.A., José Luis Calvo-Guirado, Prados-Frutos J.C. A Finite Element Analysis of the Fatigue Behavior and Risk of Failure of Immediate Provisional Implants. Metals. 2019;9(5):535. https://doi.org/10.3390/met9050535

10. Chang Y., Tambe A.A., Maeda Y., Wada M., Gonda T. Finite element analysis of dental implants with validation: to what extent can we expect the model to predict biological phenomena? A literature review and proposal for classification of a validation process. International journal of implant dentistry. 2018;4(1):7. https://doi.org/10.1186/s40729-018-0119-5

11. Gallardo Y.N.R., da Silva-Olivio I.R., Gonzaga L., Sesma N., Martin W. A Systematic Review of Clinical Outcomes on Patients Rehabilitated with Complete-Arch Fixed Implant-Supported Prostheses According to the Time of Loading. Journal of Prosthodontics. 2019;28(9):958–968. https://doi.org/10.1111/jopr.13104

12. Kim W., Li X.C., Bidra A.S. Clinical outcomes of implant‐supported monolithic zirconia crowns and fixed partial dentures: A systematic review. Journal of Prosthodontics. 2022;32(2):102–107. https://doi.org/10.1111/jopr.13575

13. Prados-Privado M., Martínez-Martínez C., Gehrke S.A., Prados-Frutos J.C. Influence of Bone Definition and Finite Element Parameters in Bone and Dental Implants Stress: A Literature Review. Biology. 2020;9(8):224. https://doi.org/10.3390/biology9080224

14. Shahad Mohammed Shakir, Saja Ali Muhsin, Raad Al Marza. Finite Element Modelling Based Studies for Dental Implants: Systematic Review. Journal of techniques. 2022;4(33):155–169. http://dx.doi.org/10.51173/jt.v4i33.771

15. Tribst J.P.M., Dal Piva A.M.d.O., da Silva-Concílio L.R., Ausiello P., Kalman L. Influence of Implant-Abutment Contact Surfaces and Prosthetic Screw Tightening on the Stress Concentration, Fatigue Life and Microgap Formation: A Finite Element Analysis. Oral. 2021;1(2):88–101. https://doi.org/10.3390/oral1020009

16. González-Mederos P., Rodríguez-Guerra J., González J., Picardo A., Torres Y. A Finite Element Analysis of a New Dental Implant Design: The Influence of the Diameter, Length, and Material of an Implant on Its Biomechanical Behavior. Materials. 2025;18(12):2692. https://doi.org/10.3390/ma18122692

17. Nokar S., Jalali H., Nozari F., Arshad M. Finite Element Analysis of Stress in Bone and Abutment-Implant Interface under Static and Cyclic Loadings. Frontiers in Dentistry. 2020;17(21):1-8. https://doi.org/10.18502/fid.v17i21.4315

18. Widjaja W., Hartung C. Biomechanische Untersuchungen und Finite-Elemente-Analysen an einem Knochen-Implantat-Verbund - Biomechanical Investigations and Finite Element Analysis of a Bone-implant Interface. Biomedizinische Technik/Biomedical Engineering. 2001;46(12):351–354. http://dx.doi.org/10.1515/bmte.2001.46.12.351

19. Hussein M.O. Stress-strain distribution at bone-implant interface of two splinted overdenture systems using 3D finite element analysis. The Journal of Advanced Prosthodontics. 2013;5(3):333–340. https://doi.org/10.4047/jap.2013.5.3.333

20. Ovesy M., Voumard B., Zysset P. A nonlinear homogenized finite element analysis of the primary stability of the bone–implant interface. Biomechanics and Modeling in Mechanobiology. 2018;17(5):1471–1480. https://doi.org/10.1007/s10237-018-1038-3


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