Sonlu Elemanlar Analizi ve Endodontideki Uygulamaları

Abstract

Sonlu Elemanlar Analizi veya Sonlu Elemanlar Yöntemi, bir yapının sonlu sayıda küçük elemana bölünmesi prensibine dayanır. Tasarım optimizasyonunda ve yapısal analizde yaygın olarak kullanılan, ilk olarak havacılık endüstrisinde karmaşık uçak gövdesi yapılarındaki gerilimi incelemek için ortaya çıkan sofistike bir mühendislik aracıdır. Belirli bir soruna sayısal çözüm bulan bu yöntem karmaşık mekanik sistemlerdeki gerilimleri ve gerinimleri analiz etmek için kullanılır. Endodontik amaçlı kullanımda diş ve çevre dokuların ve kullanılan materyallerin mekanik özelliklerinin matematiksel dönüşümünü ve analizini sağlar. Ağırlıklı olarak materyallerin ve dokuların in vivo olarak ölçülemeyen mekanik yönlerini saptamak için yararlıdır. Çeşitli avantajları vardır, gerçek modeller üzerinde yapılan çalışmalarla karşılaştırılabilir ve testler doğrulukla ve etik kaygılar olmadan tekrarlanabilir. Bu makalede Sonlu Elemanlar Analizi yöntemi hakkında bilgi vermek ve bu konuda endodonti alanında yapılan çalışmaların derlenmesi amaçlanmıştır.

Keywords

• Endodonti
• FEA
• FEM
• Sonlu Elemanlar Analizi

Finite Element Analysis and Appliences in Endodontics

Abstract

Finite Element Analysis or Finite Element Method is based on the principle of dividing a structure into a finite number of small elements. Widely used in design optimization and structural analysis, it is a sophisticated engineering tool that first emerged in the aerospace industry to study stress in complex airframe structures. This method, which finds a numerical solution to a specific problem, is used to analyze stresses and strains in complex mechanical systems. In endodontic use, it provides mathematical transformation and analysis of the mechanical properties of teeth and surrounding tissues and the materials used. It is mainly useful for detecting mechanical aspects of materials and tissues that cannot be measured in vivo. It has several advantages, it is comparable to studies on real models, and tests can be repeated with accuracy and without ethical concerns. This manuscript introduce the finite element analysis and reviews the the studies carried out in the field of endodontics on this subject.

Keywords

• Endodontics
• FEA
• FEM
• Finite Element Analysis

References

1. Marcián P, Wolff J, Horáčková L, Kaiser J, Zikmund T, Borák L. Micro finite element analysis of dental implants under different loading conditions. Computers in Biology and Medicine. 2018;96:157-65.
2. Gokhale N, Deshpande S, Bedekar S, Anand T. Practical finite element analysis. 1st ed: Finite To Infinite; 2008.
3. Zienkiewicz OC, Taylor RL. The finite element method. 5th ed. Oxford ; Boston: Butterworth-Heinemann; 2000.
4. Geramy A, Sharafoddin F. Abfraction: 3D analysis by means of the finite element method. Quintessence Int. 2003;34(7):526-33.
5. Geng JP, Tan KB, Liu GR. Application of finite element analysis in implant dentistry: a review of the literature. J Prosthet Dent. 2001;85(6):585-98.
6. Tanne K, Sakuda M, Burstone CJ. Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces. Am J Orthod Dentofacial Orthop. 1987;92(6):499-505.
7. 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(1):16- 22.
8. Szucs A, Bujtar P, Sandor GK, Barabas 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.

9. Saunders HA. Book Reviews : FINITE ELEMENT ANALYSIS FUNDAMENTALS R.H. Gallagher Prentice Hall, Inc., Englewood Cliffs, New Jersey (1975). The Shock and Vibration Digest. 1977;9:28-.
10. Yettram AL, Wright KW, Pickard HM. Finite element stress analysis of the crowns of normal and restored teeth. J Dent Res. 1976;55(6):1004-11.
11. Ritz W. Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. 1909;1909(135):1-61.
12. Turner MJ. Stiffness and Deflection Analysis of Complex Structures. Journal of the Aeronautical Sciences. 1956;23:805-23.
13. Clough RW, editor The Finite Element Method in Plane Stress Analysis1960.
14. Thresher RW, Saito GE. The stress analysis of human teeth. J Biomech. 1973;6(5):443-9.
15. Farah JW, Craig RG. Finite element stress analysis of a restored axisymmetric first molar. J Dent Res. 1974;53(4):859-66.
16. Weinstein A, Klawitter J, Anand S, Schuessler R. Stress Analysis of Porous Rooted Dental Implants. Journal of dental research. 1976;55:772-7.
17. Mohammed H. Basic Concepts of Finite Element Analysis and its Applications in Dentistry: An Overview. Journal of Oral Hygiene & Health. 2014;02.
18. Hatheway A. Review of finite element analysis techniques: capabilities and limitations: SPIE; 1992.
19. Szwedowski TD, Whyne CM, Fialkov JA. Toward characterization of craniofacial biomechanics. J Craniofac Surg. 2010;21(1):202-7.
20. Pessoa RS, Muraru L, Junior EM, Vaz LG, Sloten JV, Duyck J, Jaecques SV. Influence of implant connection type on the biomechanical environment of immediately placed implants - CT-based nonlinear, three-dimensional finite element analysis. Clin Implant Dent Relat Res. 2010;12(3):219-34.
21. Lu S, Li T, Zhang Y, Lu C, Sun Y, Zhang J, Xu D. Biomechanical optimization of the diameter of distraction screw in distraction implant by three-dimensional finite element analysis. Computers in Biology and Medicine. 2013;43(11):1949-54.
22. Cen R, Wang R, Cheung GSP. Periodontal Blood Flow Protects the Alveolar Bone from Thermal Injury during Thermoplasticized Obturation: A Finite Element Analysis Study. J Endod. 2018;44(1):139-44.
23. Srirekha A, Bashetty K. Infinite to finite: an overview of finite element analysis. Indian J Dent Res. 2010;21(3):425-32.
24. Van Staden RC, Guan H, Loo YC. Application of the finite element method in dental implant research. Computer Methods in Biomechanics and Biomedical Engineering. 2006;9(4):257-70.
25. Shivakumar S, Kudagi VS, Talwade P. Applications of finite element analysis in dentistry: A review. Journal of International Oral Health. 2021;13:415 - 22.
26. Raposo LH, Armstrong SR, Maia RR, Qian F, Geraldeli S, Soares CJ. Effect of specimen gripping device, geometry and fixation method on microtensile bond strength, failure mode and stress distribution: laboratory and finite element analyses. Dent Mater. 2012;28(5):e50-62.
27. Vinod B, Saraswathi K. Finite Element Analysis and Its Applications in Dentistry. In: Mahboub B, editor. Finite Element Methods and Their Applications. Rijeka: IntechOpen; 2020. p. Ch. 8.
28. SUN J, JIAO T, TIE Y, WANG D. Three-dimensional finite element analysis of the application of attachment for obturator framework in unilateral maxillary defect. Journal of Oral Rehabilitation. 2008;35(9):695-9.
29. Gao J, Xu W, Ding Z. 3D finite element mesh generation of complicated tooth model based on CT slices. Comput Methods Programs Biomed. 2006;82(2):97-105.
30. Viceconti M, Zannoni C, Testi D, Petrone M, Perticoni S, Quadrani P, et al. The multimod application framework: A rapid application development tool for computer aided medicine. Computer Methods and Programs in Biomedicine. 2007;85(2):138-51.
31. Reddy MS, Sundram R, Eid Abdemagyd HA. Application of Finite Element Model in Implant Dentistry: A Systematic Review. J Pharm Bioallied Sci. 2019;11(Suppl 2):S85-S91.
32. Mohammed S, Desai H. Basic concepts of finite element analysis and its applications in dentistry: An overview. Oral Hyg Health. 2014;2(156):2332-0702.1000156.
33. Chandrupatla T, Belegundu A. Introduction to finite elements in engineering: Cambridge University Press; 2021.
34. Doblaré M, Garcı́a JM, Gómez MJ. Modelling bone tissue fracture and healing: a review. Engineering Fracture Mechanics. 2004;71(13):1809-40.
35. Liu S, Liu Y, Xu J, Rong Q, Pan S. Influence of occlusal contact and cusp inclination on the biomechanical character of a maxillary premolar: A finite element analysis. The Journal of Prosthetic Dentistry. 2014;112(5):1238-45.
36. O’Mahony AM, Williams JL, Spencer P. Anisotropic elasticity of cortical and cancellous bone in the posterior mandible increases peri-implant stress and strain under oblique loading. Clinical Oral Implants Research. 2001;12(6):648-57.
37. Gharechahi M, Moezzi S, Karimpour S. Comparative Analysis of Stress Distribution through Finite-Element Models of 3 NiTi Endodontic Instruments while Operating in Different Canal Types. J Dent (Shiraz). 2023;24(1):60- 5.
38. Bonessio N, Pereira ES, Lomiento G, Arias A, Bahia MG, Buono VT, Peters OA. Validated finite element analyses of WaveOne Endodontic Instruments: a comparison between M-Wire and NiTi alloys. Int Endod J. 2015;48(5):441-50.
39. Santos Lde A, Resende PD, Bahia MG, Buono VT. Effects of R-Phase on Mechanical Responses of a Nickel-Titanium Endodontic Instrument: Structural Characterization and Finite Element Analysis. ScientificWorldJournal. 2016;2016:7617493.
40. El-Anwar MI, Yousief SA, Kataia EM, El-Wahab TM. Finite Element Study on Continuous Rotating versus Reciprocating Nickel-Titanium Instruments. Braz Dent J. 2016;27(4):436-41.
41. Yuan L, Yue L, Wang JD. [A three-dimensional finite element analysis of 0.02 taper 20# stainless steel K files during root canal instrumentation]. Zhonghua Kou Qiang Yi Xue Za Zhi. 2007;42(6):346-8.
42. Nawar NN, Abdelfattah RA, Kataia M, Saber SM, Kataia EM, Kim HC. Effect of Proximal Caries-driven Access on the Biomechanical Behavior of Endodontically Treated Maxillary Premolars. J Endod. 2023;49(10):1337- 43.
43. Wang X, Wang D, Wang YR, Cheng XG, Ni LX, Wang W, Tian Y. Effect of access cavities on the biomechanics of mandibular molars: a finite element analysis. BMC Oral Health. 2023;23(1):196.
44. Nawar NN, Elkholy MMA, Ha WN, Saber SM, Kim HC. Optimum Shaping Parameters of the Middle Mesial Canal in Mandibular First Molars: A Finite Element Analysis Study. J Endod. 2023;49(5):567-74.
45. Rundquist BD, Versluis A. How does canal taper affect root stresses? Int Endod J. 2006;39(3):226-37.
46. Telli C, Gülkan P, Günel H. A critical reevaluation of stresses generated during vertical and lateral condensation of gutta-percha in the root canal. Endod Dent Traumatol. 1994;10(1):1-10.
47. Telli C, Gülkan P. Stress analysis during root canal filling by vertical and lateral condensation procedures: a three-dimensional finite element model of a maxillary canine tooth. Br Dent J. 1998;185(2):79-86.
48. Telli C, Gülkan P, Raab W. Additional studies on the distribution of stresses during vertical compaction of gutta-percha in the root canal. Br Dent J. 1999;187(1):32- 7. Hong J, Xia WW, Xiong HG. [Analysis of the effect on the stress of root canal wall by vertical and lateral condensation procedures]. Shanghai Kou Qiang Yi Xue. 2003;12(5):359-61.
49. Belli S, Eraslan O, Eskitascioglu G. Effect of Root Filling on Stress Distribution in Premolars with Endodontic-Periodontal Lesion: A Finite Elemental Analysis Study. J Endod. 2016;42(1):150-5.
50. Gümrükçü Z, Kurt S, Köse S. Effect of Root Resection Length and Graft Type Used After Apical Resection: A Finite Element Study. J Oral Maxillofac Surg. 2019;77(9):1770.e1-.e8.
51. Ashi T, Richert R, Mancino D, Jmal H, Alkhouri S, Addiego F, et al. Do the Mechanical Properties of Calcium- Silicate-Based Cements Influence the Stress Distribution of Different Retrograde Cavity Preparations? Materials (Basel). 2023;16(8).
52. Yoo YJ, Perinpanayagam H, Kim M, Zhu Q, Baek SH, Kwon HB, Kum KY. Stress Distribution on Trephine- Resected Root-end in Targeted Endodontic Microsurgery: A Finite Element Analysis. J Endod. 2022;48(12):1517- 25.e1.
53. Talati A, Disfani R, Afshar A, Fallah Rastegar A. Finite element evaluation of stress distribution in mature and immature teeth. Iran Endod J. 2007;2(2):47-53.
54. Anthrayose P, Nawal RR, Yadav S, Talwar S, Yadav S. Effect of revascularisation and apexification procedures on biomechanical behaviour of immature maxillary central incisor teeth: a three-dimensional finite element analysis study. Clin Oral Investig. 2021;25(12):6671-9.
55. Demirel A, Bezgin T, Sarı Ş. Effects of Root Maturation and Thickness Variation in Coronal Mineral Trioxide Aggregate Plugs Under Traumatic Load on Stress Distribution in Regenerative Endodontic Procedures: A 3-dimensional Finite Element Analysis Study. J Endod. 2021;47(3):492-9.e4.
56. Eram A, Zuber M, Keni LG, Kalburgi S, Naik R, Bhandary S, et al. Finite element analysis of immature teeth filled with MTA, Biodentine and Bioaggregate. Comput Methods Programs Biomed. 2020;190:105356.
57. Lertchirakarn V, Palamara JE, Messer HH. Patterns of vertical root fracture: factors affecting stress distribution in the root canal. J Endod. 2003;29(8):523-8.
58. Lertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain-gauge studies of vertical root fracture. J Endod. 2003;29(8):529-34.
59. Anantula K, Vankayala B, Yadav SS. A threedimensional finite element analysis of stress distribution in maxillary central incisor with a horizontal mid root fracture after various management protocols. J Conserv Dent. 2021;24(5):470-4.
60. Zhou Y, Hu Z, Hu Y, Gao A, Pan X, Tang R, Lin Z. Patterns of stress distribution of endodontically treated molar under different types of loading using finite element models-the exploring of mechanism of vertical root fracture. J Mech Behav Biomed Mater. 2023;144:105947.
61. Oskui IZ, Hashemi A, Jafarzadeh H, Kato A. Finite element investigation of human maxillary incisor under traumatic loading: Static vs dynamic analysis. Comput Methods Programs Biomed. 2018;155:121-5.
62. Dezzen-Gomide AC, de Carvalho MA, Lazari- Carvalho PC, de Oliveira HF, Cury A, Yamamoto-Silva FP, Silva BSF. A three-dimensional finite element analysis of permanent maxillary central incisors in different stages of root development and trauma settings. Comput Methods Programs Biomed. 2021;207:106195.
63. Vilela ABF, Soares PBF, Almeida GA, Veríssimo C, Rodrigues MP, Versluis A, Soares CJ. Three-dimensional finite element stress analysis of teeth adjacent to a traumatized incisor. Dent Traumatol. 2019;35(2):128-34.
64. Askerbeyli Örs S, Aksel H, Küçükkaya Eren S, Serper A. Effect of perforation size and furcal lesion on stress distribution in mandibular molars: a finite element analysis. Int Endod J. 2019;52(3):377-84.
65. Ozkurt-Kayahan Z, Turgut B, Akin H, Kayahan MB, Kazazoglu E. A 3D finite element analysis of stress distribution on different thicknesses of mineral trioxide aggregate applied on various sizes of pulp perforation. Clin Oral Investig. 2020;24(10):3477-83.
66. Aslan T, Esim E, Üstün Y, Dönmez Özkan H. Evaluation of Stress Distributions in Mandibular Molar Teeth with Different Iatrogenic Root Perforations Repaired with Biodentine or Mineral Trioxide Aggregate: A Finite Element Analysis Study. J Endod. 2021;47(4):631-40.
67. Celik E, Aydinlik E. Effect of a dilacerated root on stress distribution to the tooth and supporting tissues. J Prosthet Dent. 1991;65(6):771-7.
68. Oyama K, Motoyoshi M, Hirabayashi M, Hosoi K, Shimizu N. Effects of root morphology on stress distribution at the root apex. Eur J Orthod. 2007;29(2):113- 7.
69. Kishen A, Vedantam S. Hydromechanics in dentine: role of dentinal tubules and hydrostatic pressure on mechanical stress-strain distribution. Dent Mater. 2007;23(10):1296-306.
70. Er O, Yaman SD, Hasan M. Finite element analysis of the effects of thermal obturation in maxillary canine teeth. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2007;104(2):277-86.
71. Zhou X, Chen Y, Wei X, Liu L, Zhang F, Shi Y, Wu W. Heat transfers to periodontal tissues and gutta-percha during thermoplasticized root canal obturation in a finite element analysis model. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2010;110(2):257-63.
72. Stănuși A, Popa DL, Ionescu M, Cumpătă CN, Petrescu GS, Ţuculină MJ, et al. Analysis of Temperatures Generated during Conventional Laser Irradiation of Root Canals-A Finite Element Study. Diagnostics (Basel). 2023;13(10).
73. Kim HC, Sung SY, Ha JH, Solomonov M, Lee JM, Lee CJ, Kim BM. Stress generation during self-adjusting file movement: minimally invasive instrumentation. J Endod. 2013;39(12):1572-5.
74. Zelic K, Vukicevic A, Jovicic G, Aleksandrovic S, Filipovic N, Djuric M. Mechanical weakening of devitalized teeth: three-dimensional Finite Element Analysis and prediction of tooth fracture. Int Endod J. 2015;48(9):850-63.
75. Ni N, Ye J, Wang L, Shen S, Han L, Wang Y. Stress distribution in a mandibular premolar after separated nickel-titanium instrument removal and root canal preparation: a three-dimensional finite element analysis. J Int Med Res. 2019;47(4):1555-64.
76. Askerbeyli Örs S, Küçükkaya Eren S. Effects of different treatment modalities on biomechanical behavior of maxillary incisors with external invasive cervical resorption at different progression levels. Dent Traumatol. 2023;39(6):605-15.
77. Rajawat A, Kaushik M. Stresses in Teeth with External Cervical Resorption Defects Restored with Different Biomimetic Cements: A Finite Element Analysis. J Endod. 2023;49(8):995-1003.
78. Eskibağlar M, Erdem S, Kaman MO. Evaluation of the effect of different rubber dam clamps on the mandibular first molar with Finite element analysis. Comput Methods Biomech Biomed Engin. 2023:1-10.
79. Aslan T, Üstün Y, Esim E. Stress distributions in internal resorption cavities restored with different materials at different root levels: A finite element analysis study. Aust Endod J. 2019;45(1):64-71.
80. Durmus B, Hale AA, Oguz E, Sema B. The effect of different irrigation protocols on elastic modulus of dentine and biomechanics of single-rooted premolar tooth: A nano-indentation and finite element analysis study. Niger J Clin Pract. 2019;22(1):101-7.
81. Kırmalı Ö, Türker N, Akar T, Yılmaz B. Finite element analysis of stress distribution in autotransplanted molars. J Dent. 2022;119:104082.
82. Uzunoglu-Özyürek E, Küçükkaya Eren S, Eraslan O, Belli S. Critical evaluation of fracture strength testing for endodontically treated teeth: a finite element analysis study. Restor Dent Endod. 2019;44(2):e15.