隨著植牙技術經過數十年的發展，All-on-4®全口速定植牙已廣泛應用於治療全口無牙患者，和傳統植牙相比，有著治療時間短、恢復快速和避免補骨風險等優點。執行植牙手術前，大多使用有限元素分析評估植體、贋復物和顎骨的生物力學變化，因此為了確保All-on-4®數值模型的準確性，本研究對適用性分析框架中的使用環境 (R-COU、M-COU) 和驗證證據 (R-VAL、M-VAL) 進行分析及討論。
首先在R-COU中探討影響植牙成功率的不確定性因素，而M-COU於4種骨質條件的顎骨中模擬肌肉施力及分析植牙風險，模擬結果顯示在BT4骨下高應變區體積遠高於其他骨質，有較大的骨骼損傷風險，植體則不受影響，在任何骨質下植體的最大應力值皆遠低於降伏強度，植體遭破壞的風險很小。接著在R-VAL中透過兩種方式收集驗證證據，包含應變規和DIC實驗，而M-VAL則是將模擬結果和實驗數據相互比較，兩種實驗方式皆和模擬結果呈現高度相關。
最後評估真實 (ΔR) 和模型 (ΔM) 元素間的差異，在ΔR中，模型通過考量不同顎骨幾何形狀、材料性質和負載條件的變化，使其更貼近實際情況，能準確呈現顎骨的力學行為，在ΔM中，針對顎骨材料性質、負載和邊界條件的差異進行比較，模擬結果均能在高應力應變區域表現出相似趨勢，證明了數值模型具有良好的可信度。
本研究開發一套結合ASME V&V 40和All-on-4®全口速定植牙的適用性分析框架，針對All-on-4®數值模型進行逐步的驗證，確保有限元素模擬結果的可靠性並證明該模型的可信度，提供臨床醫師正確的力學分析資訊。

Clinically, the All-on-4® treatment concept has been widely used to treat edentulous patients. Prior to implant surgery, finite element analysis is commonly used to evaluate the biomechanical changes in implants, prostheses, and jawbones. To ensure the accuracy of the All-on-4® numerical model, this study conducted an analysis and discussion of differences in the applicability analysis framework, including the context of use (R-COU, M-COU) and validation evidence (R-VAL, M-VAL).
First, the R-COU is used to investigate the uncertainty factors that affect the success rate of dental implantation. Meanwhile, the M-COU model simulates muscle forces on four different bone types of the jawbone to analyze the implantation risks. The simulation results show that the volume of the high-strain region under the type 4 bone is significantly larger than other bone types, indicating a higher risk of bone damage. However, the implants themselves remain unaffected as the maximum stress levels in the implants are well below the yield strength, minimizing the risk of implant failure in any bone quality. Then, validation evidence is collected by two methods in R-VAL, including strain gauge and Digital Image Correlation (DIC) experiment, while M-VAL model compares the simulation results and experimental data with each other. Both experimental methods are highly correlated with the simulation results.
This study develops an applicability analysis framework for the All-on-4® treatment concept that integrates ASME V&V 40 standards. This framework enables a step-by-step verification process of the All-on-4® numerical model, ensuring the reliability of finite element simulation results and establishing the credibility of the model. It is designed to provide clinicians with accurate mechanical analysis information.

[1] Sheiham, A. and J. Steele, Does the condition of the mouth and teeth affect the ability to eat certain foods, nutrient and dietary intake and nutritional status amongst older people? Public health nutrition, 2001. 4(3): p. 797-803.
[2] Gumrukcu, Z., Y.T. Korkmaz, and F.M. Korkmaz, Biomechanical evaluation of implant-supported prosthesis with various tilting implant angles and bone types in atrophic maxilla: A finite element study. Computers in Biology and Medicine, 2017. 86: p. 47-54.
[3] Takahashi, T., I. Shimamura, and K. Sakurai, Influence of number and inclination angle of implants on stress distribution in mandibular cortical bone with All-on-4 Concept. Journal of Prosthodontic Research, 2010. 54(4): p. 179-184.
[4] Dogan, D.O., et al., Evaluation of "All-on-Four" Concept and Alternative Designs with 3D Finite Element Analysis Method. Clinical Implant Dentistry and Related Research, 2014. 16(4): p. 501-510.
[5] Liang, R., et al., Biomechanical analysis and comparison of 12 dental implant systems using 3D finite element study. Computer Methods in Biomechanics and Biomedical Engineering, 2015. 18(12): p. 1340-1348.
[6] Tribst, J.P.M., et al., Influence of Framework Material and Posterior Implant Angulation in Full-Arch All-on-4 Implant-Supported Prosthesis Stress Concentration. Dentistry Journal, 2022. 10(1).
[7] Ahmadi, A., et al., The all-on-4 concept in the maxilla-A biomechanical analysis involving high performance polymers. Journal of Biomedical Materials Research Part B-Applied Biomaterials, 2021. 109(11): p. 1698-1705.
[8] Viceconti, M., et al., In silico trials: Verification, validation and uncertainty quantification of predictive models used in the regulatory evaluation of biomedical products. Methods, 2021. 185: p. 120-127.
[9] Assessing Credibility of Computational Modeling through Verification and Validation: Application to Medical Devices. 2018; Available from: https://www.asme.org/codes-standards/find-codes-standards/v-v-40-assessing-credibility-computational-modeling-verification-validation-application-medical-devices.
[10] Maló, P., B. Rangert, and M. Nobre, “All‐on‐Four” immediate‐function concept with Brånemark System® implants for completely edentulous mandibles: a retrospective clinical study. Clinical implant dentistry and related research, 2003. 5: p. 2-9.
[11] Malo, P., et al., "All-on-4" Immediate-Function Concept for Completely Edentulous Maxillae: A Clinical Report on the Medium (3 Years) and Long-Term (5 Years) Outcomes. Clinical Implant Dentistry and Related Research, 2012. 14: p. e139-e150.
[12] Lopes, A., et al., The NobelGuide (R) All-on-4 (R) Treatment Concept for Rehabilitation of Edentulous Jaws: A Prospective Report on Medium- and Long-Term Outcomes. Clinical Implant Dentistry and Related Research, 2015. 17: p. E406-E416.
[13] Malo, P., et al., The All-on-4 treatment concept for the rehabilitation of the completely edentulous mandible: A longitudinal study with 10 to 18 years of follow-up. Clinical Implant Dentistry and Related Research, 2019. 21(4): p. 565-577.
[14] La Monaca, G., et al., Immediate flapless full-arch rehabilitation of edentulous jaws on 4 or 6 implants according to the prosthetic-driven planning and guided implant surgery: A retrospective study on clinical and radiographic outcomes up to 10 years of follow-up. Clinical Implant Dentistry and Related Research, 2022. 24(6): p. 831-844.
[15] Lopes, A., et al., The NobelGuide((R)) All-on-4((R)) Treatment Concept for Rehabilitation of Edentulous Jaws: ARetrospective Report on the 7-Years Clinical and 5-Years Radiographic Outcomes. Clinical Implant Dentistry and Related Research, 2017. 19(2): p. 233-244.
[16] Francetti, L., et al., Medium- and Long-Term Complications in Full-Arch Rehabilitations Supported by Upright and Tilted Implants. Clinical Implant Dentistry and Related Research, 2015. 17(4): p. 758-764.
[17] Lekholm, U., Patient selection and preparation. Tissue integrated prothesis, 1985: p. 199-209.
[18] Sugiura, T., et al., Micromotion analysis of different implant configuration, bone density, and crestal cortical bone thickness in immediately loaded mandibular full-arch implant restorations: A nonlinear finite element study. Clinical Implant Dentistry and Related Research, 2018. 20(1): p. 43-49.
[19] Huang, H.L., et al., Biomechanical Evaluation of Bone Atrophy and Implant Length in Four Implants Supporting Mandibular Full-Arch-Fixed Dentures. Materials, 2022. 15(9).
[20] Liu, C.W., et al., Bone quality effect on short implants in the edentulous mandible: a finite element study. Bmc Oral Health, 2022. 22(1).
[21] Goiato, M.C., et al., Longevity of dental implants in type IV bone: a systematic review. International Journal of Oral and Maxillofacial Surgery, 2014. 43(9): p. 1108-1116.
[22] Staedt, H., et al., Potential risk factors for early and late dental implant failure: a retrospective clinical study on 9080 implants. International Journal of Implant Dentistry, 2020. 6(1).
[23] Pathmanathan, P., et al., Applicability analysis of validation evidence for biomedical computational models. Journal of Verification, Validation and Uncertainty Quantification, 2017. 2(2): p. 021005.
[24] Ramella, A., et al., Applicability assessment for in-silico patient-specific TEVAR procedures. Journal of Biomechanics, 2023. 146: p. 111423.
[25] Dharia, M.A., S. Snyder, and J.E. Bischoff, Computational Model Validation of Contact Mechanics in Total Ankle Arthroplasty. Journal of Orthopaedic Research, 2020. 38(5): p. 1063-1069.
[26] Weinstein, A.M., et al., Stress analysis of porous rooted dental implants. Journal of dental research, 1976. 55(5): p. 772-777.
[27] Merema, B.B.J., et al., Patient‐specific finite element models of the human mandible: Lack of consensus on current set‐ups. Oral diseases, 2021. 27(1): p. 42-51.
[28] Chang, Y., et al., 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: p. 1-14.
[29] Shen, Y.W., et al., Biomechanical Analyses of Porous Designs of 3D-Printed Titanium Implant for Mandibular Segmental Osteotomy Defects. Materials, 2022. 15(2).
[30] Omaish, H.H.M., A.M. Abdelhamid, and A.F. Neena, Comparison of the strain developed around implants with angled abutments with two reinforced polymeric CAD-CAM superstructure materials: An in vitro comparative study. Journal of Prosthetic Dentistry, 2022. 127(4).
[31] Lin, T.S., et al., Biomechanical Evaluation and Factorial Analysis of the 3-Dimensional Printing Self-Designed Metallic Reconstruction Plate for Mandibular Segmental Defect. Journal of Oral and Maxillofacial Surgery, 2022. 80(4): p. 775-783.
[32] Chakraborty, A., et al., Probing the Influence of Hybrid Thread Design On Biomechanical Response of Dental Implants: Finite Element Study and Experimental Validation. Journal of biomechanical engineering, 2022.
[33] Xu, X., et al., Experimental validation of finite element simulation of a new custom-designed fixation plate to treat mandibular angle fracture. BioMedical Engineering Online, 2021. 20(1).
[34] Shu, J.H., et al., 3D Printing Experimental Validation of the Finite Element Analysis of the Maxillofacial Model. Frontiers in Bioengineering and Biotechnology, 2021. 9.
[35] Wu, A.Y.J., et al., Effects of Positions and Angulations of Titanium Dental Implants in Biomechanical Performances in the All-on-Four Treatment: 3D Numerical and Strain Gauge Methods. Metals, 2020. 10(2).
[36] Wu, A.Y.J., et al., Biomechanical effect of implant design on four implants supporting mandibular full-arch fixed dentures: In vitro test and finite element analysis. Journal of the Formosan Medical Association, 2020. 119(10): p. 1514-1523.
[37] Tribst, J.P.M., et al., Effect of Framework Type on the Biomechanical Behavior of Provisional Crowns: Strain Gauge and Finite Element Analyses. International Journal of Periodontics and Restorative Dentistry, 2020. 40(1): p. E9-E18.
[38] Al-Zordk, W., M. Ghazy, and M. El-Anwar, Stress Analysis Around Reduced-Diameter Zirconia and Titanium One-Piece Implants With and Without Microthreads in the Neck: Experiments and Finite Element Analysis. International Journal of Oral & Maxillofacial Implants, 2020. 35(2): p. 305-312.
[39] Paes-Junior, T.-J.d.A., et al., Stress distribution of complete-arch implant-supported prostheses reinforced with silica-nylon mesh. Journal of clinical and experimental dentistry, 2019. 11(12): p. e1163-e1169.
[40] Tribst, J.-P.-M., et al., The importance of correct implants positioning and masticatory load direction on a fixed prosthesis. Journal of clinical and experimental dentistry, 2018. 10(1): p. e81-e87.
[41] Datte, C.-E., et al., Influence of different restorative materials on the stress distribution in dental implants. Journal of clinical and experimental dentistry, 2018. 10(5): p. e439-e444.
[42] Matsuzaki, M., et al., A comparison of the peri-implant bone stress generated by the preload with screw tightening between ‘bonded’ and ‘contact’ model. Computer Methods in Biomechanics and Biomedical Engineering, 2017. 20(4): p. 393-402.
[43] Wu, A.Y.J., et al., Biomechanical evaluation of one-piece and two-piece small-diameter dental implants: In-vitro experimental and three-dimensional finite element analyses. Journal of the Formosan Medical Association, 2016. 115(9): p. 794-800.
[44] Shimura, Y., et al., Biomechanical effects of offset placement of dental implants in the edentulous posterior mandible. International Journal of Implant Dentistry, 2016. 2(1): p. 1-13.
[45] Ramos, A. and M. Mesnard, A new condyle implant design concept for an alloplastic temporomandibular joint in bone resorption cases. Journal of Cranio-Maxillofacial Surgery, 2016. 44(10): p. 1670-1677.
[46] Mesnard, M. and A. Ramos, Experimental and numerical predictions of Biomet(®) alloplastic implant in a cadaveric mandibular ramus. Journal of cranio-maxillo-facial surgery : official publication of the European Association for Cranio-Maxillo-Facial Surgery, 2016. 44(5): p. 608-615.
[47] Rezende, C.E., et al., Stress Distribution in Single Dental Implant System: Three-Dimensional Finite Element Analysis Based on an In Vitro Experimental Model. The Journal of craniofacial surgery, 2015. 26(7): p. 2196-2200.
[48] Cardoso, M., et al., Stress distribution around implants with abutments of different materials: a comparison of photoelastic, strain gage and finite element analyses. Revista Odonto Ciencia, 2015. 30(4): p. 132-137.
[49] Arat Bilhan, S., et al., Effect of attachment types and number of implants supporting mandibular overdentures on stress distribution: A computed tomography-based 3D finite element analysis. Journal of Biomechanics, 2015. 48(1): p. 130-137.
[50] Mobilio, N., et al., Experimental and numeric stress analysis of titanium and zirconia one-piece dental implants. The International journal of oral & maxillofacial implants, 2013. 28(3): p. e135-e142.
[51] Chu, C.M., et al., Biomechanical evaluation of subcrestal placement of dental implants: In vitro and numerical analyses. Journal of Periodontology, 2011. 82(2): p. 302-310.
[52] Hsu, J.T., et al., Bone strain and interfacial sliding analyses of platform switching and implant diameter on an immediately loaded implant: Experimental and three-dimensional finite element analyses. Journal of Periodontology, 2009. 80(7): p. 1125-1132.
[53] Eser, A., et al., Nonlinear finite element analysis versus ex vivo strain gauge measurements on immediately loaded implants. The International journal of oral & maxillofacial implants, 2009. 24(3): p. 439-446.
[54] Kromka, M. and G. Milewski, Experimental and numerical approach to chosen types of mandibular fractures cured by means of miniplate osteosynthesis. Acta of Bioengineering and Biomechanics, 2007. 9(2): p. 49-54.
[55] Al-Sukhun, J., J. Kelleway, and M. Helenius, Development of a three-dimensional finite element model of a human mandible containing endosseous dental implants. I. Mathematical validation and experimental verification. Journal of Biomedical Materials Research - Part A, 2007. 80(1): p. 234-246.
[56] Heckmann, S.M., et al., Loading of bone surrounding implants through three-unit fixed partial denture fixation: A finite-element analysis based on in vitro and in vivo strain measurements. Clinical Oral Implants Research, 2006. 17(3): p. 345-350.
[57] Huang, H.L., et al., Effects of splinted prosthesis supported a wide implant or two implants: a three-dimensional finite element analysis. Clinical oral implants research, 2005. 16(4): p. 466-472.
[58] Iplikçioglu, H., et al., Comparison of non-linear finite element stress analysis with in vitro strain gauge measurements on a Morse taper implant. The International journal of oral & maxillofacial implants, 2003. 18(2): p. 258-265.
[59] Yuan, C.C.A., et al., The research on the dental bridge model-making process based on the curing shrinkage epoxy and residual stress reduction. Journal of Mechanics, 2021. 37: p. 659-668.
[60] Borges, G.A., et al., Is one dental mini-implant biomechanically appropriate for the retention of a mandibular overdenture? A comparison with Morse taper and external hexagon platforms. The Journal of prosthetic dentistry, 2021. 125(3): p. 491-499.
[61] Pirmoradian, M., et al., Finite element analysis and experimental evaluation on stress distribution and sensitivity of dental implants to assess optimum length and thread pitch. Computer Methods and Programs in Biomedicine, 2020. 187.
[62] Herraez-Galindo, C., et al., A Comparison of Photoelastic and Finite Elements Analysis in Internal Connection and Bone Level Dental Implants. Metals, 2020. 10(5).
[63] Dhatrak, P., et al., Finite Element Analysis and Experimental Investigations on Stress Distribution of Dental Implants around Implant-Bone Interface. Materials Today: Proceedings, 2018. 5(2): p. 5641-5648.
[64] Torezan, J.F.R., et al., Fixation of sagittal split ramus osteotomy of the mandible: a comparative assessment of three techniques based on mechanical, photoelastic and finite element analysis. Oral Surgery, 2017. 10(4): p. e48-e54.
[65] Sato, F.R.L., et al., A comparative evaluation of the hybrid technique for fixation of the sagittal split ramus osteotomy in mandibular advancement by mechanical, photoelastic, and finite element analysis. Oral Surgery, Oral Medicine, Oral Pathology and Oral Radiology, 2012. 114(SUPPL. 5): p. S60-S68.
[66] van Kootwijk, A., et al., Semi-automated digital workflow to design and evaluate patient-specific mandibular reconstruction implants. Journal of the Mechanical Behavior of Biomedical Materials, 2022. 132.
[67] Cantó-Navés, O., et al., Comparison between experimental digital image processing and numerical methods for stress analysis in dental implants with different restorative materials. Journal of the Mechanical Behavior of Biomedical Materials, 2021. 113.
[68] Tribst, J.P.M., et al., Digital Image Correlation and Finite Element Analysis of Bone Strain Generated by Implant-Retained Cantilever Fixed Prosthesis. The European journal of prosthodontics and restorative dentistry, 2020. 28(1): p. 10-17.
[69] Messias, A., et al., Effect of round curvature of anterior implant-supported zirconia frameworks: finite element analysis and in vitro study using digital image correlation. Computer Methods in Biomechanics & Biomedical Engineering, 2017. 20(11): p. 1236-1248.
[70] Sutradhar, A., et al., Designing patient-specific 3D printed craniofacial implants using a novel topology optimization method. Medical and Biological Engineering and Computing, 2016. 54(7): p. 1123-1135.
[71] Tiossi, R., et al., Validation of finite element models for strain analysis of implant-supported prostheses using digital image correlation. Dental materials : official publication of the Academy of Dental Materials, 2013. 29(7): p. 788-796.
[72] Gröning, F., et al., Improving the validation of finite element models with quantitative full-field strain comparisons. Journal of Biomechanics, 2012. 45(8): p. 1498-1506.
[73] Gröning, F., et al., Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry. Journal of Biomechanics, 2009. 42(9): p. 1224-1229.
[74] Chang, Y.H., et al., 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.
[75] Pesqueira, A.A., et al., Use of stress analysis methods to evaluate the biomechanics of oral rehabilitation with implants. The Journal of oral implantology, 2014. 40(2): p. 217-228.
[76] Karl, M., et al., Biomechanical methods applied in dentistry: a comparative overview of photoelastic examinations, strain gauge measurements, finite element analysis and three-dimensional deformation analysis. The European journal of prosthodontics and restorative dentistry, 2009. 17(2): p. 50-57.
[77] Goiato, M.C., et al., Methods used for assessing stresses in buccomaxillary prostheses: Photoelasticity, finite element technique, and extensometry. Journal of Craniofacial Surgery, 2009. 20(2): p. 561-564.
[78] Assunção, W.G., et al., Biomechanics studies in dentistry: Bioengineering applied in oral implantology. Journal of Craniofacial Surgery, 2009. 20(4): p. 1173-1177.
[79] Demenko, V., et al., FE study of bone quality effect on load-carrying ability of dental implants. Computer Methods in Biomechanics and Biomedical Engineering, 2014. 17(16): p. 1751-1761.
[80] Ishigaki, S., et al., Biomechanical stress in bone surrounding an implant under simulated chewing. Clinical oral implants research, 2003. 14(1): p. 97-102.
[81] 志賀博、町博之、小泉順一、竹井利香, 口顎功能學. 2017: 合記圖書出版社，台灣.
[82] 皮昕, 口腔解剖生理學. 2007: 合記書局出版社，台灣.
[83] Horita, S., et al., Biomechanical analysis of immediately loaded implants according to the "All-on-Four" concept. Journal of Prosthodontic Research, 2017. 61(2): p. 123-132.
[84] Reina, J.M., et al., Numerical estimation of bone density and elastic constants distribution in a human mandible. Journal of Biomechanics, 2007. 40(4): p. 828-836.
[85] Peng, W.M., et al., Biomechanical and Mechanostat analysis of a titanium layered porous implant for mandibular reconstruction: The effect of the topology optimization design. Materials Science and Engineering C-Materials for Biological Applications, 2021. 124.
[86] ASTM, S., Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials. ASTM D790. Annual book of ASTM Standards, 1997.
[87] Kageyama, T., et al., A morphological study of the relationship between arch dimensions and craniofacial structures in adolescents with Class II Division 1 malocclusions and various facial types. American Journal of Orthodontics and Dentofacial Orthopedics, 2006. 129(3): p. 368-375.
[88] KYOWA Measuring Equipment General Catalog 2022. 2022.
[89] Solav, D. and A. Silverstein, Duodic: 3d digital image correlation in Matlab. Journal of Open Source Software, 2022. 7(74): p. 4279.
[90] Fedorov, A., et al., 3D Slicer as an image computing platform for the Quantitative Imaging Network. Magnetic Resonance Imaging, 2012. 30(9): p. 1323-1341.
[91] Pattin, C.A., W.E. Caler, and D.R. Carter, Cyclic mechanical property degradation during fatigue loading of cortical bone. Journal of Biomechanics, 1996. 29(1): p. 69-79.
[92] Hellmich, C., C. Kober, and B. Erdmann, Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible. Annals of Biomedical Engineering, 2008. 36(1): p. 108-122.
[93] Adell, R., et al., A 15-YEAR STUDY OF OSSEOINTEGRATED IMPLANTS IN THE TREATMENT OF THE EDENTULOUS JAW. International Journal of Oral Surgery, 1981. 10(6): p. 387-416.
[94] Linetskiy, I., et al., Impact of annual bone loss and different bone quality on dental implant success - A finite element study. Computers in Biology and Medicine, 2017. 91: p. 318-325.
[95] Boyer, R., Materials Properties Handbook: Titanium Alloys. 1994: ASM International, USA.
[96] 林揚民, 用於All-on-4®全口重建之生物力學分析計算模型之可信度評估. 2023: 國立成功大學機械工程學系碩士論文.
[97] Hebert, J. and M. Khonsari, The application of digital image correlation (DIC) in fatigue experimentation: A review. Fatigue & Fracture of Engineering Materials & Structures, 2023. 46(4): p. 1256-1299.
[98] Mugnai, F., P. Caporossi, and P. Mazzanti, Exploiting image assisted total station in digital image correlation (DIC) displacement measurements: insights from laboratory experiments. European Journal of Remote Sensing, 2022. 55(1): p. 115-128.