{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T05:01:15Z","timestamp":1789966875074,"version":"4.0.1"},"reference-count":44,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T00:00:00Z","timestamp":1789344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Ministry of Investments and European Projects"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Background: Implant-prosthetic rehabilitation of single-tooth edentulism often requires orthodontic reshaping of the potential implant-prosthetic space because its dimensions change due to the migration of adjacent teeth. In this context, it is very important to understand the force system generated by orthodontic arches in order to control tooth movement and to achieve, at the end of orthodontic treatment, the correct dimensions of the potential implant-prosthetic space for dental implant placement. Materials and Methods: The study was based on CBCT images acquired from a 25-year-old female patient with maxillary and mandibular lateral edentulism. The images were processed using InVesalius and Geomagic to obtain a patient-specific three-dimensional reconstruction of the dento-maxillary structures. Orthodontic brackets, adhesive components, and round-section nickel\u2013titanium archwires were subsequently modeled and positioned within a common three-dimensional coordinate system. The reconstructed geometry was used to extract local geometric parameters of the archwire. These parameters were subsequently introduced into a local equivalent Euler\u2013Bernoulli beam formulation to estimate elastic force components and transverse reactions associated with the bracket-related points. Results: The study revealed an uneven distribution of forces along the orthodontic arches. For the upper arch, the elastic force values ranged from 0.044 to 0.383 N, and for the lower arch, from 0.050 to 0.308 N. The calculated reactions at the bracket components also varied depending on the orthodontic archwire geometry and the position of the support points. Conclusions: Patient-specific three-dimensional reconstruction combined with a local analytical beam approximation provides a framework for estimating geometry-dependent elastic force components within an orthodontic appliance. The calculated values should be interpreted as equivalent local force estimates derived from the reconstructed geometry and not as a complete three-dimensional force\u2013moment system.<\/jats:p>","DOI":"10.3390\/bioengineering13091069","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T17:01:00Z","timestamp":1789405260000},"page":"1069","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evaluation of the Force System Acting Within an Orthodontic Appliance"],"prefix":"10.3390","volume":"13","author":[{"given":"Amelia Smaranda","family":"Ro\u0219ianu","sequence":"first","affiliation":[{"name":"Department of Oral Rehabilitation, University of Medicine and Pharmacy of Craiova, 200349 Craiova, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Drago\u0219 Lauren\u021biu","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Automotive, Transportation and Industrial Engineering, Faculty of Mechanics, University of Craiova, 200478 Craiova, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gabriel","family":"Buciu","sequence":"additional","affiliation":[{"name":"Department of General Nursing, Faculty of Nursing-T\u00e2rgu Jiu, Titu Maiorescu University, 210102 T\u00e2rgu Jiu, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2395-6975","authenticated-orcid":false,"given":"Stelian-Mihai-Sever","family":"Petrescu","sequence":"additional","affiliation":[{"name":"Department of Orthodontics, University of Medicine and Pharmacy of Craiova, 200349 Craiova, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"ref_1","first-page":"377","article-title":"Maxillary implants and the growing patient","volume":"8","author":"Oesterle","year":"1993","journal-title":"Int. J. Oral Maxillofac. Implant."},{"key":"ref_2","first-page":"421","article-title":"Clinical and radiographic findings following placement of single-tooth implants in young patients: Case reports","volume":"16","author":"Brugnolo","year":"1996","journal-title":"Int. J. Periodontics Restor. Dent."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1093\/ejo\/23.6.715","article-title":"Orthodontic aspects of the use of oral implants in adolescents: A 10-year follow-up study","volume":"23","author":"Thilander","year":"2001","journal-title":"Eur. J. Orthod."},{"key":"ref_4","unstructured":"Proffit, W.R., Fields, H.W., Larson, B., and Sarver, D.M. (2019). Contemporary Orthodontics, Elsevier. [6th ed.]."},{"key":"ref_5","unstructured":"Misch, C.E. (2008). Contemporary Implant Dentistry, Mosby Elsevier. [3rd ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.sdentj.2019.08.004","article-title":"Pre-prosthetic orthodontics","volume":"32","author":"Alfallaj","year":"2020","journal-title":"Saudi Dent. J."},{"key":"ref_7","first-page":"91","article-title":"Pre-prosthetic orthodontics for aesthetics and function in restorative dentistry","volume":"59","author":"Small","year":"2011","journal-title":"General. Dent."},{"key":"ref_8","unstructured":"Bennett, J.C., and McLaughlin, R.P. (2019). Fundamentals of Orthodontic Treatment Mechanics, Le Grande Publishing."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"770","DOI":"10.4028\/www.scientific.net\/AMM.657.770","article-title":"Virtual and experimental studies on human walking. Virtual lower leg environment. Innovative design of a tibial nail","volume":"657","author":"Buciu","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_10","first-page":"161","article-title":"The 3D Virtual Model of a Classical Hip Joint Prosthesis","volume":"826","author":"Calin","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"167","DOI":"10.4028\/www.scientific.net\/AMM.823.167","article-title":"Virtual Model and Simulation of the Normal and Affected Human Hip Joint","volume":"823","author":"Calin","year":"2016","journal-title":"Appl. Mech. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Duta, A., Popa, D.L., Vintila, D.D., Buciu, G., Dina, N.A., Ionescu, A., Berceanu, M.C., and Calin, D.C. (2022). An Experimental and Virtual Approach to Hip Revision Prostheses. Diagnostics, 12.","DOI":"10.3390\/diagnostics12081952"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"62","DOI":"10.2991\/978-94-6463-152-4_8","article-title":"A Personalized Three-Dimensional Model of a Patient Using CT Images","volume":"Volume 15","author":"Duta","year":"2023","journal-title":"Proceedings of the International Conference on Mechanical Engineering (ICOME 2022)"},{"key":"ref_14","first-page":"461","article-title":"About the Experimental and Virtual Analysis of Orthopedic Implant Systems for the Revision of the Hip Prosthesis with Morcellated Bone Graft and Reconstruction Net","volume":"47","author":"Popa","year":"2021","journal-title":"Curr. Health Sci. J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Katta, M., Petrescu, S.-M.-S., Dragomir, L.P., Popescu, M.R., Voinea Georgescu, R., \u021auculin\u0103, M.J., Popa, D.L., Du\u021b\u0103, A., Diaconu, O.A., and Dasc\u0103lu, I.T. (2023). Using the Finite Element Method to Determine the Odonto-Periodontal Stress for a Patient with Angle Class II Division 1 Malocclusion. Diagnostics, 13.","DOI":"10.3390\/diagnostics13091567"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Petrescu, S.-M.-S., Rauten, A.-M., Popescu, M., Popescu, M.R., Popa, D.L., Buciu, G., Ciuc\u0103, E.-M., Dudan, T.-C., and B\u0103t\u0103iosu, M. (2025). Analysis of Extreme Thermal Variations in the Oral Cavity of a Patient with a Fixed Metallic Orthodontic Appliance Using the Finite Element Method. Bioengineering, 12.","DOI":"10.20944\/preprints202507.2109.v1"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Petrescu, S.-M.-S., Rauten, A.-M., Popescu, M., Popescu, M.R., Popa, D.L., Ilie, D., Du\u021b\u0103, A., Racil\u0103, L.D., Vintil\u0103, D.D., and Buciu, G. (2024). Assessment of Thermal Influence on an Orthodontic System Using the Finite Element Method. Bioengineering, 11.","DOI":"10.20944\/preprints202409.0865.v1"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Petrescu, S.-M.-S., Tuculina, M.J., Popa, D.L., Duta, A., Salan, A.I., Voinea Georgescu, R., Diaconu, O.A., Turcu, A.A., Mocanu, H., and Nicola, A.G. (2022). Modeling and Simulating an Orthodontic System Using Virtual Methods. Diagnostics, 12.","DOI":"10.3390\/diagnostics12051296"},{"key":"ref_19","first-page":"471","article-title":"The use of virtual direct and reverse engineering techniques for the reconstruction of an orthodontic system","volume":"68","author":"Popa","year":"2025","journal-title":"Acta Tech. Napoc.\u2014Ser. Appl. Math. Mech. Eng."},{"key":"ref_20","unstructured":"Popa, A.G., Botez, M.D., Buru, M.\u0218., Besoiu, T.S., Marchi\u0219, A.G., and Bredean, L. (2020). Guide to Assignments in Strength of Materials (I), UTPRESS. [2nd ed.]. Revised and Expanded."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"279","DOI":"10.5937\/fmet1902279P","article-title":"CAD, CAE, and Rapid Prototyping Methods Applied in Orthopedics for Long Bones","volume":"47","author":"Popa","year":"2019","journal-title":"FME Trans."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"012086","DOI":"10.1088\/1757-899X\/997\/1\/012086","article-title":"Virtual and experimental device for testing hip revision prostheses","volume":"997","author":"Popa","year":"2020","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"012087","DOI":"10.1088\/1757-899X\/997\/1\/012087","article-title":"A virtual approach to orthopedic systems based on implants and prostheses","volume":"997","author":"Popa","year":"2020","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"101","DOI":"10.4028\/www.scientific.net\/AMM.880.101","article-title":"3D Virtual Skull Model Based on CT or MRI Images Used for Dental Simulations","volume":"880","author":"Vintila","year":"2018","journal-title":"Appl. Mech. Mater."},{"key":"ref_25","first-page":"20","article-title":"Determination of Resistance Forces from Mandibular Movements through Dynamic Simulation Using Kinematic Analysis and the Finite Element Method","volume":"10","author":"Popescu","year":"2018","journal-title":"Romanian J. Oral Rehabil."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.archoralbio.2016.02.012","article-title":"Biomechanical investigation into the role of the periodontal ligament in optimizing orthodontic force: A finite element case study","volume":"66","author":"Liao","year":"2016","journal-title":"Arch. Oral Biol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"e26spe1","DOI":"10.1590\/2177-6709.31.1.e26spe1","article-title":"Orthodontic creative mechanics","volume":"31","author":"Machado","year":"2026","journal-title":"Dent. Press J. Orthod."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1259\/dmfr\/12615645","article-title":"The current status of cone-beam computed tomography imaging in orthodontics","volume":"40","author":"Kapila","year":"2011","journal-title":"Dentomaxillofac. Radiol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1016\/j.cden.2008.05.005","article-title":"What is cone-beam CT and how does it work?","volume":"52","author":"Scarfe","year":"2008","journal-title":"Dent. Clin. N. Am."},{"key":"ref_30","first-page":"E610","article-title":"Biomechanical aspects of external root resorption in orthodontic therapy","volume":"12","author":"Abuabara","year":"2007","journal-title":"Med. Oral Patol. Oral Cir. Bucal"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1016\/S0011-8532(22)00110-0","article-title":"Biomechanical considerations for orthodontic treatment of adults","volume":"40","author":"Lindauer","year":"1996","journal-title":"Dent. Clin. N. Am."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00056-021-00324-z","article-title":"Numerical and biomechanical analysis of orthodontic treatment of patients with recovered periodontal disease","volume":"83","author":"Bourauel","year":"2022","journal-title":"J. Orofac. Orthop."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0889-5406(86)90021-1","article-title":"The super-elastic properties of Japanese NiTi alloy wire for use in orthodontics","volume":"90","author":"Miura","year":"1986","journal-title":"Am. J. Orthod."},{"key":"ref_34","first-page":"197","article-title":"A review of contemporary archwires: Their properties and characteristics","volume":"67","author":"Kusy","year":"1997","journal-title":"Angle Orthod."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"347","DOI":"10.3233\/THC-174689","article-title":"Biomechanical investigation of orthodontic treatment planning based on orthodontic force measurement and the finite element method prior to implementation: A case study","volume":"26","author":"Wu","year":"2018","journal-title":"Technol. Health Care"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/ocr.12089","article-title":"Personalized and precision orthodontic therapy","volume":"18","author":"Iwasaki","year":"2015","journal-title":"Orthod. Craniofac. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/S0889-5406(99)70212-X","article-title":"Gingival response to orthodontic force","volume":"116","author":"Redlich","year":"1999","journal-title":"Am. J. Orthod. Dentofac. Orthop."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"e3889","DOI":"10.1002\/cnm.3889","article-title":"Precision Orthodontic Force Simulation Using a Nodal Displacement-Based Archwire Loading Approach","volume":"40","author":"Ahmad","year":"2024","journal-title":"Int. J. Numer. Methods Biomed. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1016\/0002-9416(67)90118-2","article-title":"Clinical and histologic observations on tooth movement during and after orthodontic treatment","volume":"53","author":"Reitan","year":"1967","journal-title":"Am. J. Orthod."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/0002-9416(73)90353-9","article-title":"The nature of tooth movement","volume":"63","author":"Storey","year":"1973","journal-title":"Am. J. Orthod."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5656","DOI":"10.1007\/s12598-025-03387-8","article-title":"Effects of PHB and PLA coatings on the corrosion behavior of ultrathin Mg sheets in artificial blood plasma containing BSA","volume":"44","author":"Sun","year":"2025","journal-title":"Rare Met."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"10491","DOI":"10.1007\/s12598-025-03639-7","article-title":"Engineered manganese phosphate coatings on titanium implants: Synergistic photothermal antibiosis and ion-stimulated osteogenesis via zinc\/calcium co-doping","volume":"44","author":"Li","year":"2025","journal-title":"Rare Met."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"22501","DOI":"10.1021\/acs.langmuir.5c03007","article-title":"Friction-Induced PTFE Coating on Dental Restorative Resin with Ultralow Friction and Wear","volume":"41","author":"Lin","year":"2025","journal-title":"Langmuir"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"131849","DOI":"10.1016\/j.ijbiomac.2024.131849","article-title":"Gelatin\/heparin coated bio-inspired polyurethane composite fibers to construct small-caliber artificial blood vessel grafts","volume":"269","author":"Xiang","year":"2024","journal-title":"Int. J. Biol. Macromol."}],"container-title":["Bioengineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2306-5354\/13\/9\/1069\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T04:14:43Z","timestamp":1789964083000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2306-5354\/13\/9\/1069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,14]]},"references-count":44,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["bioengineering13091069"],"URL":"https:\/\/doi.org\/10.3390\/bioengineering13091069","relation":{},"ISSN":["2306-5354"],"issn-type":[{"value":"2306-5354","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,14]]}}}