下顎近心第二大臼齒阻生是罕見的牙齒萌發障礙，某些案例是可以利用矯正的方式治療。在國立成功大學醫學院附設醫院齒顎矯正科，臨床上常使用改良式舌側弓加上遠心鉤來治療此類問題，但臨床上的困難點是如何選定一個合適的施力點來減少矯正力的副作用，關於此問題仍無文獻特別討論。本研究的目的有二，第一，利用六軸荷重元在體外模型中分析扶正臼齒的力量系統；第二，利用三維有限元素阻生齒模型 並改變參數來分析扶正臼齒的力量系統。研究方法分為三個部分。首先，選擇了一位下顎第二大臼齒阻生的病患，並拍攝錐束電腦斷層。於矯正期間使用口內掃描機紀錄扶正下顎阻生第二大臼齒的過程;第二，建立三維有限元素模型及三維列印模型，並利用六軸荷重元來量測三維列印模型，並以不同水平位置之掛鉤所產生的力量來拉動阻生齒，再比較其顯示的力及力矩，進而驗證對應之有限元素分析模型的可應用性;第三，建立各種三維有限元素分析模型，藉此來分析不同的施力向量、施力位置或不同的牙齒角度及深度時，模型的應力與應變分布及位移變化。實驗顯示，臨床病患的口內掃描影像重疊發現阻生齒移動的形式類似於有限元素分析的結果。關於三維列印模型的結果顯示，在垂直力的部分，越靠近牙齒的掛鉤會產生較多的突出的力量，反之遠離牙齒的掛鉤是產生下壓內縮的力量，而且在相對應三維模型上的有限元素分析，趨勢是相同的。最後於各種不同參數的有限元素模型中，發現若是增加阻生齒深度，產生扶正的效果越差；而力量的向量是影響牙冠的移動量的因素；且在越遠離牙齒的掛鉤上拉動牙齒，牙齒位移的旋轉中心會往牙冠方向靠近。所以本篇研究的結論是利用改良式舌側弓來拉動阻生齒，若能增加遠心鉤到阻生齒的距離，便能夠減少牙齒突出的力量；從有限元素分析的結果可發現，若能增加遠心鉤阻生齒的距離，阻生齒位移的旋轉中心會往牙冠方向靠近，而扶正阻生齒的效果是與阻生齒的深度成反比的，另外力量施予的向量會產生的不同大小的力矩並影響阻生第二大臼齒的扶正。

Impactions of mesially-inclined mandibular second molar are rare and some of them can be treated with various orthodontic techniques. The modified lingual arch with distal hook is used for uprighting mesially-impacted second molars in Department of Orthodontic, National Cheng Kung University Hospital (NCKUH) in Tainan, Taiwan. But determining the optimal site to apply force with proper vector is still unclear which the literatures have not discussed yet. The aims of the study are: (1) to evaluate the force system during molar uprighting using different force vectors via six-axis load cell (2) to evaluate the force system with different parameters in three-dimensional (3D) second-molar finite element (FE) models. The study comprises three parts. First, a patient with second molar impaction was selected and cone beam computed tomography images of the patient were taken. During orthodontic treatment, images of the patient’s mandibular dentition were obtained by intraoral scanner. Second, 3D-printed model including a six-axis load cell was set up. Constant forces which were exerted from hooks which were at the same vertical level to the impacted tooth. Then forces and moments were recorded. The correspondent FE model was verified with the results. Last, 3D models with different angulations, different depths of impacted tooth, and different positions of force application were analyzed with different force vectors to the impacted teeth. According to the superimposition of the 3D oral scan images, tooth movement in the patient was comparable with the one in FE simulations. Regarding with 3D-printed model, mesial hook generated extrusive force, whereas distal hook exerted intrusive force. In addition, FE analysis was verified and showed similar trends with 3D-printed model. FE simulations revealed that displacement of the tooth would be less if increasing the tooth depth. Moreover, the results demonstrated that vector of force is one of the factors which influence the crown displacement. On the other hand, coronal migration of center of rotation was found when increasing the distance from hook to the impacted tooth. It is concluded that increasing the distance from the hook to the impacted tooth using modified lingual arch may reduce extrusive force on the mesially-impacted lower second molar. From the data of FE analysis, increasing the distance from the hook to the impacted tooth would cause the center of rotation to migrate coronally. Besides, when depth of impacted second molar increases, it would be less effective to upright the tooth. Also, the vector of forces could generate different amounts of moments and affect the effectiveness of uprighting impacted MM2 in FE simulated models.

Abrão, A. F., Domingos, R. G., de Paiva, J. B., Laganá, D. C., & Abrão, J. (2018). Photoelastic analysis of stress distribution in mandibular second molar roots caused by several uprighting mechanics. American Journal of Orthodontics and Dentofacial Orthopedics, 153(3), 415-421. doi:https://doi.org/10.1016/j.ajodo.2017.07.023
Aitasalo, K., Lehtinen, R., & Oksala, E. (1972). An orthopantomographic study of prevalence of impacted teeth. Int J Oral Surg, 1(3), 117-120.
An, K., Jang, I., Choi, D.-S., Jost-Brinkmann, P.-G., & Cha, B.-K. (2015). Identification of a stable reference area for superimposing mandibular digital models. Journal of Orofacial Orthopedics / Fortschritte der Kieferorthopädie, 76(6), 508-519. doi:10.1007/s00056-015-0310-8
Bondemark, L., & Tsiopa, J. (2007). Prevalence of Ectopic Eruption, Impaction, Retention and Agenesis of the Permanent Second Molar. The Angle Orthodontist, 77(5), 773-778. doi:10.2319/072506-306.1
Cantrell, J., Rohde, S., Damiani, D., Gurnani, R., DiSandro, L., Anton, J., Young,A., Jerez, A., Steinbach, D., Kroese,C., Ifju, P. (2017). Experimental Characterization of the Mechanical Properties of 3D Printed ABS and Polycarbonate Parts, In: Yoshida S., Lamberti L., Sciammarella C. (eds) Advancement of Optical Methods in Experimental Mechanics, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham, 89-105
Cassetta, M., Altieri, F., Di Mambro, A., Galluccio, G., & Barbato, E. (2013). Impaction of permanent mandibular second molar: A retrospective study. Medicina Oral, Patología Oral y Cirugía Bucal, 18(4), e564-e568. doi:10.4317/medoral.18869
Chang, C. H., Lin, Joshua S., Eugene Roberts, W. (2018). Seminars in Orthodontics, 24(1), 135-154.
Cho, S. Y., Ki, Y., Chu, V., & Chan, J. (2008). Impaction of permanent mandibular second molars in ethnic Chinese schoolchildren. J Can Dent Assoc, 74(6), 521.
Davis, P. J. (1988). Findings from 1163 panelipse radiographs taken of 12-year-old children living in Hong Kong. Community Dent Health, 5(3), 243-249.
Evans, R. (1988). Incidence of Lower Second Permanent Molar Impaction. British Journal of Orthodontics, 15(3), 199-203. doi:10.1179/bjo.15.3.199
Farah, J. W., & Craig, R. G. (1974). Finite element stress analysis of a restored axisymmetric first molar. J Dent Res, 53(4), 859-866. doi:10.1177/00220345740530041701
Farah, J. W., Craig, R. G., & Meroueh, K. A. (1989). Finite element analysis of three- and
four-unit bridges. Journal of Oral Rehabilitation, 16(6), 603-611.
doi:doi:10.1111/j.1365-2842.1989.tb01384.x
Farman, A. G., Eloff, J., Nortjé, C. J., & de V. Joubert, J. J. (1978). Clinical Absence of the First and Second Permanent Molars. British Journal of Orthodontics, 5(2), 93-97. doi:10.1179/bjo.5.2.93
Ferro, F., Funiciello, G., Perillo, L., & Chiodini, P. (2011). Mandibular lip bumper treatment and second molar eruption disturbances. Am J Orthod Dentofacial Orthop, 139(5), 622-627. doi:10.1016/j.ajodo.2009.07.024
Frank, C. A. (2000). Treatment options for impacted teeth. J Am Dent Assoc, 131(5), 623-632.
Frost, H. M. (1983). The regional acceleratory phenomenon: a review. Henry Ford Hosp Med J, 31(1), 3-9.
Fu, P. S., Wang, J. C., Wu, Y. M., Huang, T. K., Chen, W. C., Tseng, Y. C., . . . Hung, C. C. (2012). Impacted mandibular second molars. Angle Orthod, 82(4), 670-675. doi:10.2319/102111-656.1
Geramy, A., & Ghadirian, H. (2008). Comparison of methods used to correct a lingually tilted mandibular molar: 3-D analysis using the finite element method (FEM). Aust Orthod J, 24(2), 96-101.
Grover, P. S., & Lorton, L. (1985). The incidence of unerupted permanent teeth and related clinical cases. Oral Surg Oral Med Oral Pathol, 59(4), 420-425.
Huang C., Chang, C., Eugene Roberts, W. (2018). Journal of Digital Orthodontics, 50, 26-46.
Jacob, H. B., LeMert, S., Alexander, R. G., & Buschang, P. H. (2014). Second molar impaction associated with lip bumper therapy. Dental Press J Orthod, 19(6), 99-104. doi:10.1590/2176-9451.19.6.099-104.oar
Johnsen, D. C. (1977). Prevalence of delayed emergence of permanent teeth as a result of local factors. The Journal of the American Dental Association, 94(1), 100-106. doi:10.14219/jada.archive.1977.0268
Johnson, J. V., & Quirk, G. P. (1987). Surgical repositioning of impacted mandibular second molar teeth. American Journal of Orthodontics and Dentofacial Orthopedics, 91(3), 242-251. doi:https://doi.org/10.1016/0889-5406(87)90454-9
Kenrad, J., Vedtofte, H., Andreasen, J. O., Kvetny, M. J., & Kjær, I. (2011). A retrospective overview of treatment choice and outcome in 126 cases with arrested eruption of mandibular second molars. Clinical Oral Investigations, 15(1), 81-87. doi:10.1007/s00784-009-0364-3
Kojima, Y., Mizuno, T., & Fukui, H. (2007). A numerical simulation of tooth movement produced by molar uprighting spring. Am J Orthod Dentofacial Orthop, 132(5), 630-638. doi:10.1016/j.ajodo.2005.07.035
Ledbetter, H. M. (1981). Stainless‐steel elastic constants at low temperatures. Journal of Applied Physics, 52(3), 1587-1589. doi:10.1063/1.329644
Lee KJ, P. Y., Hwang WS, Seong EH. (2007). Uprighting Mandibular Second Molars with
Direct Miniscrew Anchorage. Journal of Clinical Orthodontics, 41(10), 627-635.
Liu, Y. (2017). Effects of Modeling Methods on the Finite Element Analysis Results of Orthodontic Applications. (Master of Science in Mechanical Engineering), Purdue University, Indianapolis, Indiana. Retrieved from https://search.proquest.com/docview/2019151347?accountid=12719 Available from ProQuest Dissertations & Theses A&I
Magnusson, C., & Kjellberg, H. (2009). Impaction and retention of second molars: diagnosis, treatment and outcome. A retrospective follow-up study. Angle Orthod, 79(3), 422-427. doi:10.2319/021908-97.1
Marghalani, T. Y., Hamed, M. T., Awad, M. A., Naguib, G. H., & Elragi, A. F. (2012). Three-dimensional finite element analysis of custom-made ceramic dowel made using CAD/CAM technology. J Prosthodont, 21(6), 440-450. doi:10.1111/j.1532-849X.2012.00860.x
Larson M. E. (2012). Biomechanical modeling of canine retraction. (Master), University of North Carolina, Chapel
Hill Retrieved from: https://cdr.lib.unc.edu/indexablecontent/uuid:5a31b94c-dc55-47d2-93a7-fcc16c120b27
McCormack, S. W., Witzel, U., Watson, P. J., Fagan, M. J., & Groning, F. (2017). Inclusion of periodontal ligament fibres in mandibular finite element models leads to an increase in alveolar bone strains. PLoS One, 12(11), e0188707. doi:10.1371/journal.pone.0188707
Melsen, B., Fiorelli, G., & Bergamini, A. (1996). Uprighting of lower molars. J Clin Orthod, 30(11), 640-645.
Nguyen, T., Cevidanes, L., Franchi, L., Ruellas, A., & Jackson, T. (2018). Three-dimensional mandibular regional superimposition in growing patients. American Journal of Orthodontics and Dentofacial Orthopedics, 153(5), 747-754. doi:https://doi.org/10.1016/j.ajodo.2017.07.026
Raghoebar, G. M., Boering, G., Vissink, A., & Stegenga, B. (1991). Eruption disturbances of permanent molars: a review. Journal of Oral Pathology & Medicine, 20(4), 159-166. doi:10.1111/j.1600-0714.1991.tb00913.x
Roberts, W. W., Chacker, F. M., & Burstone, C. J. (1982). A segmental approach to mandibular molar uprighting. Am J Orthod, 81(3), 177-184. doi:https://doi.org/10.1016/0002-9416(82)90051-3
Shapira, Y., Borell, G., Nahlieli, O., & Kuftinec, M. M. (1998). Uprighting mesially impacted mandibular permanent second molars. The Angle Orthodontist, 68(2), 173-178.
Shapira, Y., Finkelstein, T., Lai, Y. H., Kuftinec, M. M., Vardimov, A., & Shpack, N. (2012). Prevalence and Characteristic Features of Mandibular Second Molar Impaction in Chinese-American School Children. Acta stomatologica Croatica, 46(3), 215-221.
Shapira, Y., Finkelstein, T., Shpack, N., Lai, Y. H., Kuftinec, M. M., & Vardimon, A. (2011). Mandibular second molar impaction. Part I: Genetic traits and characteristics. American Journal of Orthodontics and Dentofacial Orthopedics, 140(1), 32-37. doi:https://doi.org/10.1016/j.ajodo.2009.08.034
Shintcovsk, R. L., Martins, L. P., Shintcovsk, L. K., Tanaka, O. M., & Martins, R. P. (2018). Continuous arch and rectangular loops for the correction of consistent and inconsistent load systems in extruded and tipped maxillary second molars. American Journal of Orthodontics and Dentofacial Orthopedics, 153(3), 396-404. doi:https://doi.org/10.1016/j.ajodo.2017.07.021
Sifakakis, I., & Eliades, T. (2017). Laboratory evaluation of orthodontic biomechanics: The clinical applications revisited. Semin Orthod, 23(4), 382-389. doi:10.1053/j.sodo.2017.07.008
Slootweg, P. (2016). Dental and oral pathology. New York, NY: Springer Berlin Heidelberg.
Sonis, A., & Ackerman, M. (2011). E-space preservation. Angle Orthod, 81(6), 1045-1049. doi:10.2319/030711-165.1
Varpio, M., & Wellfelt, B. (1988). Disturbed eruption of the lower second molar: clinical appearance, prevalence, and etiology. ASDC J Dent Child, 55(2), 114-118.
Vedtofte, H. (1999). Arrested eruption of the permanent lower second molar. The European Journal of Orthodontics, 21(1), 31-40. doi:10.1093/ejo/21.1.31
Wellfelt, B., & Varpio, M. (1988). Disturbed eruption of the permanent lower second molar: treatment and results. ASDC J Dent Child, 55(3), 183-189.