臺灣博碩士論文加值系統

研究背景：
垂直牙根斷裂常見於接受過根管治療的牙齒，因為臨床表現和根尖片皆無典型的特徵，導致診斷上相對比較困難，目前未接受過根管治療卻發生垂直牙根斷裂的牙齒只有在台灣人和中國人有病例報告，對其致病原理也所知甚少。

研究材料與方法：
利用因垂直牙根斷裂且未接受過根管治療而拔除的下顎第一大臼齒，以微型電腦斷層攝影掃描的影像建立有垂直牙根斷裂及無垂直牙根斷裂的有限元素模型，並分析兩組模型在咀嚼狀態及緊咬狀態下牙根的應力分佈。

研究結果：
在以300 N斜向力模擬咀嚼狀態下，無垂直牙根斷裂的有限元素模型其最大等效應力為243.8 MPa，位於施力位置的近心頰側牙釉質上，而有垂直牙根斷裂的模型其最大等效應力為259.0 MPa，位於近心牙根的根尖三分之一處。而在以800 N垂直力模擬緊咬狀態下，無垂直牙根斷裂的模型其最大等效應力為319.6 MPa，位於施力位置的中心窩牙釉質上，而有垂直牙根斷裂的模型其最大等效應力為551.6 MPa，位於近心牙根的根尖三分之一處。

結論：
在有限元素分析法的限制及假設條件下，可得到以下幾點結論：(1)牙齒在受力狀態下，應力會集中於有裂紋或缺損的區域。(2)在咀嚼狀態下，有垂直牙根斷裂及無垂直牙根斷裂的牙齒兩者的最大等效應力數值差距不大，但應力集中位置不同。(3)在緊咬狀態下，有垂直牙根斷裂及無垂直牙根斷裂的牙齒兩者的應力集中位置不同，且垂直牙根斷裂的牙齒有較高的等效應力數值。

Background:
Vertical root fracture (VRF) is often noted in endodontically treated teeth. There are no typical clinical and radiographic findings of VRFs, which makes accurate diagnosis of VRFs difficult. Currently there are only case reports in Taiwanese and Chinese population of VRFs in nonendodontically treated teeth, and also little information about their pathogenesis.

Material and Methods:
An nonendodontically treated mandibular first molar extracted for VRFs was scanned with micro-computed tomography (micro-CT) scanners. Then using micro-CT data to generate finite element (FE) models of teeth with VRFs and without VRFs. The analysis of two FE models were focused on the stress distribution of root dentin under chewing and clenching stage.

Results:
Under 300 N oblique force to simulate chewing stage, the maximum equivalent stress was 243.8 MPa observed in mesiobuccal cusp of FE model without VRF, and 259.0 MPa in mesial root apical third of FE model with VRF. Under 800 N vertical force to simulate clenching stage, the maximum equivalent stress was 319.6 MPa observed in central fossa of FE model without VRF and 551.6 MPa in mesial root apical third of FE model with VRF.

Conclusion:
Within the limitation of finite element analysis and current assumption, the following conclusion can be drawn: (1) Crack line or defects would concentrate the stress at these regions after applying load to teeth. (2) In chewing stage, there was little difference of maximum equivalent stress between teeth with VRF and without VRF but the stress concentrated in different location. (3) In clenching stage, the stress concentrated in different location of teeth with VRF and without VRF, and higher equivalent stress was observed in teeth with VRF.

目錄
誌謝 i
中文摘要 iii
Abstract v
目錄 vii
圖目錄 x
表目錄 xiii
第一章 緒論 1
1.1 垂直牙根斷裂 1
1.2 未接受過根管治療牙齒之垂直牙根斷裂 6
1.3 未接受過根管治療牙齒之垂直牙根斷裂病因探討 7
1.4 研究動機與目的 10
第二章 研究材料與方法 11
2.1 三維幾何模型之建立 11
2.1.1 樣本蒐集及選擇 11
2.1.2 微型電腦斷層攝影 12
2.1.3 三維曲面模型之建立與修正 14
2.1.4 三維實體模型之建立與修正 16
2.2 有限元素模型(Finite element model)之建立 16
2.2.1 建立幾何模型(Geometric model) 16
2.2.2 元素選擇(Element types) 18
2.2.3 設定材料性質(Material properties) 18
2.2.4 幾何模型網格化(mesh)成有限元素模型 19
2.2.5 介面接觸設定(Interface) 20
2.2.6 拘束設定(Boundary condition) 21
2.2.7 外力設定(Loading condition) 21
2.3 分析目標 22
第三章 研究結果 23
3.1 在咀嚼狀態下承受負荷之表現 23
3.1.1 等效應力 23
3.1.2 第一主應力 23
3.1.3 第三主應力 24
3.2 在緊咬狀態下承受負荷之表現 24
3.2.1 等效應力 24
3.2.2 第一主應力 24
3.2.3 等三主應力 25
第四章 討論 26
4.1 未接受過根管治療合併垂直牙根斷裂之牙齒 26
4.2 微型電腦斷層攝影 28
4.3 幾何模型之建立 29
4.4 承受負荷結果之分析討論 30
4.5 模型驗證 33
4.6 有限元素法及研究限制 35
4.7 臨床意涵 36
第五章 結論與未來研究方向 38
5.1 結論 38
5.2 未來研究方向 38
參考文獻 67

圖目錄
圖一：病患8的牙齒外形 40
圖二：自製微型電腦斷層掃描儀Dual-Modality Micro-Fluorescence/Computed Tomography (FTCT) 40
圖三：商用微型電腦斷層掃描儀FLEX Triumph Regular FLEX-O, CT, SPECT CZT 3 Head System, LabPET4 Trimodality System 41
圖四：商用微型電腦斷層掃描儀SkyScan 1076 in-vivo micro-CT 41
圖五：四台微型電腦斷層影像於軸向切面上的比較 42
圖六：SkyScan 1076 in-vivo micro-CT的斷層影像輸入Avizo Lite 9.1.1的三維表面示意圖 42
圖七：Avizo Lite 9.1.1軟體影像分割示意圖 43
圖八：牙齒影像分割完成示意圖 43
圖九：牙髓影像分割完成示意圖 44
圖十：Stereolithography(STL)檔案三角網格的修正前後示意圖 44
圖十一：經布林運算(Boolean operation)的STL檔案示意圖 45
圖十二：建立牙周韌帶示意圖 45
圖十三：左下正中門齒至左下第三大臼齒的咬合接觸點分布圖 46
圖十四：咬合接觸點示意圖 46
圖十五：從Meshmixer軟體輸出無垂直牙根斷裂牙齒的STL檔案透視圖 47
圖十六：從Meshmixer軟體輸出有垂直牙根斷裂牙齒的STL檔案透視圖 47
圖十七：三維實體模型示意圖 48
圖十八：下顎骨區塊外形參考 48
圖十九：ANSYS Workbench軟體內建立的下顎骨區塊示意圖 49
圖二十：無垂直牙根斷裂之幾何模型示意圖 49
圖二十一：有垂直牙根斷裂之幾何模型示意圖 50
圖二十二：無垂直牙根斷裂之有限元素模型示意圖 50
圖二十三：有垂直牙根斷裂之有限元素模型示意圖 51
圖二十四：拘束設定示意圖 51
圖二十五：咀嚼狀態下的外力設定示意圖 52
圖二十六：緊咬狀態下的外力設定示意圖 52
圖二十七：咀嚼狀態下等效應力(equivalent stress)分佈圖 53
圖二十八：咀嚼狀態下等效應力於軸向切面分佈圖 53
圖二十九：咀嚼狀態下張應力(Maximum principal stress)分佈圖 54
圖三十：咀嚼狀態下張應力於軸向切面分佈圖 54
圖三十一：咀嚼狀態下壓應力(Minimum principal stress)分佈圖 55
圖三十二：咀嚼狀態下壓應力於軸向切面分佈圖 55
圖三十三：緊咬(clenching)狀態下等效應力分佈圖 56
圖三十四：緊咬狀態下等效應力於軸向切面分佈圖 56
圖三十五：緊咬狀態下張應力分佈圖 57
圖三十六：緊咬狀態下張應力於軸向切面分佈圖 57
圖三十七：緊咬狀態下壓應力分佈圖 58
圖三十八：緊咬狀態下壓應力於軸向切面分佈圖 58
圖三十九：未接受過根管治療合併垂直牙根斷裂牙齒的根尖片影像 59
圖四十：研究垂直牙根斷裂之有限元素模型幾何外形比較 59
圖四十一：在緊咬狀態下於根尖面觀的主應力向量圖(vector principal stress) 60
圖四十二：在緊咬狀態下於軸向切面的主應力向量圖 60
圖四十三：Lertchirakarn等學者研究門牙在根管充填時的張應力分佈圖 61

表目錄
表一：未接受過根管治療之牙齒合併垂直牙根斷裂的病例報告 62
表二：本實驗蒐集的未接受過根管治療合併垂直牙根斷裂之牙齒 63
表三：材料性質設定 64
表四：收斂測試結果 65
表五：承受負荷之結果 66

1. Cracking the cracked tooth code: detection and treatment of various longitudinal tooth fractures [Online]. American Association of Endodontists; 2008. Available from: https://www.aae.org/uploadedfiles/publications_and_research/endodontics_colleagues_for_excellence_newsletter/ecfesum08.pdf.
2. Tsesis I, Rosen E, Tamse A, Taschieri S, Kfir A. Diagnosis of vertical root fractures in endodontically treated teeth based on clinical and radiographic indices: a systematic review. J Endod 2010;36:1455-8.
3. Tamse A, Fuss Z, Lustig J, Kaplavi J. An evaluation of endodontically treated vertically fractured teeth. J Endod 1999;25:506-8.
4. Fuss Z, Lustig J, Katz A, Tamse A. An evaluation of endodontically treated vertical root fractured teeth: impact of operative procedures. J Endod 2001;27:46-8.
5. Cohen S, Berman LH, Blanco L, Bakland L, Kim JS. A demographic analysis of vertical root fractures. J Endod 2006;32:1160-3.
6. Rud J, Omnell KA. Root fractures due to corrosion. Diagnostic aspects. Scand J Dent Res 1970;78:397-403.
7. Tamse A. Vertical root fractures in endodontically treated teeth: diagnostic signs and clinical management. Endod Topics 2006;13:84-94.
8. Wenzel A, Haiter-Neto F, Frydenberg M, Kirkevang LL. Variable-resolution cone-beam computerized tomography with enhancement filtration compared with intraoral photostimulable phosphor radiography in detection of transverse root fractures in an in vitro model. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2009;108:939-45.
9. Hassan B, Metska ME, Ozok AR, van der Stelt P, Wesselink PR. Comparison of five cone beam computed tomography systems for the detection of vertical root fractures. J Endod 2010;36:126-9.
10. Melo SL, Bortoluzzi EA, Abreu M, Jr., Correa LR, Correa M. Diagnostic ability of a cone-beam computed tomography scan to assess longitudinal root fractures in prosthetically treated teeth. J Endod 2010;36:1879-82.
11. Hassan B, Metska ME, Ozok AR, van der Stelt P, Wesselink PR. Detection of vertical root fractures in endodontically treated teeth by a cone beam computed tomography scan. J Endod 2009;35:719-22.
12. Wang P, Yan XB, Lui DG, et al. Detection of dental root fractures by using cone-beam computed tomography. Dentomaxillofac Radiol 2011;40:290-8.
13. Huang CC, Chang YC, Tsai YL, Jeng JH. The radiological diagnosis of vertical root fracture - a literature review [in Chinese, with abstract in English]. JES 2010;1:30-6.
14. Hayashi M, Kinomoto Y, Takeshige F, Ebisu S. Prognosis of intentional replantation of vertically fractured roots reconstructed with dentin-bonded resin. J Endod 2004;30:145-8.
15. Sugaya T, Kawanami M, Noguchi H, Kato H, Masaka N. Periodontal healing after bonding treatment of vertical root fracture. Dent Traumatol 2001;17:174-9.
16. Yang SF, Rivera EM, Walton RE. Vertical root fracture in nonendodontically treated teeth. J Endod 1995;21:337-9.
17. Yeh CJ. Fatigue root fracture: a spontaneous root fracture in non-endodontically treated teeth. Br Dent J 1997;182:261-6.
18. Chan CP, Tseng SC, Lin CP, et al. Vertical root fracture in nonendodontically treated teeth--a clinical report of 64 cases in Chinese patients. J Endod 1998;24:678-81.
19. Chan CP, Lin CP, Tseng SC, Jeng JH. Vertical root fracture in endodontically versus nonendodontically treated teeth: a survey of 315 cases in Chinese patients. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 1999;87:504-7.
20. Wang P, Su L. Clinical observation in 2 representative cases of vertical root fracture in nonendodontically treated teeth. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2009;107:e39-42.
21. Tang L, Zhou XD, Wang Y, et al. Detection of vertical root fracture using cone beam computed tomography: report of two cases. Dent Traumatol 2011;27:484-8.
22. Zou X, Liu D, Yue L, Wu M. The ability of cone-beam computerized tomography to detect vertical root fractures in endodontically treated and nonendodontically treated teeth: a report of 3 cases. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2011;111:797-801.
23. Wang P, He W, Sun H, Lu Q, Ni L. Detection of vertical root fractures in non-endodontically treated molars using cone-beam computed tomography: a report of four representative cases. Dent Traumatol 2012;28:329-33.
24. Liao WC, Tsai YL, Wang CY, et al. Clinical and radiographic characteristics of vertical root fractures in endodontically and nonendodontically treated teeth. J Endod 2017;43:687-93.
25. Rivera EM, Walton RE. Longitudinal tooth fractures: findings that contribute to complex endodontic diagnoses. Endod Topics 2007;16:82-111.
26. Walton RE, Michelich RJ, Smith GN. The histopathogenesis of vertical root fractures. J Endod 1984;10:48-56.
27. Xu H, Zheng Q, Shao Y, et al. The effects of ageing on the biomechanical properties of root dentine and fracture. J Dent 2014;42:305-11.
28. Okeson JP. Management of Temporomandibular Disorders and Occlusion. 7th ed. St. Louis, Mo.: Elsevier/Mosby; 2013.
29. Bakke M, Holm B, Jensen BL, Michler L, Moller E. Unilateral, isometric bite force in 8-68-year-old women and men related to occlusal factors. Scand J Dent Res 1990;98:149-58.
30. Ferrario VF, Sforza C, Serrao G, Dellavia C, Tartaglia GM. Single tooth bite forces in healthy young adults. J Oral Rehabil 2004;31:18-22.
31. Lertchirakarn V, Palamara JE, Messer HH. Patterns of vertical root fracture: factors affecting stress distribution in the root canal. J Endod 2003;29:523-8.
32. White SC, Pharoah MJ. Oral Radiology: Principles and Interpretation. 6th ed. St. Louis, Mo.: Mosby/Elsevier; 2009.
33. Nanci A. Ten Cate's Oral Histology: Development, Structure, and Function. 8th ed. St. Louis, Mo.: Elsevier; 2013.
34. Nelson SJ. Wheeler's Dental Anatomy, Physiology and Occlusion. 10th ed. St. Louis, Mo.: Elsevier/Saunders; 2015.
35. Sultana M, Yamada K, Hanada K. Changes in occlusal force and occlusal contact area after active orthodontic treatment: a pilot study using pressure‐sensitive sheets. J Oral Rehabil 2002;29:484-91.
36. Angelopoulos C. Cone beam tomographic imaging anatomy of the maxillofacial region. Dent Clin North Am 2008;52:731-52.
37. Katranji A, Misch K, Wang HL. Cortical bone thickness in dentate and edentulous human cadavers. J Periodontol 2007;78:874-8.
38. Sheng L, Qu W, Li Y, Qu Z, Wang J. Three-dimensional survey of the whole mandibular canal and mandibular morphology by cone beam computed tomography in normal young people [in Chinese, with abstract in English]. Hua Xi Kou Qiang Yi Xue Za Zhi 2016;34:156-61.
39. Teixeira E, Sato Y, Akagawa Y, Shindoi N. A comparative evaluation of mandibular finite element models with different lengths and elements for implant biomechanics. J Oral Rehabil 1998;25:299-303.
40. 李輝煌. Finite Element Simulations with ANSYS Workbench 15. 初版. 台北: 全華圖書股份有限公司; 2014.
41. Field C, Ichim I, Swain MV, et al. Mechanical responses to orthodontic loading: a 3-dimensional finite element multi-tooth model. Am J Orthod Dentofacial Orthop 2009;135:174-81.
42. Hidaka O, Iwasaki M, Saito M, Morimoto T. Influence of clenching intensity on bite force balance, occlusal contact area, and average bite pressure. J Dent Res 1999;78:1336-44.
43. Bjorndal L, Carlsen O, Thuesen G, Darvann T, Kreiborg S. External and internal macromorphology in 3D-reconstructed maxillary molars using computerized X-ray microtomography. Int Endod J 1999;32:3-9.
44. Huang CC, Chang YC, Chuang MC, et al. Analysis of the width of vertical root fracture in endodontically treated teeth by 2 micro-computed tomography systems. J Endod 2014;40:698-702.
45. Newman MG, Takei H, Klokkevold PR, Carranza FA. Carranza's Clinical Periodontology. St. Louis, Mo.: Elsevier/Saunders; 2015.
46. Carvalho RM, Santiago SL, Fernandes CA, Suh BI, Pashley DH. Effects of prism orientation on tensile strength of enamel. J Adhes Dent 2000;2:251-7.
47. Haines DJ. Physical properties of human tooth enamel and enamel sheath material under load. J Biomech 1968;1:117-25.
48. Craig RG, Peyton FA. Elastic and mechanical properties of human dentin. J Dent Res 1958;37:710-8.
49. Lertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain-gauge studies of vertical root fracture. J Endod 2003;29:529-34.
50. Benazzi S, Kullmer O, Grosse IR, Weber GW. Using occlusal wear information and finite element analysis to investigate stress distributions in human molars. J Anat 2011;219:259-72.
51. Smith BH. Patterns of molar wear in hunger-gatherers and agriculturalists. Am J Phys Anthropol 1984;63:39-56.
52. Chen WP, Lee BS, Chiang YC, Lan WH, Lin CP. Effects of various periodontal ligament elastic moduli on the stress distribution of a central incisor and surrounding alveolar bone. J Formos Med Assoc 2005;104:830-8.
53. Jang Y, Hong HT, Roh BD, Chun HJ. Influence of apical root resection on the biomechanical response of a single-rooted tooth: a 3-dimensional finite element analysis. J Endod 2014;40:1489-93.
54. Ausiello P, Franciosa P, Martorelli M, Watts DC. Mechanical behavior of post-restored upper canine teeth: a 3D FE analysis. Dent Mater 2011;27:1285-94.
55. Dejak B, Mlotkowski A, Romanowicz M. Finite element analysis of stresses in molars during clenching and mastication. J Prosthet Dent 2003;90:591-7.
56. Magne P. Efficient 3D finite element analysis of dental restorative procedures using micro-CT data. Dent Mater 2007;23:539-48.
57. Santos AF, Tanaka CB, Lima RG, et al. Vertical root fracture in upper premolars with endodontic posts: finite element analysis. J Endod 2009;35:117-20.
58. Rees JS, Jacobsen PH. Elastic modulus of the periodontal ligament. Biomaterials 1997;18:995-9.
59. Taschieri S, Tamse A, Del Fabbro M, Rosano G, Tsesis I. A new surgical technique for preservation of endodontically treated teeth with coronally located vertical root fractures: a prospective case series. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2010;110:e45-52.