本研究的主要目的在於分析探討全口下顎齒槽骨植入不同數量與不同位置的植體，並裝上固定式全口牙橋後，在正常輕度咬合之下，植體附近齒槽骨的應力分佈情形。本研究利用電腦斷層掃描(computer tomography，CT)影像圖結合電腦輔助設計(computer aided design，CAD)系統建構双骨質(皮質骨(cortical bone)與鬆質骨(cancellous bone))的下顎齒槽骨模型。此外，利用逆向工程(reverse engineering，RE)方法與CAD (Rhinoceros 5.1.1-10 & Pro/Engineering 2000i)系統建構出包含前牙區與後牙區的14顆牙齒以及植體與支台模型； 另外，延著每一顆牙齒的齒頸線(cervical line)切除牙根以獲得各顆牙齒的齒冠, 同時利用有限元素(finite element，FE)分析軟體(MSC/PATRAN)將各顆牙齒齒冠連接起來而得到全口牙橋。利用MSC/PATRAN軟體將所有的3D 數位實體模型予以網格化後，以程式中的布林運算(Boolean operation)將各模型予以組合，形成有限元素分析模型，組合後的一階元素個數與節點數分別為1,101,954 與252,693個。此外，依植體植入的數量與植入位置的不同，本研究將所欲分析的一階有限元素模型概分為6個植體系統共27個FE模型。之後，依據27個一階FE模型分析所得之結果，在各植體系統中選出最佳設計的模型(共計6個)進行二階元素的網格化與應力分析工作。二階FE模型元素個數與節點個數分別為1,101,954與1,298,347個。在分析軟體方面，對所有的數學計算來說，MSC/PATRAN與MSC/NASTRAN軟體具有前處理器與後處理器的功能，可評估牙體與下顎齒槽骨的生物力學現象。在負載條件的選擇上，根據上下顎輕度咬合時的咬合力作為本研究的施載條件。在應力評估方面，本研究以等效應力 (von Mises stress，VMS)降伏法則作為評估各模型於受力後，模型內皮質骨、鬆質骨與植體上應力大小的表示方式。 依電腦模擬結果顯示，各FE模型的應力分佈大大地受到植體植入數目與植入位置的影響。在齒槽骨上，與單顆牙齒類似，皮質骨上的最大等效應力 (maximal von Mises stress，MVMS)均集中於皮質骨上緣與植體接觸處。 在四根植體系統方面，F-8模型的MVMS最低；在六根植體系統方面，S-6模型的MVMS最低；在八根植體系統方面，E-3模型的MVMS最低；在十根植體系統方面，T-3模型的MVMS最低；在十二根植體系統方面，各模型的MVMS均低；在十四根植體系統方面，由於所有缺牙處均植入植體，因此在其內各植體處所產生之應力值為最低。此外，在二階FE模型的分析結果顯示，F-8、S-6、E-3、T-3、TW-2及FT-1等6個FE模型分析所得的MVMS值均較一階FE模型之MVMS為高，其值約31 ~ 49 %。若依照文獻資料(即皮質骨的最大極限強度為100 ~ 170 MPa，植體的最大極限強度為550 MPa)及線彈性原理(負載大小增加為5倍，則應力值亦增加5倍)，所有的二階FE模型皮質骨與植體上之MVMS均未超過極限強度，而且，隨著植體植入愈多，MVMS有逐漸下降之趨勢。由此可知，植體植入愈多，手術治療後的安全性愈高。

The purpose of this study was to compare the effects of various designs of implants’ placement on stress distribution in bone around the implants supporting one-unit fixed prosthesis. A computer tomography image was redrawn to reconstruct a digital three-dimensional solid model of a mandible including the cortical bone and cancellous bone. Moreover, the reverse engineering method and computer-aided design were employed to construct fourteen pieces of digital three-dimensional solid model of teeth including the anterior and posterior regions as well as implant and abutment. Each tooth was cut along the cervical line to obtain the crown, and all of the crowns were connected by using the MSC/PATRAN software and called the fixed prosthesis. All of the digital three-dimensional solid models were combined and transformed to the FE models by using the MSC/PATRAN software, and they were classified into 27 configurations according to the number and location of the implants. The MSC/PATRAN software was used to develop the FE mesh of each model comprising of 1,101,954 elements with 252,693 nodes. The MSC/NASTRAN software was utilized as pre and post-processor for all mathematical calculations necessary to evaluate dental and mandibular biomechanics. One set of multiple vertical loads was used to simulate the possibility of occlusion status. And the von Mises stress values in the cortical bone, cancellous bone and implants were evaluated. The simulated results indicated that the stress distributions for FE models were largely affected by the number and location of implants. In the bone, similar to the single-tooth case, the von Mises stresses were all concentrated toward the cortical bone around the collar of the implants for FE models. In the 4-implants system, the model F-8 was generated the lowest MVMS in the position L6 of the cortical bone; in the 6-implants system, the model S-6 was generated the lowest MVMS in the position L5 of the cortical bone; in the 8-implants system, the model E-3 was generated the lowest MVMS in the position L5 of the cortical bone; in the 10-implants system, the model T-3 was generated the lowest MVMS in the position L5 of the cortical bone; in the 12-implants system, all of models were generated lower VMS in the cortical bone ; in the 14-implants system, the model FT-1 was generated the lowest MVMS in the position R6 of the cortical bone. From the literatures, the ultimate strength in the cortical bone surrounding the cervical regions of implants and the implant were about 100 and 550 MPa, respectively. If the loadings were increased to 5 times in this study, the MVMS of all materials would be increased to 5 times, too. According to these conditions, the model of F-8, S-6, E-3, T-3, TW-3 and FT-1 would be the best designs for each implant system and suitable to use in the clinical surgery. From the above statements, with more supporting implants, the treatment may be safer.

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