本研究旨在提出並評估使用統計形狀模型，重建受試者個人化踝關節的可行性。本研究從27名年輕健康志願者蒐集其踝關節三維影像作為訓練模型以建立統計形狀模型。使用“增生和自行適應網格”演算法，對所有已對齊之形狀模型進行預先處理，產生具有相應性且一致數量界標的訓練模型，這些訓練模型將進行主成分分析以獲取踝關節每一塊骨骼形狀的所有變化模式。將分析出的特徵值和特徵向量作為形狀參數，變更其加權值以決定模型之形狀變異量。形狀變異量和平均形狀共同組成統計形狀模型。為獲取踝關節模型之形狀並計算模型在空間中的擺位，本研究開發了一種雙層式優化方法（基因演算法）來更新擺位和形狀參數，直到模型之數位重建透視影像與6個視野的X光透視影像達到最佳匹配。外層優化旨在搜索前3筆最佳形狀參數，而內層優化計算6個位置參數的最佳組合。為評估提出流程之可行性，進行計算機模擬，以志願者脛骨、距骨與跟骨之電腦斷層掃描影像生成六個視野的虛擬X光透視影像。將本方法重建的踝關節模型，與作為參照標準的受試者電腦斷層影像進行比較，得出脛骨的平均（標準偏差）重建誤差為0.59（0.05）mm，距骨為0.94（0.08）mm，跟骨為0.84（0.09）mm。本研究提出一種新的雙層優化方案，經測試能以高精確度重建個人踝關節骨骼模型。

This purpose of the study was to propose and evaluate the feasibility of an optimization procedure to customize subject-specific ankle joint complex (AJC) using a statistical shape model (SSM). The SSM model was established by utilizing a number of training shape models obtained from 27 young healthy volunteers. All the shape models were preprocessed to have a corresponding and a consistent number of landmarks using the “growing and adaptive meshes” algorithm. Principle component analysis for these best-aligned training shape model sets gave the primary modes of shape variations. Taking the shape parameters as weighting factors, a linear combination of shape variations gave the overall variation of the shape. Summation of the overall variation and mean shape determined the SSM. To customize the shape of the AJC models and determine the 3-D pose of the model, we developed a dual-level heuristic optimization scheme (genetic algorithm) to update pose and shape parameters until the model-projected digitally reconstructed radiographs (DRRs) best-matched to 6 view x-ray images. The outer-level optimization aimed to search for an optimal set of first 10 shape parameters while the inner-level optimization was operated to determine an optimal set of 6 pose parameters. To evaluate the feasibility of the proposed optimization pipeline, a computer simulation study was carried out. Six view x-ray images were generated by virtually projecting a volunteer’s CT volumes of the tibia, talus, and calcaneus. The reconstructed AJC models using the proposed method were compared with the subject-specific CT-derived surface bone models, giving mean (standard deviation) shape errors of 0.59(0.05) mm for the tibia, 0.94(0.08) mm for the talus and 0.84(0.09) mm for the calcaneus. In conclusion, the study proposed a new dual-level optimization scheme to customize the subject-specific AJC shape models. The accuracy of the reconstructed shape models showed that the proposed method may provide a feasible approach to customize the individual AJC models.

摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1 研究背景 1
1.2 踝關節解剖構造 2
1.3 統計形狀模型 3
1.4 文獻回顧 4
1.5 研究目的 6
第二章 材料與方法 7
2.1 試體來源 8
2.2 受試者骨骼模型 9
2.3 統計形狀模型 10
2.4 模型對應關係(Shape Correspondence) 12
2.5 建構模型結構變異(Shape Variation) 16
2.6 電腦模擬 18
2.7 重建立體關節幾何結構 21
2.8 重建誤差之量化 26
第三章 模擬結果 28
3.1 對齊方式對建立模型對應點之影響 28
3.2 統計形狀模型 30
3.3 不同視野數量下的成品比較 33
3.4 位置誤差 41
3.5 角度誤差 47
3.6 不同骨頭之重建誤差 53
3.7 在已知骨骼擺位下進行重建 54
第四章 討論 56
4.1 對齊方式對於建立模型對應點之影響 58
4.2 視野數量對於重建誤差之影響 58
4.3 不同骨頭之位置誤差 58
4.4 不同骨頭之角度誤差 59
4.5 不同骨頭之重建誤差 60
4.6 由位置誤差造成重建形狀誤差 60
4.7 研究限制 61
第五章 結論 62
參考文獻 63

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