磁振造影技術目前已廣泛應用於臨床診斷與學術研究上，其中擴散磁振造影技術已發展成為探討大腦白質神經束的主要方法，現今已有許多不同的擴散磁振造影技術。藉由量測多張使用不同擴散梯度方向的擴散磁振影像，在水分子的擴散機率分布為高斯分布的假設下，擴散張量造影可有效預估某一體素內水分子的主要擴散方向。若我們假設此主要擴散方向與神經束走向一致，我們便能夠在活體上找出白質神經束的路徑。但擴散張量造影法於某一體素內僅能預估單一個主要擴散方向，為解決此問題，擴散頻譜造影使用不同擴散梯度方向與強度的組合，進而量測水分子的擴散機率分布。因此，擴散頻譜造影法可以更有效地找出白質神經束的路徑。
然而不論是擴散張量造影或擴散頻譜造影，在比較分析不同群組的資料時，他們都面臨一個棘手的問題：如何將這些來自不同個體的資料進行影像對位？問題源自於這些擴散磁振資料並非一般常見的純量影像，擴散張量造影的資料結構為張量影像，而擴散頻譜造影則為機率分布影像，因此不能使用常見的純量影像對位方法。此類擴散磁振影像的對位，除了解剖結構，還須將擴散訊息（如擴散張量或擴散機率分布）進行對齊。對於擴散張量影像，已有許多學者提出不同的對位方法，但尚未有文獻提出擴散頻譜影像的對位方法。本論文的主要目的為使用新近發展的「高度形變微分同胚度量映射法」，針對擴散頻譜影像的資料結構發展相對應的對位方法。
高度形變微分同胚度量映射法將兩個影像間的對位過程模擬成液體的流動，並定義兩影像間的差異函數。此法推導出，當差異函數於最小值時，此流動液體之速度場所須遵循的公式。因此高度形變微分同胚度量映射法所得之液體流動路徑為測地線，亦即此兩影像間的最短路徑。另外，此測地線可僅由初始動量（或初始速度）決定，故此法可將高度變異的非線性解剖影像置於同一座標空間進行線性分析。由於這些重要特性，本研究目的乃在將原發展於二維或三維的高度形變微分同胚度量映射法擴展至六維的擴散頻譜影像（三維影像空間，三維Ｑ空間）。
本研究針對擴散頻譜影像的六維資料結構，定義適當的形變轉換動作：令影像空間的形變場為影像空間的函數，並令Ｑ空間的形變場同時為影像空間與Ｑ空間的函數。在此定義下，本研究提出高度形變微分同胚度量映射法應用於擴散頻譜影像時所遵循的液體流動公式，此法稱之為LDDMM-DSI。慮及擴散頻譜影像的豐富資料量及數值運算時面臨的龐大電腦運算量，本論文亦提出有效的實施方案。此外，本研究進行數個驗證實驗，除探討參數的影響外，並比較LDDMM-DSI與其他對位方法的優劣。實驗顯示使用LDDMM-DSI法對擴散頻譜影像進行影像對位可獲得較佳之結果。除了完整提出LDDMM-DSI的數學架構與數值實施方案外，本論文亦以擴散頻譜影像模板示範LDDMM-DSI可能的應用。
總結而言，在高度形變微分同胚度量映射法的架構下，本論文提出針對擴散頻譜影像的對位方法，LDDMM-DSI。不論以實驗的驗證結果來看，或以擴散頻譜影像模板的示範來觀察，LDDMM-DSI皆為擴散頻譜影像的有效對位方法。此法將有助於日後擴散頻譜影像的群組分析。

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