臺灣博碩士論文加值系統

核子醫學具有提供活體生理資訊的功能，臨床上可應用至臟器功能或代謝作用之定量分析。假設待測的器官滿足線性非時變系統的特性，則器官之輸出函數，可從器官之輸入函數與反應函數進行摺積（Convolution）運算求得。經由核子醫學所使用之偵檢器或掃描儀測量器官之輸入與輸出之相關時間-活度曲線，可以反向推導出器官之反應函數，此過程稱為解摺積（Deconvolution）。實際臨床作業上因為時間的限制，會使得輸入及輸出函數取樣不足，若運用傳統的解摺積方法會造成求得的反應函數產生高頻的震盪甚至出現負值，不利於臨床應用。本研究以腎圖（Renogram）為例，探討在取樣資料不足的情況下，如何利用數學方法來增進解摺積的正確性，使得腎圖所呈現的腎臟反應函數能精確提供相關腎臟功能的量化資料。由於臨床上取樣不足是造成解摺積誤差最主要的來源，所以可根據已取得的資料再配合核醫藥物衰減的特性，將取樣的訊號作曲線延伸或外插以補足點數，再去做解摺積求得反應函數，將可有效的減少高頻雜訊的影響及產生負值的問題。傳統作法上先將這些不完整的訊號作曲線擬合（Curve Fitting），以減少雜訊的影響，然後再依據已知訊號做線性、半餘弦、多項式等外插方法，使曲線延伸至原始訊號3-4倍，最後再做解摺積得到新的反應函數。從實驗模擬中，先做曲線擬合再做非線性外插來解摺積所得到之反應函數，除了可有效解決臨床因取樣不足所造成的問題，這些方法所求得之均方根差可有效降至10%以下。而本研究的重點在於應用多解析度分析法，使用一些常用的小波濾波器搭配多項式曲線擬合，將訊號先做小波轉換再做曲線延伸，解摺積所求得之反應函數比起傳統的曲線延伸方法更能有效的減少均方根差，尤其是對於越不正常的腎臟活度曲線，亦即曲線下降越緩慢能量越大的曲線有更明顯的效果，可將均方根差減少30%以上。

The accurate distribution of transit times and mean transit times of organ’s metabolism is an important quantitative tool in nuclear medicine, having applications within renal, cardiac, liver and cerebral examinations. A deconvolution algorithm is such a technique that can be used to isolate the response of an organ from variations, which occur due the shape of the input function. Practical application of deconvolution requires the incorporation of additional information describing what constitutes an acceptable impulse response into the deconvolution process. Previous studies with several of the algorithms have suggested that sensitivity to noise is a significant problem and may account for some of the oscillatory impulse response computed from studies done with fragmented injections. It is thus desirable to evaluate a deconvolution algorithm capable of accurately handling the range of functions found in shunt quantification. Development of such an algorithm may extend the range of clinical studies that are correctable by deconvolution. Probabilistic and more accurate information concerning the impulse response may be weighted with the data into a statistical estimate of the impulse response. Our study applies curve fitting and wavelet transform based on appended curve technique to improve the accuracy of the impulse response curve and reduce the deconvolution error effectively. Compare with the traditional methods, our study can effectively reduce the root mean square error more than 30%.

第 1 章、 前言 1
第 2 章、 腎臟活度曲線 3
第 1 節、 腎臟解剖與生理 3
第 2 節、 腎臟核醫藥物(Radiopharmaceuticals) 6
第 3 節、 核子醫學腎臟功能檢查 8
第 4 節、 腎功能評估 9
第 5 節、 臨床上的應用 15
第 6 節、 平均穿流時間(Mean Transit Time) 17
第 3 章、 腎圖的分析 19
第 1 節、 腎臟系統模型 19
第 2 節、 解摺積方法 24
第 3 節、 解摺積的誤差 26
第 4 節、 曲線延伸 28
第 5 節、 曲線擬合 30
第 4 章、 多解析度分析於腎圖解摺積技術的應用 32
第 1 節、 小波的基礎原理 (Fundamentals of Wavelet) 32
第 2 節、 應用小波轉換於曲線延伸 36
第 5 章、 實驗方法與討論 40
第 1 節、 解摺積誤差的觀察 40
第 2 節、 線性曲線延伸 41
第 3 節、 非線性曲線延伸 43
第 4 節、 加入雜訊及曲線擬合 45
第 5 節、 小波轉換的運用 48
第 6 章、 結論與未來方向 60
參考資料…………………………………………………………..62

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