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| Title: | 誤差、線性化和取樣如何影響核磁共振訊號的初始值和時間常數
How Errors, Linearization, and Sampling Affect Initial Values and Time Constants of NMR Signals |
| Authors: | 林宜興
Yixing, Lin |
| Contributors: | 蔡尚岳
Tsai, Shang-Yueh
林宜興
Lin Yixing |
| Keywords: | 核磁共振譜學
代謝物濃度
代謝物橫向鬆弛時間
回訊時間
Nuclear Magnetic Resonance Spectroscopy
Metabolite Concentration
Metabolite T2
Echo Time |
| Date: | 2025 |
| Issue Date: | 2025-05-02 15:05:43 (UTC+8) |
| Abstract: | 研究目的
從多個回訊時間所測得的訊號大小來擬合出代謝物濃度可以避免掉只從單一個回訊時間與單一個固定的時間常數去回推代謝物濃度的不準確之處，但是用擬合的方式也有三個面向要考慮：在回訊時間所測得的訊號大小會有各種誤差、不同的擬合方法可能會計算出不同的初始濃度與時間常數、也許不需要用到很多個回訊時間就可以有不錯的準確度。
研究方法
我們用程式模擬的方式來探討誤差、線性化和取樣如何影響代謝物的初始濃度和時間常數。我們針對時間常數是五十毫秒到四百毫秒的代謝物，施加百分之零點五到百分之十的測量誤差，並觀察訊號大小在兩組不同的回訊時間下有何變化。
研究結果
關於線性化，應透過非線性擬合而不是線性擬合來計算代謝物的初始濃度和時間常數，因為當存在測量誤差時，非線性擬合計算出來的初始濃度誤差較小，時間常數誤差也較小。關於誤差，初始濃度的誤差約為測量誤差的一半，時間常數的誤差約為測量誤差的兩倍。關於取樣，若將回訊時間從八個減少到四個，則初始濃度的誤差增加不到測量誤差的一半，時間常數的誤差增加不到測量誤差的兩倍。
Purposes
Fitting from multiple echo times to obtain the concentration of a metabolite circumvents the inaccuracy of extrapolation from just one echo time and from a rigid time constant to obtain the concentration, but three considerations regarding fitting arise: Echo signals picked up by the induction coil suffer various sources of errors, different fitting methods may compute different initial concentrations or time constants, and the number of echo times needed may possibly be reduced for efficiency.
Methods
We run simulations to see how errors, linearization, and sampling affect the initial concentration and the time constant of a metabolite having a T2 between 50 ms and 400 ms if there is a fixed measurement error between 0.5 % and 10 % from the two sets of echo times: 30, 50, 74, 101, 135, 179, 241, 350 ms and 1, 2, 5, 13, 30, 72, 170, 400 ms.
Results
Regarding linearization, the initial concentration and the time constant of a metabolite should be computed by nonlinear fitting instead of linear fitting because nonlinear fitting produces a smaller error of initial concentration and a smaller error of time constant when there is a measurement error. Regarding errors, the error of initial concentration is approximately one half of the measurement error and the error of time constant is approximately twice the measurement error. Regarding sampling, reducing the number of echo times from the set {1, 2, 5, 13, 30, 72, 170, 400} to the set {1, 7, 54, 400} increases the error of initial concentration by less than one half of the measurement error and increases the error of time constant by less than two times the measurement error. |
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| Description: | 碩士
國立政治大學
應用物理研究所
111755003 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111755003 |
| Data Type: | thesis |
| Appears in Collections: | [應用物理研究所 ] 學位論文
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