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研究生：	洪郁晴 Hung, Yu-Ching
論文名稱：	藉由延遲性波分解估計動脈硬度指標 Estimate Stiffness Index of Vessel by Delayed Wave Decomposition
指導教授：	舒宇宸 Shu, Yu-Chen
學位類別：	碩士 Master
系所名稱：	理學院 - 數學系應用數學碩博士班 Department of Mathematics
論文出版年：	2016
畢業學年度：	104
語文別：	英文
論文頁數：	46
中文關鍵詞：	光體積描述訊號、血管硬度指標、血管反射指標、複合波分解
外文關鍵詞：	photoplethysmography, stiffness index, reflection index, wave decomposition
相關次數：	點閱：107 下載：4
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血管的硬度指標(Stiffness Index,SI) 是一個很重要的生理指標，它能預測心肌梗塞，還能預測中風等心血管疾病。實際上，血管硬度指標(SI) 是由手指頭所量測出來的周期性的光體積描述訊號波(Photoplethysmogram Wave) 的兩個波峰之間的時間差所計算出來的。在本研究中，我們利用延遲波分解方法去估計該時間差。關鍵的想法就是把PPG 訊號分解為主波與副波兩個波，其中主波是由超音波所量測出的頸動脈的血流速度波型所造成，而副波為其延遲波，也可以想成是從動脈的主要分支所產生的反射波。我們利用複合波分解方法去求得延遲的時間，並以此來估計硬度指標(SI)。透過延遲波與主波的高度比例來估計反射指標(RI)。我們透過最小化平均波形與心臟波形及其經過一段時間延遲波疊合波形的差異，來決定該延遲多少時間與回傳波的大小。我們也比較了Nelder-Mead 的方法。而且我們使用Penalty
function 的方法來平衡誤差與重組係數。最後，我們增加延遲回傳波的數量，並發現若透過12個回傳波以上疊合，可以疊合出與原始平均波形吻合的波形。

Stiffness index (SI) of vessel is an important physiological index and a predictor of cardiovascular disease such as myocardial infarction and stroke. In practice, the stiffness index is computed by finding the time difference of two peaks in a period of the photoplethysmogram (PPG) wave from fingertip. In this study, we use delayed wave decomposition to estimate the time difference instead. The key idea is to decompose the
PPG signal into the velocity waves from the carotid arteries measured by ultrasound transducer and its delayed wave, which is considered as the reflection wave from main branch of artery. The method of the wave decomposition is used to determine the delayed time, which is a parameter relating to the stiffness index; and the ratio of delayed wave and dominant wave, which is used to estimate the reflection index. We determine the time delay and the amplitude of the delayed wave by minimizing the difference between the average waveform and the heart waveform and its delayed wave in a period. We also compared with the Nelder-Mead method. And we used the penalty functions to balance the errors and the delayed coefficients. Moreover, we increase the number of delayed waves and we found that the reconstruction wave is almost the same as the averaged waveform if we used twelve delayed waves at least.

1 Introduction 1
1.1 The Physiologic Indices Presented by Photoplethysmograph Signals . . 1
1.2 Functions of Cardiac Blood Flow Waveforms . . . . . . . . . . . . . . . 7
1.3 The Motivation of Study . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Model Establishment of the PPG Signal and the Waveform of the
Blood Flow Velocity in Carotid Arteries 11
2.1 Definitions of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Delayed Wave Decomposition . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Characteristics of the PPG Signal Waves . . . . . . . . . . . . . . . . . 14
2.3.1 Pretreatment of the PPG Signal Waves . . . . . . . . . . . . . . 14
2.3.2 Characteristics of the Dominant PPG Signal Wave . . . . . . . 15
2.4 The Dominant Wave of the Delayed Wave Decomposition from the Ultrasound
Data about the Waveforms of the Blood Flow Velocity in the
Carotid Artery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Waveform Modification of the Blood Flow Velocity in the Carotid
Artery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Filtering out the Unnecessary Reflected Waves from the Representative
Wave of the Blood Flow Velocity in the Carotid Artery 19
2.4.3 Adjustments of the Waveforms of the Blood Flow Velocity in the
Carotid Artery in Accordance with the Representative Wave of
the PPG Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Establishment and Methodology of the Optimization Model 24
3.1 Optimization Model of the Complex Wave Decomposition on Two Single
Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Optimization model of the Complex Wave Decomposition on Multiple
Single Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Optimization Model with A Constraint . . . . . . . . . . . . . 32
3.2.2 Method of Penalty Functions . . . . . . . . . . . . . . . . . . . 34
4 Numerical Results 36
5 Conclusion and Future Prospects 42
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Bibliography 45
                                    

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校內：2022-07-31公開
校外：2022-07-31公開

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