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Title: | 修正傅立葉級數並應用於心電圖分析 Modified Fourier series and its application in ECG analysis |
Authors: | Ming-Hsiu Song 宋明修 |
Advisor: | 管傑雄(Chieh-Hsiung Kuan) |
Keyword: | 心電圖,頻譜,非週期函數,週期性函數,隨機行為,奇函數,偶函數, electrocardiogram,spectrum,aperiodic function,periodic function,random behavior,even function,odd function, |
Publication Year : | 2018 |
Degree: | 碩士 |
Abstract: | 根據世界衛生組織(World Health Organization)的統計,心血管疾病已成為全球十大死因的第一位。專家估計,在2012年就有1750萬人死於心血管疾病,佔全球死亡總數的31%。心血管疾病致死率相當高卻又難以預期,所以發展一套早期預防暨檢測系統去區別出正常人和心律不整病患是很重要的,區別出正常人和心律不整病患可以幫助醫生有效評估病人情況,給予調養的建議,進一步降低心血管疾病死亡率,達到預防醫學所提倡”預防勝於治療” 之目的。
在眾多心臟檢測技術中,利用心電圖來檢測心臟疾病最簡便有效,且心電圖有非侵入性、即時偵測和容易取得等優點,因此在臨床上被廣泛使用。 傳統心電圖分析技術,使用心律變異分析來區別正常人和心律不整病患,此方法統計多個心電圖尖峰區間(RR-interval)的變異數作為區分標準,變異數較大者歸類為心律不整病患,反之變異數較小者歸類為正常人。 我們則提出一套不同於傳統心律變異分析之新技術。使用MIT的資料庫,在研究心電圖的過程中,我們發現即使是正常人的心電圖,心跳週期的信號也不會完全重疊,也就是說,有非週期性的成分存在,非週期性信號可能來自於心理因素,尤其是主意識的影響。 因此心臟不像汽車引擎固定動作,而是有隨機行為,非週期性信號可代表隨機行為。因為心電圖由週期性和非週期性信號組成,因此我們將心電圖信號同時用兩組基底:一組週期性基底和另一組非週期性基底去做展開,週期性基底採用傅立葉基底,傅立葉基底的缺點是在邊界的誤差會較大,我們加入非週期性基底後,發現可以改善誤差,並從頻譜分析中觀察到心臟有隨機行為。 本研究可再細分成兩套不同方法來分析心電圖信號,第一套方法稱為駐波展開解,展開式中包含駐波成分。第二套方法稱為行進波展開解。兩種展開的原理都是前面所述,在週期性基底中加入非週期性基底,展開後再由頻譜去做進一步分析。 結果顯示,心臟隨著時間變化,有隨機行為的存在,時間域上不同的心動週期,頻譜上可以找到不同大小的非週期性成分。並且,有多樣化的組合方式可以去描述同一個心電圖的心動週期,例如駐波解和行進波解最後會對應到很相似的偶函數和奇函數,但偶函數的組成卻分別可以有兩種。此外,利用偶函數奇函數的功率指標或是週期性和非週期性的功率指標作為依據,可以對正常人與心律不整病患做初步的區分。 未來我們將以此技術和傳統的心律變異分析做比較,應用在臨床疾病的治療方面,可以協助醫生判斷病情,並提供病人自身病情的資訊,進一步採取預防疾病的措施,達到預防醫學的效果。 According to WHO (World Health Organization) statistics, cardiovascular disease has become the top one among ten leading causes of death worldwide. Experts estimate that in 2012,17 million 500 thousand people died of cardiovascular disease, accounting for the 31% total number of worldwide deaths. Cardiovascular disease mortality rate is very high and it was difficult to be expected, so the development of a prevention and early detection system to distinguish between the normal and arrhythmia patients is very important, the difference between normal and arrhythmic patients can help doctors evaluate the conditions of the patients ,give them drugs or advice on medical cares, to further reduce the mortality of cardiovascular disease. Among many cardiac detection techniques, using an electrocardiogram to detect heart disease is the most simple and effective method. Because electrocardiogram has the advantage of non-invasive, real-time detection, it is widely used in clinic application. Traditional ECG analysis techniques uses HRV (Heart rate variability) to differentiate between normal and arrhythmogenic patients. This method counts multiple RR interval variants as the criterion, the larger number of variants were classified as arrhythmia patients, and the small number of variants were classified as normal people. Normal ECG are considered to be period according to traditional ECG analysis as well. In the course of studying MIT database’s electrocardiogram, we found that even in normal people, the signal of heartbeat cycle does not overlap completely, that is,there are aperiodic components, aperiodic signals may come from psychological factors, especially the influence of main consciousness. So the heart is not fixed like a car engine, but there's random behavior in it,and aperiodic signal is representative of random behavior. Because ECG is composed of periodic and aperiodic signal,we use two sets of bases: one periodic and the other aperiodic. The periodic base is the Fourier base,the disadvantage of Fourier base is larger boundary error. After adding the aperiodic base, we find that aperiodic base can lower the boundary error and stand for random behavior in the spectrum analysis. This study can be subdivided into two different ways to analyze the ECG signal. The first method is called standing wave expansion solution,which includes standing wave in it, and the second method is called propagating wave expansion solution. The principle of the two expansion is described earlier, adding aperiodic base in the periodic base, and then using the spectrum for further analysis. The results show that there is random behavior in the heart, that is, there are different aperiodic components in the spectrum with different cardiac cycles in the time domain. And there are a variety of combinations that can be used to describe the cardiac cycle of the same ECG, such as standing wave solutions and traveling wave solutions, which eventually correspond to very similar waveforms of even and odd functions. However, the even function can be decomposed of two different functions. In addition, based on the power index, we can make a preliminary distinction between normal people and arrhythmia patients. In the future, we will compare this technique with traditional Heart rate variability analysis. Applying in the treatment of clinical disease, we can help doctors to determine the patients’ disease, and provide the patients’ with their disease information. This way, they can take measures to prevent heart disease, and the goal of preventive medicine will be achieved. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70212 |
DOI: | 10.6342/NTU201704204 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 電子工程學研究所 |
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