第二心音 (S2s) 是一個具有不同頻率聽覺振動的短脈衝且其包含兩個成分，稱為主動脈 (aortic, A2) 和肺動脈 (pulmonic, P2) 的閉合聲音。S2 的臨床評估已被認定為 “心臟聽診的關鍵”。A2s 和 P2s 之間的延遲在醫學術語上被稱為分裂 (split)，其攜帶著重要的臨床線索。此外，其他參數如 S2s (即 A2s, P2s, 和分裂) 的持續時間和 A2s 和 P2s 的瞬時頻率能量 (EIF) 也可以提供重要的臨床線索。但是，由於 A2–P2 之間的重疊及 P2 的低能量模型導致分裂偵測的問題是難解的。就此而言，有可能將 S3 (第三心音) 誤判為一個帶有 “固定分裂” 問題的不正常的 S2。在文獻中，先前研究僅注重經驗上的分裂量測，其是基於 S2s時頻表示 (TFR) 的目視檢查，而兩個不可或缺的議題 A2–P2 重疊及 S2s 的低能量模型則被
忽略。此外，S2s、A2s和 P2s的持續時間並沒有被利用。而且，該方法無法提供任何基於S2s 分析的診斷原則。更進一步地說，S3 和不正常 S2s (特別是 “固定分裂” 問題) 之間的誤判議題並沒有被解決。前述所提之議題在此博士論文中透過發展基於非線性訊號處理的方法被處理，其中包含非線性訊號分解、瞬時頻率估計和非線性時頻局部化。據此，發展的方法可以非常有效率的應付這兩個嚴重的議題 — A2s 和 P2s 之間的重疊以及 P2s 的低能量模型。本博士論文以三個主要的部份達到這些目標。
在敘述方法之前，與發展方法有關的所有理論會被個別的闡明。在那之後，發展方法包括方法、實驗、結果和討論會在接下來的章節中被詳盡的說明。在第一個部分，基於稱為希爾伯特振動分解 (Hilbert vibration decomposition, HVD) 的非線性訊號分解，發展的方法可以定量的測量 S2s 的分裂。HVD 將 S2 拆解為一定數量的分量同時完整地保存相位資訊。接下來，透過使用平滑式魏格納 - 韋立分佈 (smoothed pseudo Wigner-Ville distribution, SPWVD) 和重新分配方法將 A2s 和 P2s 局部化。最後，A2s 和 P2s 的時間索引的均值之間的差異被用來計算分裂。實驗結果顯示分裂的均值 ± 標準差 (SD) 是 34.7±46ms。此方法能有效率的測量分裂，即使當 A2–P2 重疊 ≤ 20 ms 及 P2 對 A2 的正規化峰值時間比是低的 (≥0.22)。
在第二部分，發展方法透過識別 A2s 和 P2s 的起始和結束位置可以測量持續時間、分裂和瞬時頻率的能量。與 A2s–P2s 的持續時間和 IFs 的能量 (EIFs) 有關的診斷也會被檢驗。發展方法精確地指示以識別出正常/不正常的 S2s 同時包含 S2 分裂的類型。此方法的特點是基於 Hilbert 轉換的 IF 估計和基於 SPWVD 重新分配的局部化技術。結果顯示 A2s和 P2s 的持續時間之 mean ± SD 分別為 46.7±2.5 ms 和 41.8±2.4 ms。A2s 和 P2s 的 EIFs 之mean ± SD 分別為 13.8±2.4 和 10.5±1.7。
第三部分發展了 S3 偵測，其可以解決 S3 和帶有 “固定分裂” 的不正常 S2 之間的誤判問題。發展方法基於非線性訊號分解和時頻局部化來偵測 S3。S3 基於位置的資訊被識別並透過測量 S2-S3 之間的時間延遲來確定。結果分析顯示此方法可以正確地偵測 S3s，即使當 S3s 的正規化時間能量和頻率分別 > 0.15 和 > 35 Hz。最後，在結論中提出了限制和未來的展望。

The second heart sounds (S2s) are a short burst of auditory vibration of varying frequencies and it includes two components, called aortic (A2) and pulmonic (P2) closure sounds. The clinical evaluations of the S2s have been recognized as “key to auscultation to the heart.” The delay between the A2s and P2s is called split in medical term, which carries significant clinical clues. Besides, the other parameters such as duration of the S2s (i.e., A2s, P2s and split) and energy of instantaneous frequencies (EIF) of the A2s and P2s can provide significant clinical clues. However, the detection of split is obscured due to overlap between A2–P2 and low energy model of the P2. In this regard, there is a chance of misreading the S3 (third heart sounds) as an abnormal S2 with “fixed split” problem. In literature, the previous works were focused only the measurement of the split empirically based on the visual inspections of the time-frequency representation (TFR) of the S2s only and two vital issues A2–P2 overlap and low energy model of P2s were ignored. Besides, the durations of the S2s, A2s, and P2s were not taken into account. Moreover, the methods could not provide any diagnostic principle based on the analysis of the S2s. Furthermore, the misreading issue between the S3 and abnormal S2s (especially “fixed split” problem) was not addressed. The aforementioned issues were handled in this dissertation by developing methods based on nonlinear signal processing which include nonlinear signal decomposition, instantaneous frequency estimation, and nonlinear time-frequency localization. In accordance, the developed methods could tackle the two serious issues of the S2s — Overlap between A2s and the P2s and low energy model of P2s very efficiently. This dissertation achieves these goals in three main parts.

Before describing the methods all the theories concerned with the developed methods are enlightened in particulars. After that, the developed methods are explained including methods, experiments, results and discussions in subsequent chapters with full details. In the first part, the developed method can measure the split of the S2s quantitatively based on nonlinear signal decomposition called Hilbert vibration decomposition (HVD). The HVD decomposes the S2 into certain number of components while preserving the phase information intact. Further, A2s and P2s are localized by using smoothed pseudo Wigner-Ville distribution (SPWVD) followed by reassignment method. Finally, the split is calculated by taking the differences between the means of time indices of A2s and P2s. The result shows that the mean ± standard deviations (SD) of the split is 34.7±46 ms. The method measures the split efficiently, even when A2–P2 overlap is ≤ 20ms and the normalized peak temporal ratio of P2 to A2 is low (≥0.22).

In the second part, the developed method can measure the duration, splits, and energy of instantaneous frequency by identifying start and end positions of the A2s and P2s. The diagnosis related to duration and energy of IFs (EIFs) of A2s-P2s is also examined. The developed method explicitly guides to distinguish the normal/abnormal S2s including the types of S2 splits. The method is characterized by Hilbert transform-based IF estimation as well as the localization technique based on the reassignment of SPWVD. The results show that the mean ± SD of the duration of A2s and P2s are 46.7±2.5ms and 41.8±2.4ms, respectively for normal subjects. The mean ± SD of the EIFs of A2s and P2s are 13.8±2.4 and 10.5±1.7, respectively.

The third part, the detection of the S3 has been developed which could solve the misreading problem between the S3 and the abnormal S2 with ‘fixed split’ problem. The developed method detects the S3 based on nonlinear single decomposition and time-frequency localization. Based on the positional information, the S3 is distinguished and confirmed by measuring time delay between S2–S3. The result analysis shows that the method can detect the S3s correctly, even when normalized temporal energy and frequency of S3s are > 0.15, and > 35 Hz respectively. Finally the conclusions are drawn mentioning the limitation followed by future scopes.

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