應用稀疏時頻表現式解析生理系統間非線性耦合機轉

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許境恩(Ching-En-Hsu) 查詢紙本館藏

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生物醫學工程研究所

論文名稱

應用稀疏時頻表現式解析生理系統間非線性耦合機轉
(Probing the Nonlinear Mechanisms Between Physiological Systems by Time- Frequency Sparse Representation)

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至系統瀏覽論文 (2025-9-6以後開放)

摘要(中)

跨頻率耦合（Cross Frequency Coupling, CRC）可用來定義不同系統之前的交互作用，當兩系統開始耦合時，兩系統的訊號可被觀察到有相似特徵，交互作用的訊息可能會載在訊號的頻率、相位或者振幅之中。
在生理系統中，跨頻率耦合現象廣泛出現，例如腦波中存在相位-振幅調變
(Phase-Amplitude Coupling, PAC)，也就是存在兩震盪子之間的相互作用，低頻訊號的相位，會改變高頻訊號的振幅，因此高頻震盪訊號除了自己的調頻(Carrier Frequency)外，其振幅能量強度由低頻訊號控制。其中腦波中的PAC便可應用於麻醉場域，而PAC的強度可用來監控患者的麻醉深度與意識狀態。
欲將低頻震盪子的信息載到高頻震盪子上，便牽涉的通訊領域的震幅調變(Amplitude Modulation)與頻率調變(Frequency Modulation)，不同於應用於通訊領域，將訊息(Message)載於已知載波(Carrier)上，在探勘生理系統中的非線性耦合現象，並無法訊息或載波的性質，因此本文的主要目的是提出訊號處理的方法，可針對非線性耦合訊號進行估測。
頻率調變與振幅調變是一種時變且非線性轉換，然而確保有一定的穩定性(Stationary)，因此本文欲針對調變的頻率響應進行分析，且採用時頻展開式(Time Frequency Representation)針對非線性的調變進行觀測，數理證明以時頻轉換解析訊號調變與頻率調變的可行性，提出一套訊號處理方法，可以對訊號中的振幅與頻率調變進行估測，最終以此方法為基礎，檢測生理系統中未知的跨頻率耦合反應，以分析系統間交互作用。

摘要(英)

Cross-frequency coupling (CFC) serves a critical role to define the interaction and synchronization between different systems. When systems begin to communicate, the phase, frequency, or amplitude of these systems may indicate similar pattern.
In electroencephalogram (EEG), the low frequency oscillators’ phase could modulate the high frequency oscillators’ amplitude, which is known as phase-amplitude coupling (PAC). PAC occurs in EEG especially when the subject losses consciousness. Therefore, PAC is an important factor to monitor both the depth of unconsciousness due to anesthesia in surgery and sleepiness in sleep medicine. Moreover, phase frequency coupling (PFC) , another kind of CFC, reflects the interaction between respiratory system and the cardiovascular system. The respiratory sinus arrhythmia (RSA) is defined as the increase and decrease of the rate of heartbeat during inhalation and expiration, respectively. Subject with terrible autonomic nervous function has poor RSA. That is, PFC is a practical tool to evaluate autonomic nervous system.
Given that different modulations are able to explain mechanisms between systems, it is essential to develop the signal processing tool that precisely quantitate coupling activities. CFCs are phenomena comprised of amplitude modulation (AM) and the frequency modulation (FM) in communication domain. AM and FM are non-linear frequency interactions that pose obstacle for Fourier-based method to access correct frequency. The traditional method is to acquire modulation index with constant bandwidth band-pass filter, through this method is not able to discover non-stationary coupling. In this paper, we aim to propose a method based on time frequency representation (TFR) that distinguishes different CFC precisely. TFR also provides an opportunity to deal with non-stationary coupling. We are looking forward to applying our method to other CFCs, including amplitude-amplitude coupling (AAC) and phase-phase coupling (PPC). Eventually, with proposed toolbox, we expect to establish a standard to observe the CFC correctly.

關鍵字(中)

★ 跨頻率耦合
★ 鎮幅調變
★ 頻率調變
★ 時頻展開式
★ 時頻分析

關鍵字(英)

★ Cross Frequency Coupling
★ Amplitude Modulation
★ Frequency Modulation
★ Time Frequency Representation

論文目次

摘要 i
Abstract ii
Table of Contents iii
List of Figures v
Chapter 1 Introduction 1
Chapter 2 Background 3
2.1 Amplitude Modulation 3
2.2 Frequency Modulation 5
2.3 Time Frequency Representation (TFR) Based Measurement Method 7
2.3.1 Short Term Fourier Transform (STFT) 8
2.3.2 Continuous Wavelet Transform (CWT) 9
2.3.3 Inverse Transform of CWT 12
2.3.4 The Mathematical Foundation of CWT 12
2.3.5 Improvement of Time Frequency Representation 17
Chapter 3 Probe the Nonlinear Mechanism in Electrocardiography, ECG 20
3.1 Autonomic Neural Network Model 20
3.2 Integral Pulse Frequency Modulation Model (IPFM) 21
3.3 Unevenly Sampled Pulse Measurement with Synchrosqueezing Transform 24
3.4 Simulated Signal Model Measurement 26
3.5 Factors in Real-World Cardiac-Related Signal Measurement 27
3.6 The algorithm of the CWT Based Autonomic Function Measurement 30
3.7 CWT Based ECG-Derived Respiration (EDR) Measurement 31
Chapter 4 Proposed Nonlinear Measurement Method 34
4.1 The Amplitude Modulation Spectrum 35
4.1.1 Observation on the CWT-based Amplitude modulation Spectrum 37
4.1.2 The Reassignment Process in Amplitude modulation 37
4.2 The Frequency Modulation Spectrum 39
4.2.1 The Reassignment Process in Frequency modulation 41
4.3 Probing Cross Frequency Coupling 44
4.3.1 Phase amplitude Coupling (PAC) Measurement 44
4.3.2 2D Phase Reassignment on Cross Frequency Comodulogram 46
Chapter 5 Conclusion 47
5.1 Conclusion 47
5.2 Future Work to Cross Frequency Coupling 48
5.3 Future Work to Cardiac Dynamic Model 49
Reference 49

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指導教授

林澂(Chen Lin)

審核日期

2022-9-6

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