分形高斯雜訊之維度估測及其生理訊號上之應用

Dimension Estimation of Fractional Gaussian Noise and Its Application to Physiological Signals

李旬政(Shiun-Jeng Li)

指導教授 ： 張 翔

國立清華大學/電機資訊學院/電機工程學系/博士(2007年)

https://doi.org/10.6843/NTHU.2007.00328

摘要

從生理系統擷取的節律性訊號經常具有記憶（memory）和長程相關（long-term correlation）的特質。依據它們的來源，這類的訊號可以用兩種數學模型來描述。若訊號是直接源自於神經與肌肉，則以離散分形高斯雜訊的模型來描述。若訊號是源自於神經與肌肉的累加性效果（cumulative effects），則以離散分形布朗運動(discrete-time fractional Brownian motion) 的模型來描述。也就是說，我們可以將訊號視為具有非整數維度的特質，而後使用分形維度來捕捉生理訊號強度的特徵。本估測方法是以離散分形高斯雜訊為理論。在實際訊號估測維度的過程中，需計算訊號的自相關函數與頻譜分佈函數（spectral distribution function, SDF），而後以勒讓德多項式（Legendre polynomials, LPs）為基底集來分解頻譜分佈函數。當資料長度增加時，估測子的標準差會減少。因此，此分形維度估測是統計學上相容的（statistically consistent）。當系統是正相關（positive correlation）時，估測子的標準差會較小。因此，此估測子特別適合用於探討共濟的生理功能。
因為使用了頻譜分佈函數，本估測方法可同時獲得分形維度與頻譜節律這兩個指標。當分形維度搭配上頻譜節律一起使用時，這兩個指標除了可用以區別正常鼠不同的排尿狀態，還可以用於研究脊髓損傷鼠用藥與否的共濟模式之探討。正常鼠的排尿過程中，EMG與CMG可以利用分形維度與頻譜特性明確地分為儲尿、排尿及排尿後三個階段，此為尿道外括約肌與膀胱逼尿肌共濟模式之常態特性，可做為比對藥物影響的依據。對於脊髓損傷鼠施加蕃椒素或RTX的研究，藉由排尿與儲尿期間EMG、CMG之分形維度與頻譜特性，發現其共濟模式已經與正常鼠不同。結果顯示，整體而言，以RTX的效果較佳，RTX產生弱共濟（weak synergy），而蕃椒素已不存有共濟（no synergy）的特徵。相信本研究提供的方法適用於評估其它共濟的生理功能，與評估藥物對具有動態疾病的動物的影響。

關鍵字

分形維度 ； 分形高斯雜訊 ； 頻譜分佈函數 ； 蕃椒素 ； 動態疾病 ； 效能評估 ； 排尿的共濟行為

並列摘要

Rhythmic signals from physiological systems usually have memory and long term correlation. They can be modeled as fractional Brownian motion or fractional Gaussian noise depending on if the signals are derived from cumulative effects of nerves and muscles. That is, they can be treated as signals with fractional dimension and the value of its fractal dimension (FD) can be used to characterize the intensity of physiological signals. In this study, a novel method of dimension estimation based on the calculation of spectral distribution function (SDF) of discrete-time fractional Gaussian noise using Legendre polynomials (LPs) as basis set is proposed. The dimension estimation is statistically consistent and its standard deviation is small when the system is under positive correlation. Hence, this estimator is especially suitable for investigating synergic physiological functions. Due to SDF, two indicators, FD and spectral frequency, can be obtained simultaneously. These two indicators can be applied in illustrating the synergic behavior of detrusor of the bladder and external urethral sphincter (EUS) during micturition. Another application of these two indicators is the dynamical performance evaluation of the pharmacological effects on micturition in spinal-cord-injury (SCI) rats. Capsaicin and resiniferatoxin (RTX) are administered and their effects are compared. Results indicate that the synergy of micturition using RTX is better than that of capsaicin. It is believed that this methodology would be useful in the assessing of other synergic physiological functions and studying functional effects of pharmacology for animals under dynamical diseases.

並列關鍵字

Fractal dimension ； fractional Gaussian noise ； spectral distribution function ； capsaicin ； resiniferatoxin ； dynamical diseases ； performance evaluation ； synergy of micturition

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