生醫訊號解構分析與數學模型

Mathematical Modeling and Decomposition Analysis for Biomedical Signals

黃聖澄(Sheng-Cheng Huang)

指導教授 ： 林康平

中原大學/電機資訊學院/電機工程研究所/博士(2017年)

https://doi.org/10.6840/cycu201700723

摘要

在生醫訊號處理領域上，數學模型扮演重要角色，許多不同模型已經發展應用於各種應用上，包含藥物動力學(pharmacokinetics)、血液動力學(hemodynamics)和呼吸生理(respiratory physiology)等領域。本篇論文提出三種不同模型在解構分析分別應用於上述三種不同之領域。兩個指數模型應用於PET影像，多項式模型用於評估呼吸限流(IFL)，進而診斷是否有睡眠呼吸中止症，伽瑪-高斯模型使用於光體積描計圖(PPG)波形分類。
在正子影像，本研究開發出自適性權重非線性最小平方法(AWNLS)，用於解決在量測時的雜訊，所導致在FDG動態模型估算小參數(microrate constant)不穩定的問題。AWNLS方法根據組織時間-活性曲線(TTAC curve)調整成本函數，依據TTAC曲線前半部平均值來修正成本函數。本研究使用不同參數集合，不同雜訊進行模擬，並且比較AWNLS、NLS、WNLS、LLS、GLLS方法之精準度。本研究結果顯示，在高強度雜訊條件之下，NLS法k1-k3有低準確度。NLS法和WNLS法對於起始值敏感。LLS和GLLS法則因存有偏差，在k4十分不準確。相形之下，AWNLS法不受雜訊與起始值影響，均可得到準確的小參數(k1-k4)和FDG代謝率(K)和FDG分佈量(k1/k2)。
在呼吸氣流上，吸氣限流(IFL)是一種睡眠呼氣障礙患者之特別的症狀，時間-氣流曲線表示表示吸氣時，最大的氣流阻抗。本論文研究為一即時演算法用於偵測睡眠時的吸氣限流。本研究發展集合共分成三類，有16個筆被分為正常，78筆被歸類為有IFL，其中有20筆為輕微等級，58筆為嚴重等級。本研究使用多項式逼近方法來擷取IFL曲線特徵，我們使用一階至三階的多項式，計算其平均絕對誤差。本研究提出演算法使用一三階權重多項式模型。在驗證上,總共有1093筆資料被收集為本研究之測試集合，且使用錯誤分類蜘蛛網(misclassification cobweb)分析每一個分類之準確度。研究結果顯示，本研究提出之演算法在IFL分類上有94.14%之正確率。本研究提出一有效且自動化偵測睡眠呼吸限流之演算法。
PPG是一種非侵入式即時量測技術，被廣泛應用於居家與遠端照護。本研究根據DVP訊號前半段陡峭，後半段平滑之特性，提出一結合伽瑪函數與高斯函數之數學模型。本研究收集850筆經由專業醫師分類成五類之DVP訊號，並且使用兩種類模型多高斯模型(multi-Gaussian models)和伽瑪-高斯複合模型(multi-Gaussian models)，並且分別執行兩核心至五核心來驗證。研究結果顯示，本研究提出之數學模型比其他模型有較小的誤差，更適合用於DVP訊號解構分析。因此，本研究已成功證明此模型在PPG訊號分類與曲線擬合更為準確。

關鍵字

數學模型 ； 解構分析

並列摘要

Mathematical modeling plays a crucial role in biomedical signal processing. Many different models have been developed for several applications, including pharmacokinetics, hemodynamics, and respiratory physiology models. This study developed three types of models for decomposition analysis. Two exponential models were used for quantification of positron emission tomography (PET) images. A polynomial model was used to evaluate respiratory flow for distinguishing patients with and without obstructive sleep apnea. A Gamma–Gaussian complex model was used with a photoplethysmographic waveform for clustering.
Regarding PET images, this study developed an adaptive weighted nonlinear least squares (AWNLS) method for solving the problem of measurement-noise-caused high variability in the estimation of the microrate constants of fluorodeoxyglucose (FDG) kinetics. In the AWNLS method, the cost function is adjusted according to the characteristics of the tissue time–activity curve (TTAC). In particular, the average of the early part of the TTAC is used to modify the cost function when fitting the FDG model to the TTAC. A computer simulation applying different sets of parameter values and noise conditions was performed. The accuracy and reliability of the parameters estimated from AWNLS were compared with those estimated from nonlinear least squares (NLS), weighted nonlinear least squares (WNLS), linear least squares (LLS), and generalized linear least squares (GLLS). The errors in k1–k3 obtained using NLS indicate this method’s poor precision in the presence of high noise levels. NLS and WNLS were sensitive to the initial values. Moreover, the k4 estimated using LLS and GLLS were inaccurate because of large bias. By contrast, the microrate constants (k1–k4), FDG metabolic rate (K), and volume of distribution (k1/k2) obtained using AWNLS were stable and accurate irrespective of the noise level and initial values. The AWNLS method could estimate the FDG metabolic rate (K) and the microrate constants (k1–k4) of the FDG model accurately at various noise levels, irrespective of the initial values.
Regarding respiratory flow, inspiratory flow limitation is a critical symptom of sleep breathing disorders. A characteristic flattened flow–time curve indicates the presence of highest resistance flow limitation. This study investigated a real-time algorithm for detecting IFL during sleep. Three categories of inspiratory flow shape were collected from previous studies for use as a development set. Among these, 16 cases were labeled as non-IFL and 78 as IFL, which were further categorized into a minor level (20 cases) and severe level (58 cases) of obstruction. In this study, algorithms using polynomial functions were proposed for extracting the features of IFL. Methods using first- to third-order polynomial approximations were applied to calculate the fitting curve and obtain the mean absolute error. The proposed algorithm is described by the weighted third-order (w.3rd-order) polynomial function. For validation, a total of 1,093 inspiratory breaths were acquired as a test set. The accuracy levels of the classifications produced by the presented feature detection methods were analyzed, and the performance levels were compared using a misclassification cobweb. The results revealed that the algorithm using the w.3rd-order polynomial approximation achieved an accuracy of 94.14% for IFL classification. We concluded that this algorithm achieved effective automatic IFL detection during sleep.
Photoplethysmography (PPG) technology is a noninvasive and real-time optical method that is widely used in primary healthcare and remote clinics. This study proposed a mathematical model that combines the Gamma and Gaussian functions and is based on the characteristics of the digital volume pulse (DVP) waveform—that the front of the curve is steep and the tail of the curve is smooth. This study collected 850 DVP data items, which were divided into five types. We performed decomposition from two to five kernel models by using Gamma–Gaussian and multi-Gaussian models. The results showed that the proposed model was suitable for deconstruction of the DVP waveform, and the residual error was less than that of others. In this study, we proved that the proposed model is more accurate at curve-fitting and more effective in the classification of PPG signals than other models.

並列關鍵字

Mathematical Modeling ； Decomposition Analysis

參考文獻

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