生醫訊號解構分析與數學模型

黃聖澄

doi:10.6840/cycu201700723

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生医讯号解构分析与数学模型

Mathematical Modeling and Decomposition Analysis for Biomedical Signals

黄圣澄 , 博士　　导师：林康平　　

英文 DOI： 10.6840/cycu201700723

数学模型；解构分析； Mathematical Modeling ； Decomposition Analysis

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摘要 │ 参考文献 (94) │ 国际计量

摘要〈TOP〉

在生医讯号处理领域上，数学模型扮演重要角色，许多不同模型已经发展应用於各种应用上，包含药物动力学(pharmacokinetics)、血液动力学(hemodynamics)和呼吸生理(respiratory physiology)等领域。本篇论文提出三种不同模型在解构分析分别应用於上述三种不同之领域。两个指数模型应用於PET影像，多项式模型用於评估呼吸限流(IFL)，进而诊断是否有睡眠呼吸中止症，伽玛-高斯模型使用於光体积描计图(PPG)波形分类。
在正子影像，本研究开发出自适性权重非线性最小平方法(AWNLS)，用於解决在量测时的杂讯，所导致在FDG动态模型估算小参数(microrate constant)不稳定的问题。AWNLS方法根据组织时间-活性曲线(TTAC curve)调整成本函数，依据TTAC曲线前半部平均值来修正成本函数。本研究使用不同参数集合，不同杂讯进行模拟，并且比较AWNLS、NLS、WNLS、LLS、GLLS方法之精准度。本研究结果显示，在高强度杂讯条件之下，NLS法k1-k3有低准确度。NLS法和WNLS法对於起始值敏感。LLS和GLLS法则因存有偏差，在k4十分不准确。相形之下，AWNLS法不受杂讯与起始值影响，均可得到准确的小参数(k1-k4)和FDG代谢率(K)和FDG分布量(k1/k2)。
在呼吸气流上，吸气限流(IFL)是一种睡眠呼气障碍患者之特别的症状，时间-气流曲线表示表示吸气时，最大的气流阻抗。本论文研究为一即时演算法用於侦测睡眠时的吸气限流。本研究发展集合共分成三类，有16个笔被分为正常，78笔被归类为有IFL，其中有20笔为轻微等级，58笔为严重等级。本研究使用多项式逼近方法来撷取IFL曲线特徵，我们使用一阶至三阶的多项式，计算其平均绝对误差。本研究提出演算法使用一三阶权重多项式模型。在验证上,总共有1093笔资料被收集为本研究之测试集合，且使用错误分类蜘蛛网(misclassification cobweb)分析每一个分类之准确度。研究结果显示，本研究提出之演算法在IFL分类上有94.14%之正确率。本研究提出一有效且自动化侦测睡眠呼吸限流之演算法。
PPG是一种非侵入式即时量测技术，被广泛应用於居家与远端照护。本研究根据DVP讯号前半段陡峭，後半段平滑之特性，提出一结合伽玛函数与高斯函数之数学模型。本研究收集850笔经由专业医师分类成五类之DVP讯号，并且使用两种类模型多高斯模型(multi-Gaussian models)和伽玛-高斯复合模型(multi-Gaussian models)，并且分别执行两核心至五核心来验证。研究结果显示，本研究提出之数学模型比其他模型有较小的误差，更适合用於DVP讯号解构分析。因此，本研究已成功证明此模型在PPG讯号分类与曲线拟合更为准确。

并列摘要〈TOP〉

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.

参考文献 ( 94 ) 〈TOP〉

[1] Sokoloff, L., Reivich, M., Kennedy, C., Des Rosiers, M., Patlak, C. S., Pettigrew, K., Sakurada, O. & Shinohara, M. (1977). The [14C] deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat. Journal of neurochemistry, 28(5), 897-916.
连结：
[2] Phelps, M., Hoffman, E., Huang, S. C., & Kuhl, D. (1977). Positron tomography:" in vivo" autoradiographic approach to measurement of cerebral hemodynamics and metabolism. Acta neurologica Scandinavica. Supplementum, 64, 446-477.
连结：
[3] Su, K. H., Lee, J. S., Li, J. H., Yang, Y. W., Liu, R. S., & Chen, J. C. (2009). Partial volume correction of the microPET blood input function using ensemble learning independent component analysis. Physics in medicine and biology, 54(6), 1823-1846.
连结：
[4] Chen, I., Hsu, Y. Y., Chen, C. C., & Lin, K. P. (2002). Multi-Parameter Evaluation of Brain Tumor with a WWW Based Multimedia Database System. Journal of Medical and Biological Engineering, 22(1), 41-48.
连结：
[6] Huang, S. C., Phelps, M. E., Hoffman, E. J., Sideris, K., Selin, C. J., & Kuhl, D. E. (1980). Noninvasive determination of local cerebral metabolic rate of glucose in man. American Journal of Physiology-Endocrinology And Metabolism, 238(1), E69-E82.
连结：

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