| Summary: | 博士 === 中原大學 === 電機工程研究所 === 105 === 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.
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