Doctor of Philosophy Dissertation Linear and Nonlinear Analysis for Transduced Current Curves of Electrochemical Biosensors Graduate School of Chonnam National University Department of Computer Engineering HUYNH TRUNG HIEU Directed by Professor Yonggwan Won February 2009 TABLE OF CONTENTS TABLE OF CONTENTS.i LIST OF FIGURES .v LIST OF TABLES .ix LIST OF ABBREVIATIONS .1 Statement of the Problem .2 Objective and Approach.2 Approaches and Contributions .2 Parameter Estimation in the Linear Model.13 a) Minimum Variance Unbiased estimation .13 b) Maximum Likelihood Estimation (MLE) .16 d) Linear Bayesian Estimators.2 Feedforward Neural Networks.1 Neural Networks and Feedforward Operation .2 Gradient-descent based Learning Algorithms .3 Practical Techniques for Improving Backpropagation .4 Theoretical Foundations for Improving Backpropagation .5 Approximation Capabilities of Feedforward networks and SLFNs .3 Support Vector Machine. TRAINING ALGORITMS FOR SINGLE HIDDEN LAYER FEEDFORWARD NEURAL NETWORKS .1 Single Hidden Layer Feedforward Neural Networks.2 Extreme Learning Machine (ELM).3 Evolutionary Extreme Learning Machine (E-ELM) .4 Least-Squares Extreme Learning Machine .1 Least-Squares Extreme Learning Machine (LS-ELM) .2 Online Training with LS-ELM .5 Regularized Least-Squares Extreme Learning Machine (RLS-ELM) .6 Evolutionary Least-Squares Extreme Learning Machine (ELS-ELM). OUTLIER DETECTION AND ELIMINATION .1 Distance-based outlier detection .2 Density-based local outlier detection .3 The Chebyshev outlier detection.4 Area-descent-based outlier detection .5 Two-stage area-descent outlier detection .6 ELM-based outlier Detection and Elimination. HEMATOCRIT ESTIMATION FROM TRANSDUCED CURRENT CURVE.1 Review of Hematocrit and Previous Measurement Methods.1 Typical Methods for Measuring Hematocrit .2 Hematocrit Determination from Impedance.3 Hematocrit Measurement by Dielectric Spectroscopy .2 Hematocrit Estimation from Transduced Current Curve .1 Transduced Current Curve from Electrochemical Biosensor for Glucose Measurement .2 Linear Models for Hematocrit Estimation.3 Neural Network for Hematocrit Estimation .4 Hematocrit Estimation by Using Support Vector Machine.
ERROR CORRECTION FOR GLUCOSE BY REDUCING EFFECTS OF HEMATOCRIT .1 Effects of Hematocrit on Glucose Measurement .2 Error Correction for Glucose Measured by a Handheld Device .3 Error Correction for Glucose Computed Using a Single Transduced Current Point. DIRECT ESTIMATION FOR GLUCOSE DENSITY FROM TRANSDUCED CURRENT CURVE.1 Effects of Critical Care Variables.2 Glucose Estimation from the Transduced Current Curve .1 Experimental Results for Hematocrit Estimation .2 Experimental Results for Glucose Correction.1 Error Correction for Glucose Measured by the Handheld Device .2 Error Correction for Glucose Computed Using a Single Transduced Current Point .3 Experimental Results for Direct Estimation for Glucose from the Transduced Current Curve. CONCLUSIONS AND FUTURE WORKS .3 Reducing Effects of Other Factors .4 Applying Improvements of ELM in Medical Diagnosis .150 iv LIST OF FIGURES Figure .1 Overview of the proposed systems: (a) Error correction for glucose values by reducing the effects of hematocrit. (b) Glucose estimation from transduced current curve .2 The transduced current curve.
The first eight seconds may be incubation time which waits for chemical reaction.1 A typical feedforward neural network.2 Loss functions can be used in SVR, in which ε-insensitive loss function allows obtaining a sparse set of support vectors .3 Soft margin loss setting corresponds for a linear SV machine.1 The architecture of single hidden layer feedforward neural network (SLFN) .1 A simple 2D dataset contains points belonging to two clusters C1 and C2. C1 forms a denser cluster than C2. Two additional points o1 and o2 can be considered as outliers .2 Detecting outliers by the area descent method.3 A simple dataset with closed outliers o1 and o2. These outliers cannot be detected by area-descent based method.1 An example of anodic current curve corresponding to the first 14s.
v The first 8 seconds may be incubation time, which waits for chemical reaction.2 Transduced anodic current points used in estimation of hematocrit. They are obtained by sampling the second part of current curve at frequency of 10Hz.3 Current measurements at the time instants. They seem to be an exponential function of time.4 Hematocrit estimation by using LRCP approach. Current curve together with its two extra features are the input of linear model.5 Hematocrit estimation using the neural network model.
Input features are current points sampled from the transduced current curve with/without extra features.1 Effects of Hematocrit on Glucose Measurement: (a) same measured value on current curve but different glucose value, (b) different measured value on current curve but same glucose value.2 Plot of the paired-differences of glucose measurements by portable device minus the primary reference glucose measurements as function of hematocrit [5].3 Glucose correction process. Finding a mapping from tm to tc so that dependency of hematocrit is reduced and errors are also reduced.4 An illustration of glucose correction of handheld devices.5 An illustration of glucose correction measured from a single point on the transduced current curve.6 Plot of the primary reference glucose against current point x57. We can diagnose that there would be a linear relationship between the primary reference glucose and current-point xk.1 Effects of PO2 on glucose measurement by handheld devices [5]. The glucose is underestimated at higher levels of PO2.2 Effects of PCO2 on glucose measurement by handheld devices [5].
The measured glucose is underestimated at the higher levels of PCO2.3 Effects of pH on glucose measurement by handheld devices [5].4 Illustration of estimating glucose from the transduced current curve. Glucose values are estimated directly from multiple current points, which include changing information of the transduced current curve.5 SLFNs for estimating glucose. Input features are current points sampled from the transduced current curve.1 Distribution of collected hematocrit. This distribution is fairly representing the general trend of hematocrit values for human.2 Distribution of glucose collected from YSI 2300.3 Plot of paired-differences of glucose measurements by handheld device minus the YSI2300 glucose measurements.
The dependency of hematocrit on residuals is significant.4 The paired-differences of a testing set corresponding to glucose measurements by handheld device without error correction. The dependency of hematocrit on residuals is significant.5 The paired-differences of a testing set corresponding to glucose measurements by handheld device after error correction. The dependency of hematocrit on residuals is reduced significantly.6 Comparison of glucose results from handheld meter and the primary reference instrument, YSI 2300: (a) before error correction and (b) after error correction.7 The plot of paired-differences of estimated glucose on the test set minus the YSI 2300 glucose measurements with respect to the hematocrit density. The dependency of hematocrit on residuals is almost removed.8 The comparison of glucose value between the neural network and the primary reference instrument corresponding to criterion of ±15mg/dL for glucose levels ≤100 mg/dL and ±15% for glucose levels > 100 mg/dL.129 viii LIST OF TABLES Table .1 Symbols and Notations .1 Correlation coefficients between the current points and the primary reference glucose .2 Correlation test for normality corresponding to time points.1 Root mean square errors (RMSE) compared to the reference hematocrit measurements .2 Mean percentage error (MPE) compared to the reference hematocrit measurement .3 Comparison results for different criteria of error tolerance .4 Comparison results on different criteria of error tolerance.5 Comparison results on RMSE of approaches .6 Comparison results for different criteria of error tolerance .128 ix LIST OF ABBREVIATIONS Abbr.
Description BLUE Best linear unbiased estimator Bmse Bayesian mean square error BP Backpropagation C(Rp) Set of all continuous functions defined in the extended Rp DE Differential evolution E-ELM Evolutionary extreme learning machine ELM Extreme learning machine ELS-ELM Evolutionary least squares extreme learning machine HCT Hematocrit KKT Karush-Kuhn-Tucker condition LMMSE Linear minimum mean square error LRCP Linear model with Reduced Current Points LS Least squares LS-ELM Least squares extreme learning machine LWCP Linear model with Whole Current Points MCV Mean corpuscular volume MLE Maximum likelihood estimator MMSE Minimum mean square error MP Moore-Penrose generalized inverse MPE Mean percentage error MSE Mean square error x MVU Minimum variance unbiased estimator OS-ELM Online sequential extreme learning machine PCO2 Carbon dioxide partial pressure PDF Probability density function pH A measure of the acidity of alkalinity PO2 Oxygen partial pressure POCT Point-of-care testing RBC Red blood cell RLS-ELM Regularized least-squares extreme learning machine RMSE Root mean squared error SLFN Single hidden layer feedforward neural network SV Support vector SVC Support vector classification SVD Single value decomposition SVM Support vector machine SVR Support vector regression ε-SVR Support vector regression with ε-insensitive loss function ν-SVR SVR proposed by Schölkopf et al. [47] TCC Transduced current curve WBC White blood cell WGN White Gaussian noise WHO World Health Organization WLS Weighted least squares xi Linear and Nonlinear Analysis for Transduced Current Curves of Electrochemical Biosensors HUYNH TRUNG HIEU Department of Computer Engineering Graduate School of Chonnam National University (Directed by Professor Yonggwan Won) Abstract Since the development of science and technology, a wide range of diagnostic tests can be done quickly and simply without the need for sophisticated laboratory equipment, in which the biosensors play a role as key technology. They are very useful in medicine and healthcare as well as in chemical and biochemical industry to determine and analyze complex mixtures and analytes. Normally, biosensors can be classified and evaluated based on the design and functional characteristics such as accuracy, cost, availability, range, simplicity, etc.
On these bases, electrochemical biosensors are favored due to accuracy, cost and availability. After the expenditure of an enormous amount of effort, the electrochemical biosensors for blood glucose measurement become the most widespread commercial biosensors to date. They can be used along with the handheld devices to monitor daily blood glucose levels of diabetic patients to maintain their blood glucose concentrations at or near normal levels, which can reduce substantially complications xii due to diabetes. Although handheld devices are conveniently used for monitoring and controlling the blood glucose levels, their accuracies are greatly affected by interferences such as uric acid, ascorbic acid, PO2, PCO2, pH, hematocrit, etc, in which the hematocrit is the most highly influencing factor affecting glucose measurements by handheld devices.
While interferences from oxidizable substances can be reduced by chemical methods, few practical solutions have been proposed to reduce effects of hematocrit. However, these solutions increase cost and complexity of manufacturing procedures. They are also very difficult to implement in handheld devices. This research focuses on developing intelligent computing methods for improving accuracies of handheld devices in glucose measurements, which use electrochemical biosensors.
The analytical principle of the electrochemical biosensors in glucose measurements is based on a bio-interaction process, in which an electrochemical current signal called transduced current is produced by the interaction of blood glucose with glucose oxidase and the oxidation of reduced form of the enzyme by electrode. This transduced current changes along the time, which is represented by a curve called as transduced current curve (TCC). In some ways, TCC has been used to determine the concentration of glucose by handheld devices. However, our research was started from the belief that the changing pattern of TCC includes not only glucose information but also various other factors including interferences.
Therefore, analysis of TCC can play a crucial role in enhancing performance of measurement by using electrochemical biosensors. xiii In this research, linear and nonlinear models including support vector machines (SVM) and neural networks are investigated to analyze the transduced current curves. They can provide proper methods for determining critical factors such as hematocrit and improving accuracy of glucose measurement for the whole blood. These models are simple; they do not require complicated chemical procedures and take less cost for handheld devices.
Novel methods have been devised for hematocrit estimation from the transduced current curve. The first one is linear models, in which the hematocrit is estimated by linear combination of current points sampled from the transduced current curve. The second method for hematocrit estimation is using single hidden layer feedforward neural networks (SLFNs) which are trained by extreme learning machine (ELM) algorithm and its improvements to obtain compact networks. The input features are also sampled current points.
An application of support vector machine (SVM) for hematocrit estimation is our third method, in which support vector regression (SVR) was used in mapping the current points to hematocrit. The results obtained from measuring methods are the important factor in reducing or eliminating effects of hematocrit level on portable glucose meters. In addition, it shows that the clinical indicator can be estimated by cheep handheld devices with fast measuring time.