Linear and nonlinear analysis for transduced current curves of electrochemical biosensors :Doctor of Philosophy - Major: Computer Science

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 ....................................................................................x

Abstract.....................................................................................................................xii

CHAPTER I. INTRODUCTION ...........................................................................1

1.1 Statement of the Problem..............................................................................1

1.2 Objective and Approach................................................................................3

1.2.1 Overview .............................................................................................3

1.2.2 Approaches and Contributions ............................................................5

1.2.3 Data Acquisition ..................................................................................8

1.3 Organization..................................................................................................8

CHAPTER II. LITERATURE REVIEW..............................................................10

2.1 Linear Models ...............................................................................................11

2.1.1 Overview .............................................................................................11

2.1.2 Parameter Estimation in the Linear Model..........................................13

a) Minimum Variance Unbiased estimation ........................................13

b) Maximum Likelihood Estimation (MLE).......................................15

c) Least Squares (LS)..........................................................................16

d) Linear Bayesian Estimators.............................................................19

2.2 Feedforward Neural Networks......................................................................22

2.2.1 Neural Networks and Feedforward Operation ....................................23

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2.2.2 Gradient-descent based Learning Algorithms .....................................24

2.2.3 Practical Techniques for Improving Backpropagation ........................26

2.2.4 Theoretical Foundations for Improving Backpropagation ..................27

2.2.5 Approximation Capabilities of Feedforward networks and SLFNs....30

2.3 Support Vector Machine................................................................................34

CHAPTER III. TRAINING ALGORITMS FOR SINGLE HIDDEN

LAYER FEEDFORWARD NEURAL NETWORKS ...........................................43

3.1 Single Hidden Layer Feedforward Neural Networks....................................43

3.2 Extreme Learning Machine (ELM)...............................................................45

3.3 Evolutionary Extreme Learning Machine (E-ELM).....................................49

3.4 Least-Squares Extreme Learning Machine ...................................................51

3.4.1 Least-Squares Extreme Learning Machine (LS-ELM) .......................51

3.4.2 Online Training with LS-ELM ............................................................54

3.5 Regularized Least-Squares Extreme Learning Machine (RLS-ELM)..........59

3.6 Evolutionary Least-Squares Extreme Learning Machine (ELS-ELM).........61

CHAPTER IV. OUTLIER DETECTION AND ELIMINATION .......................64

4.1 Distance-based outlier detection ...................................................................64

4.2 Density-based local outlier detection............................................................66

4.3 The Chebyshev outlier detection...................................................................68

4.4 Area-descent-based outlier detection ............................................................69

4.5 Two-stage area-descent outlier detection ......................................................72

4.6 ELM-based outlier Detection and Elimination .............................................74

CHAPTER V. HEMATOCRIT ESTIMATION FROM TRANSDUCED

CURRENT CURVE.................................................................................................78

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5.1 Review of Hematocrit and Previous Measurement Methods........................79

5.1.1 Typical Methods for Measuring Hematocrit .......................................79

5.1.2 Hematocrit Determination from Impedance........................................80

5.1.3 Hematocrit Measurement by Dielectric Spectroscopy........................82

5.2 Hematocrit Estimation from Transduced Current Curve ..............................83

5.2.1 Transduced Current Curve from Electrochemical Biosensor for

Glucose Measurement ..................................................................................84

5.2.2 Linear Models for Hematocrit Estimation...........................................86

5.2.3 Neural Network for Hematocrit Estimation ........................................90

5.2.4 Hematocrit Estimation by Using Support Vector Machine .................91

CHAPTER VI. ERROR CORRECTION FOR GLUCOSE BY REDUCING

EFFECTS OF HEMATOCRIT..............................................................................92

6.1 Effects of Hematocrit on Glucose Measurement ..........................................92

6.2 Error Correction for Glucose Measured by a Handheld Device ...................95

6.3 Error Correction for Glucose Computed Using a Single Transduced

Current Point .......................................................................................................99

CHAPTER VII. DIRECT ESTIMATION FOR GLUCOSE DENSITY

FROM TRANSDUCED CURRENT CURVE.......................................................107

7.1 Effects of Critical Care Variables..................................................................107

7.2 Glucose Estimation from the Transduced Current Curve .............................109

CHAPTER VIII. EXPERIMENTAL RESULTS ..................................................114

8.1 Experimental Results for Hematocrit Estimation .........................................115

8.2 Experimental Results for Glucose Correction...............................................119

8.2.1 Error Correction for Glucose Measured by the Handheld Device ......120

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8.2.2 Error Correction for Glucose Computed Using a Single

Transduced Current Point.............................................................................125

8.3 Experimental Results for Direct Estimation for Glucose from the

Transduced Current Curve ..................................................................................127

CHAPTER IX. CONCLUSIONS AND FUTURE WORKS................................130

9.1 Conclusions...................................................................................................130

9.2 Future Works.................................................................................................133

9.2.1 Feature Selection .................................................................................133

9.2.2 Optical Biosensors...............................................................................133

9.2.3 Reducing Effects of Other Factors ......................................................134

9.2.4 Applying Improvements of ELM in Medical Diagnosis.....................134

REFERENCES.........................................................................................................135

ACKNOWLEDGMENTS.......................................................................................148

CURRICULUM VITAE..........................................................................................150

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LIST OF FIGURES

Figure ......................................................................................................................Page

Figure 1.1 Overview of the proposed systems: (a) Error correction for glucose

values by reducing the effects of hematocrit. (b) Glucose estimation

from transduced current curve .......................................................................4

Figure 1.2 The transduced current curve. The first eight seconds may be

incubation time which waits for chemical reaction. ......................................5

Figure 2.1 A typical feedforward neural network......................................................24

Figure 2.2 Loss functions can be used in SVR, in which ε-insensitive loss

function allows obtaining a sparse set of support vectors .............................35

Figure 2.3 Soft margin loss setting corresponds for a linear SV machine.................37

Figure 3.1 The architecture of single hidden layer feedforward neural network

(SLFN)...........................................................................................................44

Figure 4.1 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.....................................................................65

Figure 4.2 Detecting outliers by the area descent method.........................................70

Figure 4.3 A simple dataset with closed outliers o1 and o2. These outliers

cannot be detected by area-descent based method.........................................71

Figure 5.1 An example of anodic current curve corresponding to the first 14s.

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The first 8 seconds may be incubation time, which waits for chemical

reaction...........................................................................................................84

Figure 5.2 Transduced anodic current points used in estimation of hematocrit.

They are obtained by sampling the second part of current curve at

frequency of 10Hz. ........................................................................................85

Figure 5.3 Current measurements at the time instants. They seem to be an

exponential function of time..........................................................................87

Figure 5.4 Hematocrit estimation by using LRCP approach. Current curve

together with its two extra features are the input of linear model. ................89

Figure 5.5 Hematocrit estimation using the neural network model. Input

features are current points sampled from the transduced current curve

with/without extra features. ...........................................................................91

Figure 6.1 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.............................93

Figure 6.2 Plot of the paired-differences of glucose measurements by portable

device minus the primary reference glucose measurements as function

of hematocrit [5]. ...........................................................................................94

Figure 6.3 Glucose correction process. Finding a mapping from t

m to t

c

so that

dependency of hematocrit is reduced and errors are also reduced. ...............95

Figure 6.4 An illustration of glucose correction of handheld devices. ......................97

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Figure 6.5 An illustration of glucose correction measured from a single point

on the transduced current curve.....................................................................100

Figure 6.6 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.............................................101

Figure 7.1 Effects of PO2 on glucose measurement by handheld devices [5].

The glucose is underestimated at higher levels of PO2. .................................108

Figure 7.2 Effects of PCO2 on glucose measurement by handheld devices [5].

The measured glucose is underestimated at the higher levels of PCO2..........108

Figure 7.3 Effects of pH on glucose measurement by handheld devices [5].............109

Figure 7.4 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...........110

Figure 7.5 SLFNs for estimating glucose. Input features are current points

sampled from the transduced current curve...................................................111

Figure 8.1 Distribution of collected hematocrit. This distribution is fairly

representing the general trend of hematocrit values for human.....................114

Figure 8.2 Distribution of glucose collected from YSI 2300.....................................119

Figure 8.3 Plot of paired-differences of glucose measurements by handheld

device minus the YSI2300 glucose measurements. The dependency of

hematocrit on residuals is significant.............................................................120

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Figure 8.4 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. ...................................122

Figure 8.5 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....................122

Figure 8.6 Comparison of glucose results from handheld meter and the

primary reference instrument, YSI 2300: (a) before error correction

and (b) after error correction..........................................................................124

Figure 8.7 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..............................................................................................127

Figure 8.8 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

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LIST OF TABLES

Table ..................................................................................................................Page

Table 4.1 Symbols and Notations ...........................................................................69

Table 6.1 Correlation coefficients between the current points and the primary

reference glucose ........................................................................................102

Table 6.2 Correlation test for normality corresponding to time points...................104

Table 8.1 Root mean square errors (RMSE) compared to the reference

hematocrit measurements ...........................................................................116

Table 8.2 Mean percentage error (MPE) compared to the reference hematocrit

measurement ...............................................................................................118

Table 8.3 Comparison results for different criteria of error tolerance ....................123

Table 8.4 Comparison results on different criteria of error tolerance.....................126

Table 8.5 Comparison results on RMSE of approaches .........................................126

Table 8.6 Comparison results for different criteria of error tolerance ....................128

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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

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