Theoretical Investigation of Bioactive Papers

Using the Kubelka-Munk Theory

By

Elina Levi Gendler

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Chemical Engineering and Applied Chemistry

University of Toronto

© Copyright by Elina Levi Gendler, 2015

ii

Theoretical Investigation of Bioactive Papers Using

the Kubelka-Munk Theory

Elina Levi Gendler

Masters of Applied Science

Chemical Engineering and Applied Chemistry

University of Toronto

2015

Abstract

This work demonstrates a theoretical study of colorimetric detection of analytes via bioactive

papers. A mathematical model incorporating the Kubelka-Munk theory, which analyzes light

propagation through paper, was developed. It provides the correlation of color with the

concentration of chromophores generated in a reaction between biosensor and analyte as a

function of the paper characteristics and optical properties. Accordingly, we evaluate the degree

of error of colorimetric readings obtained under various conditions. Theoretical results show that

a 5 % variation in reflectance could yield a significant error in detected chromophore

concentration. The reflectance is highly affected by environmental illumination and changes in

chromophore distribution profile. Confining color detection to the surface of paper is

advantageous yet prone to variability due to non-uniformity in analyte or biosensors penetration

depth. This work will be, hopefully, incorporated in the initial steps of the bioactive papers

design, to obtain more efficient and accurate performance.

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Acknowledgments

Special thanks to Professor Ramin Farnood,

for the kind and intelligent supervision, and the guidance you offered along the way.

I have learned a lot from you, professionally and personally

***

I would like to express my gratitude to Sentinel and FIBRE Networks,

for the generous funding, for the exposure with the pulp and paper industry,

and for the enriching conferences across Canada

***

To my dearest friends,

those who are near and those who are an ocean away,

thank you for filling my days with humor and tremendous support

***

I would like to thank my family,

my loving parents, Bella and Miron Gendler, and incredible sister, Diana Borenshtein.

The warmth and wisdom you provided from distance gave me strength and comfort

***

Last but not least, I would like to thank my husband, Amir Ben Levi,

for the endless love and care. As always, you motivate me the most and provide the patience and

the encouragement I need. This thesis could not have been possible without you

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Table of Contents

List of Figures ............................................................................................................................................. vii

List of Tables ................................................................................................................................................. x

Chapter 1 .......................................................................................................................................................1

1. Introduction ...........................................................................................................................................2

1.1 Colorimetric Detection via Bioactive Papers ................................................................................2

1.2 Objective .......................................................................................................................................2

1.3 Applying the Kubelka-Munk Theory to a Mathematical Model ...................................................3

1.4 New Possibilities with the Application of a Theoretical model ....................................................4

1.5 Structure of the Thesis ...................................................................................................................4

Chapter 2 .......................................................................................................................................................5

2. Literature Review ..................................................................................................................................6

2.1 Bioactive Papers ............................................................................................................................6

2.1.1 Paper-based Biosensors Are Lab-On-Chip Analytical Devices ............................................6

2.1.2 The Design of Bioactive Papers ............................................................................................7

2.1.3 Colorimetric Detection ..........................................................................................................9

2.1.4 Cellphone As a Colorimetric Device .................................................................................. 11

2.1.5 Challenges to Overcome ..................................................................................................... 11

2.2 The Kubelka-Munk Theory ........................................................................................................ 13

2.2.1 The Fundamentals of the Kubelka-Munk Theory .............................................................. 13

2.2.2 Light Absorption and Scattering Effects ............................................................................ 16

2.2.3 The Additivity Law ............................................................................................................ 18

2.2.4 Non-homogeneous Papers: Multi-layer Structures ............................................................. 19

2.2.5 Limitations of the Kubelka-Munk Theory .......................................................................... 20

2.3 Mathematical Representation of Color ....................................................................................... 21

2.3.1 CIE Universal Standard System ......................................................................................... 21

2.3.2 The Calculation of XYZ Tristimulus Values ..................................................................... 22

2.3.3 CIELAB Standard System .................................................................................................. 24

2.3.4 RGB Color Model .............................................................................................................. 25

2.3.5 The Application of Color Models and Spaces in Bioactive Papers .................................... 26

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2.4 Summary of the Existing Literature ........................................................................................... 26

Chapter 3 .................................................................................................................................................... 28

3. Methodology ...................................................................................................................................... 29

3.1 Developing a Theoretical Model Based on the Kubelka-Munk Theory ..................................... 29

3.1.1 Homogeneous Bioactive Paper ........................................................................................... 29

3.1.2 The Effect of Porosity on the Colorimetric Detection ........................................................ 31

3.1.3 Non-homogeneous Bioactive Paper: Multi-layer Theory ................................................... 32

3.2 Mathematical Representation of Color ....................................................................................... 35

3.2.1 Reflectance Measurement of Dyed Paper .......................................................................... 35

3.2.2 Calculating XYZ Tristimulus Values ................................................................................. 36

3.2.3 Color Quantification Based on CIELAB Color Space ....................................................... 38

3.2.4 Color Quantification Based on sRGB Color Space of RGB Color Model ......................... 38

Chapter 4 .................................................................................................................................................... 39

4. Results and Discussion ....................................................................................................................... 40

4.1 The Application of the Kubelka-Munk Theory .......................................................................... 40

4.1.1 Homogeneous Bioactive Paper ........................................................................................... 40

4.1.2 The Effect of Paper Porosity on the Colorimetric Detection .............................................. 51

4.1.3 Sensitivity Analysis ............................................................................................................ 54

4.1.4 Non-homogeneous Paper: Multi-Layer K-M Theory ......................................................... 55

4.2 Effect of illuminants on color ..................................................................................................... 66

4.2.1 XYZ Tristimulus Colors for Various Illuminants .............................................................. 66

4.2.2 Color Strength According to CIELAB Values ................................................................... 68

4.2.3 Color Difference According to CIELAB Values................................................................ 69

4.2.4 Generating Color Pallets According to RGB Values ......................................................... 70

Chapter 5 .................................................................................................................................................... 73

5. Concluding Remarks .......................................................................................................................... 74

5.1 The Application of the K-M Theory........................................................................................... 74

5.1.1 Key Findings ...................................................................................................................... 75

5.1.2 Limitations of the Present Work ......................................................................................... 76

5.2 Mathematical Representation of Color ....................................................................................... 78

6. Bibliography ....................................................................................................................................... 80

Appendices ................................................................................................................................................. 85

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Appendix A – Model Codes in Mathematica Software .......................................................................... 85

A-1: Homogeneous Paper ................................................................................................................... 85

A-2: Homogeneous Paper with the Application of Porosity Functions ............................................. 86

A-3: Multi-layer Paper ....................................................................................................................... 87

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List of Figures

Figure 2-1: Basic design of bioactive paper ..................................................................................................7

Figure 2-2: Paper-based analytical devices in: (A) 1D, (B) 2D, and (C) 3D. The area where the sample is

collected is denoted by S, and T expresses the testing area used for the diagnosis (adapted from [2]) ........9

Figure 2-3: Cross-section of a paper sample: the light entering the paper is scattered several times and

either absorbed by the paper, transmitted through it, or reflected out of it (Adapted from [29]) ............... 14

Figure 2-4: The fundamentals of the K-M theory. Light fluxes propagating through paper, only in one

axis (Adapted from [29]) ............................................................................................................................ 14

Figure 2-5: CIELAB color space (adapted from [31]) ............................................................................... 24

Figure 3-1: A two-layer system, where the bottom layer is the base paper and the upper layer is the active

layer containing the chromophore. The penetration depth of the analyte is correlated to the grammage

fraction fW .................................................................................................................................................. 33

Figure 3-2: Schematic diagram of a three-layer device structure. The middle layer is the active layer

containing the chromophore ....................................................................................................................... 34

Figure 3-3: Preparation of dyed paper samples .......................................................................................... 36

Figure 3-4: Generating palette based on calculated RGB values for each illuminant and dye concentration

.................................................................................................................................................................... 38

Figure 4-1: Calculated light reflectance as a function of chromophore concentration in paper and paper

grammage: (a) 3D plot and (b) 2D plot (W = 0.001, 0.005, 0.01, and 0.2). Model parameters are

according to Table 3-1 ................................................................................................................................ 41

Figure 4-2: Calculated light reflectance as a function of chromophore concentration and absorption

coefficient of paper: (a) 3D plot, and (b) 2D plot (kp = 1, 8, and 15). Model parameters are according to

Table 3-1..................................................................................................................................................... 43

Figure 4-3: The relative change in R as function of chromophore concentration for increase in kp from 1 to

5 (white bars) and 1 to 15 (black bars). Model parameters are according to Table 3-1 ............................. 44

Figure 4-4: Calculated light reflectance as functions of chromophore concentration and absorption

coefficient (a) 3D plot, and (b) 2D plot (ka = 0, 1000, 2000... 10000). Model parameters are according to

Table 3-1..................................................................................................................................................... 45

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Figure 4-5: Estimated relative change in R as a function of chromophore concentration for increasing ka

from 100 to 1000 (white bars) and from 100 to 10,000 (black bars). Model parameters are according to

Table 3-1..................................................................................................................................................... 46

Figure 4-6: Calculated light reflectance as functions of chromophore concentration and paper scattering

coefficient: (a) 3D plot, and (b) 2D plot (s = 10, 50, 100, 200, and 500). Model parameters are according

to Table 3-1 ................................................................................................................................................ 47

Figure 4-7: Calculated light reflectance as a function of chromophore concentration for various backing

materials (a) 3D plot, and 2D (b) 2D plot (Rg =0,0.1,0.2,…,1).Modelparametersareaccordingto

Table 3-1..................................................................................................................................................... 49

Figure 4-8: Calculated light reflectance as function of backing material reflectance for different values of

paper grammage at the chromophore concentrations of 0.0001 g/g (a) and 0.01 g/g (b). Model parameters

are according to Table 3-1 .......................................................................................................................... 50

Figure 4-9: Calculated light reflectance as functions of chromophore concentration and paper porosity: (a)

3D plot, and (b) 2D plot ( = 0.1, 0.3, 0.5, and 0.7). Model parameters are according to Table 3-1 ........ 52

Figure 4-10: % change in calculated reflectance R as a function of chromophore concentration for a

decrease in porosity from 0.7 to 0.5 (white bars), 0.7 to 0.3 (grey bars), and 0.7 to 0.1 (black bar). Model

parameters are according to Table 3-1 ....................................................................................................... 53

Figure 4-11: % change in R as a function of chromophore concentration for 10 % fluctuation in the paper

properties. Rg is varied from 0 to 1. Model parameters are given in Table 3-1 .......................................... 54

Figure 4-12: The calculated light reflectance of a two-layer structure, where the chromophore is

distributed uniformly at the top half of the sheet, as a functions of Ca and ka: (a) 3D plot, and (b) 2D plot

(ka = 0, 1000, 2000... 10000). Model parameters are according to Table 3-1 ............................................ 56

Figure 4-13: The calculated light reflectance of a three-layer structure where the chromophore is

distributed in the middle layer of the sheet, as functions of Ca and ka: (a) 3D plot, and (b) 2D plot (ka = 0,

1000, 2000... 10000). Model parameters are according to Table 3-1 ......................................................... 57

Figure 4-14: Paper reflectance vs. chromophore concentration for homogeneous (white bar), two-layer

(grey bar), and three-layer (black bar) bioactive papers. The relative change in the reflectance readings

from homogeneous case with uniform chromophore distribution is inserted in the plot. Model parameters

are according to Table 3-1 .......................................................................................................................... 58

Figure 4-15: Reflectance of a two-layer bioactive device versus chromophore absorption coefficient ka

and fraction of the active layer f at various chromophore concentrations: 0.001g/g (top), 0.01 g/g

(middle), and 0.1 g/g (bottom). Left: 3D plots, and right: 2D plots for various chromophore absorption

coefficients (ka = 1000, 2000, 5000, 10000)............................................................................................... 60

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Figure 4-16: The relative change in R012 as a function of analyte concentration for different variabilities in

grammage fraction fW of the top layer in a two-layer structure ................................................................. 62

Figure 4-17: The relative change in reflectance of a two-layer structure vs. the relative change in active

layer fraction f for initial values of f=0.1, f=0.2, and f=0.5, at chromophore concentration Ca=0.0001 g/g

.................................................................................................................................................................... 62

Figure 4-18: The relative change in reflectance of a two-layer structure vs. the relative change in active

layer fraction f for initial values of f=0.1, f=0.2, and f=0.5, at chromophore concentration Ca=0.001 g/g 63

Figure 4-19: The relative change in reflectance of a two-layer structure vs. the relative change in active

layer fraction f for initial values of f=0.1, f=0.2, and f=0.5, at chromophore concentration Ca=0.01 g/g .. 63

Figure 4-20: The relative change in reflectance of a two-layer structure vs. the relative change in active

layer fraction f for initial values of f=0.1, f=0.2, and f=0.5, at chromophore concentration Ca=0.1 g/g .... 64

Figure 4-21: Reflectance of a two-layer bioactive device versus chromophore absorption coefficient ka

and fraction of the active layer f at various chromophore concentrations: 0.001 g/g (top), 0.01 g/g

(middle), and 0.1 g/g (bottom), while maintaining a constant amount of chromophore with the application

of adjusted concentration as described in Equations (35) and (36). Left: 3D plots, and right: 2D plots for

various chromophore absorption coefficients (ka = 1000, 2000, 5000, 10000) .......................................... 65

Figure 4-22: Chroma vs. dye concentration for illuminants D65, D55, C, and F2 .................................... 68

Figure 4-23: vs. dye concentration for illuminants D55, C, and F2 compared to illuminant D65 ....... 69

Figure 4-24: The impact of different illuminants on perceived color for dyed paper samples using RGB

colormodel.EachboxwascoloredinMicrosoftPowerPointaccordingtotheR‟G‟B‟valuescalculated

for a given illuminant and various dye concentrations ............................................................................... 71

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List of Tables

Table 2-1: Typical values of k and s for paper ........................................................................................... 17

Table 2-2: Selected CIE standard illuminants ............................................................................................ 23

Table 3-1: Typical values for the mathematical model and their ranges .................................................... 31

Table 3-2: Dyed paper samples used in this study ..................................................................................... 35

Table 3-3: The calculation of XYZ values for dye solution no.1 for standard illuminant D65 [50] .......... 37

Table 4-1: The effect of grammage change on light reflectance for different chromophore concentrations

at ka=10,000 m2/kg and ka=1300 m

2/kg. Model parameters are according to Table 3-1 ............................ 42

Table 4-2: The effect of change in scattering coefficient on the calculated light reflectance for different

chromophore concentrations, model parameters are according to Table 3-1 ............................................. 48

Table 4-3: % change in light reflectance as the backing material is changed from perfectly black to

perfectly white for various paper grammage values at chromophore concentration of 0.0001 g/g............ 51

Table 4-4: XYZ tristimulus values for different dye solutions and illuminations ...................................... 67

Table 4-5: The average change in percentage of the XYZ tristimulus values of illuminants D50, C, and F2

compared to illuminant D65 ....................................................................................................................... 67

Table 4-6: % difference between the chroma based on illuminants D50, C, and F2 compared to

illuminant D65 at two dye concentrations .................................................................................................. 69

Table 4-7:R‟G‟B‟valuesofsRGBcolorspacefordifferentdyesolutionsandilluminations .................. 70

1

Chapter 1

Introduction

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1. Introduction

1.1 Colorimetric Detection via Bioactive Papers

The use of bioactive papers for the immediate detection of bioagents could become a vital asset

in the food industry, medical treatment, and hazardous work environments. These paper-based

analytical devices are promised to be low-cost, portable, disposable, and easy to use.

The simplest and the most common assays applied in bioactive papers are based on colorimetric

detection. Such devices rely on visual observation, which gives a qualitative result.

Unfortunately, quantitative results require sophisticated equipment such as spectrophotometers,

which are bulky, massive, and expensive. Moreover, their operation requires the expertise of

trained personnel and a long analysis time, making it difficult to obtain an immediate point-of-

care diagnosis.

Currently, the quantification of an analyte concentration as a function of the assay color relies on

calibration curves and regression models. To the best of our knowledge, there is no predictive

model that can correlate color to the concentration of the specimen as a function of the paper-

based sensor design, structure, and method of operation.

1.2 Objective

The overall objective of this study is to provide a theoretical foundation based on fundamental

principles that can be used to design bioactive papers with highly efficient and sensitive

quantitative colorimetric detection. Specific objective of this project are:

1- developing a theoretical model for colorimetric bioactive papers based on the Kubelka-

Munk theory;

2- studying the effect of paper structure and properties on the performance of colorimetric

bioactive paper sensors using the theory above;

3

3- developing a fundamental understanding of the influence of detection method on the

bioactive paper sensor readings.

Such a theoretical model has the potential to be incorporated into the development of various

optical sensors and devices, such as cellphones.

1.3 Applying the Kubelka-Munk Theory to a Mathematical Model

Bioactive paper devices are “paper-like products, cardboard, fabrics and their combinations, with

active recognition and/or functional material capabilities” [1]. In such a device, a biosensor (e.g.

antibodies, enzymes, bacteriophages and DNA aptamers) is immobilized on the paper and is

brought to contact with a target analyte. The biochemical reaction between biosensor and analyte

produces color that could be used for (semi-) quantitative detection assays. In order to achieve a

sensitive and selective detection method, it is important to develop a better understanding of

factors that could affect the colorimetric reading.

In this study, we examine the effects of structure and properties of paper as well as the method of

detection of analyte on the intensity and characteristics of reflected light in bioactive paper

devices. The location of biosensors within the device, whether between capturing layers or at the

surface, affects the intensity of the perceived color. The distribution profile of the biosensor can

alter the pigment generation profile and thus the color interpretation. In addition, the device

could be immersed in a solution, or a drop of a sample could be placed onto its surface. The

method of application of the analyte into the bioactive paper is expected to have an impact on the

colorimetric reading. Variations in paper characteristics such as grammage, porosity, and optical

properties, along with the background used underneath the paper samples, can also cause

variations in the results. Moreover, the colorimetric measurements obtained by optical devices,

such as cellphones, are influenced by environmental conditions including the ambient

illumination.

To investigate effects of the above factors on bioactive paper assays, a mathematical model is

developed based on the Kubelka-Munk theory to analyze light propagation through a

colorimetric bioactive paper device. This model is used to estimate the theoretical error in

4

colorimetric detection due to variations in the paper properties, device structure, detection

method, and ambient conditions. The expression of color is achieved by incorporating the XYZ

tristimulus values that can be readily translated to color spaces such as RGB and CIELAB. The

present work demonstrates the calculation of XYZ tristimulus values, CIELAB and RGB

coordinates, according to reflectance measurements, and evaluates its sensitivity to various

illuminants.

1.4 New Possibilities with the Application of a Theoretical model

To our knowledge, this is the first time that the Kubelka-Munk theory is applied in the study of

bioactive papers. It is our hope that the present work will pave the way to gain a better

fundamental understanding of the colorimetric reading obtained by paper-based analytical

devices. An early assessment of the physical and optical properties of a desired medium could

shorten the development time and provide an efficient start in the first steps of the bioactive

paper development and optimization. Such a model could also serve as a basis for rapid and

more accurate interpretation of colorimetric readings. Therefore, this study has the potential to

help optimize the design and use of bioactive papers to obtain more accurate and sensitive

results.

1.5 Structure of the Thesis

This chapter provides an introduction and overview, including the objectives for performing a

theoretical study of colorimetric bioactive papers with the application of the Kubelka-Munk

theory. The literature review is provided in Chapter 2, including the state of the art in bioactive

papers, the fundamentals of the Kubelka-Munk theory, and the mathematical representation of

colors. The methodology used for developing the theoretical model to correlate light reflectance

with chromophore concentration under different conditions, and the calculation of XYZ

tristimulus values to be incorporated in RGB and CIELAB color spaces are presented in Chapter

3. In Chapter 4, results of the present work are provided and discussed in details. Finally,

concluding remarks based on the above findings and their implication are presented in Chapter 5.

5

Chapter 2

Literature Review

6

2. Literature Review

2.1 Bioactive Papers

2.1.1 Paper-based Biosensors Are Lab-On-Chip Analytical Devices

Real-time detection of biomolecules and chemical specimens, such as bacteria, pathogens and

contaminants, has great importance, especially in developing countries. For example, toxin

identification can make it possible to detect potential contaminants in drinking water or to

perform immediate preliminary medical care.

Bioactive papers are cellulose-based analytical tools used to identify the presence of chemical

and biological agents with the potential to provide clinical analysis, food and water regulation,

and safety in hazardous work environments. These analytical devices offer easy, immediate

diagnosis; they are inexpensive, portable, and readily used [2], [3].

Accordingly, the bioactive paper is a type of a lab-on-chip (LOC) device, yielding a prompt, one-

process diagnosis in a small scale, which could replace the long and tedious analysis work

performed in laboratories. The miniaturization process can shorten the time required for analysis

and promote the development of independent detection devices. This tool requires only small

amounts of reagents and fluidic sample [4], [5]. Furthermore, paper is an attractive substrate for

the biosensors, as it is a low-cost, abundant, and disposable material [2], [4].

Many paper-based biosensors have been developed in the recent years [1], [6]–[10]. A paper-

based analytical device could be used for physiological needs, including blood group typing,

DNA extraction and detection, cancerous biomarkers detection, glucose detections in blood or

urine samples for diabetes validation, and liver function monitoring. Pathogenic diseases, such as

malaria, hepatitis B and C, and HIV-1, could be easily diagnosed. It is a simple, cost effective,

and life-saving technology. Considering these attributes, paper-based analytical devices can be

appealing for point-of-care (POC) diagnosis in military, remote areas, and developing countries

for environmental monitoring, medical treatment and emergency care [2], [11].

7

2.1.2 The Design of Bioactive Papers

Bioactive paper sensors can be prepared in techniques including inkjet, wax, and screen printing

[12]. Most of them incorporate lateral flow of the liquid sample into a sensing area embedded

with active labeling reagents, typically proteins or enzymes [4]. In colorimetric bioactive papers,

theses reagents, or biosensors, react with the analyte of interest to generate chromophores that

are responsible for the appearance of color. Therefore, the appearance of color indicates the

presence of chemical or biological targets in the sample and color intensity may be used to

quantify the concentration of the analyte.

The paper device could be immersed in a solution, for instance wastewater, saliva, blood or urine

sample, or a drop of a sample could be placed onto its surface, as depicted in Figure 2-1.

However, the principle of generation of chromophores via biochemical reaction in both schemes

remains the same.

Figure 2-1: Basic design of bioactive paper

Paper-based biosensors are classified into three main types according to their detection

techniques: dipstick assays, lateral flow assays (LFAs), and microfluidic paper analytical devices

(µPADs). A detailed description of each technique is given below.

Dipstick assays are the most unsophisticated diagnostic tools among the three as they contain

reagents used for a single reaction. When the dipsticks are immersed in a solution, the fluid

dissolves the reagents, which were dried upon the paper during manufacture, enabling a chemical

8

reaction. Although these instruments are simple to design and easy to use, their detection method

is based only on qualitative results: an observable change in color indicates the presence or the

absence of the analyte. A well-known example for such a device is the pH strip [12].

In LFAs, the aqueous sample flows laterally through the paper strip due to capillary force

provided by the porous and hydrophilic composition of the cellulose fibers. Therefore, there is no

need for using an external pump [2]. The sample reaches a series of reagents deposited on the

paper, thus enabling various detection possibilities. A well-established example for a device

based on lateral flow is the pregnancy test. Some of the major drawbacks of such an instrument

are the long time needed to manufacture and optimize it and the relatively large volume of a

sample it requires for detection. In addition, despite its simplicity, these assays do not

incorporate multi-step processes required to produce robust and sensitive readings; they are not

suited for multi-targets analysis; and they often provide only qualitative detection, i.e. a „yes‟ or

„no‟ result [4], [12].

Rapid diagnostic paper-based tools as demonstrated above have been introduced to the world

since 1950‟s, yet only in the recent years there has been a growing interest in developing µPADs.

In terms of structure, µPADs are similar to LFAs, with the added feature of integrating

microfluidic mechanism. These sensors comprise hydrophobic barriers typically formed by

patterning a paper with microstructures, yielding hydrophilic channels as narrow as 250 µm. This

makes it possible to control the flow of aqueous sample and direct it to distinguished

independent sensing areas. Thus, multiple reactions can occur simultaneously on a singular

sensor without cross-contamination of other sensing areas. Common patterning methods for

creating the hydrophobic barriers include photolithography, wax printing, inkjet printing, plasma

etching, and laser cutting [2], [13]–[15]. In this technology, the miniaturized patterned structures

enable applying limited amounts of reagents on the paper and also use smaller amounts of

samples than those in traditional paper-based sensors [1]. These instruments have numerous

advantages over other paper-based tools: they are more versatile, and most important, they could

provide a quantitative reading [12].

The familiar examples of pH strips and pregnancy tests are based on a one-dimensional design:

the liquid sample flows only in a single direction. With the application of microfluidics, the

paper devices can become a two-dimensional network, in which the liquid sample is spread from

9

a single region to multiple locations. This makes it possible to perform multiple assays with

higher complexity in one device. Three-dimensional designs incorporate vertical flow within

multiple 2D layers. Thesedesignsaretheclosestformto“universaldevices”,enablingtotesta

wide range of analytes at once and increase diagnosis functionality, yet they sacrifice simplicity

and cost-effectiveness [2]. For simplicity, this thesis will focus only on 1D device structures.

Figure 2-2: Paper-based analytical devices in: (A) 1D, (B) 2D, and (C) 3D. The area where the sample is

collected is denoted by S, and T expresses the testing area used for the diagnosis (adapted from [2])

2.1.3 Colorimetric Detection

The simplest and the most common assays applied in paper-based analytical devices are based on

colorimetric detection. They rely on visual change, i.e. color, induced by a chemical reaction

between the reagents and the analytes. Other visual detection techniques, such as florescence and

light absorbance, can be used for accurate and sensitive assays, but they typically require

specialized, sophisticated laboratory instrumentation [2]. There are many paper characteristics

influencing the sensitivity of the colorimetric reading; some of the key factors are described

below.

10

Types of paper

The choice of base paper for colorimetric biosensors is an important consideration. Optical

properties of paper affect light reflectance measured by the device and hence could influence the

colorimetric readings. Regular office paper, for example, contains optical brightening agents

typically added to a paper during its manufacture to increase its whiteness. These optical

brighteners absorb ultraviolet light and emit blue light within the range 400 to 500 nm [16], thus,

they could shift the assay colorimetric readings. Therefore, for the use of bioactive papers, the

base paper should be free of additives or fillers that could interfere with the colorimetric reading

and cause additional error [2]. Another potential case of optical interference is papers containing

mechanical pulps. Mechanical pulp papers contain lignin that develops a yellowish color when

exposed to light [17]. This phenomenon is called yellowing, and it could affect the overall color

perceived for diagnostics.

In many studies, the substrate used for the bioactive paper production is a filter paper, mainly

due to its wicking ability. Filter paper is considered relatively homogeneous, and it is usually

made of one type of cellulose fiber, mostly cotton [2]. The most popular type used in the

development of bioactive devices is Whatman grade no.1 filter paper [3]. According to the

information provided by the supplier, this is an unbleached and un-calendered paper with no

binders or resins and a low content of fines. Lu et al. suggested the use of nitrocellulose (NC)

membrane as a substrate for µPADs, for its pore size is considerably smaller than traditional

filter papers, which contributes to product robustness and reliability [1].

Paper thickness and porosity

In a dipstick device, paper thickness affects the volume of the sample that could be absorbed

within the paper. The porosity of a paper is also important as it could affect the accessibility and

dispersion of target analytes within the paper [2]. Similarly, the porosity of a coating layer

influences the penetration profile of bio-ink during the device preparation, which could affect the

appearance of color upon exposure to the analyte [18].

11

Paper wetness

Being a hygroscopic material, paper can be subjected to changes in the fiber structure and

network in the presence of water, including increase in its roughness and thickness [19], [20].

Such structural changes could introduce variability and hence error in the colorimetric readings.

Also, it can be presumed that with the addition of moisture content in the bioactive paper, the

color obtained is more intense [10].

2.1.4 Cellphone As a Colorimetric Device

Recent studies have reported the development of rapid, portable, and cost-effective optical

devices used for colorimetric assay. These devices are typically based on light transmission [21]

and reflectance [22] measurements. Nonetheless, the integration of such equipment into

applications will take time and investment in production, and even then, it may not be widely

accessible, especially in developing countries.

Recent studies demonstrated the application of mobile phones as an affordable alternative for

colorimetric diagnosis [10], [23]–[26]. Today, cellphones are within reach to the majority of the

population [15]. They are used for a wide array of applications; colorimetric detection should not

be any different. The aim is that any individual could rapidly interpret and analyze assays with

the aid of accessible applications, which can be easily downloaded, and communicate data

online. However, current developments are based on calibration models, rather than on

theoretical equations. In addition, assay analysis via cellphones application will have to consider

environmental conditions, including ambient lighting and the possibility that dust and dirt

particles will contaminate the sample. The distance of the cellphone from the assay and its

alignment might also affect the readings.

2.1.5 Challenges to Overcome

The advantages for the use of LOC diagnostic systems are vast and well-acknowledged;

however, surprisingly, these tools are not yet successfully commercialized [4]. In their simplest

form, colorimetric paper-based assays produce only qualitative results. Nonetheless, there are

12

certain clinical tests that require accurate quantification of analyte concentration, for example,

the glucose level in the blood sample of a diabetic patient. A high level of accuracy often

requires performing several analytical steps, yet standard paper-based detection devices are

typically limited to single-step assays. The design of biosensors with multiple reactions can

increase their analysis sensitivity, but at the expense of complexity and cost [2].

Another challenge is that current paper-based sensors typically analyze only one designated

target. There is an increasing interest in designing devices that can detect more than one analyte

simultaneously. However, multi-purpose analytical devices require greater sophistication, which

could render them commercially less appealing. The device complexity could undermine the

biosensor robustness, reliability, ease of use, and cost-effectiveness.

A key issue facing bioactive paper sensors is their sensitivity. Current paper-based biosensors are

capable of identifying bioagent concentrations as small as 10-6

M. However, this sensitivity is not

sufficient for many applications. For example, the concentration of cancerous target entities

present in a blood sample could be in a range from 10-9

to 10-12

M. Therefore, a higher analytical

sensitivity is required [2], [4].

Additional challenge is the shelf-life of the paper analytical devices. Reagents and analytes might

evaporate, degrade or oxidize and thus introduce error in the assay. There is also the risk of

contamination by exposing the paper device to dust, wind, and particles in the air [2].

It is imperative that the bioactive paper will combine a simple design with efficient operation to

provide accurate diagnosis without sacrificing reliability. As discussed before, µPADs rely on

microfluidics for the delivery of analytes to biosensors. Complexity of the structure of µPADs

could cause additional errors in colorimetric readings and reduce device sensitivity. However, so

far, there has been no study in the literature to explore the effect of paper composition, porosity,

surface chemistry, etc. on the flow rate in such microfluidic devices [2].

Thus, developing paper-based analytical devices with increased versatility and sensitivity

without compromising their cost-effectiveness and simplicity remains to be a challenging task. It

is our hope that with the development of theoretical models describing the appearance of color as

a function of the bioactive paper design, it will be possible to achieve this goal.

13

2.2 The Kubelka-Munk Theory

As stated previously, the objective of the present study is to develop a mathematical model to

study colorimetric bioactive papers as functions of the paper structure and properties. Various

mathematical models have been developed previously to quantify the optical properties of paper

and to predict its color and appearance [27]. In particular, the Kubelka-Munk (K-M) theory has

been widelyusedincolorscienceandpaperindustrysincethe1930‟s[28]. Due to its simplicity,

it is incorporated in various applications, including producing inks for printers, paint

manufacturing, and coloring textiles and papers [29]. Originally developed for paint films and

later applied to paper by Steele and Judd, the theory involves the analysis of interactions and

propagation of light through a layer of a turbid material [30]. It enables to examine the optical

properties of materials and effects of light reflectance, transmittance, and absorbance [31].

Despite its broad applications, the K-M theory has not been employed in the study of

colorimetric bioactive papers. To use this theory in the design of bioactive papers, we assume

that these devices, containing the color-generating analytes, are comparable to dyed papers.

2.2.1 The Fundamentals of the Kubelka-Munk Theory

The K-M theory is a two-stream simplification of radiative transfer model of light, traveling

within a layer of a material [32]. The theory assumes that the incoming light is monochromatic

and perfectly diffused, and that it propagates only along one axis. In applying this theory to

paper, it is also assumed that the paper is a homogeneous, isotropic, and non-fluorescent medium

with infinite width and length, that is, there are no boundary effects. Moreover, surface reflection

of the material is ignored [29], [33]. Theoretically, only the processes of light scattering,

absorption, reflectance, and transmittance are taken into consideration.

Figure 2-3 is a schematic diagram showing propagation of light in the cross-section of paper.

Light entering paper is scattered several times and is either absorbed by the paper, or transmitted

through it, or reflected out of it. The scattering coefficient S and the absorption coefficient K

represent how well the light is being either scattered or absorbed, respectively, in paper [34]. The

14

optical parameters are assumed to be constant and independent of paper thickness [29].

However, K and S depend on the wavelength of light and could change significantly within the

visible spectrum.

Figure 2-3: Cross-section of a paper sample: the light entering the paper is scattered several times and

either absorbed by the paper, transmitted through it, or reflected out of it (Adapted from [29])

Figure 2-4: The fundamentals of the K-M theory. Light fluxes propagating through paper,

only in one axis (Adapted from [29])

A schematic diagram showing fluxes of light traveling through a layer of paper as per the K-M

theory is illustrated in Figure 2-4. If I represents the light flux entering the paper and J represents

the light flux leaving the paper, then the reflectance R is defined as the ratio, or J/I. Considering

15

an infinitesimal thickness of paper , the downward and upward fluxes of light entering this

element, i.e. and , will be absorbed and scattered within this element according to [29],

[33]:

After integrating the two equations, assuming that K and S are constants, we arrive at the

following equation for an infinitely thick paper [29]:

The reflectivity, denoted by , is the reflectance of an opaque pad, or the reflectance of a paper

so thick that further increase in its thickness will not affect [35]. To isolate , Equation (3)

can be rewritten as:

√

Paper thickness impacts its scattering effect and hence its optical properties [21]. It can be shown

that the reflectance of a single sheet of paper with finite thickness of X can be expressed by [29]:

( ) (

) *(

) +

( ) (

) *(

) +

where denotes the reflectance of an opaque backing placed as a substrate underneath the

layer. When the paper sheet is backed by an ideal, non-reflective black cavity,

Van Den Akker introduced a new approach in which grammage W is used instead of the paper

thickness in the above derivations [31], [35]. Grammage, or basis weight, is the mass of paper

per unit area, expressed in units of kg/m2. The use of grammage in K-M equations is

advantageous since paper thickness might change due to compression without affecting the paper

optical properties [30]. Absorption and scattering coefficients corresponding to basis weight are

16

denoted by k and s, respectively, in units of m2/kg. Similar to Equation (5), the reflectance for

every wavelength as a function of grammage can be written as follows [31]:

( ) (

) *(

) +

( ) (

) *(

) +

where

√

In general, k and s, and therefore and are functions of the wavelength of incident light .

The national technical pulp and paper association (TAPPI), which issued standard methods for

optical measurements of paper brightness and opacity, adopted the application of paper

grammage as the preferred method for calculations, rather than the use of thickness [36].

Furthermore, reported in the literature are only few typical values for optical properties

correlated with paper thickness. For this reason, in this study, we focus on using paper grammage

and the absorption and scattering coefficients expressed in units of m2/kg.

Equations required for calculating reflectance and paper optical properties were summarized by

Robinson [35]. The development of the K-M theory in detail can be found in many textbooks

involving color and light reflectance [31], [37].

2.2.2 Light Absorption and Scattering Effects

In practice, the absorption and scattering coefficient are determined by reflectance

measurements. They are subjected to paper manufacturing processes, including pulping,

bleaching, beating and calendaring. The optical properties are also a function of the type and

amount of fibers, fillers and pigments added to a paper [32].

The light scattering in a medium depends on its structure and composition. Paper mostly consists

of cellulose fibers, fines, fillers, and additives, and the incident light entering a paper scatters at

17

the surface of these particles and their interfaces. Due to its packed structure, paper is a highly

light-scattering material [29], [37]. The higher the density of paper, the lower is the scattering

effect: pulp beating and wet pressing during papermaking reduce the free surface area in paper,

decreasing s in the process. In the case of coated papers, the pigment type, the amount of binder,

and the coating weight affect its optical properties. In this study, we will only discuss the

porosity of paper and not the pigment particles. The absorption coefficient is mostly dependent

on the degree of pulp bleaching: k decreases with increased bleaching, but increases with aging

and yellowing [37], [38].

Table 2-1: Typical values of k and s for paper

Ref. Absorption Coefficient k (m2/kg) Scattering Coefficient s (m

2/kg)

[37] Typically 40

For mechanical pulps >100

For chemical pulps 5

[29] For coated and uncoated bleached

papers

502

For mechanical pulps 3-6 For mechanical pulps 40-702

For unbleached kraft pulps 14

[39] Unbleached handsheet of

mechanical pulp at 560 nm

(function of fines)

1.67-3.46 Unbleached handsheet of

mechanical pulp at 560 nm

(function of fines)

56.8-117

Bleached handsheet of mechanical

pulp at 560 nm (function of fines)

0.46-0.61 Bleached handsheet of mechanical

pulp at 560 nm (function of fines)

50.3-96.2

Undyed wood-free copy paper 35

[40] Uncoated wood-free fine paper

without fillers

0.3 Uncoated wood-free fine paper

without fillers

30

[38] Unbleached Thermochemical pulp

(TMP) at 457 nm

7.4 Unbleached Thermochemical pulp

(TMP) at 457 nm

64

Unbleached TMP at 457 nm, low

content of fines

6.1 Unbleached TMP at 457 nm, low

content of fines

43

Unbleached Stone Ground-wood

(SGW) pulp at 457 nm

5.4 Unbleached Stone Ground-wood

(SGW) pulp at 457 nm

69

Unbleached SGW pulp at 457 nm,

low content of fines

4.5 Unbleached SGW pulp at 457 nm,

low content of fines

52

[39] Colored paper with yellow dye at

440 nm (function of C)

4.0-11.9 Colored paper with yellow dye at

440 nm

32

Colored paper with magenta dye at

560 nm (function of C)

6.5-9.1 Colored paper with magenta dye

at 560 nm

29

Colored paper with cyan

dye at 620 nm

5.6 Colored paper with cyan dye at

620 nm

29.5

18

Theoretically, k and s are independent properties. However, in practice, it has been reported that

these optical coefficients are dependent on one another: the scattering coefficient decreases for a

high absorbing medium [32], [39]. This phenomenon, that is called the“Footeeffect” [41], is

encountered when absorbing pigments and dyes are added to paper, influencing the surface

reflectance and the internal light absorption of the medium [42], [43].

It is worth noting that k and s are model-dependent parameters, and they do not represent actual

physical light phenomena in the medium [27], [32], [37]. Typical values of k and s for paper and

dyed paper are illustrated in Table 2-1.

2.2.3 The Additivity Law

In the case of papers composed of multiple components, absorption and scattering coefficients

could be estimated using the rule of mixtures, or the additivity law:

.

Where , , and are absorption coefficient, scattering coefficient, and the mass fraction of

component i , respectively [44]. Therefore, for a chromophore-containing paper, the above

equations can be simplified as:

.

The coefficients , and express the optical properties of the base paper, while , , and

denote the concentration and optical properties of the chromophore. When applying the K-M

equations, we get the following function:

(

)

Based on the above equation and assuming that the substrate paper coefficients are known, only

two constants are required to correlate reflectivity to component concentration [44].

19

If the scattering effect of the color pigment can be neglected, Equation (11) could be further

simplified to what is known as the One-constant theory, correlating reflectivity to only one

unknown constant ka:

(

)

The additivity law could yield sufficiently accurate results for k. The prediction of s might be

accurate enough when the paper density remains constant. This is not the case, however, for dyed

or coated papers [37]. As discussed before, earlier studies have reported that k increases with

increasing the pigment concentration, while s decreases. This phenomenon could stem from the

addition of the absorbing sites of the pigments masking over the scattering sites in a paper; the

non-homogeneity of the pigment colorants, migrating and aggregating into different forms; or

the non-homogeneity of the paper structure [31], [44].

2.2.4 Non-homogeneous Papers: Multi-layer Structures

Multi-layer materials, such as coated papers, can be treated as heterogeneous sheets of paper

with different optical properties [29], [31], [32]. The K-M equations, however, for these

materials are more complex than those presented so far.

The light reflectance and transmittance of a system consisting two layers, where layer 1 is on top

of layer 2, can be derived from the equations Kubelka had published in 1948 [30], [33]:

where, and denote the reflectance calculated for layers 1 and 2, respectively. In the

above equation, the reflectance R012 is calculated based on R values of each layer, where it is

assumed that every layer is backed by a black backing. The transmittance of a single

homogeneous sheet backed by a black backing is obtained by [40]:

20

(

) [ √ ]

[ √ ]

Similarily, the equations above can be extended to a multi-layer system. For a three-layer

material, the reflectance is calculated as follows:

The reflectance R021 is calculated similarily to R012 according to Equation (13), only layer 2 is on

top of layer 1.

An equivalent approach for multi-layer materials adopted by many researches incorporates the

successive addition of the classic K-M equations for each layer [34], [35], [45]. This approach

yields the same results as the multi-layer equations developed by Kubelka in 1948.

For a coating layer, s depends on the coating weight and the reflectance of the paper substrate

underneath it. Leskelä proposed that the changes in the light angular distribution through the

different layers might cause errors in the predicted optical properties based on K-M theory [37].

2.2.5 Limitations of the Kubelka-Munk Theory

The K-M theory has been generally accepted in paper science and incorporated in most standard

analytical methods. Nonetheless, despite its simplicity and vast applicability, this theory has

several limitations [30], [31].

First, the assumption that paper is a homogeneous medium is nonrealistic. Pauler claimed that

paper should be considered as a layered structure due to retention and dewatering processes

during paper manufacture, yielding different optical properties at the outer and inner layers of a

single sheet [30]. In addition, the additivity law is appropriate for homogeneous mixtures, yet

there is no indication that the colorants are distributed homogeneously through a sheet of paper.

Moreover, colorant particles can migrate and aggregate into different forms so that the scattering

effect is not uniform across the paper, especially when the dye concentration is altered [31].

21

Second, The K-M theory demonstrates a simplified model disregarding surface reflectance and

fluorescence effects. The calculations also neglect the angular variations of light reflection

within a layer of a material arising from the instrument geometry; therefore, additional error

might be introduced [27], [31].

Finally, the reflectance measurements are not accurate enough to correspond to theoretical

calculations. Since three measurements are required ( , , and ), the level of error is

elevated. The assumption of an ideal black or white backing might reduce the degree of error, but

this does not mean that the optical properties obtained are reliable and representative [27], [31].

In practice, paper does not apply to all the assumptions of this theory, yet the K-M equations

provide satisfactory color prediction in the industry. Although many studies have proposed

improvements to address the above limitations [27], [46], [47], no suitable alternative has been

found for the K-M theory yet [30], [37].

2.3 Mathematical Representation of Color

As discussed previously, incorporating color detection in various optical devices, with the

emphasis on digital multimedia such as cellphones, is of great interest for the wide acceptance of

bioactive paper technology. For this reason, the visual color needs to be interpreted accurately by

the device, in order to provide readings with adequate sensitivity, which then could be translated

to the analyte concentration. To do this, color should be expressed in the form of color

coordinates. However, due to differences in illumination conditions, standard methods or

corrections schemes are required to convert raw optical readings to the universal color systems.

This section is focused on the conversion of colorimetric data into various color coordinates.

2.3.1 CIE Universal Standard System

The international commission in illumination (CIE) has established universal standards for

testing optical properties of paper. These standards rely on a set of three color-matching

22

functions, representing the red, green and blue colors perceived physiologically by the human-

eye cone receptors [31], [37]. The experiments performed by the CIE in 1931 for generating the

color-matching functions were based on human observation at a 2° viewing angle, known as the

CIE1931“standardobserver”.Later, in 1964, a second set of color matching functions were

introduced for a viewing angle of 10° [31].

The color-matching functions yield three primaries, called the XYZ tristimulus values, which are

essentially the foundation for generating almost any color model, as presented below. A color

model includes the combination of three light sources that can be presented in a triangular

diagram, also known as the color gamut. The combination of two primaries fall within one line

of the triangle, and the combination of the three primaries in various proportions can extract all

possible colors within the triangle [48].

2.3.2 The Calculation of XYZ Tristimulus Values

The tristimulus values in the CIE standard system X, Y, and Z are the basis for calculating the

coordinates of various color models and spaces. They are given as [49]

∑ ̅

∑ ̅

∑ ̅

where denotes the normalizing factor expressed by:

∑ ̅

Fora“standardobserver”,according to CIE 1931 (2o) or CIE 1964 (10

o), ̅, ̅, and ̅ represent

the color matching functions; is the wavelength; is the spectral energy distribution per

each illuminant; is the light reflectance at a specific wavelength; and is the wavelength

increment [49]. The lightness or luminosity, i.e., color intensity, is expressed by Y coordinate

[31].

23

The factors k, ̅ , ̅ , ̅ , , and , which are multiplied by the measured reflectance

values in Equations (17)-(20), are called Tristimulus Weighing Factors , , and . Tables

of the Tristimulus Weighing Factors for various illuminants, standard CIE observers, and

wavelength measurement intervals can be found in the literature [50].

Varying illuminant characteristics affects the perceived color, and hence chromatic coordinates.

As a result, CIE has established standard illuminants representing various ambient conditions,

such as daylight and indoor fluorescent lighting. These standard illuminants were defined by

using several lamps with alternating filters [31]. In this study, we will focus on four selected

illuminants, as presented in Table 2-2 [48], [50].

Table 2-2: Selected CIE standard illuminants

Illuminant Description Correlated to

Temperature1

D65 CIE standard illuminant representing daylight 6504 K

D50 CIE illuminant representing daylight;

it is used for prints and color rendering in the graphic arts industry 5000 K

C CIE standard illuminant representing daylight 6774 K

F2 Cool white fluorescent light 4200 K

To save computation time and data storage, instead of collecting colorimetric data for every

illuminant, it is possible to transform XYZ values taken for one illuminant to the corresponding

values for another using the Bradford matrix:

[ ]

[

] [ ]

Components of the Bradford matrix depend on the source and target illuminants and can be

found in the literature.

1 Theilluminantiscorrelatedtoa“colortemperature”,thatis,thetemperaturetowhichablackbodyisheatedto

produce the same color stimuli [31]

24

2.3.3 CIELAB Standard System

Another standard, issued later by the CIE, is the L*a

*b

* chromatic representation, also called

CIELAB. This color coordinate system is used widely in the paper industry. The lightness scale

is denoted by L*, whereas the components a

* and b

*, related to color hue and saturation, represent

the red-green scale and the yellow-blue scale, respectively (see Figure 2-5). These three

coordinates are derived from the XYZ tristimulus values and expressed by the following

equations [48], [49]:

⁄ ⁄

[ ⁄ ⁄

⁄ ⁄

]

[ ⁄ ⁄

⁄ ⁄

].

Here, , , and coordinates are the tristimulus values for a “perfectwhite”colorofa

specific illuminant. Equation (22) can be applied as long as ⁄ .

Figure 2-5: CIELAB color space (adapted from [31])

The components a* and b

*yield the expression for color strength, or chroma, denoted by C

*:

√

25

From the above, the visual appearance of an object depends on its lightness, hue, and saturation.

The change in color is dependent on the change in one of these aspects or all of them. The color

difference between two measurements is denoted by , and it is expressed by:

√ ,

where , , and are the differences in CIELAB coordinates. Of course, a color

difference expressed by a single scalar is not enough to characterize the shift in the three-

dimensional coordinates, yet it could be useful for comparing performance characteristics [31].

2.3.4 RGB Color Model

TheRGBcolormodelisanadditivemodelinwhichthreeprimarycolors,red(R‟),green(G‟),

andblue(B‟),ofdifferentintensitiesarecombinedtogethertoproduce a broad range of colors. It

is widely used in electronic systems to project a colored image. Each primary color is correlated

to digital representation of 8 bits in a 24-bit color system, and it varies from 0 to 255. A perfect

white color is represented by the coordinates {255,255,255}; whereas a perfect black color is

expressed by {0,0,0} coordinates [15], [48].

The RGB color model yields numerous color spaces; they are defined differently from one

software to another, such as Apple or Adobe, when incorporated in various devices. Hence, RGB

color spaces are device-dependent, where the same color will be represented by different

coordinates for various digital instruments. On the other hand, the XYZ color space is source

independent, i.e., a set of the tristimulus values will be perceived as the same color in different

optical devices [48].

RGB values could be obtained by transforming the tristimulus primaries derived from reflectance

measurements. To convert XYZ coordinates into RGB, there are designated matrices for various

color spaces. The general form of such a transformation is as follows:

[ ] [

] [

].

26

ToobtainR‟G‟B‟values for a 24-bit color system, we use the following expression2 [48]:

,

whereγisa transform correction specific for every color space. With the application of a chosen

γ,theresultsareroundedtothenearestintegerbetween0and255.Theimportanceofγisnot

discussed within the scope of this study, but it can be found elsewhere [48]. Similar expressions

can be applied to determine G‟andB‟values.

2.3.5 The Application of Color Models and Spaces in Bioactive Papers

In this work, we focus on the RGB color model, as most of the recent studies in the field of bio-

sensors use RGB coordinates for image analysis [24]. However, there are other color models and

spaces commonly used in the digital media. For example, the CMYK model is a subtractive

color model, using cyan, magenta, yellow, and black colors. A Greyscale model combines black

and white colors in different intensities. An HSV color space is derived from the RGB values,

and its coordinates represent hue, saturation, and brightness [15].

Lopez-Ruiz et al. defined assay colors in HSV coordinates that were correlated to the target

specimen concentration [10]. Cantrell et al. also presented a good response obtained for optical

sensors using the HSV color space [51]. The RGB values are used more often to describe a

change in the intensity of color; to express the change of color, or hue, the HSV space might be

more appropriate.

2.4 Summary of the Existing Literature

Bioactive papers are promised to be a simple, low-cost, and portable detection tool of bioagents

and analytes, which could be used in the food industry, medical treatments and hazardous work

environments. These paper-based analytical deices are embedded with biosensors that generate

2 Equation (28) is applicable when R, G, and B values are between 0 and 1

27

color in the presence of target specimen. Analysis based on colorimetric detection could

potentially replace the long and tedious work performed in laboratories.

An accurate and sensitive quantification of target bioagent concentrations in a sample requires a

better fundamental understanding of the appearance of chromophores during the biochemical

reaction in the paper biosensors. For this purpose, this thesis presents the application of the

Kubelka-Munk theory, which analyzes light propagation through a paper based on scattering and

absorption effects, and the investigation of paper properties and environmental attributes

affecting the measurements of paper light reflectance. To the best of our knowledge, this is the

first time that this theory is investigated in terms of application in bioactive papers.

The conversion of colorimetric data into various color coordinates is obtained with the

application of universal standards developed by the CIE. The XYZ tristimulus values are the

foundation for generating almost any color model, including RGB and CIELAB, often applied in

multimedia. By incorporating the theoretical foundation to commonly used optical devices such

as digital cameras and cellphones, the diagnosis of contaminants and pathogenic specimens

could become universally accessible.

28

Chapter 3

Methodology

29

3. Methodology

3.1 Developing a Theoretical Model Based on the Kubelka-Munk

Theory

In this work, we explore the theoretical principles for the colorimetric detection using bioactive

papers. This section describes the methodology of applying the K-M theory to develop a

theoretical model correlating the light reflectance to analyte concentration as function of the

paper optical properties, design, and environmental conditions.

Throughout this work, the additivity law is incorporated into expressing k, in order to integrate

the chromophore concentration within the K-M equations. Since studies reported that s does not

obey the additivity law, the scattering coefficient is considered to remain constant. Furthermore,

we distinguish between two major cases, namely homogeneous and non-homogeneous bioactive

paper devices. All the calculations and plots were performed using “Wolfram Mathematica 8.0

for Students”software (Wolfram Research, USA).

3.1.1 Homogeneous Bioactive Paper

This is the simplest case in which we assume that the paper sheet is homogeneous and that the

biosensor is spread uniformly within it. For calculating the light reflectance of paper, Equations

(6) and (7) were used. The absorption coefficient k was calculated according to Equation (9). An

example for the Mathematica code is found in Appendix A-1. Table 3-1 gathers the numeric

values of the optical properties and paper characteristics to be applied in the K-M equations.

These variables were chosen for the purpose of illustration, based on the literature. The table also

includes the range of change of each property, which could potentially affect the reflectance.

30

Paper grammage:

As mentioned previously, the most common paper applied in the production of bioactive papers

is Whatman no.1 filter paper. This paper is characterized with grammage of 0.087 kg/m2 and

thickness of 180 µm. According to Then et al. the typical W of a filter paper ranges from 0.09 to

0.2 kg/m2 [2]. Thus, the range tested for this parameter is between 0 and 0.200 kg/m

2.

Scattering coefficient of the paper:

Based on Table 2-1, the typical scattering coefficient of unbleached mechanical paper is around

40 m2/kg, which was assumed to be the value in our model. However, it could reach to 10-fold

higher values. Therefore, s was varied in the range 0-500 m2/kg.

Absorption coefficient of the paper:

As shown in Table 2-1, unbleached mechanical pulp is between 3 to 6 m2/kg and unbleached

kraft paper is about 14 m2/kg. Therefore, for the Whatman no.1 filter paper, the absorption

coefficient was assumed to be 5 m2/kg, and the chosen range for changing was from 0 to 15

m2/kg.

Absorption coefficient of the analyte:

Unfortunately, there is not much of information in the literature about the absorption coefficients

of dyes and other colorants. It was found, however, that the maximal absorption coefficient of

black carbon ink at 700 nm is 10,000 m2/kg [41], [52]. This value was taken for an extreme

scenario for a highly absorbing analyte ka.

Analyte (chromophore) concentration:

Experimental protocols report using dye concentrations, expressed as mass fractions, in the range

from 0.000002 to 0.016 grams of dye in 1 gram of dyed sheet [42]. Conventional bioactive

papers can absorb analyte concentrations roughly from 4x10-5

to 0.01 grams of analyte per gram

of paper [11]. For the purpose of illustration and convenience, it was decided that the analyte

(expressed by chromophore) concentration Ca will range between 0.0001 and 0.1 g/g.

31

Table 3-1: Typical values for the mathematical model and their ranges

Parameter Selected Value Range of Change Units

- 0-0.1 g/g

0.087 0-0.2 kg/m2

5 0-15 m2/kg

10,000 0-10,000 m2/kg

40 0-500 m2/kg

0 0-1 -

3.1.2 The Effect of Porosity on the Colorimetric Detection

To examine the effect of variations in porosity on colorimetric reading, porosity was integrated

into the K-M model, as described below. The pore volume fraction of a multi-particle system ϕ is

dependent on the bulk and the particle densities. For paper made of cellulosic fibers, we get the

following expression:

The cellulose particle density is denoted by , and the paper density is expressed by . The

porosity and density calculated for Whatman no. 1 filter paper are 0.69 and 483 kg/m3,

respectively, and the cellulose density is typically 1540 kg/m3 [53].

The density of paper is the ratio between its grammage and thickness ; therefore,

and paper grammage becomes:

Thus, by applying Equation (31), it is possible to investigate the effect of paper porosity on light

reflectance.

In addition, as was mentioned previously, the porosity of paper affects the scattering coefficient.

An increase in porosity reduces the paper density, and increases s as a result. Here, scattering

coefficient is assumed to be proportional to the paper porosity, with zero scattering for a fully

32

collapsed paper, i.e. s=0 at ϕ=0. Therefore, for Whatman paper with a porosity of 0.69 and

scattering coefficient of 40 m2/kg:

The Mathematica code for this case is provided in Appendix A-2.

3.1.3 Non-homogeneous Bioactive Paper: Multi-layer Theory

If the analyte is not evenly distributed within the paper, bioactive paper no longer can be treated

as a homogeneous medium. Therefore, the effect of the analyte disposition and depth of

penetration within paper on the reflectance needs to be taken into account. In this case, the paper

biosensor was addressed as a compound material with several layers with different optical

properties. It was assumed, though, that the analyte within each layer is evenly distributed.

Here we distinguish two cases: two-layer structure, where the analyte is distributed at the surface

layer of a bioactive paper device; and a three-layer structure, where the analyte is introduced

only in the middle layer located inside a bioactive paper. The Mathematica codes of the models,

based on the K-M equations for two and three-layer materials, are presented in Appendix A-3.

Two-layer Structure

Figure 3-1 illustrates the theoretical two-layer structure of a bioactive paper, where the bottom

layer (layer 2) is a paper substrate, and the top layer (layer 1) is the active layer containing

chromophores generated in the biochemical reaction between biosensor and target analyte. The

reflectance of each layer, assuming that it is backed by a black backing, and the transmittance of

layer 1 were calculated according to Equations (6) and (15), respectively; whereas, Equation (13)

was used to calculate the total reflectance of the two-layer system.

Assume W represents the total grammage of the paper, and f is the grammage fraction of the top

layer. Thus, the top layer grammage becomes fW, and (1-f)W represents the grammage of the

bottom layer. To examine the effect of thickness (i.e. grammage) of the top layer, the fraction f

33

was varied from 0 to 0.5, which means that the analyte penetrates paper from the top to its

middle point.

Figure 3-1: A two-layer system, where the bottom layer is the base paper and the upper layer is the active

layer containing the chromophore. The penetration depth of the analyte is correlated to the grammage

fraction fW

Two cases were considered in this investigation: 1) constant chromophore concentration in

paper, and 2) constant chromophore amount in paper. In the first case, with the increase of

grammage fraction f the amount of the chromophore will also increase. In the second case,

however, the concentration of chromophore varies based on the mass of the chromophore

and the mass of paper . For a homogeneous paper, where chromophore is evenly

distributed through paper thickness, chromophore concentration can be expressed by:

Similarly, if chromophore is confined within a layer, we can write the expression for the adjusted

concentration for a fraction f of W:

34

After placing Equation (33) into Equation (34), we arrived at the following expression,

correlating between the apparent chromophore concentration and the adjusted one:

Then, the absorption coefficient was calculated according to

Three-layer Structure

In this case, we assumed that the layer of paper containing chromophore is located in the middle,

between two layers of paper (Figure 3-2). The grammage fraction of the middle layer was

considered constant at the value of 0.5, to compare the reflectance results with those obtained for

the same fraction in the two-layer structure. The reflectance of this three-layer material was

calculated according to Equation (16). Similar to the case of two-layer structure, additivity rule

was used to estimate the absorption coefficient of the middle layer.

Figure 3-2: Schematic diagram of a three-layer device structure. The middle layer is the active layer

containing the chromophore

35

3.2 Mathematical Representation of Color

In this chapter, we illustrate the process of expressing color in mathematical coordinates. We

calculated the XYZ tristimulus values and then transformed them into CIELAB and RGB values.

For each of the three color representations, we examined the magnitude of error in the results as

function of the ambient illumination. To extract XYZ coordinates, we measured the light

reflectance of dyed paper samples prepared in the lab.

3.2.1 Reflectance Measurement of Dyed Paper

Samples of a simple office paper were dyed with methylene blue in solutions of different

concentrations. Table 3-2 provides a list of the dyed paper samples, and their preparation is

depicted in Figure 3-3.

Table 3-2: Dyed paper samples used in this study

Solution no. 1 2 3 4 5 6 7 8

Conc. (M) 0.0001 0.0002 0.0005 0.001 0.002 0.005 0.01 0.02

Conc. (g/g) 0.0018 0.0021 0.0023 0.0030 0.0031 0.0050 0.0058 0.0077

The solutions of methylene blue dye with water were prepared from 0.1 mM to 20 mM in

logarithmic scale. To make sure that there was no influence of additives and fillers dissolved in

the water on the weight measurements, the paper samples were washed in distilled water for

about 90 min, dried and weighed prior to the dyeing process. For each dye solution, three

samples of washed paper were dipped for 60 sec in the dye solution and 60 sec in RO water, to

wash out the dye residue, and then they were dried and weighed again to estimate the amount of

the absorbed dye in the paper. The drying process of the paper samples, at any stage, included

air-drying followed by drying in a desiccator to remove any moisture in the paper.

36

Figure 3-3: Preparation of dyed paper samples

The reflectance values of each dyed paper sample were measured using a 530 X-Rite

spectrodensitometer at the range of 400-700nm, with the interval of 10nm, over a black backing.

The optical device was calibrated to illuminant D65 and CIE 1931 (2°) standard observer.

3.2.2 Calculating XYZ Tristimulus Values

The XYZ values for the paper samples dyed with Methylene Blue were calculated as described

in Section 2.3.2 using the Tristimulus Weighing Factors ( , , and ) for illuminant D65,

CIE 1931 (2°) standard observer, and with measurement interval of 10nm. Table 3-3 illustrates

the procedure for solution no. 1 (dye concentration = 0.0018 g/g).

The Bradford matrices used to transform the XYZ coordinates obtained for illuminant D65 into

the values corresponding to illuminants D50, C, and F2 are [48]:

[ ]

[

] [ ]

[ ]

[

] [ ]

[ ]

[

] [ ]

.

37

Accordingly, the tristimulus values obtained for various illuminants were determined to evaluate

the magnitude of error introduced due to variations in illuminant characteristics.

Table 3-3: The calculation of XYZ values for dye solution no.1 for standard illuminant D65 [50]

So