How can chemometrics improve microfluidic research?

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How Can Chemometrics Improve Microfluidic Research? Mehdi Jalali-Heravi, Mary Arrastia, and Frank Anthony Gomez Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/ac504863y • Publication Date (Web): 04 Feb 2015 Downloaded from http://pubs.acs.org on February 10, 2015

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Analytical Chemistry

Feature How Can Chemometrics Improve Microfluidic Research? Mehdi Jalali-Heravi, Mary Arrastia, and Frank A. Gomez*

Department of Chemistry and Biochemistry California State University, Los Angeles 5151 State University Drive Los Angeles, California 90032-8202, USA E-Mail: [email protected] 323-343-2368 Fax: 323-343-6490

*Author to whom correspondence should be addressed.

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Abstract Chemometrics has the potential to embolden microfluidics to become that enabling technology for so long sought after. In this Feature article, we describe a historical perspective on microfluidics and its current challenges, a perspective on chemometric methods including response surface methodology (RSM), and how a combination of artificial neural network with experimental design (ANN-ED) have demonstrated promise in addressing basic microfluidic problems.

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Microfluidics: A Historical Perspective

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Challenges in microfluidics

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What is chemometrics?

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Perspective on the use of chemometric methods in microfluidics

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Optimizing the factors affecting the results: Response surface methodology

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Combination of artificial neural network with experimental design (ANN-ED)

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Conclusions and future outlook

Microfluidics: A Historical Perspective It has been almost a quarter of a century since the first seminal publication detailed what is now termed a microelectromechanical (MEM) system, “lab-on-a-chip”, or microfluidic device (MD).1 Since that initial work in 1990, the number of ISI publications found with “microfluidic” in the title has grown from less than 100 in 1994, to nearly 1000 in 2004, to over 3000 today. In fact, the term “lab-on-a-chip” (LOC) has become nearly passé in the sheer numbers of works and researchers who espouse the notion of miniaturizing everything larger than a finger nail. And yet, why not? Microfluidic LOC technologies allow researchers the flexibility for laboratory experimentation and, thereby, the benefits of miniaturization, integration, and automation to many industries. Microfluidic platforms are advantageous over non-microfluidic techniques as they offer speed to analysis, ability to multiplex, portability, and compatibility with other techniques. The most exciting aspect of microfluidics is its potential for producing practical devices; hence, its enabling technology label. Much of this can be seen in the milieu of

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microfluidics technologies that have enabled applications related to LOC or micro total analysis systems (µTAS). Microfluidic technologies has allowed for the facile manipulation of minute quantities of liquids in channels and, in many case, the ability to perform several analytical steps (for example, sample pretreatment, reaction, separation, and detection) on a microfluidic platform effectively and automatically.2,3 Applications for microfluidic devices (MDs) over the past two decades are similar to the great increase in microelectronics subsequent to the invention of the integrated circuit and show great potential in many applications today. These applications shown the most promise in the biomedical area where these devices have been used in cellular analysis,4-12 enzymatic assays,13-22 viral detection,23-33 and the polymerase chain reaction.34-40 just to name a few. There are many advantages microfluidics offer including small minute volumes that lead to optimized efficiency of chemical reagents; fast sampling times; manufacturing costs that are lower per device than other currently available analytical techniques that allow for facile disposability; parallel processing of samples; the ability to control multiple samples and reagents simultaneously both accurately and precisely reducing the need for pipetting; low power consumption, and; versatile format for the integration of a number of detection schemes. Several years ago, Gervais and Delamarche described what could be stated is a scientists ideal microfluidic-based device for use as a point-of-care (POC) diagnostic device.41 Here, the microfluidic device would not be very invasive and would use only a small amount of sample (as low as 1 µL) from the patient. Sampling would be accurate and be done by the microchip and have the potential of larger volumes. The microfluidic

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device would be flexible enough such that it would have the ability to be multiplexed in order to analyze many analytes including multiple proteins and nucleic acids within one minute. Selectivity of analytes in solution would be easily accomplished with little chance for false positives. Furthermore, there would be little chance for cross contamination between samples from different patients or different runs. The sensitivity limit of the microfluidic device is expected to be in the pico- to femtomolar range which will allow for the detection of sample components in low concentrations and in the micromolar quantities. It would be integral that the device be constructed of a transparent material and have a long battery life that would not require recharging for years. It is desirable that the device be impervious to both water and other organic solutions and that if the device is dropped onto the ground, it would still remain operable. The device would be stored between −55 °C and 55 °C for a number of years and could be used in both a hospital setting and at home by patients. Finally, the cost of fabrication and manufacturing of the microfluidic device would be less than one dollar.41 Today, many areas of science (chemical, biological, medicinal, and agricultural, just to name a few) have integrated some type of platform to study some molecular species at some rate at some level of detection. Specifically, microfluidics has provided the foundation for a number of biochemical advancements in POC diagnostics, drug discovery, and bioterrorism detection. Among the areas where microfluidics has seen most integration in include pharmaceuticals, biotechnology, the life sciences, public health, defense, and agriculture. Just to point out one area that has benefited from the inclusion of microfluidic technologies, the pharmaceutical industry has integrated miniaturization, integration, and automation into many of its research and development

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sectors such that nearly every company conducting research is aware of microfluidic technologies and are modifying their strategic plans with miniaturization in mind. It is no longer cost-efficient for pharmaceutical companies to utilize robotic automation systems due to their expense and maintenance. Instead, microfluidic platforms present a viable option due to low costs, minor maintenance and space requirements, and small sample volume needs.

Challenges in Microfluidics Even since that initial pioneering work by Manz many have opined that microfluidics would (and some boasted should) eventually supplant traditional, larger, and costlier instruments as well as provide analysis at levels of detection and at speeds never before possible.3 So why has microfluidics yet reached its full potential? Why is there not the ability to run a myriad of tests in the privacy of one’s home reliably and accurately? Why is there not a pile of “chips” in every biochemistry, medicinal, agricultural, etc. lab? The first reason is an economical one caused by the pharmaceutical industries need to continue to sell medication to as many people as possible with marginal consideration to predictive, personalized, and preemptive medicine. It is this philosophy that determines trends in funding for biomedical innovation. The second reason is the lag in microfluidic technology which has hindered the development of integrated and foolproof POC devices. The third reason is problems with the biology and how conclusive results to patient tests cannot be guaranteed. Finally, technological challenges, commercial and intellectual property concerns, and regulatory hurdles, have further impeded the potential of microfluidics.

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The aforementioned are not the only reasons microfluidics have yet reached the market en masse. While many previous studies have demonstrated the application of microfluidic technologies toward high-throughput and high-content chemical and biological assays, for example, only a limited few have used statistical methods and computational techniques to examine the effect of experimental variables on output response, data classification, and signal processing capabilities, and/or the soundness of the device output to variations in the platform design.42-44 Sans this optimization, there exists the inherent difficulty in developing technologies that may one day lead to commercialization and products that would serve a useful purpose by the society at large. Microfluidics can benefit most in the biomedical sector and in particular POC diagnostic devices. It is expected that the market for POC diagnostics will increase to almost $17 billion by 2016 and $35 billion by 2021. Presently, the main markets for POC diagnostics include but are not limited to glucose monitoring, pregnancy and fertility, blood chemistry and electrolyte, cholesterol, drug and alcohol, and cardiac markers. Future growth areas will include HIV testing, drugs contributing to abuse, and diagnostics for diagnosing infections. Certainly, optimization of applications would have a great benefit for mankind here.

What is Chemometrics? Chemometrics is the chemical discipline that uses mathematical and statistical methods, to design or select optimal measurement procedures and experiments, and to provide maximum chemical information by analyzing chemical data. Recent advances have led to new analytical tools– microprocessor controlled “intelligent” instrumentation,

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and data analysis systems. The flood of data generated by modern analytical instrumentation is a major reason that chemists, in particular, have developed chemometric applications. The term chemometrics was coined by the young Swedish scientist Svante Wold in 1972.45 His collaboration with the American analytical chemist Bruce Kowalski resulted in the foundation of the International Chemometrics Society.46 Before the development of the chemometrics discipline chemists would utilize as much mathematics possible to solve the problem at hand. Yet, the more complex the problem, and especially if it involved statistical experimental design and data analysis, the more likely it would be relegated to an engineer or statistician. Today, science has few borders, and collaboration is the name of the game. So too can be said in data analysis and interpretation as the current trend in scientific thinking across disciplines involves a multivariate approach. Problems need to be approached from different perspectives and similarly there are frequent linkages, correlations, and relationships between variables that can only be determined surmised by using the most modern of data analysis techniques. Hence, chemometrics becomes a necessity, not the luxury it once might have been. Brown et al.47 covered the most significant developments in the field in a series of reviews entitled Chemometrics in Analytical Chemistry. In this review, group reviews and tutorials focusing on specific methods were covered.47, 48 This review and other articles have demonstrated that the field of chemometrics has enjoyed a steady growth. A large variety of problems exist in the microfluidic field that either chemometric methods have solved or can address them. For example, viruses can be detected using a microfluidic biochip with molecularly imprinted polymers (MIP) integrated on the chip using contact-less dielectric microsensors.49 This method was based on the differences

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between the dielectrics of the virus sample and the polymers used to fabricate the MIP. The method of principal component analysis (PCA) can be used to distinguish between the data points obtained in the presence of de-ionized water (DI), buffer, and virus solution using native and molecularly imprinted polymers. In PCA, the principal components only represent linearly independent coordinate axes for multivariate data clusters and do not have a real physical meaning. It is shown that dielectric spectroscopy with the help of chemometrics is able to distinguish between the native- and molecular imprinted- polymers.49In another contribution, a quartz microfluidic chip has been used to identify tumor cells using Raman spectroscopy.50The cells can be identified based on Raman spectra by using the classification algorithm of linear discriminant analysis (LDA).50This aspect of classification is often referred to as the ‘likelihood’ approach. This likelihood perspective will minimize the total theoretical probability of misclassification. It is demonstrated that Raman-based tumor cell identification has improved using this algorithm.50 Nowadays, there are concerns for bacteria identification and, therefore, the development of a reliable, fast and high specific detection method is helpful.51 Vibrational spectroscopy can be used for the verification of bacteria in microfluidic devices.51 However, the statistical analysis of data requires a reproducible and specific spectral pattern as well as the establishment of large databases. This means that a fast technique such as surface enhanced Raman spectroscopy (SERS) is needed to reduce the recording time. Walter et al.51 implemented SERS in a microfluidic device and were able to reduce the recording time to 1 s per spectrum. They measured bacteria cells of nine different E. coli strains to avoid the spectral fluctuations that are common to SERS

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measurements on bacterial samples. Here, a chemometric technique was required to obtain useful information from the flood of data provided by this approach. Support vector machine (SVM), as a classifier, was used in this research to validate the classification of E. coli strains.51The dataset was split in two sets. The training of the classifier was carried out using the first dataset, and the second dataset was used for the validation. The application of SVM resulted in accuracies up to 92.6%. In general, developing a fast, highly specific and reliable method for identifying bacteria in a microfluidic device is not feasible without the assistant of chemometrics. One of the biological and biomedical application areas for chemometric assisted-vibrational spectroscopy is the characterization of different types of microorganisms.52 Chemometrics and multivariate methods of analysis have opened a new dimension for the clinical application of NIR spectroscopy. A comprehensive review presented by Trietsch et al.53 introduces LOC technology and its potential for the life sciences. In developing LOC platforms, to ensure low experimental variability and thus higher data quality, a large number of experiments should be performed in parallel. Therefore, chemometric methods will be required to analyze the extensive amount of data generated by such techniques. For instance, screening of large chemical compound libraries at higher rates and reduced costs is essential for the lead compound screening in drug development processes.53 An ultimate goal of using chemometrics is to optimize biomedical and related microfluidics applications that require small amounts of sample, which are routinely operated by untrained personnel, and at low cost.

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Perspective on the Use of Chemometric Methods in Microfluidics Chemometrics and computational methods have been integrated in many scientific disciplines, and they certainly can be useful in improving the performance of microfluidic-based processes. Due to the large quantity of variables affecting the performance of microfluidic-based devices, the procedure of developing a lab-on-a-chip device cannot be considered a simple task. In this context, the term “optimization” refers to improving the performance by determining the best conditions at which the best response is obtained. Optimization and modeling can shorten the method development, which is often a time-consuming process. Unfortunately, it is still a common practice to use the classical experimental approach based on the single variable approach (SVA) or one-variable-at-a-time strategy.54 While the use of SVA might work in some specific cases it frequently requires too much experimental data. Besides, it has a serious problem when variables interact with each other. In this context, multivariate methods whereby all factors are varied simultaneously is an important issue. In addition, these approaches require less time, effort, and resources compared to univariate procedures.55 The approach to process the optimization is called response surface methodology (RSM). RSM can be used for modeling and analysis of a process in which the response is influenced by several parameters. The objective of this approach, which is a collection of mathematical and statistical methods is to optimize the response of interest. These techniques have been extensively used in bioprocesses56-59, the industrial world60-62, and analysis of very complex mixtures 54, 63-65. Although the application of RSM to microfluidic processes

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with different unpredictable variables would seem logical, there is a dearth of work in this area. An aim of this article is to address the advantages of using multiparametric approaches in optimizing microfluidic-based devices. Multivariable techniques are based on experiments, yet our plan or design of experimentation first requires some preliminary experiments prior to extensive experimentation. In fact experimental design (ED) will be adopted to design the experiments. Response surface modeling would be used to optimize the data of ED. These data are obtained by using a limited number of experiments and they may not represent the thorough optimized factors. Therefore, the ED data can be modeled with a category of artificial intelligence (AI) techniques called artificial neural networks (ANNs). ANNs are a family of statistical learning algorithms that mimics the human brain. These networks have several advantages, including the capacity of selflearning and modeling of complex data without the need for a detailed information on the underlying phenomena.66-67 Consequently, thorough optimized conditions require the combination of ANN with the experimental design (ANN-ED).We will not present an exhaustive review of ANNs applications here. However, we do demonstrate the fundamental principles and, on selected examples, the ability and advantages of the ANN-ED applications in microfluidic processes.

Optimizing the Factors Affecting the Results: Response Surface Methodology

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This article focuses on planning and conducting experiments using the microfluidic systems. Our focus is on defining, and then optimizing the factors affecting the performance of a microfluidic system using the discipline of chemometrics. The process of development of a microfluidic-based system can be represented by the model shown in Figure 1.

Figure 1. Development of a microfluidic-based system

The process of development of a microfluidic device (MD) is a combination of machines, methods, materials, and other resources that convert some inputs, often chemicals, into outputs that have an observable response. In general, the miniaturized devices are very sensitive in variation of several controllable and uncontrollable variables influencing the response. The objective of the experimenter is to determine the influence that these factors have on the output response of the system. This means that the trial and error strategy is not efficient in developing or improving the performance of a pre-developed system. In this context, ED can play an important role in developing new MDs or improving the existing ones. In ED a series of experiments is performed to generate data from the process, and then use the information from the experiments to establish a mathematical model, by which the factors can be optimized.

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A major disadvantage of the one-factor-at-a-time strategy is that it fails to consider the interaction between variables. The correct approach to consider several factors with probable interactions is to conduct a factorial design (FD). In this strategy, factors are varied together instead of one at a time. The most common design is a full factorial design denoted as 2k-designs, where the base 2 stands for the number of factor levels and k is the number of factors. In this design two levels (the lower and upper levels) are chosen for each factor in such a way that they cover the entire factor space. Often two levels, the lower and upper level is chosen. In the case of a large number of factors, where the number of experiments increases fractional factorial design (FFD) is superior to full factorial design. In FFD, the number of experiments is reduced by a number p according to a 2k-p design. The FD and FFD mainly are used for the screening portion of the experiments. As a simple example, we will illustrate the different steps of applying the experimental design with an ongoing microfluidic project in our laboratory. The aim of this project was to simulate the mixing of two food dyes (blue and yellow) on a paper microfluidic platform and to optimize the parameters affecting the response. The proposed paper microfluidic platform consists of two inlets for each of the food dyes, a straight channel containing the detection zone, and a waste reservoir for excess solution (Figure 2). The two level FD was used for the screening step followed by RSM to optimize the factors affecting the response. After mixing the dyes on the paper MD, it was scanned and the scanned images were analyzed using Adobe Photoshop CS2.

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Figure 2. Schematic representation of the paper chip

Based on preliminary studies, three parameters including (A) the length of the channel, (B) the width of the channel and, (C) the volume of the sample, were considered. Table 1 shows the main factors, their notations, and levels. In addition, the color intensity obtained at the halfway of the channel was selected as response. Eight experiments were randomized and executed in predetermined levels of factors in a 23 FD. The design matrix is shown in Table 2.

Table 1. Factors and their levels in factorial design. Factor Channel length (mm) Channel width (mm) Sample volume (µL)

Notation A B C

Levels -1 7.5 1.5 1.5

+1 12.5 2.2 3.0

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Table 2. Design matrix together with the responses for full factorial design. Run Order 1 2 3 4 5 6 7 8

Channel length (A) 1 -1 -1 1 1 -1 -1 1

Channel width (B) 1 1 1 -1 1 -1 -1 -1

Sample volume (C) -1 -1 1 1 1 1 -1 -1

Response 220.47 211.06 198.65 206.39 208.89 195.5 206.37 214.91

Analysis of variance (ANOVA) can be used to estimate the significances of the main effects and interactions. ANOVA is an appropriate procedure for testing the equality of several means. When one wishes to compare more than two experiments or sample means, the null hypothesis is that the sample means are the same, and the alternative hypothesis is that they are not. ANOVA is a useful method for making decisions about these hypothesis. Therefore, this procedure can be applied in estimating the significances of each effect. The effects of a main effect or interaction and its rank relative to other variables can be estimated via least squares estimation. Having the estimated factors in hand, one could prepare a list of the main effects and interactions ordered by the magnitude of each effect. The normal probability plots are useful tools to assess the influence of each factor on the response. Therefore, in addition to ANOVA, the normal probability plots were used to find the most influential effects and interactions. In these plots, all the effects that lie along the line are not significant, whereas, important effects are far from the line. Figure 3 demonstrates that all three factors are important. However, analysis of the effects demonstrated a low contribution (7.8%) for the channel length and no noticeable interactions between the factors. Analysis of the FD results

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shows that the response increases when the width and height of the channel increases. In contrast, the color intensity decreases by increasing the volume of the sample. Consequently, only the width of the channel and volume of the sample were used in the next step for developing a proper model by using response surface designs.

Figure 3. Normal probability plot of effects for the full factorial design.

The next step is to process optimization for which we have to use RSM. In the present project, we are interested to find the levels of the width of the channel (B) and the volume of the sample (C) that maximize the color intensity (y) of the mixed dyes.

The first step in RSM is to define a reasonable approximation for the true functional relationship between the response y and the independent variables (B and C). Designs for fitting response surfaces are called response surface designs. RSM is a sequential procedure. For the points on the response surface that are remote from the optimum, or

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for where there is little curvature in the system a first-order model will be appropriate. Polynomials of higher degree must be used for the systems with the curvature. There are different second order methods of ED among which the three methods of central composite design (CCD)68, Box Behnken design (BBD)69, and uniform shell (Doehlert) design (DD)70 have large applications in fitting the second order models. Central composite design (CCD) presented by Box and Wilson 68 is the most common and efficient design for fitting the second-order models. Generally, a CCD for k factors consists of a 2k factorial with nF runs, 2k axial or star runs denoted by na, and nc center runs. A sequential experimentation is required to deploy a CCD practically. That is, a 2k runs is needed to fit a first-order model, and the axial runs must be added to allow the quadratic terms to be incorporated into the model. The nc center points provide protection against curvature from second-order effects as well as allow an independent estimate of error to be obtained. In CCD designs the distance α of the axial points from the design center and the number of center points nc must be specified. By choosing a proper α, one may make a rotatable central composite design. It means developing a design that provides equal precision of estimation in all direction. The value of α for rotatability depends on the number of points in the factorial portion of the design. In fact, α = (nF)1/4 yields a rotatable CCD where nF is the number of points used in the factorial portion of the design. On the other hand, the value of the axial spacing, α, can be chosen in such a way that the design be orthogonal. In this context, the axial spacing needed to ensure orthogonality may be calculated from

=

( )

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(1)

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Therefore, orthogonality of the design depends on the number of the center runs. In general, a CCD for k factors, coded as (x1,.., xk), consists of 2k + 2k + nc runs. 2k factorial points with the following coordinates xi = -1 or xi = +1, for i = 1,…, k. It contains 2k axial points with all their coordinates null except for one that has been set equal to a specific value α (or –α). Lastly, a total of nc runs have been performed at the center point of the experimental region, where, x1 = x2 =……= xk = 0. Box and Behnken have proposed a class of three-level designs for fitting response surfaces.69 This is called a spherical design, where all the points lie on a sphere of radius (2)1/2. BB design does not have any points at the vertices of the cubic region that have been created by the upper and lower limits for each factor. This could be advantageous when it is not feasible to test the points on the corners due to physical process constrains or they are extraordinarily expensive. BBDs of k factors composed of 2k (k+1) + Cο runs, where Cο represents the number of center points. The uniform shell (Doehlert) designs are generated from a k-dimensional simplex.70 DD for a 2 factor system will be made up by the vertices of a regular hexagon. DDs of k factors consist of k2 + k + Cο experiments, for which Cο denotes the number of experiments performed at the center of the design. The uniform shell designs have interesting properties about displacing and expanding by adding a new factor.70 Here CCD is presented in more detail due to the fact that this design is the most common design for fitting the response surfaces. A rotatable CCD with α = 1.41421 was used for the optimization of the effective parameters on the intensity of the color of the

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mixed food dyes using a paper microfluidic platform. Table 3 represents the design matrix for the rotatable CCD design.

Table 3. Design matrix together with the responses for central composite design (CCD). Run Order

Point type

1 2 3 4 5 6 7 8 9 10 11 12 13

Center Center Axial Axial Center Fact Center Fact Center Axial Axial Fact Fact

Channel width (B) 0 0 1.41421 -1.41421 0 -1 0 -1 0 0 0 1 1

Sample volume (C) 0 0 0 0 0 1 0 -1 0 1.41421 -1.41421 1 -1

Response

212.38 214.25 217.23 201.85 211.70 204.76 213.95 207.62 213.70 211.01 217.93 213.21 219.22

Similar to the screening step, ANOVA was used to choose an appropriate response surface model and explore the significances of the model equation, and the model terms. A quadratic model based on a higher F- and R-value and lower lack of fit (LOF) and prediction error sum of squares (PRESS) to fit the experimental data was selected. Equation 2 shows the generated response surface model in a coded form,

Response (y) = 213.20 + 5.23 B – 2.33 C _ 0.79 BC _ 2.03 B2 + 0.44 C2

(2)

The next step is evaluation of the generated model by calculating several statistical parameters. In order to certify the reliability of a model, the significance of the

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regression model, the weights of individual model coefficients and the significance of the lack-of-fit must be examined using an ANOVA table. To assess the significance of a regression model we have to calculate the mean square values for the treatment and the residuals. This sum of the squares are by definition estimates of the variance of the results. These estimates should be similar if the regression model does not account for a significant portion of the total variance. Considering the null hypothesis, one should calculate the F-value which is the ratio of these variances. If the calculated F-value in the ANOVA table exceeds the critical value found in the probability table, the model is significant. The ANOVA table showed a F-value of 62.97indicating that the model is significant. Also, the very low Fvalue of 0.48 for the lack of fit confirms the validity of the model, because it is not significant compared to the pure experimental error . In addition to these two statistics, the standard deviation and coefficient of variation (C.V.) of 0.97 and of 0.46% , respectively are reasonably low and acceptable. The parameter of R-squared is loosely interpreted as the proportion of the variability in the data explained by the analysis of variance. Clearly, we must have 0 ≤ R2 ≤ 1, with larger values being more desirable. Therefore, in the case of the paper microfluidic system the generated model with R2 = 0.978, explains about 97.8% of the variability in the color intensity. A disadvantage of this parameter is that its value depends upon the number of terms added to the model. This statistic increases as the number of the terms increases, even though they are not significant. To nullify this drawback, the adjusted coefficient of determination, the adjusted R-squared can be used. This parameter can be considered as a measure of the amount of variation around the

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mean explained by the model adjusted for the number of terms in the model. The addition of nonsignificant terms to the model can usually decrease this statistic.71 The predicted Rsquare is a measure of the predictive ability of the model. The predicted R-square of 0.934 for the model reveals that the generated model is able to predict about 93.4% of variability in new data. The adjusted R-squared and the predicted R-squared should be within 0.20 of each other, otherwise there may be a problem with either the model/ or data. The “Adequate Precision” statistic is a parameter which represents the signal-tonoise (S/N) ratio. This term is computed by dividing the difference between the maximum and the minimum predicted response by the average standard deviation of all predicted responses. The adequate models should have a ratio greater than 4.0. For the generated model, this value is 27.61 indicating a very good S/N ratio. For further evaluation of the model, Leverage and Cook’s distance72 should be considered. Leverage must be calculated to assess how each point influences the model fit. The value of one for the leverage of a point means that the model has gone through that point. A high leverage is not good because if an unexpected error accompanies a point that error strongly influences the model. The Cook’s distance can be used to explore the existence of the outliers or unexpected errors in the model .72 Cook’s distance is a measure of how the regression changes if a point is deleted. A case with high leverage incorporates a relatively large value for the Cook’s distance and may be outlier and must be investigated. Inspection of the Cook’s results shows that no outlier or unexpected errors exist in the proposed model. One of the advantages of the response surface models relies on their threedimensional plots to visualize the relationship between the responses and the

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experimental level of each factor.73 These plots should tell you the approximate shape of the response surface and whether or not an optimization of the factors is possible. Depending on the values of the coefficients in the second-order equation, the response surface could be a parabola opening upward (stationary point is a minimum), a parabola opening downward (stationary point is a maximum), or a saddle (stationary point is neither a minimum nor a maximum). Canonical analysis can be used to obtain the coordinates of the stationary point on the response surface. In the case of flatter response surfaces, there is considerable flexibility in locating an acceptable set of operating conditions. In other words, there is essentially an entire plane rather than merely a point when the response is approximately at its optimum value. The model response (in our case color intensity) is mapped against two experimental factors (channel width and sample volume) while the other factors are held constant at their central levels. Figures 4 and 5 are the response surface and contour plot, respectively, showing the effect of channel width (B) and sample volume (C) on the color intensity (response) at the fixed value of channel length in its center value. These figures clearly show a positive effect for the channel width and a negative effect for the sample volume. It can be seen that when channel width was increased, the color intensity increased. In contrast, larger color intensities were obtained at lower sample volumes.

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Figure 4. Three-dimensional response surface for channel width (B)-sample volume (C).

Figure 5. Contour plot for channel width (B)-sample volume (C).

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The main aim and the final step of the optimization is to determine the optimum values of influential factors on the responses using the generated model. The maximum value of 225 was obtained for the color intensity by using the optimum values of 2.30 mm and 0.75 µL for the channel width and sample volume, respectively. The value of 229 was obtained experimentally using the optimum values for the width and the volume factors while the channel length was kept constant. The closeness of the predicted and experimental values demonstrate the strength of chemometrics in developing microfluidic platforms.

Combination of artificial neural network with experimental design (ANN-ED) To the best of our knowledge, research combining the application of experimental design and artificial neural networks (ANNs) in the optimization of the parameters affecting a microfluidic-based system is scarce. In general, compared with classical statistical optimization techniques, such as RSM, the use of the ANN approach appears to be well-suited to solving problems where the relationship between variables are neither linear nor complex.74 As opposed to ANN, classical RSM requires the specification of a polynomial function to fit the relationship and, thus, is incapable in approximating complicated non-linear relationships. In addition, ANNs are robust and can yield generalizations from precedent even from incomplete or noisy data. Also, ANNs can yield universal approximation functions flexible in modeling linear and non-linear relationships. Optimization can result via a search for the optimal value of an objective function (OF) that depends on several factors. The OF is the response which varies for different

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processes. Usually the development of microfluidic-based systems is interdisciplinary and so too will the OF vary and be, for example, the yield of a reaction, the efficiency of a fuel cell, reproducibility, fluorescence and so on. The OF can principally be predicted using a hard or soft model. The hard model requires the exact physicochemical description of the process taking place and also the determination of the physicochemical constants. In the case of microfluidic-based systems, this approach is exhausting as many physicochemical constants must be determined. In contrast, for the soft models there is no need to know the processes involved in the techniques and the number of experiments can be significantly reduced especially if a multivariate approach is used. In any experiment, the value of OF (response) is dependent on the processes in the system. Therefore, a soft model can be used to estimate or predict the response for possible values of the input variables. Polynomial fitting, partial least squares, and multiple linear regression (MLR) are examples of common soft methods. However, among the soft models, ANNs have gained popularity in modeling and optimization. This may be attributed to their distinguished features and advantages including: (1) ANNs are robust and have the ability of generalizations even if the data are noisy or incomplete; (2) ANNs are able to model the linear and non-linear phenomena by providing flexible functions, and; (3) ANNs can learn from examples and capture subtle functional relationships among case data. This means that prior assumptions about the underlying relationships in a particular problem need not be made. The ability of ANNs to model nonlinear systems with no prior knowledge of the system concerned makes them attractive for different research areas. These methods have been applied to classify 1H NMR spectra75, to correct mass spectral drift76, for classification and source determination of petroleum distillates77,

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and for prediction of chromatographic retention time in high-resolution anti-doping screening data78, just to name a few. Artificial neural networks (ANNs) are based on the cerebral networks of the human brain, and have the capacity of learning by example. The basic processing units of an ANN are simulated neurons, which are interconnected in a group that are able to process the information. An ANN is a computing paradigm formed from hundreds of artificial neurons or nodes (processing elements). The neurons are connected with different weights (coefficients) and work together to produce an output function. Each artificial neuron (processing element) consists of weighted inputs, transfer function, and one output and in fact is an equation which balances inputs and outputs. When a network is structured based on its application, it should be trained. The networks can be trained by using the supervised or unsupervised learning approaches. In supervised learning both inputs and outputs should be known. This type of learning is useful to predict one or more target values from one or more input variables. ANNs with unsupervised algorithms are known as Self Organizing Maps and for these there is no need to know the inputs and outputs. In a supervised approach the training data will be taken as numerical inputs and would be transferred to a desired output. The network approach consists of three stages: (1) Choosing the variables that are to be used as inputs from the selected data. Also dividing the dataset into training, monitoring and prediction sets. (2) Designing the network topology and implementing the algorithms. (3) Assessment of the predictive ability of the generated ANN model and validation of its results. The choice of the experimental data to train the network is crucial. On the other hand, from the economical and practical point of view the number of experiments should be as low as possible 27



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without losing much information. This can be achieved by combining the ED techniques and ANNs. The process of this combination is illustrated in Figure 6.

Figure 6. Combination of ED and ANN for optimization purposes.

The structure of an ANN plays a significant role on its efficiency and operation. The neurons of a network are divided into several groups called layers. Generally, the ANNs can have single- and multiple-layer architectures. There are two ways that the neurons can be connected to each other, feed-forward and feedback architectures. There are many types of ANNs all described by the transfer functions of their neurons, by the learning rule and by the connection formula. The most popular one is a supervised

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network with back-propagation learning rule. The back-propagation (BP) networks are multilayer perceptons (one input layer, one or more hidden layers and one output layer). The number of nodes in input layer depends on the number of possible parameters we have in our data file, while the number of responses determines the number of the neurons in the output layer. The number of neurons in the hidden layer cannot be defined in advance and must be optimized. A BP network learns by example that means we have to provide a learning set with some input examples and a known output for each case. Therefore, the BP algorithm works in a supervised mode of learning. The BP learning process works in an iterative steps. The initial value of the inputs is applied to the network and the network produces the output by using the current weights (coefficients). Then the calculated output is compared to the known value of the output and a mean-squared error signal is calculated. The error value is propagated backwards through the network and a small changes are made to the weights to reduce the errors. This process is repeated until the overall error value drops below a pre-defined threshold. The network will never be trained completely, but the goal is changing the weights between the layers until the error, E is minimized:

= ∑ ∑( − )

(3)

The error E of a network can be defined as the squared differences between the target value t and the output y of the output neurons summed over p training patterns and k output nodes. For each microfluidic system, the network can be trained and verified using the proper training and validation sets. The points lying on the borders of the experimental design can be included in the training set. Validation points can be chosen randomly on the working space. The training would be stopped when the minimum RMSE for verification step is reached.

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When the ANN is trained the weights are saved. These weights can be used to predict the response for a new set of data. When the trained network is validated, it can be used to predict the responses on the entire working space using a grid with a given dimension. It should be noted that the network’s parameter should be re-initialized several times, randomly changing their initial values to prove the robustness of the model and the reproducibility of the results. At this stage it would be useful to find out which parameters have considerable impact on the value of the output. The relevance of each of the ANN inputs can be computed via sensitivity analysis.79 To perform this analysis one should run the network in feed-forward mode, varying each input by a small amount and determining how much the output changes. The greater the changes, the higher the impact of the parameter on the output. The trained network is able to predict the response variables for the training dataset. However, the goal is to develop a model that is robust and generalized and has the potential of producing accurate values for the responses taken from other datasets. Therefore, those ANN models that memorizes the weight links of the training set and have the ability to reproduce only the response variables of the training sets are poor models. The ANN model which has poor generalization and good memorization is said to have been overfitted. The overfitting should be prevented. This can be done by keeping the ratio of the number of data points to the number of connections higher than some threshold. To prevent overfitting, one may stop the training (early stopping) when the lowest generalization error is reached. This means that for monitoring the overfitting an additional validation data set that was not used in the training process is required. Recently we implemented a genetically tuned neural platform to optimize the fluorescence upon binding a fluorescent ligand (5-carboxyfluorescein-D-Ala-D-Ala-DAla (5-FAM-(D-Ala)3) to teicoplanin that has been electrostatically attached onto a 30


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microfluidic surface.43 Three parameters were examined: (i) time the ligand was in the microfluidic channel; (ii) time the antibiotic was in the microfluidic channel, and; (iii) time the buffer flowed through the microfluidic channel. Box-Behnken experimental design was used to feed the neural network. Genetic algorithms (GA)80 was used to search for the optimal neural network structure to be used for optimizing the fluorescence. A genetic algorithm is a highly parallel, randomly searching algorithm that emulates evolution according to the Darwinian survival of the fittest principle. Figure 7 shows the hybrid neural network platform employing a Levenberg-Marquardt (LM) algorithm 43 combined with GA to optimize the experimental conditions. The ANN-GA approach used in this work consisted of training the ANN model and using GA as a searching tool to find the solution space of the trained network.

Figure 7. Schematic of the genetically tuned neural network platform (Taken from reference 43)

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The method proposed in this work has the advantage of combining an ANN with a flexible learning characteristics and the global solution exploratory nature of GA. The results of this study has shown that all three parameters have a significant impact on the extent of fluorescence and, hence, binding of the ligand to teicoplanin in the microchannel.43 The largest fluorescence was observed when the receptor and the ligand incubation times are maximum and the washing time is low. This work demonstrated the robustness of ANN-GA in modeling and optimizing the fluorescence resulted upon binding a fluorescent ligand to a receptor. Scampicchio et al. was the first to show the coupling of capillary electrophoresis (CE) microchips with multivariate techniques to classify wines.42 They used principal component analysis (PCA) to choose the most influential variables for discrimination models. The statistical method of PCA reduces the dimension of data by converting a set of observations of possibly correlated variables into a set of linearly uncorrelated variables called principal components. The principal components are the directions where the data is most spread out. Samples are plotted using new axes and the resulting graphic is called Score Plot. Loadings are the coefficients by which the original variables must be multiplied to obtain the PC. In the latter case the resulting graphic is called Loading Plot. These plots show the relationship between the variables and how much they influence the system. These plots can be used to separate the samples (in this work wines) into different groups. In this effort, three Cabernet-Sauvignon wines from different regions (Italy, Australia, and New Mexico) were classified using CE on the chip and chemometrics in less than 60 seconds without any pretreatment of the samples.42 The

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main aim of this work was revealing a simple method to obtain data from the electropherogram and using multivariate data analysis to provide the most information possible. It is apparent that numerous important applications can benefit from the coupling of microfluidics with chemometric techniques. Recently Tohid and Pacheco-Vega used parametric analysis, by means of numerical simulation, to study the effect of geometrical parameters and operating conditions on the performance of a microfluidic direct methanol fuel cell (DMFC).44 To optimize the power density, they first kept the operating conditions constant while varying the width of the flow channel (a geometrical parameter). The results of parametric analysis in obtaining the optimal FC geometry and its range of operating conditions have been promising. However, in contrast to ANN-ED approach, a noticeable shortcoming of this technique is the inability to ascertain the potential interactions between the geometrical and operating parameters.

Conclusions and future outlook Chemometrics and its methods are versatile and can be applied to a variety of scientific disciplines extensively utilizing a number of statistical and mathematical methods, namely multivariate ones. There are various algorithms to process and evaluate the data and that can be implemented to various fields, namely, medicine, pharmacy, food control, and environmental monitoring. To date, though, chemometrics has yet been embraced by the scientific community to the extent the pioneers in the field had envisaged. Marginal support from governments to establish an academic base could be a reason for the decline in chemometrics in some areas of the world. Still, we believe that

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chemometrics will continue to evolve towards increased usage and its adoption into microfluidics at all levels will bring about enabling technologies unforeseen today. Some chemometric methods such as, multivariate curve resolution (MCR), Hadamard, self-organized systems, newer multi-way analysis, etc. have been proven to be very potent tools to handle responses of varying complexity, from single spectra to data matrices coming from various analytical instruments. Although, these techniques show great promise in different analytical disciplines, but to date, though, that promise has yet been born out in the microfluidic area. These chemometric methods are flexible, and therefore can be generalize across all analytical disciplines. Clearly, combining microfluidics with these techniques will increase the analytical potential of the microfluidic platforms. Improved sensitivity and selectivity, the possibility of thorough analysis in the presence of uncalibrated interferents, analysis of megavariate data structures for classification purposes, are some of the advantages which can be achieved. Applying these methods cause saving time, money and manpower and at the same time bring more accurate and more precise analytical results. However, the mathematical nature of chemometric methods is their most important drawback, and the development of user-friendly softwares for non-expert users in public domain is a critical limitation of chemometric methods. Generally, chemometrics shows great promise in all analytical disciplines. We believe that microfluidics will have a much brighter future if scientists integrate chemometric methodologies into the field.

Acknowledgements

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The authors gratefully acknowledge financial support for this research by grants from the National Science Foundation (HRD-0934146, EEC-0812348, and OISE0965911).

Financial & competing interests disclosure The authors have no relevant affiliations or financial involvement, either previous or current, with an organization or entity with a financial interest in or financial conflict with the subject mater or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties. No writing assistance was utilized in the production of this manuscript.

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Biography Frank A. Gomez obtained his Ph.D. in 1991 from the University of California, Los Angeles and was a Damon Runyon Walter Winchell Cancer Research Fund Postdoctoral Fellow at Harvard University prior to joining the faculty at California State University, Los Angeles in 1994 where he is currently a Professor in the Department of Chemistry and Biochemistry as well as Research Development Liaison for the university. His research group is engaged in developing fundamental and applied research in the area of microfluidics focusing on developing new microfluidic devices for use in point-of-care (POC) diagnostics and chemical and biochemical separations. Current work involves the development of paper microfluidic and bead-based assays, enzyme microreactors, surface plasmon resonance (SPR) on chips, microfluidic fuel cells (methanol, formic acid, and hydrogen), and novel materials for microfluidics. His group also employs response surface methodology (RSM) and artificial neural networks (ANN) to experimentally optimize conditions in microfluidics. He has trained many B.S. and M.S. students and published numerous papers on microfluidics with students as co-authors. Biography Mehdi Jalali-Heravi received his Ph.D. in 1978 from Surrey University (U.K.) and is an Emeritus Professor of Chemistry at Sharif University of Technology (Iran). He is a Visiting Research Associate at California State University, Los Angeles and is involved in optimizing different microfluidic platforms using response surface methodology (RMS) and artificial neural networks (ANN). He pioneered the development of chemometrics in Iran. He has published numerous peer-reviewed papers in chemometrics and has trained a number of MS and PhD students in this area. He has extended QSPR studies to the biological systems and his researches have had a profound impact in thorough analysis of complex mixtures. His main research interests are in chemometrics, especially in multivariate data analysis methods and optimization. His research covers many parts of the spectrum of neural network uses in analytical chemistry. Biography Mary Arrastia is an undergraduate student in the Department of Chemistry and Biochemistry at California State University, Los Angeles majoring in chemistry. Her research focus is on paper microfluidics and its application in the biomedical sciences and point-of-care diagnostics.

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