Evaluation of Two Statistical Tools ( Least Squares Regression and Artificial Neural Network ) in the Multivariate Optimization of Solid-Phase Extraction for Cadmium Determination in Leachate Samples

Este trabalho propõe a otimização multivariada de um procedimento para determinação de cádmio em amostras de chorume usando-se espectrometria de absorção atômica com chama após a extração em fase sólida usando-se uma minicoluna empacotada com Amberlite XAD-4 modificada com ácido 3,4-diidróxibenzoico. As variáveis relacionadas à pré-concentração (pH, razão de amostragem e concentração do tampão) foram otimizadas usando-se planejamento Doehlert. Duas ferramentas para modelagem estatística (regressão por mínimos quadrados e redes neurais artificiais) foram aplicadas aos dados e seus desempenhos foram comparados. Procedimentos de digestão do chorume por aquecimento em meio ácido e por radiação ultravioleta foram avaliados sendo este último mais adequado para evitar a perda de Cd por volatilização. O procedimento desenvolvido apresentou um fator de enriquecimento de 9 vezes com limites de detecção e de quantificação (3sb) de 0,72 e 2,4 μg L, respectivamente, e precisão expressa como porcentagem do desvio padrão relativo de 4,0 e 6,4% (RSD%, n = 4 para 5,0 e 20,0 μg L, respectivamente). Testes de adição/recuperação de Cd foram realizados obtendo-se valores entre 97 e 112%. O procedimento foi aplicado na determinação de cádmio em amostras de chorume coletadas no aterro sanitário do município de Jaguaquara-BA, Brasil.


Introduction
The production of a dark liquid called leachate is common in sanitary landfills.This residue results from the decomposition of waste mass plus the rainwater percolating into the landfill, and the trash moisture. 1The contamination of soil, air or water by composites such as the leachate is extremely harmful to the environment.Leachate can contain high concentrations of chemical compounds and potentially toxic metals that can modify the ideal conditions of the ecosystem. 2admium concentrations can increase in the environment through the release of waste and/or contaminated effluents.Amongst the wastes with a contaminant potential those Vol.26, No. 1, 2015   resulting from the production of alloys, the manufacture of products containing Cd, batteries and leachate from sanitary landfills can be mentioned.Cadmium is very toxic to humans and other animals.Products containing Cd (inks, enamels and alloys) are possible sources of contamination to foods and beverages and can cause acute toxicity.Among the adverse health effects caused by exposure to this metal or its derivatives, the following are noteworthy: chronic lung diseases, emphysema, kidney disorders, anemia, liver and bone diseases, and others. 3mongst the types of metals present in the complex matrix of leachate, Cd can hardly be quantified by flame atomization atomic absorption spectrometry (FAAS), since the quantification limit of the analytical technique is not sufficiently low.Furthermore, the difficulties increase with losses provoked by the volatility of this analyte when the sample is digested by heating in open systems, the low metal concentrations in the examined matrices, and the occurrence of matrix effects.5][6] This procedure allows quantifying Cd by FAAS, since the interfering substances are eliminated and the analyte is isolated from the matrix components at a higher concentration. 5olid phase extraction (SPE) is one of the preconcentration methods commonly applied in environmental analyses.SPE methods are based on analyte sorption onto the solid surface of a determined material (commonly silica, XAD resins, polyurethane foam, etc., impregnated or modified with a complexing agent) followed by elution with adequate solvents. 7Solid phase extraction in minicolumns is a procedure that involves variables that must be optimized for each type of analyte and type of solid phase used such as pH, sample flow rate and buffer volume.Nowadays, multivariate optimization is used in this optimization, since it does not either require a great deal of experiments and reagents or consumes much time; in addition, it allows the evaluation of interactions between the different variables. 8,9s for the work involving SPE, the use of multivariate experimental design methodologies for response surface generation, such as the Doehlert design, is possible in the search for the optimum extraction conditions.The use of this methodology allows simultaneous improvements of the responses that are influenced by factor-level combinations.In the case of SPE, the major contributing factors in the extraction are pH, which is a key parameter in the retention of the analyte, 10 sampling flow rate and buffer concentration.Fitting the mathematical functions to the results obtained by combining different levels of variables allows predicting the result as well as the influences of each factor in a given experiment.This type of methodology has advantages such as savings in time, materials and costs. 11In conjunction with the statistical techniques, the Doehlert matrix can be applied to generate response surfaces and study the behavior of the variables.This methodology allows finding the optimum conditions of an experiment.Essentially, the most efficient way is to look at a combination of factors which result in the best response of a process or in the best features of a product. 12athematical functions that generate response surfaces can be fitted to experimental data using the classical least square methodology or alternative methodologies, such as artificial neural networks (ANN).ANN provide an attractive possibility for providing non-linear modeling for response surfaces.In classical response surface methodology (RSM), the number of terms in the polynomial equation is limited to the number of experimental design points.On the other hand, ANN methodology allows the modeling of complex relationships without this limitation.Its analysis is quite flexible in regard to the number and form of the experimental data having better predictive power than regression models.Regression analyses are dependent on predetermined statistical significance levels, and less significant terms are usually not included in the model.With the ANN method, all data are used making the models more accurate. 12,15ccordingly, the objective of this study was to determine the Cd concentrations at trace level in landfill leachate samples through the development of an effective methodology that makes use of solid phase extraction and flame atomic absorption spectrometry.The response surfaces methodology, associated with least squares regression and artificial neural networks, was applied in the mathematical optimization and search of optimum values for the most significant variables in the preconcentration process.

Instrumentation
Metal concentrations were measured using a Perkin Elmer AAnalyst 200 model flame atomic absorption spectrometer (Norwalk, USA) equipped with deuterium arc lamp for background correction.The hollow cathode lamp was used as a source of radiation at a wavelength of 228.8 nm for the spectral bandwidth of Cd.The flame composition for determining the studied metals was acetylene (flow rate: 2.0 mL min -1 ) and air (flow rate: 13.5 mL min -1 ).The nebulizer flow rate was 5.0 mL min -1 .
A peristaltic pump (MILAN) was used to control the flow rate of samples during solid-phase extraction.A portable pHmeter ML 1010 (MISURA LINE) was used to measure the pH.A TE007MP block digester (Tecnal) with temperature control and a laboratory-made ultraviolet digester craft equipped with 20 W mercury low-pressure lamps (Mercury) were respectively used in the acid and ultraviolet digestion of leachate samples.An ultrasonic bath with controlled heating (Visque Model 1450A) was used to facilitate outgassing of the samples after digestion by ultraviolet radiation.

Reagents and solutions
The reagents used were of analytical grade.Water was deionized with Elga purifier (model Purelab Classic).Working solutions of Cd were diluted from stock solutions of 1000 mg mL -1 (Merck).The pH of solutions was adjusted with acetate (pH 3.8 to 5.8), phosphate (pH 6.2 to 7.5), borate (pH 7.5 to 9.0) and ammoniacal (pH 10.0) buffer solutions.The solutions of nitric acid and hydrochloric acid were prepared from solutions of concentrated acid (Merck, Darmstadt, Germany).
The working glassware was washed with deionized water after decontamination with nitric acid solution (10%) for 24 hours.

Sample collection
Leachate samples were collected from the sanitary landfill of Jaguaquara (lat.13°31'51" S and long.39°58'15" W) in the southwest region of Bahia, northeastern Brazil.Samples were collected from November 2011 to May 2012.The leachate was collected directly into the primary reservoir where it is stored after passing through the collector arrays.The samples were stored in polyethylene flasks and were immediately taken to the laboratory for pH determination and placing in a refrigerator.All collection vials were subjected to triple washing with deionized water, kept in a nitric acid solution (5% v/v) for 24 hours and then rinsed again with deionized water.

Optimization procedure
The Doehlert design matrix was applied in the optimization procedure for Cd preconcentration in leachate samples.The procedure consisted in the solid phase extraction (SPE) of the metal in a minicolumn packed with 0.1 g of a polymeric resin (Amberlite XAD-4) modified with 3,4-dihydroxybenzoic acid (DHB), elution and subsequent determination by FAAS.The variables optimized in the design were: pH, buffer concentration and flow rate sampling and their level combinations are presented in Table 1.All of the studied factors were explored on at least three levels.At the central point, three replicates were carried out for calculating the experimental error.The generated data were analyzed using Statistica 7 software, and the experiments were performed in duplicate.
Cadmium solutions were prepared in 20 mL volumetric flasks to which a specific pH buffer was added along with the pre-established metal concentration of 30 µg L -1 .After that, the analytes were eluted from the SPE column using 1 mL of 1.0 mol L -1 HCl and transferred to vials for analysis by FAAS.

Synthesis of XAD-4/DHB resin
This modified resin has been used before by our research group. 13Amberlite XAD-4 beads (5 g) were treated with 10 mL of concentrated HNO 3 and 25 mL of concentrated H 2 SO 4 and the mixture stirred at 60 o C for 1 h in a water bath.Afterwards, the reaction mixture was poured into an ice-water mixture.The nitrated resin was filtered, washed repeatedly with water until free from acid and thereafter treated with a reducing mixture of 40 g of SnCl 2 , 45 mL of concentrated HCl and 50 mL of ethanol.The mixture was refluxed for 12 h at 90 o C. The solid precipitate was filtered and washed with water and 2 mol L -1 NaOH.The amino resin was first washed with 2 mol L -1 HCl and finally with distilled water to remove the excess of HCl.It was suspended in an ice-water mixture (150 mL) of 1 mol L -1 HCl and 1 mol L -1 NaNO 2 .The diazotized resin was filtered, washed with ice-cold water and reacted with DHB

Mathematical modeling
Mathematical modeling was carried out using two modeling tools: least squares regression and artificial neural network.The surfaces were obtained by fitting polynomial functions to the absorbances obtained for each combination of levels regarding the variables set by a Doehlert design.The performances of two modeling methods were compared using the coefficient of determination (R 2 ).

UV digestion of leachate
Leachate samples were digested with UV radiation. 14 sample of 6.5 mL leachate was placed in a Petri dish in which another 0.5 mL of hydrogen peroxide (VETEC) plus another 3.0 mL of an ammoniacal buffer solution (pH 10) were added.The solutions were subjected to UV photodigestion for 40 minutes using a laboratory-made digester and were then transferred to 20 mL volumetric flasks.After that, the solutions were subjected to an ultrasonic bath for removal of residual bubbles.Finally, 4 mL of the ammoniacal buffer solution (pH 10) were added to each sample and the liquid was diluted with deionized water up to 20 mL so as to perform the preconcentration procedure.

Acid digestion of leachate on a heating plate
The acid digestion was carried out with 5 mL of leachate.It was placed in a digestion tube and 2 mL of concentrated HNO 3 (65%) were added.Next, the solutions were heated in the temperature range of 100-120 °C up to nearly dryness and complete digestion.The digested samples were cooled to room temperature.The sample solution was neutralized with 5% NaOH and 4 mL of ammoniacal buffer solution was added.The solutions were transferred to volumetric flasks and had their volumes completed with deionized water up to 20 mL before preconcentration.This process was carried out in duplicate for each sample.

Preconcentration system
Both digested samples (UV and acid procedures) were followed by solid phase extraction.Using a peristaltic pump, the samples were individually subjected to a minicolumn packed with an Amberlite XAD-4 polymer resin functionalized with 3,4-dihydroxybenzoic acid (DHB) at a flow rate of 10.92 mL min -1 .In addition, 1.0 mL of 1 mol L -1 HCl was used to elute the analyte of interest and the final solutions were stored in vials for analysis by FAAS.

Optimization of experimental conditions for solid phase extraction
Amongst the multivariate optimization procedures, response surface methodology (RSM) has been widely applied in analytical chemistry, since it allows the simultaneous optimization of variables in a very efficient manner.Among the experimental design used in RSM, the use of Doehlert matrix in the optimization of analytical methods has been increasing over the last years due to its efficiency and ease of application to a number of analytical systems. 10Accordingly, Doehlert was used in the multivariate optimization of the factors that most affect the solid phase extraction in order to simultaneously define the desired optimum values in this work: an efficient enrichment of the analyte during the sample preconcentration allowing instrumental analysis with better performance.The analytical signal of FAAS (absorbance) is the response of interest in this modeling and the results from Doehlert design application are shown in Table 2.

Modeling of response surfaces using least squares regression
Least squares regression is a multiple regression technique used to fit the mathematical models to a set of experimental data with the purpose of generating the least possible residue.The residue is the difference between the experimentally observed value and that calculated on the basis of the fitted mathematical function.Small residues denote a good predictive ability of the mathematical model.A quadratic function, using least squares regression, was fitted (equation 1) to depict the behavior of data from Table 2. w = 0.23 -0.035x + 0.0036x 2 -0.0018y + 0.0001y 2 -15.4z + 328z 2 -0.0004xy + 0.33xz + 0.052yz (1)   where w is the response (absorbance), x denotes the pH of the preconcentrate solution, whilst y is the sample flow rate and z refers to the buffer concentration.The Pareto chart exhibited in Figure 1 reveals that, with regard to the quadratic equation, the quadratic term of flow rate (y 2 ) and the interaction term between flow rate and buffer (yz) are not significant and can be removed without compromising the prediction.Therefore, pH is the most significant variable in the extraction process.Its positive value indicates that Cd extraction can be increased with pH elevation.
The quality of the fitted model can be also evaluated by the graph of predicted values vs. the experimentally observed values (Figure 2) and by the coefficient of determination (R 2 ).The R 2 value observed for the linear model was 0.7332, while that for the quadratic model was 0.9174.Despite the analysis of variance (ANOVA) indicating that there is lack of fit (p < 0.05 for a confidence level of 95%), the R 2 from both the linear and the quadratic models reveals that the quadratic model is a better predictor.Residuals from the quadratic model do not follow random tendency, however it presents the lowest residuals than a linear model.Therefore, it was applied to obtain the optimum conditions to extract the analyte.
The critical point for the quadratic model is characterized as a minimum point.Given that the goal is to maximize the extraction of Cd in the solid phase, the coordinates of this point will not provide the desired optimum values.Hence, the surfaces generated from the quadratic model should be visually inspected in the search for values that generate the greatest possible response within the experimental field set out by the Doehlert matrix.The surfaces generated from equation 1 are exhibited in Figure 3.
Basic pH favors the extraction process.The influence of this factor on the SPE for the preconcentration of metals based upon complexation is remarkable given how the retention of metals depends upon active sites that arise from the deprotonation of functional groups.Therefore, in order to retain analytes of acidic character, the pH should be increased.It can be noted, then, that the variation in the pH range controls the formation of Cd-DHB complex.Although the effect is not as pronounced as in the case of variable pH, buffer concentration was the second most important factor in the studied preconcentration procedure.This can be justified in view of its role in maintaining the optimum pH when reconditioning the column after elution with HCl.The relatively low response variation for this variable probably has happened due to the short experimental field chosen in relation to the variation of buffer concentration.The sampling flow rate in many SPE processes in minicolumn plays a major role in the retention of the analyte.A high sampling flow rate can reduce the time of contact of the analyte with the solid phase and thereby diminish its retention.Yet, as the flow rate observed in these experiments was seen to be less significant as compared to other variables, a higher flow rate was used so as to reduce the extraction time and enable faster analyses.
In analyzing surfaces, it was found that the largest extractions of the analyte occur at a basic pH level (10); sampling flow rate of 10.92 mL min -1 and higher buffer concentration values (0.03 mol L -1 ).These values were chosen as optimum in the implementation of the extraction process.

Modeling of response surfaces by artificial neural networks
Artificial neural networks (ANN) are computational operating systems inspired by the brain operations and consist of groups of highly interconnected processing elements known as neurons.ANN offer alternatives to the classical polynomial regression tools (such as least squares regression) in the mathematical modeling of response surfaces. 15he data obtained by the application of Doehlert design were modeled by neural networks for obtaining the response surfaces that better describe the behavior of data.The parameters adopted for the supervised learning of the tested networks are presented in Table 3.
Backpropagation has been used as a learning mechanism for networks.So the outputs, which are predicted values, have been compared vs. the observed values (obtained experimentally) to produce the smallest possible errors.The following learning algorithms were tested under the same conditions for selecting the most appropriate algorithm to the available data: linear, radial basis function networks (RBF) and multilayer perceptrons (MLP).For the training phase were used all experimental points of Doehlert design.
The network algorithm No. 5 (Table 4) was the one that exhibited the lowest training error (0.0376) and, because of that, this algorithm was chosen for the construction of response surfaces relative to the optimization of Cd solid phase extraction.As illustrated in Figure 4, this architecture is a quite simple network with an efficient predictive ability.The error obtained in testing this network was also small (0.0596).Another parameter that proves the superiority of this algorithm is the value of R 2 .The graph of observed values vs. predicted values for the algorithm No. 5 is shown in Figure 5.Note that algorithm No. 5 has the highest R 2 (0.9869).
Algorithm No. 5 is a multilayer perceptron (MLP) whose neural network architecture is characterized by having three neurons in the input layer, a single middle layer with six neurons, and an output layer with one neuron.The network algorithm MLP 3:3-6-1:1 was adopted in the construction of response surfaces (Figure 6).The surface shapes are very similar to those obtained by least squares regression.Nevertheless, its fit to experimental data is higher.Therefore, in this work, the optimized values obtained by visual inspection are virtually identical to those obtained by least squares regression.
In general, ANN is able to better describe the experimental domain studied but in the case study discussed in this manuscript, the two modeling techniques showed the same efficiency of optimization.

Analytical characteristics of the optimized preconcentration method
Under the optimum extraction conditions, the analytical characteristics of the system were obtained for Cd preconcentration via solid phase extraction and determination by FAAS.The calibration curve obtained by the preconcentration of standard solutions was   is capable of attenuating the migration of various metals into the leachate. 28Christensen et al. 29 argue that the main processes of Cd attenuation in leachate are: dilution, complexation, sorption and precipitation.Furthermore, Cd sources such as rechargeable batteries and ferrous alloys are withdrawn by collectors, who have a shed on site.This contributes to a considerable reduction of the element in the landfill cells.The pH from the acidic or basic medium is crucial in defining the age of the leachate and consequently the age of the landfill.The phases wherein leachate can be classified according to pH variation are methanogenic and acid. 30A leachate sample collected in the acid phase in a landfill in operation for a few years and subjected to unstable anaerobic fermentation shows high acidic pH, chemical oxygen demands (COD) and total organic carbon (TOC) levels.In the methanogenic phase, chemical oxygen demands and total organic carbons decrease as pH increases. 31s illustrated in Table 6, the pH determined in the leachate samples from the sanitary landfill of Jaguaquara is alkaline.Alkaline pH favors the precipitation and removal of Cd from the leachate, making it stationary on the soil.One can therefore assert that the analyzed leachate derives from the waste mass that is under methanogenic decomposition.When considering that the landfill has been operating for more than 10 years, the pH values corroborate the findings of previous works and indicate low concentrations of potentially toxic metals. 32n a study conducted at the municipal landfill of Ribeirão Preto city, São Paulo State (Brazil), the Cd contents of leachate samples collected in 2000 and 2004 have been dosed, respectively, at concentrations of 10 and 12 µg L -1 . 19In the quantification of levels of

Figure 1 .
Figure 1.Pareto chart relative to the terms of the quadratic function fitted to the data obtained from the application of Doehlert design in the optimization of solid phase extraction for Cd.

Figure 2 .
Figure 2. Graphical display of observed values vs. predicted values for the quadratic function on the absorbance data generated from the system of Cd preconcentration.

Figure 3 .
Figure 3. Two response surfaces generated by fitting the quadratic model to the data obtained from Cd absorbance.

Table 4 .
Characteristics of neural networks retained in the training phase during the analysis of data from Doehlert design for optimizing Cd extraction of neurons in the input layer; B: number of neurons in the first intermediate layer; C: number of neurons in the second middle layer; D: number of neurons in the output layer; GRNN: general regression neural network; RBF: radial basis function network; MLP: multilayer perceptron.

Figure 4 .Figure 5 .
Figure 4. Architecture of the neural network algorithm No. 5 with three neurons in the input layer, six in the intermediate layer and one in the output layer.

Table 1 .
Experimental matrix of Doehlert design for optimizing the SPE method NaOH solution) at 0-3 o C for 24 h.The resulting brown-colored resin was filtered, washed with water and dried in air.The mass of the resin used to fill the column and the type and concentration of the eluent (1.0 mol L -1 HCl) was established in accordance with previous studies.

Table 2 .
Responses (absorbance) from the application of Doehlert design in the preconcentration of Cd

Table 3 .
Parameters adopted in the supervised learning of neural networks

Table 5 .
Comparisons of the analytical performance of the present off line system with those reported in the literature with FAAS detection techniques EF: enrichment factor; DHB: 3.4-dihydroxybenzoic acid; TAR: thiazolylazo-resorcinol; DAAB-VP: diazoaminobenzene-vinylpyridine.

Table 6 .
Amount of Cd and pH in the leachate samples collected from the Jaguaquara Sanitary Landfill-BA a CONAMA resolution 430/2011.