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Multivariate optimization techniques in food analysis – A review
Accepted Manuscript Multivariate optimization techniques in food analysis - A review Sergio L.C. Ferreira, Mario M. Silva Junior, Caio S.A. Felix, Daniel L.F. da Silva, Adilson S. Santos, João H. Santos Neto, Cheilane T. de Souza, Raineldes A. Cruz Junior, Anderson S. Souza PII: DOI: Reference:
S0308-8146(17)31933-7 https://doi.org/10.1016/j.foodchem.2017.11.114 FOCH 22091
To appear in:
Food Chemistry
Received Date: Revised Date: Accepted Date:
1 September 2017 27 October 2017 30 November 2017
Please cite this article as: Ferreira, S.L.C., Silva Junior, M.M., Felix, C.S.A., da Silva, D.L.F., Santos, A.S., Santos Neto, J.H., de Souza, C.T., Cruz Junior, R.A., Souza, A.S., Multivariate optimization techniques in food analysis A review, Food Chemistry (2017), doi: https://doi.org/10.1016/j.foodchem.2017.11.114
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Multivariate optimization techniques in food analysis - A review
Sergio L.C. Ferreira1,2*, Mario M. Silva Junior1,2, Caio S.A. Felix1,2, Daniel L.F. da Silva1,2, Adilson S. Santos1,2, João H. Santos Neto1,2, Cheilane T. de Souza1,2, Raineldes A. Cruz Junior1,2, Anderson S. Souza1,2
1- Universidade Federal da Bahia, Instituto de Química, Grupo de Pesquisa em Química e Quimiometria, Campus Ondina, 40170-115, Salvador, Bahia, Brazil
2- Instituto Nacional de Ciência e Tecnologia, INCT, de Energia e Ambiente, Universidade Federal da Bahia, 40170-115, Salvador, Bahia, Brazil
*Correspondence author: Sergio L. C. Ferreira E-mail: [email protected] FAX: + 55 71 32836831
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Abstract This work presents a critical review of multivariate techniques employed for optimization of methods developed in food analysis. A comparison between the response surface methodologies has been performed, it evidencing advantages and drawbacks of these. Applications of the main chemometric tools (central composite and Box Behnken designs and Doehlert matrix) often utilized for optimization of sample preparation procedures and also instrumental conditions of analytical techniques for determination of organic and inorganic species in food samples are shown. Also, a brief discussion on the use of multiple responses and robustness test in food analysis has been presented.
Keywords: Food; Doehlert matrix; Central composite design, Box Behnken design; Robustness; Experimental design; Factorial design.
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1. Introduction Currently, multivariate optimization techniques have often been used in analytical chemistry, and they have been subjects for the publication of several review papers (Bezerra, dos Santos, Santos, Novaes, Ferreira, & de Souza, 2016; Bezerra, Santelli, Oliveira, Villar, & Escaleira, 2008; Candioti, De Zan, Camara, & Goicoechea, 2014; Novaes, Bezerra, da Silva, dos Santos, Romao, & Neto, 2016). In food analysis, these tools can be employed for evaluation preliminary of the factors (factor screening) and also for determination of the critical conditions of these. So, the optimization techniques can be divided into two kinds of designs.
1.1. Tools for evaluation preliminary of the factors The main technique employed for factor screening is the two-level full factorial design, whose number of experiments established by the matrix is determined by the expression (2k), being (k) the number of factors investigated. It allows the determination of the effects and the significances of the factors and their interactions of the processes. However, when the number of factors is large, the use of two-level full factorial design becomes unacceptable. So, in this case, the fractional factorial designs (2k-x) may be the most recommended, where (x) is the reduction of the number of experiments. These designs have the disadvantage that the effects of the main factors are confounded with the effects of interactions of other factors. A strategy to improve interpretation and decrease the risk of error is to establish designs whose the main effects are confounded with effects of highorder factor interactions. This approach is defined by the design resolution that is represented by Roman numerals. Thus, for a fractional factorial of resolution III, the main effects are not confounded with other main effects, but they are confounded with twofactor interactions. In a fractional factorial of resolution IV the main effects are confounded with three-factor interactions, and also two-factor interactions are confounded with other two-factor interactions (Friedrich, Martins, Prestes, & Zanella, 2016; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003).
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1.2. Response surface methodologies (RSM) The response surface methodologies (RSM) establish quadratic models, they allowing the obtaining of the critical conditions of the factors (maximum or minimum). The RSM´s more employed by analytical chemistry are central composite design (CCD), Doehlert matrix (DM), three-level factorial (3K) and Box Behnken designs (BBD). All these tools have their advantages and drawbacks. During the optimization of experimental factors using RSM, the validation study of the quadratic model is obligatory because in this case, the critical conditions of the method are being determined in this step. So, the analysis of variance (ANOVA) has been one of the best options for this evaluation. Also, the model obtained should not have lack of fit to ensure the efficiency of the optimization. By another hand, for the linear models, this requirement is lower because the two-level factorial designs full or fractional are employed for preliminary evaluation of the factors (S.L.C. Ferreira, 2015; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003).
1.2.1 Central composite design This methodology consists of a two-level factorial design, a star design, and the central point. For two and three factors, this design requires nine and fifteen experiments, respectively, and the factors are studied with 3 and 5 levels. In two-factors CCD designs, in general, the variables are studied at 5 levels: -√2, -1, 0, +1, +√2. However, when α=1 the factors are studied with 3 levels (-1, 0, +1). One of the advantages of this tool is the two-level full factorial design, which can be performed preliminarily as a step for evaluation of the factors. By another hand, this design contemplates experiments with all factors at the negative or positive level, which is a disadvantage because runs performed under extreme conditions can induce unsatisfactory results. The number of experiments required by this design is defined by the expression N = 2k + 2k + Co, being that k is the number of factors and Co the number of central points (S. L. C. Ferreira, Bruns, Ferreira, Matos, David, Brandao, et al., 2007; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003). Table 1 shows methods proposed for food analysis optimized using central composite designs.
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1.2.2. Box Behnken design Box Behnken matrix for three factors is a spherical, rotatable design, which viewed on a cube, it consists of the central point and the middle points of the edges (S.L.C. Ferreira, 2015; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003). In this design, all the factors are studied with three levels, and the number of experiments required for obtaining the model is defined as N=2k(k−1) +Co, where k is the number of factors and Co is the number of central points. (S. L. C. Ferreira, et al., 2007). Table 2 presents some applications of Box Behnken design for optimization of methods proposed for food analysis.
1.2.3. Doehlert matrix Doehlert design requires for the development of the model the number of experiments which is defined by the equation N = 2K + K +Co, where K is the number of factors and Co is the number of central points developed. For two factors, this design is established with three and five levels. For K equal to 3, the factors can be studied with three, five and seven levels. This methodology has no experiments with all factors with positive or negative levels (S. L. C. Ferreira, dos Santos, Quintella, Neto, & Bosque-Sendra, 2004). Applications of Doehlert matrix in the optimization of methods developed for food analysis are shown in Table 3.
1.2.4. Three level factorial design The full three-level factorial design (3k) is a response surface methodology, which has as a disadvantage the number required for obtaining of the quadratic model. Besides that, this design also contemplates experiments with all factors at the negative or positive level (S.L.C. Ferreira, 2015; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003).
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1.2.5. Efficiencies of the response surface methodologies A comparison between the response surface methodologies (RSM´s) has been performed by the efficiency parameter (ϕ), which is defined as being the number of coefficients in the estimated model divided by the number of experiments required by the RSM (S. L. C. Ferreira, Caires, Borges, Lima, Silva, & dos Santos, 2017; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003). The Table 4 shows the efficiencies of the RSM´s (central composite, three-level factorial and Box Behnken designs and the Doehlert matrix), where can be seen that the Doehlert matrix has the higher efficiency and the three level factorial design is unfeasible when the number of factors is higher than 2.
1.2.6. Mixture design Mixture design is also a response surface methodology, which the product resultant is an ingredient mixture, whose the proportion of the components is established by models which may be linear, quadratic or cubic (Handa, de Lima, Guelfi, Georgetti, & Ida, 2016; Sifaoui, Mecha, Silva, Chammem, Mejri, Abderabba, et al., 2016). The applications of mixture designs in food analysis are still sparse. Between these, we can cite some applications of mixture designs for optimization of: mobile phase in chromatographic processes (Borges, Bruns, Almeida, & Scarminio, 2007); acid mixture for sample digestion procedure (Nano, Bruns, Ferreira, Baccan, & Cadore, 2009); extractor solution in procedure using slurry sampling (Bezerra, Castro, Macedo, & da Silva, 2010); solvent organic for extraction of organic compound (W. D. Oliveira, de Souza, Padula, & Godoy, 2017).
2. Applications of multivariate optimization techniques in food analytical chemistry The applications of the chemometric tools in food analytical chemistry can be divided into two approaches: optimization of the experimental conditions during the sample preparation
step and also optimization of the instrumental variables of analytical techniques. Eventually, these tools have also been used in the validation step of the analytical methods in the robustness tests.
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2.1. Applications of experimental designs in the sample preparation steps The employ of chemometric tools for the optimization of sample preparation procedures in food analysis is quite diverse. Between these, we can report analytical strategies using microwave assisted radiation (Andrade & Lancas, 2017; Bagheri, Asgharinezhad, & Ebrahimzadeh, 2016; Khajeh & Sanchooli, 2010; Korn, dos Santos, Korn, & Ferreira, 2005; Marval-Leon, Camara-Martos, Perez-Rodriguez, Amaro-Lopez, & MorenoRojas, 2012), ultrasound assisted radiation (Machado, Pereira, Barbero, & Martinez, 2017), sample solubilization using tetramethylammonium hydroxide (de Figueiredo, Bonafe, Martins, Martins, Maruyama, Santos, et al., 2018; Torres, Martins-Teixeira, Cadore, & Queiroz, 2016), enzymatic extraction (Bayar, Friji, & Kammoun, 2018), pressurized water extraction (Moras, Rey, Vilarem, & Pontalier, 2017), besides preconcentration procedures involving liquid-liquid extraction (Biata, Nyaba, Ramontja, Mketo, & Nomngongo, 2017; Khazaeli, Haddadi, Zargar, Hatamie, & Semnani, 2017), cloud point extraction (Costa, Coelho, & Coelho, 2015; Heidarizadi & Tabaraki, 2016; Rezende, Nascentes, & Coelho, 2011), dispersive liquid-liquid microextraction (Souza, Siqueira, Prates, Bezerra, Rocha, Oliveira, et al., 2017), solid phase extraction in their several forms (Andrade & Lancas, 2017; Arabi, Ghaedi, & Ostovan, 2016; Bittar, Catelani, Nigoghossian, Barud, Ribeiro, Pezza, et al., 2017; Dahaghin, Mousavi, & Sajjadi, 2017; Kakavandi, Behbahani, Omidi, & Hesam, 2017; Seidi & Fotouhi, 2017) and others (J. J. Gao, Wang, Qu, Wang, & Wang, 2017; Wei, Xiao, & Yang, 2016).
2.2. Applications of experimental designs for optimization of instrumental variables of analytical techniques The instrumental conditions of many analytical strategies proposed for the determination of organic and inorganic species in food samples have been optimized using experimental designs. Between these, we can cite methods developed using analaytical techniques as: hydride generation atomic fluorescence spectrometry (Silva, Leao, Silva, Pimentel, Garcia, & Ferreira, 2017); electrothermal atomization atomic absorption spectrometry (da Silva, Junior, Silva, Portugal, Matos, & Ferreira, 2011; Junior, Silva, Leao, & Ferreira, 2014); High performance liquid chromatography (Galarce-Bustos, Alvarado, Vega, & Aranda, 2014; Jovanov, Guzsvany, Lazic, Franko, Sakac, Saric, et al., 2015; Michlig, Van de 7
Velde, Freyre, & Bernardi, 2014); Hydride generation inductively coupled plasma optical emission (Escudero, Pacheco, Gasquez, & Salonia, 2015); cold vapor atomic absorption spectrometry (Silva, Silva, Leao, dos Santos, Welz, & Ferreira, 2015).
2.3. Employment of experimental designs for the evaluation of robustness Robustness is a parameter that has been evaluated in validation studies, whose definition is: "the capacity of an analytical procedure to produce unbiased results when small changes in the experimental conditions are made voluntarily." The determination of robustness of an analytical method can be performed using several chemometric tools. The two-level full factorial design constitutes a good alternative if the number of factors is small. However, when the number of factors is large, the fractional factorial designs are the most recommended. Between these, Taguchi and Plackett-Burman designs have often been employed in robustness tests (S. L. C. Ferreira, Caires, Borges, Lima, Silva, & dos Santos, 2017; L. F. Oliveira, Braga, Filgueiras, Augusto, & Poppi, 2014). A procedure established for determination of the total antioxidant capacity of wines using sequential-injection with chemiluminescence detection employed a Plackett-Burman design for evaluation of the robustness of the method (Fassoula, Economou, & Calokerinos, 2011). Another method proposed for the determination of total arsenic in seafood, also used this same experimental design for evaluation of the robustness (C. Santos, Alava-Moreno, Lavilla, & Bendicho, 2000).
2.4. Multiple response modeling Many analytical methods have been proposed for determining of a single species, however, very often the objective of the processes is the extraction and or quantification of more than one species. So, multiple responses are required to establish conditions of compromise between the quantified analytes. This way, the desirability function (D) has been often employed for optimization of methods for food analysis using multiple responses (Derringer & Suich, 1980). Between these, we can cite some references: (Ferreres, Grosso, Gil-Izquierdo, Valentao, Mota, & Andrade, 2017; Gomes, Portugal, dos Anjos, de Jesus, de Oliveira, David, et al., 2017; Heidarizadi & Tabaraki, 2016; Marti, Valcarcel, HerreroMartinez, Cebolla-Cornejo, & Rosello, 2017; Setyaningsih, Saputro, Carrera, Palma, & 8
Barroso, 2017). Additionally, another multiple response function (MR) with a mathematic approach very simple was also proposed (Portugal, Ferreira, dos Santos, & Ferreira, 2007). This function also has been used for optimization of analytical strategies developed for food analysis. (D. Santos, Carvalho, Lima, Leao, Teixeira, & Korn, 2014; W. P. C. Santos, Castro, Bezerra, Fernandes, Ferreira, & Korn, 2009; Sousa, Goncalves, Heleno, de Queiroz, & de Marchi, 2014). Recently a comparison between the function MR and the desirability function D was reported. The results obtained in the generated models by the application of the two multiple response functions in the experimental data were quite similar (Novaes, Ferreira, Neto, de Santana, Portugal, & Goicoechea, 2016).
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Table 1. Analytical methods optimized employing central composite designs
Analytes
Sample
Process
AT*
Reference (Rezende, Nascentes, &
Cadmium
Soft drinks
CPE
FAAS Coelho, 2011)
Nickel
Edible oils
LLE
FAAS
Beverage
DLLME
HPLC
Tomatoes
MAE
HPLC
Sorbic acid and Benzoic Acid
(Tokay & Bagdat, 2016) (Kokya, Farhadi, & Kalhori, 2012)
(Li, Phenolics
Deng,
Wu,
Liu,
Loewen, & Tsao, 2012) Lumonisin B-1
Rice
Milk,
(Petrarca,
FLD
Rossi, & de Sylos, 2014)
HPLCFLD
(M. Gao, Wang, Ma, Zhang, Yin, Dahlgren, et al., 2015)
HG-ICP
(Escudero,
OES
Gasquez, & Salonia, 2015)
chicken
Fluoroquinolones egg and honey
LLME
Argentinean Selenium
HPLC-
beverages
SPE
(Dasbasi, Trace metals ions
Rodrigues,
LLE / SPE
Honey
SPE
Pacheco,
Sacmaci,
FAAS Cankaya, & Soykan, 2016)
Mercury
Seafood
SPE
CV AAS
(Seidi & Fotouhi, 2017)
Ochratoxin A
Wine
SPME
HPLC-MS
(Andrade & Lancas, 2017) (Pineda, Carrasco, Pena-
Biogenic amines
Wines
Chrom.
HPLC
Farfal, Henriquez-Aedo, & Aranda, 2012)
(Biata, Nyaba, Ramontja, Antimony and tin
Beverages
DLLME
ICP OES
Mketo,
& Nomngongo,
2017)
(Farina, Abdullah, Bibi, & Pesticide residues Plants
SPE
GC-ECD Khalik, 2017)
*AT- analytical technique
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Table 2. Box Behnken design for optimization of methods proposed for analysis food
Analytes
Sample
Process
AT*
Nicotinic Acid and Food Nicotinamide
CE
HPLC
Thiamine
Wheat Flours
SPE
HPLC
Nitrite
Meat products
Extraction
CV
(Poly)phenols
Grape
Extraction
UV-Vis
SPE
FAAS
Extraction
ICP-MS
Extraction
HPLC
DLLME
HPLC
Cadmium lead
and Seafood/ Vegetables
Cadmium
Brown flour
rice
Anthocyanins and Black rice polyphenols steroidal and phenolic Chicken, fish endocrine Several metals
Food
SPE
Antibacterial residues
Foods of HF-LPME animal origin
Antimony
Fish muscle
MAE
Flavonoids
Moringa oleifera leaf
Extraction
Aroma-active monoterpenes
Berries
SPME
Several metals
Black Leaves
Selenium
Food
d-CPE
Lead
Agricultural products
SPE
Mercury
Vinegar
UE
Tea
SPE
Reference (Mu, Luan, Liu, & Gao, 2013) (Michlig, Van de Velde, Freyre, & Bernardi, 2014) (Yildiz, Oztekin, Orbay, & Senkal, 2014) (Dominguez-Perles, Teixeira, Rosa, & Barros, 2014) (Manoochehri, Asgharinezhad, & Shekari, 2015) (Y. N. Wu, He, Wang, Yuan, Xing, Wang, et al., 2016) (Pedro, Granato, & Rosso, 2016) (H. L. Wu, Li, Liu, Hu, Geng, Chen, et al., 2016)
(Bagheri, Asgharinezhad, & Ebrahimzadeh, 2016) (Tajabadi, Ghambarian, HPLCYamini, & Yazdanfar, DAD 2016) (Silva, Leao, Silva, HG AFS Pimentel, Garcia, & Ferreira, 2017) (Y. Q. Wang, Gao, Ding, HPLC-MS Liu, Han, Gui, et al., 2017) (Chmiel, Kupska, GC-MS Wardencki, & Namiesnik, 2017) (Manoochehri & FAAS Naghibzadeh, 2017) (M. Wang, Zhong, Qin, HG AFS Zhang, Li, & Yang, 2017) (Dahaghin, Mousavi, & FAAS Sajjadi, 2017) (Silva, Silva, Leao, dos FAAS
CV AAS
Santos, Welz, & Ferreira, 2015)
*AT- analytical technique 11
Table 3. Optimization using Doehlert matrix in methods proposed for food analysis
Analytes
Sample
Nitrogen
Bean
Insecticide
Honey
residues
pollen
Process
and
AT*
MAE
Kjeldad
SPE
LC-MS/MS
Reference (Korn, dos Santos, Korn, & Ferreira, 2005) (Garcia-Chao, Agruna, Calvete, Sakkas, Llompart, & Dagnac, 2010)
(Khajeh, Zinc and Copper
Cereal
MAE
FAAS
Reza,
Moghaddam, & Sanchooli, 2010)
Water,
food
Manganese
(de Oliveira, de Oliveira, SPE
FAAS
and sediment
Segatelli, & Tarley, 2013)
(D. Santos, Carvalho, Lima, Micronutrient Coconut milk
UAE
ICP OES
Leao, Teixeira, & Korn,
minerals 2014)
(Heidarizadi & Tabaraki, Synthetic dyes
Candies
CPE
UV–Vis
Isoflavones
Soybean flour
SPE
HPLC
2016)
(Moras, Rey, Vilarem, & Pontalier, 2017)
(Teodoro, Dias, da Silva, Food Copper
and
beverages
SPE
FAAS
Bezerra, Dantas, Teixeira, et al., 2017)
*AT- analytical technique CE- capillary electrophoresis; Chrom- chromatografic conditions; CPE- cloud point extraction; CV- cyclic voltammetry; CV AAS- cold vapour atomic absorption spectrometry; d-CPE- dualcloud point extraction; DLLME dispersive liquid liquid microextraction; ET AASelectrothermal atomic absorption
spectrometry;
FAAS- flame atomic absorption
spectrometry; GC-ECD- gas chromatography-electron capture detector; GC-MS- gas chromatography-mass spectrometry; HF-LPME- hollow fiber-liquid phase microextraction; HG AFS- hydride generation atomic fluorescence spectrometry; HG-ICP OES- hydride generation-inductively coupled plasma atomic emission spectrometry; HPLC- high performance liquid chromatography; HPLC-DAD- high performance liquid chromatographydiode array detection; HPLC-FLD- high performance liquid chromatography-fluorescence 12
detector; HPLC-MS- high performance liquid chromatography-mass spectrometry; ICP OESinductively coupled plasma atomic emission spectrometry; ICP-MS- inductively coupled plasma-mass spectrometry; LC-MS/MS- liquid chromatography-triple quadrupole mass spectrometry; LLE- liquid-liquid extraction; LLME- liqui-liquid microextraction; MAEmicrowave assisted extraction; PLE- pressurized liquid extraction; SPE- solid phase extraction; SPME- solid phase microextraction; UAE-ultrasound-assisted extraction; UV-Visultraviolet and visible spectrophotometry.
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Table 4 Table 4. Comparison between efficiencies of the response surface methodologies
Factor
Number of experiments
P
Efficiency
required
(ϕ)
CCD
BBD
DM
3kD
CCD
BBD
DM
3kB
2
6
9
-
7
9
0.67
-
0.86
0.67
3
10
15
13
13
27
0.67
0.77
0.77
0.37
4
15
25
25
21
81
0.60
0.60
0.71
0.19
5
21
43
41
31
243
0.49
0.51
0.68
0.09
6
28
77
61
43
729
0.36
0.46
0.65
0.04
p- Number of coefficients of the quadratic model; CCD- central composite design; BBD- Box Behnken design; DM- Doehlert matrix; 3KD- Full three level factorial design.
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Conclusions The literature survey carried out during the execution of this study revealed that the multivariate optimization techniques have often been used in the development of food analysis methods. In this context, the central composite design is one of the most employed, although it has lower efficiency than the Doehlert matrix and Box Behnken design. Also, this work revealed that the procedures developed for food analysis had not evaluated the robustness, despite the importance of this parameter in the validation studies of analytical methods. The chemometric techniques have often been employed for optimization of procedures for food analysis aiming quantification of organic and inorganic species, because these tools allow the determination of the critical conditions of experimental factors of the analytical methods, considering the interaction between these, with lower consumption of reagents and lower time spent during the optimization step. Additionally, separation and preconcentration procedures for multi-element determinations have been optimized using multiple response functions establishing compromises between the analytes. Acknowledgements Authors are grateful to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), to the Fundação de Amparo à Pesquisa do Estado da Bahia (FAPESB) and to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for providing grants and fellowships and for financial support.
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Highlights Chemometric techniques employed for optimization in food analysis are shown. Description, advantages, and drawbacks of the experimental designs are presented. A comparison between the response surface methodologies for food analysis has been performed.
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S0308-8146(17)31933-7 https://doi.org/10.1016/j.foodchem.2017.11.114 FOCH 22091
To appear in:
Food Chemistry
Received Date: Revised Date: Accepted Date:
1 September 2017 27 October 2017 30 November 2017
Please cite this article as: Ferreira, S.L.C., Silva Junior, M.M., Felix, C.S.A., da Silva, D.L.F., Santos, A.S., Santos Neto, J.H., de Souza, C.T., Cruz Junior, R.A., Souza, A.S., Multivariate optimization techniques in food analysis A review, Food Chemistry (2017), doi: https://doi.org/10.1016/j.foodchem.2017.11.114
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Multivariate optimization techniques in food analysis - A review
Sergio L.C. Ferreira1,2*, Mario M. Silva Junior1,2, Caio S.A. Felix1,2, Daniel L.F. da Silva1,2, Adilson S. Santos1,2, João H. Santos Neto1,2, Cheilane T. de Souza1,2, Raineldes A. Cruz Junior1,2, Anderson S. Souza1,2
1- Universidade Federal da Bahia, Instituto de Química, Grupo de Pesquisa em Química e Quimiometria, Campus Ondina, 40170-115, Salvador, Bahia, Brazil
2- Instituto Nacional de Ciência e Tecnologia, INCT, de Energia e Ambiente, Universidade Federal da Bahia, 40170-115, Salvador, Bahia, Brazil
*Correspondence author: Sergio L. C. Ferreira E-mail: [email protected] FAX: + 55 71 32836831
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Abstract This work presents a critical review of multivariate techniques employed for optimization of methods developed in food analysis. A comparison between the response surface methodologies has been performed, it evidencing advantages and drawbacks of these. Applications of the main chemometric tools (central composite and Box Behnken designs and Doehlert matrix) often utilized for optimization of sample preparation procedures and also instrumental conditions of analytical techniques for determination of organic and inorganic species in food samples are shown. Also, a brief discussion on the use of multiple responses and robustness test in food analysis has been presented.
Keywords: Food; Doehlert matrix; Central composite design, Box Behnken design; Robustness; Experimental design; Factorial design.
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1. Introduction Currently, multivariate optimization techniques have often been used in analytical chemistry, and they have been subjects for the publication of several review papers (Bezerra, dos Santos, Santos, Novaes, Ferreira, & de Souza, 2016; Bezerra, Santelli, Oliveira, Villar, & Escaleira, 2008; Candioti, De Zan, Camara, & Goicoechea, 2014; Novaes, Bezerra, da Silva, dos Santos, Romao, & Neto, 2016). In food analysis, these tools can be employed for evaluation preliminary of the factors (factor screening) and also for determination of the critical conditions of these. So, the optimization techniques can be divided into two kinds of designs.
1.1. Tools for evaluation preliminary of the factors The main technique employed for factor screening is the two-level full factorial design, whose number of experiments established by the matrix is determined by the expression (2k), being (k) the number of factors investigated. It allows the determination of the effects and the significances of the factors and their interactions of the processes. However, when the number of factors is large, the use of two-level full factorial design becomes unacceptable. So, in this case, the fractional factorial designs (2k-x) may be the most recommended, where (x) is the reduction of the number of experiments. These designs have the disadvantage that the effects of the main factors are confounded with the effects of interactions of other factors. A strategy to improve interpretation and decrease the risk of error is to establish designs whose the main effects are confounded with effects of highorder factor interactions. This approach is defined by the design resolution that is represented by Roman numerals. Thus, for a fractional factorial of resolution III, the main effects are not confounded with other main effects, but they are confounded with twofactor interactions. In a fractional factorial of resolution IV the main effects are confounded with three-factor interactions, and also two-factor interactions are confounded with other two-factor interactions (Friedrich, Martins, Prestes, & Zanella, 2016; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003).
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1.2. Response surface methodologies (RSM) The response surface methodologies (RSM) establish quadratic models, they allowing the obtaining of the critical conditions of the factors (maximum or minimum). The RSM´s more employed by analytical chemistry are central composite design (CCD), Doehlert matrix (DM), three-level factorial (3K) and Box Behnken designs (BBD). All these tools have their advantages and drawbacks. During the optimization of experimental factors using RSM, the validation study of the quadratic model is obligatory because in this case, the critical conditions of the method are being determined in this step. So, the analysis of variance (ANOVA) has been one of the best options for this evaluation. Also, the model obtained should not have lack of fit to ensure the efficiency of the optimization. By another hand, for the linear models, this requirement is lower because the two-level factorial designs full or fractional are employed for preliminary evaluation of the factors (S.L.C. Ferreira, 2015; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003).
1.2.1 Central composite design This methodology consists of a two-level factorial design, a star design, and the central point. For two and three factors, this design requires nine and fifteen experiments, respectively, and the factors are studied with 3 and 5 levels. In two-factors CCD designs, in general, the variables are studied at 5 levels: -√2, -1, 0, +1, +√2. However, when α=1 the factors are studied with 3 levels (-1, 0, +1). One of the advantages of this tool is the two-level full factorial design, which can be performed preliminarily as a step for evaluation of the factors. By another hand, this design contemplates experiments with all factors at the negative or positive level, which is a disadvantage because runs performed under extreme conditions can induce unsatisfactory results. The number of experiments required by this design is defined by the expression N = 2k + 2k + Co, being that k is the number of factors and Co the number of central points (S. L. C. Ferreira, Bruns, Ferreira, Matos, David, Brandao, et al., 2007; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003). Table 1 shows methods proposed for food analysis optimized using central composite designs.
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1.2.2. Box Behnken design Box Behnken matrix for three factors is a spherical, rotatable design, which viewed on a cube, it consists of the central point and the middle points of the edges (S.L.C. Ferreira, 2015; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003). In this design, all the factors are studied with three levels, and the number of experiments required for obtaining the model is defined as N=2k(k−1) +Co, where k is the number of factors and Co is the number of central points. (S. L. C. Ferreira, et al., 2007). Table 2 presents some applications of Box Behnken design for optimization of methods proposed for food analysis.
1.2.3. Doehlert matrix Doehlert design requires for the development of the model the number of experiments which is defined by the equation N = 2K + K +Co, where K is the number of factors and Co is the number of central points developed. For two factors, this design is established with three and five levels. For K equal to 3, the factors can be studied with three, five and seven levels. This methodology has no experiments with all factors with positive or negative levels (S. L. C. Ferreira, dos Santos, Quintella, Neto, & Bosque-Sendra, 2004). Applications of Doehlert matrix in the optimization of methods developed for food analysis are shown in Table 3.
1.2.4. Three level factorial design The full three-level factorial design (3k) is a response surface methodology, which has as a disadvantage the number required for obtaining of the quadratic model. Besides that, this design also contemplates experiments with all factors at the negative or positive level (S.L.C. Ferreira, 2015; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003).
5
1.2.5. Efficiencies of the response surface methodologies A comparison between the response surface methodologies (RSM´s) has been performed by the efficiency parameter (ϕ), which is defined as being the number of coefficients in the estimated model divided by the number of experiments required by the RSM (S. L. C. Ferreira, Caires, Borges, Lima, Silva, & dos Santos, 2017; Massart, Vandeginste, Buydens, de Jong, Lewi, & Smeyers-Verbeke, 2003). The Table 4 shows the efficiencies of the RSM´s (central composite, three-level factorial and Box Behnken designs and the Doehlert matrix), where can be seen that the Doehlert matrix has the higher efficiency and the three level factorial design is unfeasible when the number of factors is higher than 2.
1.2.6. Mixture design Mixture design is also a response surface methodology, which the product resultant is an ingredient mixture, whose the proportion of the components is established by models which may be linear, quadratic or cubic (Handa, de Lima, Guelfi, Georgetti, & Ida, 2016; Sifaoui, Mecha, Silva, Chammem, Mejri, Abderabba, et al., 2016). The applications of mixture designs in food analysis are still sparse. Between these, we can cite some applications of mixture designs for optimization of: mobile phase in chromatographic processes (Borges, Bruns, Almeida, & Scarminio, 2007); acid mixture for sample digestion procedure (Nano, Bruns, Ferreira, Baccan, & Cadore, 2009); extractor solution in procedure using slurry sampling (Bezerra, Castro, Macedo, & da Silva, 2010); solvent organic for extraction of organic compound (W. D. Oliveira, de Souza, Padula, & Godoy, 2017).
2. Applications of multivariate optimization techniques in food analytical chemistry The applications of the chemometric tools in food analytical chemistry can be divided into two approaches: optimization of the experimental conditions during the sample preparation
step and also optimization of the instrumental variables of analytical techniques. Eventually, these tools have also been used in the validation step of the analytical methods in the robustness tests.
6
2.1. Applications of experimental designs in the sample preparation steps The employ of chemometric tools for the optimization of sample preparation procedures in food analysis is quite diverse. Between these, we can report analytical strategies using microwave assisted radiation (Andrade & Lancas, 2017; Bagheri, Asgharinezhad, & Ebrahimzadeh, 2016; Khajeh & Sanchooli, 2010; Korn, dos Santos, Korn, & Ferreira, 2005; Marval-Leon, Camara-Martos, Perez-Rodriguez, Amaro-Lopez, & MorenoRojas, 2012), ultrasound assisted radiation (Machado, Pereira, Barbero, & Martinez, 2017), sample solubilization using tetramethylammonium hydroxide (de Figueiredo, Bonafe, Martins, Martins, Maruyama, Santos, et al., 2018; Torres, Martins-Teixeira, Cadore, & Queiroz, 2016), enzymatic extraction (Bayar, Friji, & Kammoun, 2018), pressurized water extraction (Moras, Rey, Vilarem, & Pontalier, 2017), besides preconcentration procedures involving liquid-liquid extraction (Biata, Nyaba, Ramontja, Mketo, & Nomngongo, 2017; Khazaeli, Haddadi, Zargar, Hatamie, & Semnani, 2017), cloud point extraction (Costa, Coelho, & Coelho, 2015; Heidarizadi & Tabaraki, 2016; Rezende, Nascentes, & Coelho, 2011), dispersive liquid-liquid microextraction (Souza, Siqueira, Prates, Bezerra, Rocha, Oliveira, et al., 2017), solid phase extraction in their several forms (Andrade & Lancas, 2017; Arabi, Ghaedi, & Ostovan, 2016; Bittar, Catelani, Nigoghossian, Barud, Ribeiro, Pezza, et al., 2017; Dahaghin, Mousavi, & Sajjadi, 2017; Kakavandi, Behbahani, Omidi, & Hesam, 2017; Seidi & Fotouhi, 2017) and others (J. J. Gao, Wang, Qu, Wang, & Wang, 2017; Wei, Xiao, & Yang, 2016).
2.2. Applications of experimental designs for optimization of instrumental variables of analytical techniques The instrumental conditions of many analytical strategies proposed for the determination of organic and inorganic species in food samples have been optimized using experimental designs. Between these, we can cite methods developed using analaytical techniques as: hydride generation atomic fluorescence spectrometry (Silva, Leao, Silva, Pimentel, Garcia, & Ferreira, 2017); electrothermal atomization atomic absorption spectrometry (da Silva, Junior, Silva, Portugal, Matos, & Ferreira, 2011; Junior, Silva, Leao, & Ferreira, 2014); High performance liquid chromatography (Galarce-Bustos, Alvarado, Vega, & Aranda, 2014; Jovanov, Guzsvany, Lazic, Franko, Sakac, Saric, et al., 2015; Michlig, Van de 7
Velde, Freyre, & Bernardi, 2014); Hydride generation inductively coupled plasma optical emission (Escudero, Pacheco, Gasquez, & Salonia, 2015); cold vapor atomic absorption spectrometry (Silva, Silva, Leao, dos Santos, Welz, & Ferreira, 2015).
2.3. Employment of experimental designs for the evaluation of robustness Robustness is a parameter that has been evaluated in validation studies, whose definition is: "the capacity of an analytical procedure to produce unbiased results when small changes in the experimental conditions are made voluntarily." The determination of robustness of an analytical method can be performed using several chemometric tools. The two-level full factorial design constitutes a good alternative if the number of factors is small. However, when the number of factors is large, the fractional factorial designs are the most recommended. Between these, Taguchi and Plackett-Burman designs have often been employed in robustness tests (S. L. C. Ferreira, Caires, Borges, Lima, Silva, & dos Santos, 2017; L. F. Oliveira, Braga, Filgueiras, Augusto, & Poppi, 2014). A procedure established for determination of the total antioxidant capacity of wines using sequential-injection with chemiluminescence detection employed a Plackett-Burman design for evaluation of the robustness of the method (Fassoula, Economou, & Calokerinos, 2011). Another method proposed for the determination of total arsenic in seafood, also used this same experimental design for evaluation of the robustness (C. Santos, Alava-Moreno, Lavilla, & Bendicho, 2000).
2.4. Multiple response modeling Many analytical methods have been proposed for determining of a single species, however, very often the objective of the processes is the extraction and or quantification of more than one species. So, multiple responses are required to establish conditions of compromise between the quantified analytes. This way, the desirability function (D) has been often employed for optimization of methods for food analysis using multiple responses (Derringer & Suich, 1980). Between these, we can cite some references: (Ferreres, Grosso, Gil-Izquierdo, Valentao, Mota, & Andrade, 2017; Gomes, Portugal, dos Anjos, de Jesus, de Oliveira, David, et al., 2017; Heidarizadi & Tabaraki, 2016; Marti, Valcarcel, HerreroMartinez, Cebolla-Cornejo, & Rosello, 2017; Setyaningsih, Saputro, Carrera, Palma, & 8
Barroso, 2017). Additionally, another multiple response function (MR) with a mathematic approach very simple was also proposed (Portugal, Ferreira, dos Santos, & Ferreira, 2007). This function also has been used for optimization of analytical strategies developed for food analysis. (D. Santos, Carvalho, Lima, Leao, Teixeira, & Korn, 2014; W. P. C. Santos, Castro, Bezerra, Fernandes, Ferreira, & Korn, 2009; Sousa, Goncalves, Heleno, de Queiroz, & de Marchi, 2014). Recently a comparison between the function MR and the desirability function D was reported. The results obtained in the generated models by the application of the two multiple response functions in the experimental data were quite similar (Novaes, Ferreira, Neto, de Santana, Portugal, & Goicoechea, 2016).
v
9
Table 1. Analytical methods optimized employing central composite designs
Analytes
Sample
Process
AT*
Reference (Rezende, Nascentes, &
Cadmium
Soft drinks
CPE
FAAS Coelho, 2011)
Nickel
Edible oils
LLE
FAAS
Beverage
DLLME
HPLC
Tomatoes
MAE
HPLC
Sorbic acid and Benzoic Acid
(Tokay & Bagdat, 2016) (Kokya, Farhadi, & Kalhori, 2012)
(Li, Phenolics
Deng,
Wu,
Liu,
Loewen, & Tsao, 2012) Lumonisin B-1
Rice
Milk,
(Petrarca,
FLD
Rossi, & de Sylos, 2014)
HPLCFLD
(M. Gao, Wang, Ma, Zhang, Yin, Dahlgren, et al., 2015)
HG-ICP
(Escudero,
OES
Gasquez, & Salonia, 2015)
chicken
Fluoroquinolones egg and honey
LLME
Argentinean Selenium
HPLC-
beverages
SPE
(Dasbasi, Trace metals ions
Rodrigues,
LLE / SPE
Honey
SPE
Pacheco,
Sacmaci,
FAAS Cankaya, & Soykan, 2016)
Mercury
Seafood
SPE
CV AAS
(Seidi & Fotouhi, 2017)
Ochratoxin A
Wine
SPME
HPLC-MS
(Andrade & Lancas, 2017) (Pineda, Carrasco, Pena-
Biogenic amines
Wines
Chrom.
HPLC
Farfal, Henriquez-Aedo, & Aranda, 2012)
(Biata, Nyaba, Ramontja, Antimony and tin
Beverages
DLLME
ICP OES
Mketo,
& Nomngongo,
2017)
(Farina, Abdullah, Bibi, & Pesticide residues Plants
SPE
GC-ECD Khalik, 2017)
*AT- analytical technique
10
Table 2. Box Behnken design for optimization of methods proposed for analysis food
Analytes
Sample
Process
AT*
Nicotinic Acid and Food Nicotinamide
CE
HPLC
Thiamine
Wheat Flours
SPE
HPLC
Nitrite
Meat products
Extraction
CV
(Poly)phenols
Grape
Extraction
UV-Vis
SPE
FAAS
Extraction
ICP-MS
Extraction
HPLC
DLLME
HPLC
Cadmium lead
and Seafood/ Vegetables
Cadmium
Brown flour
rice
Anthocyanins and Black rice polyphenols steroidal and phenolic Chicken, fish endocrine Several metals
Food
SPE
Antibacterial residues
Foods of HF-LPME animal origin
Antimony
Fish muscle
MAE
Flavonoids
Moringa oleifera leaf
Extraction
Aroma-active monoterpenes
Berries
SPME
Several metals
Black Leaves
Selenium
Food
d-CPE
Lead
Agricultural products
SPE
Mercury
Vinegar
UE
Tea
SPE
Reference (Mu, Luan, Liu, & Gao, 2013) (Michlig, Van de Velde, Freyre, & Bernardi, 2014) (Yildiz, Oztekin, Orbay, & Senkal, 2014) (Dominguez-Perles, Teixeira, Rosa, & Barros, 2014) (Manoochehri, Asgharinezhad, & Shekari, 2015) (Y. N. Wu, He, Wang, Yuan, Xing, Wang, et al., 2016) (Pedro, Granato, & Rosso, 2016) (H. L. Wu, Li, Liu, Hu, Geng, Chen, et al., 2016)
(Bagheri, Asgharinezhad, & Ebrahimzadeh, 2016) (Tajabadi, Ghambarian, HPLCYamini, & Yazdanfar, DAD 2016) (Silva, Leao, Silva, HG AFS Pimentel, Garcia, & Ferreira, 2017) (Y. Q. Wang, Gao, Ding, HPLC-MS Liu, Han, Gui, et al., 2017) (Chmiel, Kupska, GC-MS Wardencki, & Namiesnik, 2017) (Manoochehri & FAAS Naghibzadeh, 2017) (M. Wang, Zhong, Qin, HG AFS Zhang, Li, & Yang, 2017) (Dahaghin, Mousavi, & FAAS Sajjadi, 2017) (Silva, Silva, Leao, dos FAAS
CV AAS
Santos, Welz, & Ferreira, 2015)
*AT- analytical technique 11
Table 3. Optimization using Doehlert matrix in methods proposed for food analysis
Analytes
Sample
Nitrogen
Bean
Insecticide
Honey
residues
pollen
Process
and
AT*
MAE
Kjeldad
SPE
LC-MS/MS
Reference (Korn, dos Santos, Korn, & Ferreira, 2005) (Garcia-Chao, Agruna, Calvete, Sakkas, Llompart, & Dagnac, 2010)
(Khajeh, Zinc and Copper
Cereal
MAE
FAAS
Reza,
Moghaddam, & Sanchooli, 2010)
Water,
food
Manganese
(de Oliveira, de Oliveira, SPE
FAAS
and sediment
Segatelli, & Tarley, 2013)
(D. Santos, Carvalho, Lima, Micronutrient Coconut milk
UAE
ICP OES
Leao, Teixeira, & Korn,
minerals 2014)
(Heidarizadi & Tabaraki, Synthetic dyes
Candies
CPE
UV–Vis
Isoflavones
Soybean flour
SPE
HPLC
2016)
(Moras, Rey, Vilarem, & Pontalier, 2017)
(Teodoro, Dias, da Silva, Food Copper
and
beverages
SPE
FAAS
Bezerra, Dantas, Teixeira, et al., 2017)
*AT- analytical technique CE- capillary electrophoresis; Chrom- chromatografic conditions; CPE- cloud point extraction; CV- cyclic voltammetry; CV AAS- cold vapour atomic absorption spectrometry; d-CPE- dualcloud point extraction; DLLME dispersive liquid liquid microextraction; ET AASelectrothermal atomic absorption
spectrometry;
FAAS- flame atomic absorption
spectrometry; GC-ECD- gas chromatography-electron capture detector; GC-MS- gas chromatography-mass spectrometry; HF-LPME- hollow fiber-liquid phase microextraction; HG AFS- hydride generation atomic fluorescence spectrometry; HG-ICP OES- hydride generation-inductively coupled plasma atomic emission spectrometry; HPLC- high performance liquid chromatography; HPLC-DAD- high performance liquid chromatographydiode array detection; HPLC-FLD- high performance liquid chromatography-fluorescence 12
detector; HPLC-MS- high performance liquid chromatography-mass spectrometry; ICP OESinductively coupled plasma atomic emission spectrometry; ICP-MS- inductively coupled plasma-mass spectrometry; LC-MS/MS- liquid chromatography-triple quadrupole mass spectrometry; LLE- liquid-liquid extraction; LLME- liqui-liquid microextraction; MAEmicrowave assisted extraction; PLE- pressurized liquid extraction; SPE- solid phase extraction; SPME- solid phase microextraction; UAE-ultrasound-assisted extraction; UV-Visultraviolet and visible spectrophotometry.
13
Table 4 Table 4. Comparison between efficiencies of the response surface methodologies
Factor
Number of experiments
P
Efficiency
required
(ϕ)
CCD
BBD
DM
3kD
CCD
BBD
DM
3kB
2
6
9
-
7
9
0.67
-
0.86
0.67
3
10
15
13
13
27
0.67
0.77
0.77
0.37
4
15
25
25
21
81
0.60
0.60
0.71
0.19
5
21
43
41
31
243
0.49
0.51
0.68
0.09
6
28
77
61
43
729
0.36
0.46
0.65
0.04
p- Number of coefficients of the quadratic model; CCD- central composite design; BBD- Box Behnken design; DM- Doehlert matrix; 3KD- Full three level factorial design.
14
Conclusions The literature survey carried out during the execution of this study revealed that the multivariate optimization techniques have often been used in the development of food analysis methods. In this context, the central composite design is one of the most employed, although it has lower efficiency than the Doehlert matrix and Box Behnken design. Also, this work revealed that the procedures developed for food analysis had not evaluated the robustness, despite the importance of this parameter in the validation studies of analytical methods. The chemometric techniques have often been employed for optimization of procedures for food analysis aiming quantification of organic and inorganic species, because these tools allow the determination of the critical conditions of experimental factors of the analytical methods, considering the interaction between these, with lower consumption of reagents and lower time spent during the optimization step. Additionally, separation and preconcentration procedures for multi-element determinations have been optimized using multiple response functions establishing compromises between the analytes. Acknowledgements Authors are grateful to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), to the Fundação de Amparo à Pesquisa do Estado da Bahia (FAPESB) and to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for providing grants and fellowships and for financial support.
15
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Highlights Chemometric techniques employed for optimization in food analysis are shown. Description, advantages, and drawbacks of the experimental designs are presented. A comparison between the response surface methodologies for food analysis has been performed.
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