Introduction

Currently, in all industries the optimization of processes is essential to establish the best operating parameters, obtaining better results and at the same time, saving costs and production time. For this, it is necessary to apply mathematical and statistical methods with scientific validity^{1, 2} that help predict the behavior of the variables of interest.³ Before the 1950s, techniques were used that only analyzed one independent variable at a time, omitting the influence of the others,^4-6 generating inaccurate results and requiring many experiments. To compensate for this, the response surface methodology (RSM) arises, a modeling technique used in the chemical, pharmaceutical⁷ and food industries, biological and medical sciences,¹ in construction, manufacturing and soil mechanics,³ due to its versatility,⁸ since it can evaluate multiple independent variables and even their interaction, essential to know their additive, synergic and/or antagonistic effects on one or more responses,^9-12 very useful for predictions and process improvements,^{13, 14} and a better interpretation.¹⁵ Additionally, for its application it is sufficient to have a minimum number of experiments, without affecting the results.^16-18 In addition, when generating a mathematical equation, it can be validated to confirm its effectiveness.¹⁹

In recent years, the application of RSM in food processes has been extensively studied and, despite promising results, optimization in this field remains a challenge due to the complexity and dynamics of the products. In this context, the objective of this review is to analyze the current state of RSM in the extraction of agri-food compounds, previously knowing the fundamentals to understand the technique. In addition, the disadvantages and limitations of the technique will be determined, which is essential to know in order to avoid possible negative effects on the results.

Fundamentals of RSM

In an experimental design, there are independent variables or also called factors, which have an influence on the dependent or response variables. The standard equation (Eq.) (1) to find the response of interest (y) is given by the different factors (x), with their respective coefficients (f), in addition to an estimated error value (ε).¹

For a better analysis, the values of each factor are coded and standardized,¹⁷ with values ​​that generally oscillate between -1 and +1,²⁰ following the Eq. (2), where the coded variable (X) is generated from the actual variable (x) with its minimum and maximum value (or level).

Steps for RSM Application

The steps, based on the proposals of different researchers, ^{1, 2, 8, 11, 14, 17, 20} have been synthesized in a concise way, divided into four stages (Figure 1).

Figure 1: RSM Flowchart. Click here to view Figure

A crucial step is the statistical validation of the model. If it is not adequate, the irrelevant factors must be filtered out and the experimental runs must be repeated.

Identification of Variables

The main step is to establish the dependent and independent variable(s), determining significant factors to reduce the number of experiments and improve modeling.^{17, 18, 20, 21}

Selection of a Response Surface Design

RSM is bases on Box-Behnken Design (BBD) and  Central Composite Design (CCD),^{11, 17, 19} among other derivates such as Face-Centered CCD (FCCCD), Rotable CCD (RCCD),²⁰ Cube Style CCD (CSCCD) and Spherical CCD (SCCD).² BBD and CCD are 3^k and 5^k designs, respectively that provide 3 and 5 levels for each “k” or factor.^20-22 With Eq. (3) and Eq. (4) we obtain the number of experiments applying BBD and CCD, where C₀ is the number of central points set.¹⁹

It is necessary to indicate that the designs are adjusted from Eq. (1) to first-degree and second-degree models, which, their form is given by Eq. (5) and Eq. (6), respectively, where x are the factors and β are their coefficients, β₀ is the intercept coefficient and ε is the error.¹⁴ In addition, the model changes due to the interactions, applying the Eq. (7), where β₀, β_i, β_ii and β_ij are the intercept, linear, quadratic and interaction coefficients.⁶

Construction and Evaluation of the Best Mathematical Model

When the model is selected, it must be statistically verified whether it correctly represents the relationship between the variables.²¹ For this purpose, analysis of variance (ANOVA) is performed, which evaluates the precision of the predictive model through the coefficient of determination (R²).¹¹ In addition, other techniques are also used, such as lack of fit test, mean absolute deviation and  residual analysis. Due to the interest in optimizing the different responses of a food process, there is a multi-criteria methodology called desirability function²⁰ that combines the values of each partial desirability (dnYn)  to generate the overall desirability (D),²³ which is the geometric mean, according to Eq. (8).²⁴

Model Plots and Determination of the Optimal Conditions

The next step is to generate the contour (two-dimensional) and surface (three-dimensional) response graphs to better observe the significant relationship between input and output variables.^{12, 14} The values are estimated, but since they are as close as possible to the real ones, it is sufficient for a good interpretation.²⁰ Once the graphs have been obtained, the optimal conditions are determined using Eq. (9), considering that the optimum value is not necessarily the maximum;¹⁷ for example, in the research of Louhichi et al.,¹² concerning the treatment of vegetable oil refinery wastewater, the objective was to achieve the lowest values of chemical oxygen demand and turbidity.

In the end, the validity of the generated equation must be confirmed. The difference between the predicted and experimental responses must be less than 5%.²⁰

RSM in the Extraction of Agri-Food Compounds

In the food industry, RSM has been used in enzymatic hydrolysis, clarification,¹ metabolite production,²⁰ microencapsulation,^{22, 25} product improvement and formulation, ^26-28 in thermal treatments such as cooking²³, non-thermal treatments such as osmotic drying²⁹ and plasma cold, ^30-32 in wastewater treatment, ^{12, 16} in packaging, ^{22, 33, 34} in germination³⁵ and especially in the extraction of compounds,^{19, 36} due to their properties and potential applications, mainly in the food and pharmacological fields.³⁷

There are thermal extraction techniques or called conventional solid-liquid, but there are also non-thermal techniques, more efficient and they have less impact on food quality.³⁸ Regarding the compounds to be extracted, they can be polysaccharides, proteins, oils, pigments, hydrocolloids or polyphenols, which are the most studied.³⁹ Regardless of the extraction method or the target compound, determining the best process conditions is a tedious task⁴⁰ and, therefore, optimization with techniques such as RSM is indispensable. In this context, in recent years, the number of investigations on its application in this field has increased substantially. For a better analysis, a recent summary is shown in Table 1.

In the extraction there are many variables that affect the response (s); the most common are time, temperature, pH, type, concentration and proportion of the solvent.⁵ There are also specific variables such as power in the case of microwave extraction. All the factors have an influence individually, but as mentioned, it is also essential to understand the effect of their interaction, in order to interpret the process as a whole. As shown in Table 1, temperature is one of the most significant factors, but it is affected when its value is very high, which is a limitation; However, it is not inconvenient for emerging techniques such as vacuum-ultrasound assisted enzymatic extraction, pulsed electric fields assisted extraction and atmospheric cold plasm assisted extraction, in which other variables have a greater influence, such as enzyme concentration, pressure and power, which, in general, soften, permeabilize and break down the matrix tissues, facilitating mass transfer without the use of high temperatures.⁴¹ Consequently, the compounds are not affected, increasing the extraction yield.

Some characteristics resulting from the conditioning of the raw material, such as particle size and shape after grinding, can also be considered as a factor.⁴⁰ In this sense, Chanioti et al.¹³ evaluated the influence of particle size of olive pomace in the ultrasound assisted extraction of oil, unsaponifiable matter and polyphenols. The optimal conditions using BBD were at 60ºC, sample/n-hexane ratio of 1:12 and 0.5 mm of particle, recovering 11.03% of oil; for the unsaponifiable matter, only at 55ºC was obtained 4.5%; regarding the content of total phenols, which was 0.261 mg GAE/g of oil, it was obtained at 50ºC, with a solid-liquid ratio of 1:8 and 0.9 mm of particle.

Table 1: Recent Findings on Application of RSM in the Extraction of Agri-Food Compounds. Click here to view Table

In other study, Ishak et al.⁵⁰ obtained 30.7% of oil from chia by optimizing with CCD the supercritical fluid extraction at 45 ºC, 335 bar, 24 s of grinding time and  100−400 μm of particle. According to Rivas et al.⁴⁸ when the particles are small, the solvent passes faster through the tissues, avoiding the innate resistance to mass transfer.

As is known, the extraction of compounds from agro-industrial by-products is common, which represent approximately 30% of the food⁵¹ and which are usually discarded,⁵ but their use affects the sustainability of the industry, reducing environmental pollution and its impact. In addition, they mainly contain antioxidants with pharmacological activity, such as polyphenols, but their yield is very low and therefore it is essential to optimize their recovery.⁵² García et al.⁵³ evaluated pressurized liquid extraction of phenols and punicalagin from pomegranate peel. They optimized it with a CCD at 200 ºC and using 77% ethanol, recovering 164.3 mg GAE/g and 17 mg of punicalagin/g dw.

Another important point is the application of the extracted compounds, especially as natural additives in other food processes. Roy et al⁵⁴ optimized the ultrasound assisted extraction of astaxanthin from the shrimp shell using deep natural eutectic solvents with a BBD. With 39 min, an amplitude of 54.43%, the HBD/HBA ratio (molar ratio of the donation of hydrogen bonds and acceptance of lactic acid) of 1:1.02, it was obtained 68.98 mg/g dw. Additionally, it was used as a plasticizer for biofilms based on chitosan, achieving high DPPH (1,1-difenil-2 picrilhidrazilo) antioxidant activity, better sensory, physical, mechanical and thermal characteristics.

Finally, extraction can focus on biological activities. Pinto et al.⁵¹ optimized the production of an extract with a high antioxidant potential from Castanea sativa shell using supercritical CO₂. With a CCD at 60ºC, 350 bar and 15% of ethanol as cosolvent, the antioxidant activity by DPPH assay was of 54.91%, with an R² of 84.817%. Subsequently, the extract was able to eliminate cancer cell lines such as Caco-2 (477.94 g/mL) and HT29-MTX (3.71 g/mL).

It is important to note that RSM can be used simultaneously with other techniques to improve optimization,⁵⁵ such as artificial neural networks (ANNs), related to the networks of the human brain. It is better in complex non-linear processes.⁷ Ciric et al.⁶ used RSM-ANNs to improve the ultrasound assisted extraction of polyphenols and flavonoids from Allium sativum L. The best parameters were at 59 ºC, for 13.5 min, using 71% methanol as solvent in a ratio of 20:1 with the sample, obtaining 19.948 mg GAE and 1.422 mg routine equivalent/g of fresh weight, with 0.9998 and 0.9885 of adjusted R², respectively. According to research of Rebollo-Hernanz et al.⁷ on the conventional extraction of polyphenols from coffee husk, RSM is first used to run the experimental runs quickly and to build and adjust the mathematical model (R²: 0.9402) that serves as the basis for ANNs; it analyzes and predicts mainly quadratic interactions, obtaining a new and more accurate model (R²: 0.9802). Considering another technique such as fuzzy logic (FL). Khamparia et al.⁵⁶ compared RSM, ANNs and FL in the conventional extraction of oleonolic acid from Ocinum sanctum, concluding that ANNs was better, followed by RSM and FL, with R² values ​​of 0.994, 0.992 and 0.703.

Regarding other methods, Sodeifian et al.⁵⁷ optimized the supercritical CO₂ extraction of essential oil from Eryngium billardieri with RSM and simulated annealing (SA), a useful algorithm for a better global optimization from the improvement of each factor. From the data obtained with RSM, thanks to SA, the kinetic behavior of the process was described, and the model was adjusted and reoptimized. A maximum yield of 0.8522% of essential oil was obtained, at 300 bar, 35ºC, 130 min and with 0.75 mm of particle size. Similarly, Vásquez-Villalobos et al.⁵⁸ optimized the conventional extraction of glucosinolates from maca (Lepidium meyenii) using RSM. They could not obtain the optimal value due to limitations of the technique, but they complemented it with genetic algorithm (GA) and finally managed to obtain a maximum of 17.1 μmol of glucosinolates/g of fresh weight, using ethanol (70.95%), sample/solvent ratio of 10:1, at 78.98 ºC and for 90 min.

Current and Future Challenges

To apply RSM, a series of steps must be carefully followed. For this, it is essential to have experience in the subject or a basic notion from previous studies, in order to make the correct choice of data and that these are close to the desired optimization; otherwise, if the range of values ​​selected is not adequate, the results will not be as expected and, therefore, the optimization will not occur in the best conditions.

Regarding the selection of the best mathematical model, it is advisable to choose for the model with the lowest degree, but that this is statistically significant. In most cases, second-degree equations are usually used, however, these do not usually represent the database and, therefore, the predicted values ​​tend to be relatively far from the experimental ones.² The main disadvantage of RSM is that the data are fitted to a second degree polynomial model due to the presence of curvatures in the process, which is incorrect because there may also be curvatures in higher degree models and even more so when considering the complexity of the extraction processes. To solve these limitations, as previously determined, RSM can be complemented with other optimization techniques such as ANNs, FL, SA and GA. Another advantage of these combinations is that with the correct description of the process dynamics, simulations can be performed, which is a current trend. This would make it possible to run an infinite number of experiments virtually, considerably reducing time and costs.

Conclusions

The application of RSM requires basic knowledge of experimental design, modeling and data validation. Currently, it is being widely used in the optimization of the extraction of bioactive compounds in the food industry, including polyphenols, carbohydrates, proteins and oils from a variety of agri-food products and using multiple extraction techniques, demonstrating the versatility and suitability of RSM. Also, according to the literature, RSM has limitations, but they can be corrected with other optimization tools, in addition to offering an enhanced technique that provides better results.

Acknowledgment

Declared none.

Funding Sources

This work is self-funded thus nothing to declare.

Conflict of Interest

The author(s) declares no conflict of interest.

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