Different biological materials of animal and plant origin (Figure 1) were used in this study. These are:

• Tubers of Dioscorea cayenensis, coming from the Plateaux department, precisely from Gamboma, and bought at the local market of Mati in the Texaco district in the north-east of Brazzaville;

• Pulses, in particular the Pigeon pea known under the scientific name Cajanus cajan, coming from the department of Bouenza and bought from the local market of Total in Bacongo, southwest of Brazzaville;

• Cereal grains of corn (Zea mays) coming from Loudima department of Bouenza in the south-west of Congo and bought from the Mati market of Texaco in the north-east of Brazzaville, which served us as malt;

• And fresh herring fish (Clupea harengus), bought in the city of Pointe-Noire in the department of Kouilou in the southwest of the country.

Before formulating the infant composite flours from the response surface by using the Box-Behnken matrix, we first proceeded separately to the elaboration of Yam, Pigeon pea and Herring flours following several unitary operations.

The optimization of the formulation conditions of infant flours was performed with the response surface method (RSM). A three-level Box-Behnken matrix was employed in this regard. Yam flour (X₁), herring flour (X₂) and pigeon pea flour (X₃) were chosen for the independent variables. The coded and uncoded independent variables and their levels are presented in Table 1. The independent variables and their ranges were selected on the basis of screening against chemical composition.

Experiments were designed according to the Box-Benhken centered matrix using Minitab software (Minitab, version 2011, n˚17.3.1.). The entire design consisted of 15 separate trials where the experimental conditions varied in a programmed manner in a completely randomized order (Table 2). Three replicates (experiments 13 - 15) in the center of the domain were conducted to determine the experimental error (analysis of variance), which error is incorporated in the calculation of the factor effects estimate. Taking into account the standard nutritional composition per 100 g of complement food [21] cited by Nago [22], eight (08) dependent variables or response noted Y contents of water (Y₁), ash (Y₂), oil (Y₃), protein (Y₄), sugar (Y₅), amount of total energy (Y₆), fiber (Y₇) and finally water absorption capacity (Y₈) were considered to evaluate the influence of independent variables on the composition of infant flour.

It should be noted that in the 15 distinct formulations, ten grams (10 g) of corn malt was incorporated in order to make the composite flour caloric and digestible, better yet infant.

A second order polynomial equation was used to express the different responses as a function of the independent variables as follows:

Y = a 0 + a 1 X 1 + a 2 X 2 + a 3 X 3 + a 12 X 1 X 2 + a 13 X 1 X 3 + a 23 X 2 X 3     + a 11 X 1 2 + a 22 X 2 2 + a 33 X 3 2 (1)

where Y represents the response variables; a₀ is a constant that fixes the response at the center point of the experiment; a₁, a₂, and a₃ represent the regression coefficients for the linear effect terms; a 1 2 , a 2 2 , and a 3 2 are the quadratic effect terms; and a₁₂, a₁₃, and a₂₃ are the interaction effect terms, coded independent variables, respectively.

Minitab software (Minitab, version 2011, n˚17.3.1.) was used to determine the

analysis of variance (ANOVA) and coefficient of determination (R²) to estimate model fit.

The significance of each coefficient was determined using the F-test and the value (p < 0.05) and the non-significant coefficients were removed to obtain a reduced model. The corresponding variables would be more significant if the absolute F-value becomes higher and the p-value becomes smaller [23] [24].

The relationship between the independent variables (X₁, X₂, and X₃) and the variable response (Y₁ to Y₈) was demonstrated by graphical representations of the 3- and 2-D response surface plots and isoresponse curves (Figure 2), respectively, generated by Minitab software, in order to derive the optimal conditions.

The analyses carried out were related to:

• Dry matter: where it was determined after drying by placing 5 g of sample in an oven at 105˚C for 24 hours [25];

• Total ash: where it was obtained after incineration of the powder sample in a muffle furnace heated to 450˚C - 550˚C for 8 h [25];

• Lipid content: where this is obtained after extraction by soxhlet with hexane for 6 h [25];

• Protein content: it is determined by measuring the total nitrogen present in the samples according to the Kjeldahl method [26];

• Total carbohydrate content: which was deduced by difference by the method of Egan et al. [27] according to the formula:

Carbohydraterate ( % ) = 100 − [ P ( % ) + L ( % ) + Te ( % ) + C ( % ) ] (2)

• Energy value: To determine the theoretical caloric value of infant formula, the products of the major constituents (carbohydrates, proteins, lipids) were summed with their Atwater heat coefficients [28] according to the formula:

Energyvalue ( Kcal / 100   g ) = ( % Carbohydrates × 4 ) + ( % Proteins × 4 ) + ( % Lipids × 4 ) (3)

• Determination of dietary fiber: it was done by a chemical method adapted to the laboratory. We have weighed one gram (1 g) of flour in a flask to which 100 mL of sulfuric acid 0.25 N were poured. The mixture was boiled under reflux for 30 min. Then 100 mL of 0.31 N sodium hydroxide was added and heated for 30 min. The extract obtained is filtered through a Whatman filter paper. Once recovered, it is dried in an oven at 130˚C for 2 h. The dry residue is then incinerated in a muffle furnace at 600˚C for 30 min and weighed for determination of the crude fiber content.

• Water absorption capacity (WAC) of the flours: it was evaluated according to the method described by Phillips R. D et al. [29].

A Box-Behnken matrix (BBD) design was used to elucidate the main effects and interactions of the parameters involved in the formulation of infant flours: influence of the amount of yam flour (X₁: 40 - 50 g), herring flour (X₂: 10 - 20 g) and pigeon pea flour (X₃: 20 - 30 g).

The eight responses of interest and the results of 15 experimental trials using the BBD design (Table 3), which include part of the design and observed experimental responses. The water and ash contents range from 3.364% - 10.214% and 0.789% - 4.668% respectively. The highest water content (10.214%) was obtained under the experimental conditions of X₁ = 40 g, X₂ = 20 g and X₃ = 25 g; while the lowest ash content (0.789%) was obtained under the conditions X₁ = 20 mL/g, X₂ = 55˚C and X₃ = 100 min. The results of Table 3 indicate that according to the standard of the global composition of infant flours (WC fixed at 5% and AC at 2%), only experiences 6, 7 and 11 for MC; 1, 3, 12 and 14 for AC meet the standard. In the same spirit of analysis, the values of LP, PC, CC, E, FC and WAC vary respectively from: 3.311% - 7.725%.; 8.400% - 16.713%; 66.864% - 78.216%; 359.598 - 630.077 Calories; 0.007% - 0.065% and finally 102 - 283 (no

MC: Moisture content; AC: Ash content; LC: Lipid content; PC: Protein content; CC: Carbohydrates content; E: Energie; FC: Fiber content; WAC: Water absorption capacity.

unit). Still in relation to the standard norm in LC (≥7%), PC (≥13%), and E (~400 Cal), five experiments for each and respectively responses (1, 4, 7, 12, and 14); (3, 4, 12, 13, and 14); (4, 6, 12, 14, and 14) are in agreement. As for the CC (norm equal to 68%) and FC (norm 5%) respectively four (4, 12, 13, and 14) and all 15 experiments obey this same norm. On the other hand, there is no norm for the WAC. Therefore, an optimization process was highlighted, in order to obtain the formulation meeting the desirable criteria of infant flours.

Tables 4(a)-(c) summarizes the ANOVA results, including the coded regression coefficients for the second-order polynomial equation, coefficients of determination (R²), and F and p-values for the response variables MC (Y₁), AC (Y₂), LC (Y₃), PC (Y₄), CC (Y₅), E (Y₆), FC (Y₇), and WAC (Y₈) under different formulation conditions. Most of the R² values of the response variables being ≥ 0.6; the developed quadratic models can be considered as valid or adequate models [30] [31]. This indicates that the regression model well explains the influence of the independent variables on the responses of the formulated infant flours. The quadratic models adjusted for the eight responses in coded variables are given in

a₀ is the constant, a_i. a_ii and a_ij are the linear, quadratic and interactive coefficients of the polynomial quadratic equation, respectively; R²: Coefficient of determination; F: Fisher’s test of equality of two variances; p: probability of obtaining the results of a test (limit value of p = 0.05).

a₀ is the constant, a_i. a_ii and a_ij are the linear, quadratic and interactive coefficients of the polynomial quadratic equation, respectively; R²: Coefficient of determination; F: Fisher’s test of equality of two variances; p: probability of obtaining the results of a test (limit value of p = 0.05).

a₀ is the constant, a_i. a_ii and a_ij are the linear, quadratic and interactive coefficients of the polynomial quadratic equation, respectively; R²: Coefficient of determination; F: Fisher’s test of equality of two variances; p: probability of obtaining the results of a test (limit value of p = 0.05).

Equations (4)-(11) as follows:

Y 1 = 7.874 − 0.136 X 1 + 0.291 X 2 − 0.162 X 3 − 0.596 X 1 X 2 + 1.490 X 1 X 3     + 0.682 X 2 X 3 − 0.014 X 1 2 + 1.159 X 2 2 − 2.224 X 3 2 (4)

Y 2 = 3.369 + 0.378 X 1 − 0.099 X 2 − 0.297 X 3 − 0.392 X 1 X 2 + 0.335 X 1 X 3     − 0.440 X 2 X 3 − 0.300 X 1 2 − 0.654 X 2 2 − 0.824 X 3 2 (5)

Y 3 = 6.065 − 0.124 X 1 + 1.035 X 2 − 0.488 X 3 + 0.966 X 1 X 2 − 0.733 X 1 X 3     − 0.543 X 2 X 3 − 0.952 X 1 2 − 0.647 X 2 2 + 0.598 X 3 2 (6)

Y 4 = 13.212 + 0.823 X 1 + 1.800 X 2 + 1.156 X 3 − 0.655 X 1 X 2 + 0.410 X 1 X 3     + 1.562 X 2 X 3 − 1.212 X 1 2 − 0.363 X 2 2 − 1.855 X 3 2 (7)

Y 5 = 69.48 − 0.941 X 1 − 3.027 X 2 − 0.185 X 3 + 0.68 X 1 X 2 − 1.50 X 1 X 3     − 1.26 X 2 X 3 + 2.48 X 1 2 + 0.50 X 2 2 + 4.31 X 3 2 (8)

Y 6 = 385.4 + 0.100 X 1 + 33.500 X 2 − 22.500 X 3 + 12.100 X 1 X 2 − 11.000 X 1 X 3     − 65.100 X 2 X 3 − 35.900 X 1 2 − 23.800 X 2 2 + 47.600 X 3 2 (9)

Y 7 = 0.040 + 0.001 X 1 + 0.002 X 2 + 0.013 X 3 − 0.001 X 1 X 2 + 0.003 X 1 X 3     + 0.001 X 2 X 3 + 0.002 X 1 2 − 0.018 X 2 2 − 0.007 X 3 2 (10)

Y 8 = 178.2 − 10.400 X 1 + 25.300 X 2 − 48.900 X 3 − 9.900 X 1 X 2 − 16.500 X 1 X 3     − 13.900 X 2 X 3 + 22.100 X 1 2 − 20.7000 X 2 2 − 1.300 X 3 2 (11)

To visualize the effect of the independent variables on the dependent variables, contour curve plots (2-D) and response surface plots (3-D) (Figure 2) of the quadric polynomial models were generated by varying two of the independent variables in the experimental range while holding one of the variables constant at its respective lowest, middle, and highest level.

The response surface method effectively identifies the optimal values of the independent variables so that the responses are maximized by taking into account the nutritional value of the components of the supplemental infant flours following the codex alimentarius recommended standard [32] and the standard norm Nago [22] cited by Adjadogbedji [33].

Optimizing the conditions composite infant flour production was achieved using a multiple response method called desirability [35] [36]. This method involves transforming each response variable (Y_i) into an individual desirability function (d_i). This method looks for a combination of factor levels that jointly optimize a set of responses by satisfying the requirements for each response in the set. The scale of the desirability function ranges from 0 to 1; d = 0, for a totally undesirable response, to d = 1 for a fully desired response above which further improvements would not matter [37].

Individual desires (d) for each response were obtained by specifying the goals and limits required for each response. There were three goals to choose from: minimize the response, target the response, or maximize the response. The upper and lower bounds for each objective should also be specified. A weighting factor, which defines the shape of the desirability function for each response, was then assigned for each response. The weights should be between 0.1 and 10, with higher weights corresponding to more important responses and lower weights corresponding to less important responses. Once the individual desirabilities were calculated for each response, they were combined to provide a composite desirability measure of the multiple response system. This composite desirability measure is the weighted geometric mean of the individual desirabilities or responses [38].

In order to optimize the response, and with reference to the standard nutritional composition for 100 g of complement flour, the objectives were to individually target the values of the MC, AC, LC, PC, CC, and E responses relative to this standard; to maximize FC and then minimize WAC. Goal setting, lower and upper limits, weights, and individual importance are shown in Table 5. For MC, the goal is to obtain a value equal to or close to the 5% target value. Values below 3.364 or above 10.214% are not acceptable. For AC, the goal is to obtain a value equal to or close to the 2% target value. Values below 0.789 or above 4.668% are not acceptable. The objectives for LC, PC, CC, and E were to obtain target values or close to 7%, 13%, 68%, and 400 calories, respectively. For each of the latter responses, values below 2.667 or above 7.725%; below 8.400 or above 16.712%; below 66.864 or above 78.216%; and below 359.598 or above 630.077 calories, respectively, were not acceptable. The objective for FC is to maximize the value where 0.065% or more is considered excellent, while those below 0.007% are not acceptable. Finally, the objective for the WAC is to minimize the value. A value

I D: Individual Desirability; Va: adjusted value; DC: Desirability Composit.

of 102.381% or less is considered excellent, while those above 283.333% are not acceptable.

All responses have the same importance value of 1 on the composite desirability. In other words, the quality of the flour is equally dependent on all evaluated responses.

From the optimization parameters, the optimal conditions for the composite infant flour formulation are obtained along with the predicted response values shown in Table 6. The individual desirability of MC, AC, LC, PC, E and WAC is 0.999; 0.895; 0.995; 0.923; 0.995 and 0.883 respectively, whereas individual desirability of CC and FC were much lower at 0.564 and 0.671 respectively. The composite desirability was evaluated at 0.850. The optimal formulation conditions for infant-type flour correspond to 46.263 g of yam flour (X₁), 15.859 g of herring flour (X₂) and 30.00 g of pigeon pea flour (X₃).

Figure 3 shows predicted responses generated from the optimized factors. Each column and row of the graph corresponds to a factor and a response variable, respectively. The upper and lower limits of the factors and the current factor setting in parentheses or square brackets are displayed in the top row. The response objective, the expected response to the current factor settings, y, and the individual desirability, d, are shown in the left column.

The vertical and horizontal lines on the graph represent the current factor parameters and response values, respectively. In general, when increasing the amount of yam flour, the MC, AC, PC and FC responses increase, while LC, CC,

E and WAC decrease. Increasing herring meal decreased energy, ash, carbohydrate, while the other responses increased. There was only an increase in fiber, protein and lipids as the pigeon pea meal load increased while the other responses decreased.