## 3 Results and Discussion
### Physical Properties of Bread and Optimization of the Bread Formulation through Experimental Design
Hardness decreased as the maize proportion increased, and very small changes were observed with the xanthan proportion (Figure 2i). In general, springiness and specific volume values were higher at higher hydration levels, while hardness was higher at lower hydration levels. Table 2 shows the results of the optimization of the variables (specific volume, springiness, and hardness) by desirability function. The maximum predicted response for specific volume was 1.728 using 100% maize, 100% psyllium husk, and 102.41% hydration, with a desirability of 0.844, while the predicted responses for springiness and hardness were 0.841 and 1561.066, respectively, both with a desirability of 1. At those optimum formulations, the theoretical or predicted values of all dependent variables were estimated using the second-order polynomial equations developed (Table 2). The average values obtained experimentally for the specific volume were 1.45 cm\({}^{3}\)/g, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{\begin{tabular}{c} **X\({}_{1}\)** \\ **(Maize Flour** \\ **Proportion**) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **X\({}_{2}\)** \\ **(Xanthan Gum** \\ **Proportion**) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **X\({}_{3}\)** \\ **(Hydration** \\ **Percentage**) \\ \end{tabular} } & \multirow{2}{*}{**Desirability**} & \multirow{2}{*}{\begin{tabular}{c} **Predicted** \\ **Response** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Experimental** \\ **Values** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **\% Error * \\ **\end{tabular} } \\ \hline
**Specific volume (cm\({}^{3}\)/g)** & 100.00 & 0.00 & 102.41 & 0.84 & 1.73 & 1.45 \(\pm\) 0.07 & 16\% \\
**Springiness** & 67.23 & 86.60 & 117.66 & 1.00 & 0.84 & 0.73 \(\pm\) 0.02 & 13\% \\
**Hardness (g)** & 75.11 & 78.33 & 98.89 & 1.00 & 1561 & 2944 \(\pm\) 109 & 88\% \\ \hline \hline \end{tabular}  
* \(\%\)Error = 100 \(\times\) (experimental value-predicted value)/predicted value.  
\end{table} 
Table 2: Optimization of variables (specific volume, springiness, and hardness) by desirability function. Figure 2: 3D response surface graphs of the effect of hydration and xanthan percentage on (**a**) springiness, (**b**) specific volume, (**c**) hardness; effect of maize proportions and hydration on (**d**) springiness, (**e**) specific volume, (**f**) hardness; effect of maize proportions and xanthan percentage on (**g**) springiness, (**h**) specific volume, (**i**) hardness. springiness had a mean value of 0.73, and hardness presented 2944 g. A variation of 16, 13, and 88% was observed between the predicted maximum value and the experimental maximum for these variables, respectively. The results for specific volume and springiness had some agreement with respect to the predicted values from the optimization analysis using the desirability function. However, in the case of hardness, they did not confirm the adequacy of the response model, and it did not achieve the expected optimization. Based on these results, the final conditions that allowed the production of bread with greater springiness were selected, since this was the variable that presented the lowest percentage of error. In this sense, based on the results obtained from the optimization of the experimental design, the final bread formulation selected was the following: 67% maize flour, 33% buckwheat flour, 87% xanthan gum, 13% psyllium husk, and 118% hydration (Table 2). This formulation was called B-ED. However, despite obtaining gluten-free bread with good springiness, some sensory defects were detected that could affect the acceptability of the product. Therefore, the formulation was modified in order to obtain the best springiness based on the information described by other authors [13], which revealed that many gluten-free bread products are also formulated with other ingredients, such as oil and sugar, as well as with a higher percentage of yeast than that initially used in the first experiments (1.5%).