## 3 Results and Discussion
### Optimization of Parameters and Validation of the Models
\[\text{Color (C*)}=17.715+1.100\text{A***} \tag{5}\]  
Fracturability (g) is the maximum force needed to break a pasta piece [35; 37]. The fracturability of dried pasta decreases with the increase of the addition of spent grain; the linear term had the greatest negative effect on the response, while the quadratic term had a significant positive effect on the dry pasta fracturability (Equation (6)). The decrease of fracturability with spent grain addition is shown in Figure 1D; the enriched fish pasta had the same decrease of fracturability, possibly because of the fiber content or fat composition of each assortment of the pasta [49]. [PERSON] and [PERSON] showed that the addition of spent grain in corn snacks decreased the fracturability of the products [15]. \[\text{Fracturability}=3635.83-2505.19\text{A***}+1909.53\text{A2***} \tag{6}\]  
A protein content increase with spent grain addition can be observed in Figure 1E. Pasta proteins were significantly influenced by the linear and quadratic terms in Equation (7). This tendency for protein levels to increase with increased levels of added spent grain was also observed in other studies [45; 50]. \[\text{Proteins}=6.658+1.115\text{A***}+0.192\text{A}^{2}\text{**} \tag{7}\]  
A total dietary fiber increase with spent grain addition can be observed in Figure 1F. The total dietary fiber of pasta was significantly influenced by the linear term in Equation (8). [PERSON] et al. obtained an increased total dietary fiber content with the increase of spent grain in pasta production [32]. The same results were obtained in other studies [14; 31; 45; 46; 50; 51]. \[\text{Total dietary fiber}=36.244+1.483\text{A***} \tag{8}\]  
The total phenolic content increased with spent grain addition (Figure 1G), and from Equation (9), it can be observed that the linear term had the highest positive effect and the quadratic term had a significant negative effect on the response. Spelt pasta can be used to produce precooked pasta with a high content of biologically active compounds compared to refined flour [14]. Pasta supplemented with native spent grain or fermented spent grain had an increase in phenolic content [34]. [PERSON] et al. obtained fortified spent grain pasta with an increase in phenolic content [33]. \[\text{Total phenolic content}=22.023+2.728\text{A***}-1.875\text{A}^{2}\text{***} \tag{9}\]  
An antioxidant activity increase with spent grain addition can be observed in Figure 1H. The DPPH test was significantly influenced by the linear and quadratic terms in Equation (10). In their study, [PERSON] and [PERSON] obtained snacks with 10-40% spent grain addition, which increased the phenolic content and antioxidant activity [52]. [PERSON] et al. obtained spent grain pasta with a total antioxidant capacity of up to 19% compared with the control durum flour pasta [48]. \[\text{Antioxidant activity}=20.654+9.327\text{A***}+5.901\text{A}^{2}\text{***} \tag{10}\]  
A value below 12% of cooking loss indicates good quality products, and cooking loss is considered an indicator of the general cooking performance of pasta [53; 54; 55]. Cooking loss increased with the increase of spent grain addition (Figure 1I), but cooking losses were below the values reported for good quality durum wheat pasta (<7%) [56]. The linear term had the most significant positive effect, as can be seen in Equation (11). Cooking loss increases as cohesiveness decreases, according to [PERSON] et al. [53]. Pasta rich in fiber tends to have a higher cooking loss, probably due to the weakening of the protein network by the presence of fiber content [32]. According to [PERSON] et al., as the amount of protein and fiber increased in the pasta recipe, the cooking loss increased [27]. \[\text{Cooking loss}=6.026+0.972\text{A}*** \tag{11}\]  
The predicted results for the responses were verified, and differences of \(\leq\)5% were obtained between the predicted and verified values.