## 3 Results and Discussion
### 3.6. Dough Rheological Properties during Heating
#### 3.6.2 Starch Gelatinization  
The regression model obtained for C3 torque, which represent maximum consistency during starch gelatinization process that occurs when dough is heated above 60 \({}^{\circ}\)C is presented in Equation (11):  
\[\text{C3 }=1.86\ +0.0397\cdot\text{X}_{1}-0.1090\cdot\text{X}_{2}\ +0.0236\cdot\text{X}_{1}\cdot\text{X}_{2}\ -0.0223\cdot\text{X}_{1}^{2}-0.0085\cdot\text{X}_{2}^{2} \tag{11}\]  
The quadratic regression equation was fitted (\(p<0.0001\)) for prediction of factors' effects on C3 torque and showed a high coefficient of determination (\(R^{2}=0.96\)).The linear coefficient of the QF addition level indicated a highly significant negative effect (\(p<0.0001\)) on the torque C3, while particle  
Figure 2: Response surface graph for combined effects of quinoa flour particle size and level added in refined wheat flour on Mixolab parameters during protein weakening stage: (**a**) C2 torque (C2) and (**b**) difference between torques C1 and C2 (C1–2). size had a positive effect (\(p<0.005\)). It was observed that interaction between PS and QF addition level had a significant effect (\(p<0.05\)) on C3. Similar observations regarding particle size effect on the starch gelatinization process were reported by [PERSON] et al. (2019) [28] for quinoa flour and may be due to low amylose content compared to the control. [PERSON] et al. (2017) [77] showed that nonstarch components such as lipids, proteins and dietary fibers could restrict swelling and gelatinization during cooking, in addition to a diluting effect due to the interaction with starch polymers (lipids and proteins), and to the competition for water (proteins and dietary fiber), interfering with starch swelling. As observed in Figure 3a, C3 gradually decreased with the QF substitution increase, and a higher level of QF (\(20\%\)) addition in wheat flour led to a decreased value for C3 torque (\(1.67\) N \(\cdot\) m) in the case of smaller particle size. This behavior could be related to the amylase activity of quinoa flour and the amylose-lipid complexes formed during heating of starch slurries. The results are in agreement with those obtained when amaranth was added in wheat flour [43]. The C3 torque decreased when the particle size of quinoa flour decreased. This was expected because the small particles fraction was a starch-rich particle and lead to a lower C3 torque compared to coarse particles that are fiber-rich particle fractions. Similar observations were reported by [PERSON] et al. (2020) [1] and, [PERSON] (2017) [76]. Additionally, the medium and small fractions had less carbohydrates content compared to large particle size fractions (Table 2). The small particle sizes presented large surfaces and competed with starch granules from wheat flour, contributing to lower dough viscosity. An opposite trend was reported by [PERSON] et al. (2019) [28] for larger particles of QF which led to a higher pasting viscosity explained by the smaller surface area with lower swelling. The differences among studied particle fractions was affected by their composition and might be due to the particle microstructure of the quinoa-starch that govern water absorption and swelling. The effects of particle size and QF addition level in wheat flour on the difference between C3 and C2 torques (C3-2) is described by Equation (12):  
\[\text{C3}-2\ =1.36\ +0.0252\text{:}\ \text{X}_{1}-0.0827\text{:}\ \text{X}_{2}\ +0.0165\text{:}\ \text{X}_{1}\cdot\text{X}_{2}\ -0.0160\text{:}\ \text{X}_{1}^{2}\ -0.0231\text{:}\ \text{X}_{2}^{2} \tag{12}\]  
The quadratic model represented the experimental data of C3-2 very well with a high \(R^{2}\) value (0.98). The linear terms of particle size and QF addition level in wheat flour on C3-2 were significant (\(p<0.0001\)). C3-2 was significantly correlated (\(p<0.05\)) with the quadratic effect of particle size and the interaction effect of particle size and QF addition level in wheat flour.