*3.2. Processing Parameter Optimization and Their E*ff*ect on the Safety and Quality of the Formulated Matrix*

The best processing conditions for treating chokeberry milkshakes when HPP is combined with added by-products with antimicrobial and antioxidant properties (chokeberry pomace) were studied by RSM. This methodology uses a sequence of designed experiments to obtain an optimal response.

First, the estimated effects of each factor (pressure, time, and concentration) and their interactions were analyzed (Figure 3). The response function for the factors and the adjusted regression coefficient (*R*<sup>2</sup> adjusted), showing the percentage of variation in the response explained by the fitted model, is shown in Equations (1)–(3) (pressure (P), time (t), chokeberry pomace concentration (C)). The value of the adjusted *R*<sup>2</sup> close to one indicates a high correlation between the experimental and fitted values.

**Figure 3.** Estimated effects of each factor (pressure, time, and concentration) and their interactions with TPC (**a**), AC (**b**), and *L. monocytogenes* inactivation (**c**) where + or − means a positive or negative relation between factor (pressure, time or concentration) and response (TPC, AC or L. monocytogenes survival fraction), respectively. A: pressure, B: time and C: concentration. The combination of letters (AA, BB, AB ... ) refer to the interactions carried out in the analysis.

$$\text{TPC} = 25.6475 + 11.2687 \times \text{C} \qquad \qquad R^2 \text{adj} = 0.85 \tag{1}$$

$$\text{AC} = 2.08477 + 1.38395 \times \text{C} \qquad \qquad R^2 \text{adj} = 0.80 \tag{2}$$

$$\mathrm{Log}\_{10}\left(\frac{\mathrm{N}}{\mathrm{N}\_{0}}\right) = -0.160277 + 0.000618685 \times \mathrm{P} + 0.285165 \times \mathrm{t} - 0.00123019 \times \mathrm{P} \times \mathrm{t} \quad R^2 \mathrm{adj} = 0.76 \tag{3}$$

Figure 3 shows the pareto chart for TPC, AC, and microbial inactivation. This chart determines the magnitude and the importance of the effects. The bars that extend beyond the line correspond to effects that are statistically significant with a 95.0% confidence level. The factor "pomace concentration in milkshakes" is the only factor that significantly affects TPC and AC concentration. However, the results in Table 2 show TPC and AC are influenced by all the factors, including time and pressure. Chokeberry pomace has been reported as a berry fruit with high phenolic content [8]. Thus, though it could exist with the effect of pressure and time, the results could be masked by the natural high phenolic content.

The low effect of treatment conditions on TPC and AC could be explained by using milk as a liquid medium. High pressure processing induces physicochemical and technological changes in milk properties. When HPP is applied to milk, the casein micelles are disintegrated into casein particles of smaller size, which is accompanied by an increase in casein and calcium phosphate levels in the serum phase of milk and by a decrease in both non-casein nitrogen and serum nitrogen fractions [18,53]. In addition, interactions between polyphenols and milk proteins have been previously described by other researchers [54–56]. In our work, these interactions could be favored by the changes in the casein structure due to HPP treatment, which would lead to the formation of complexes that restrict the accessibility of analysis, leading to lower AC and TPC and a non-significant effect of treatment conditions (pressures and time). Tadapaneni et al. [57] also observed this effect in strawberry-based beverages treated with HPP at pressures ranging from 200 to 600 MPa. They saw, when formulated with milk instead of water, the beverage presented reduced levels of AC and anthocyanins because of complexes forming between polyphenols and milk proteins. Therefore, as the effect of concentration is so pronounced in RSM and polyphenol–milk protein interactions may exist, decreasing the AC and TPC, the effect of the other parameters is much lower, leading to a non-significant effect of time and pressure.

In contrast, pressure and time are the parameters with a significant effect on the microbiological inactivation. Thus, the chokeberry pomace concentration added to the milkshake, does not have a significant effect on the inactivation results. These results confirm the hypothesis explained above (Figure 2); there is an antimicrobial effect of berry pomace. However, it is masked with the protective effect of milk on *L. monocytogenes* cells, giving as a lower inactivation result than with similar treatment conditions in products with a natural antimicrobial agents, yet without milk [49]. Despite the protective effect of milk on microorganisms, adding chokeberry pomace could help achieve higher inactivation levels than HPP without the pomace.

Once the estimated effect and its interaction were analyzed, the response optimization was carried out. The results show that the optimized factors are 500 MPa for 10 min in milk with 10% (*w*/*v*) of chokeberry pomace (Table 3). This treatment condition ensures the maximum TPC and AC with the minimum microbiological survival.


**Table 3.** Predicted and limit response values for optimum treatment conditions.

The optimum treatment conditions are the same as those of the experimental design. When comparing the results in Table 2 with the predicted values in Table 3, we see that experimental results are like the predicted values through optimization. Therefore, the RSM is proven to be a reliable tool to predict the behavior of the sample studied in terms of AC, TPC, and microbial inactivation.
