## 3 Results and Discussion
### Validation of the ASLT Methodology in Predicting the Shelf Life of Frankfurter-Type Sausages
\begin{table}
\begin{tabular}{c c c c} \hline
**Estimated** & **Kinetic Data** & **Kinetic Data** & **Kinetic Data** \\
**Parameters** & **Whole Data Set** & **3 Temperatures** & **2 Temperatures** \\ \hline E\({}_{\text{a}}\) (kJ /mol) & 125.6 \(\pm\) 18.4 a & 116.2 \(\pm\) 35.9 a & 119.3 a \\ \hline k\({}_{\text{ref}}\) (d\({}^{-1}\)) & 0.199 \(\pm\) 0.031 a & 0.219 \(\pm\) 0.074 ab & 0.183 a \\ \hline R\({}^{2}\) & 0.959 & 0.912 & - \\ \hline \end{tabular} Different letters among columns indicate significant differences between means (\(\pm\)standard deviation) according to the mean values of [PERSON]’s post hoc comparison test for a significance level of \(p\) = 0.05.  
\end{table} 
Table 4: Parameters of the Arrhenius equation for each studied case. Figure 10: Arrhenius equation considering all kinetic data for (**a**) four, (**b**) three, and (**c**) two storage temperatures of HPP frankfurter sausages (4, 8, 12, and 18 \({}^{\circ}\)C). As indicated from the obtained results, the Arrhenius equation can adequately describe the temperature dependence of lag phase duration, even when applied for a small range of data sets (R\({}^{2}\): 0.996-0.997), without statistically significant differences among predictions. Considering the above predicted parameters, the microbial growth rate of the TVC and the shelf life of the sausage samples were predicted for a wide range of storage temperatures, and the predicted values were plotted along with the experimental ones for all the isothermal and the dynamic temperature conditions, as shown in Figures 12 and 13. Considering the shelf life stated by the manufacturers for similar commercial meat products, which is 75 days, and in conjunction with the models derived from this research, it is determined that this duration corresponds to storage temperatures of 4.2, 3.2, and 3.8 \({}^{\circ}\)C. These temperatures were calculated using the produced models, including: (i) data from all four studied storage temperatures, (ii) data from three studied storage temperatures (8, 12, and 18 \({}^{\circ}\)C), and (iii) data from two studied storage temperatures (8 and 18 \({}^{\circ}\)C). The results indicate that the models developed through the ASLT methodology could provide highly accurate and reliable predictions of the shelf life of the studied products. Consequently, these models can be utilized as valuable tools for estimating product shelf life by performing tests exclusively at higher storage temperatures, which can lead to significant time savings in the testing process. This approach not only optimizes resource use but also improves the understanding of the factors affecting product stability under various conditions, thereby facilitating more efficient product development and quality assurance practices. This study demonstrated the successful validation of the ASLT methodology for HPP meat products, specifically frankfurter-type sausages. The findings confirm ASLT as a reliable and efficient tool that replicates spoilage patterns under accelerated conditions, reducing the time and cost of traditional shelf life studies. The results show that the study also provides insights into the spoilage dynamics unique to HPP-treated products, such as the role of specific spoilage organisms like lactic acid bacteria, which inform and enhance the ASLT framework. These dual contributions--validating ASLT and refining its application for HPP products--highlight its value for the meat industry. ASLT enables faster product development, optimized resource allocation, and better management of storage and distribution conditions. This work bridges the gap between HPP technology and predictive modeling, advancing the efficiency and reliability of shelf life assessment. Figure 11: Arrhenius equation considering the lag phase of the TVC growth for the whole kinetic data set (four storage temperatures: 4, 8, 12, and 18 \({}^{\circ}\)C) of HPP frankfurter sausages.