## 3 Results and Discussion
### Validation of the ASLT Methodology in Predicting the Shelf Life of Frankfurter-Type Sausages  
In order to determine the dependence of the TVC (total viable count) growth rate on the temperature, the Arrhenius equation, as described in Equation (1), was applied. The Arrhenius equation was applied to (i) the whole set of kinetic data, as well as to the cases where (ii) the data set of the three most severe temperatures (above 8 \({}^{\circ}\)C) and (iii) only a two-point data set (8 and 18\({}^{\circ}\)C) were taken into account, to validate whether the ASLT methodology could be effectively applied for the estimation of shelf life of the tested meat products. The results are presented in Figure 10a-c and Table 4.  
As indicated from the obtained results, the [PERSON] equation can adequately describe the temperature dependence of microbial growth rate, even when applied for a small range of data sets (R\({}^{2}\): 0.912-0.959), without statistically significant differences among predictions. Similarly, the dependence of the lag phase duration (\(\lambda\)) on temperature was determined with a modified [PERSON] equation, as follows:  
\[\lambda=\lambda_{ref}\cdot\exp[-\frac{Ea}{R}\cdot(\frac{1}{T}-\frac{1}{T_{ref} })] \tag{6}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Storage Temperature (\({}^{\circ}\)C)** & **Growth Rate** & **Lag Phase** & **R\({}^{2}\)** & **Doubling Time** \\  & **k (d\({}^{-1}\))** & **(d)** & & **T\({}_{d}\) (d)** \\ \hline
4 & 0.084 \(\pm\) 0.007 a & 18.9 \(\pm\) 5.43 a & 0.988 & 8.2 \\
8 & 0.183 \(\pm\) 0.018 b & 8.51 \(\pm\) 0.89 b & 0.990 & 3.7 \\
12 & 0.595 \(\pm\) 0.037 c & 4.27 \(\pm\) 0.70 c & 0.994 & 1.1 \\
18 & 1.058 \(\pm\) 0.102 d & 2.28 \(\pm\) 0.48 d & 0.992 & 0.6 \\ \hline VAR1 (T\({}_{\text{eff}}\) = 4.5 \({}^{\circ}\)C) & 0.084 \(\pm\) 0.005 a & 18.1 \(\pm\) 4.11 a & 0.994 & 8.3 \\ VAR2 (T\({}_{\text{eff}}\) = 11.1 \({}^{\circ}\)C) & 0.701 \(\pm\) 0.110 c & 7.11 \(\pm\) 1.21 b & 0.974 & 1.0 \\ \hline \hline \end{tabular} Different letters among lines 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 2: Kinetic parameters of the TVC growth in Frankfurter-type sausages after HPP at different isothermal and dynamic storage conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Storage Temperature (\({}^{\circ}\)C)** & **Shelf Life** \\  & & **(d)** \\ \hline \multirow{6}{*}{CNT} & 4 & 18 \\  & 8 & 11 \\  & 12 & 8 \\  & 18 & 3 \\ \cline{2-3}  & VAR1 & 20 \\  & VAR2 & 6 \\ \hline \multirow{6}{*}{HPP} & 4 & 89 \\  & 8 & 41 \\  & 12 & 11 \\  & 18 & 7 \\ \cline{2-3}  & VAR1 & 89 \\  & VAR2 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Shelf life based on the TVC growth in CNT and HPP frankfurter-type sausages stored at different isothermal and dynamic storage conditions. where \(\lambda\) is the lag phase duration at temperature \(T\) (d), \(\lambda_{\textit{ref}}\) is the lag phase duration at temperature \(T_{\textit{ref}}\) (d), \(T_{\textit{ref}}\) is a reference temperature (K), \(R\) is the molar gas constant (8.314 J/K\(\cdot\)mol) and \(E_{\textit{a}}\) is the apparent activation energy (J/mol). The equation was applied for the above mentioned case studies (i, ii and iii), linearized by applying the logarithm to both sides of the equation, then coefficients \(\lambda_{\textit{ref}}\) and \(E_{\textit{a}}\) were estimated using linear regression, and the results are presented in Figure 11 and Table 5.