## Results and Discussion
### Kinetics of Microbiological Data and Model Development/Validation
thermosphacta_ and LAB were significantly (_p_ < 0.05) delayed by the presence of _\"tsipouro\"_ compared to controls, at the majority of storage temperatures. In fact, for _B. thermosphacta_, ground beef packaged with _\"tsipouro\"_ showed \(\mu_{max}\) ca. 2-fold lower than the controls at 0-8 \({}^{\circ}\)C (_p_ < 0.05) (Table 1). In previous study of our research group, vapours of \"tsipouro\" was among the most effective antimicrobials along with _\"ouzo\"_, and _\"raki\"_ doubling the shelf-life of pork meat packaged under at 4 \({}^{\circ}\)C [15]. Regarding the pH, changes in controls (from 5.54 to 5.89) and in ground beef packaged with _\"tsipouro\"_ (from 5.61 to 5.83) were non-significant (_p_ \(\geq\) 0.05), at all storage temperatures (data not shown). Overall, the antimicrobial active packaging with _\"tsipouro\"_ significantly extended shelf-life of packaged ground beef as calculated by _B. thermosphacta_ growth (specific spoilage organism) and Equation (1). Specifically, shelf-life of controls versus _\"tsipouro\"_ was estimate from 28.0 \(\pm\) 3.8 to 49.3 \(\pm\) 1.7 days at 0 \({}^{\circ}\)C, from 9.5 \(\pm\) 3.5 to 14.2 \(\pm\) 6.8 days at 4 \({}^{\circ}\)C and from 5.1 \(\pm\) 0.9 to 10.1 \(\pm\) 4.0 days at 8 \({}^{\circ}\)C (_p_ < 0.05), while the shelf-life at 12 \({}^{\circ}\)C remained unaffected (_p_ \(\geq\) 0.05). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Microorganism/ Treatment** & **Temperature** & **N\({}_{\textbf{0}}\) (log CFU/g) \({}^{\textbf{1}}\)** & **\(N_{max}\) (log CFU/g) \({}^{\textbf{1}}\)** & **\(\mu_{max}\) (day\({}^{-1}\)) \({}^{\textbf{1}}\)** & **\(\lambda\) (days)** \\ \hline \hline \multirow{8}{*}{Control} & 0 & 3.91 \(\pm\) 0.96 \({}^{\textrm{A}}\) & 7.00 \(\pm\) 0.56 \({}^{\textrm{A}}\) & 0.36 \(\pm\) 0.14 \({}^{\textrm{A}}\) & N.A. \({}^{\textrm{2}}\) \\  & 4 & 4.75 \(\pm\) 0.75 \({}^{\textrm{AB}}\) & 8.32 \(\pm\) 0.31 \({}^{\textrm{C}}\) & 0.65 \(\pm\) 0.18 \({}^{\textrm{B}}\) & N.A. \\  & 8 & 4.18 \(\pm\) 1.27 \({}^{\textrm{AB}}\) & 7.55 \(\pm\) 0.34 \({}^{\textrm{AB}}\) & 1.26 \(\pm\) 0.06 \({}^{\textrm{C}}\) & N.A. \\  & 12 & 5.82 \(\pm\) 0.21 \({}^{\textrm{B}}\) & 8.04 \(\pm\) 0.24 \({}^{\textrm{BC}}\) & 1.46 \(\pm\) 0.06 \({}^{\textrm{C}}\) & N.A. \\ \hline \multirow{8}{*}{_“Tisipouro”_} & 0 & 4.10 \(\pm\) 0.89 \({}^{\textrm{A}}\) & 6.38 \(\pm\) 0.45 \({}^{\textrm{A}}\) & 0.14 \(\pm\) 0.04 \({}^{\textrm{A}*}\) & N.A. \\  & 4 & 5.06 \(\pm\) 1.09 \({}^{\textrm{A}}\) & 7.27 \(\pm\) 0.55 \({}^{\textrm{AB}*}\) & 0.37 \(\pm\) 0.16 \({}^{\textrm{A}*}\) & N.A. \\ \cline{1-1}  & 8 & 4.14 \(\pm\) 1.08 \({}^{\textrm{A}}\) & 6.66 \(\pm\) 0.50 \({}^{\textrm{A}*}\) & 0.72 \(\pm\) 0.26 \({}^{\textrm{B}*}\) & N.A. \\ \cline{1-1}  & 12 & 5.85 \(\pm\) 0.17 \({}^{\textrm{A}}\) & 7.93 \(\pm\) 0.20 \({}^{\textrm{B}}\) & 1.15 \(\pm\) 0.11 \({}^{\textrm{C}}\) & N.A. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Kinetic parameters and statistics of _B. thermosphacta_ and LAB estimated from the primary model of [PERSON] and Roberts on ground beef (500 g) packaged with absorbent pads supplemented with 50 mL of _“tsipouro”_ (40 mL under the ground beef piece and 10 mL under the labelling, facing the headspace) and stored at 0, 4, 8, and 12 \({}^{\circ}\)C under 80% O\({}_{2}\): 20% CO\({}_{2}\). Untreated samples served as controls. With regards to secondary modelling, \(\mu_{max}\) of dominant spoilage bacteria of ground beef packaged with or without \"_tsipouro_\" was described as a function of storage temperature by square root and Arrhenius models, while the estimated parameters and goodness-of-fit statistics are shown in Table 2. The average estimated activation energies of Arrhenius model for \(\mu_{max}\) of _B. thermosphacta_ and LAB in controls were 90.2 \(\pm\) 12.2 kJ/mol and 92.8 \(\pm\) 10.4 kJ/mol, respectively, while in ground beef packaged with \"_tsipouro_\" equaled to 87.2 \(\pm\) 17.1 kJ/mol (_B. thermosphacta_) and 124.8 \(\pm\) 15.0 kJ/mol (LAB) (Table 2).