## 3 Results and Discussion
### Shelf Life Estimation  
The shelf life estimation of MAP fish was performed using the acceptability limit of 10\({}^{7}\) CFU g\({}^{-1}\) for the total viable count [34]. Spoilage rejection for MAP + CO\({}_{2}\) emitter packaged fish has been reported at log 6.5-7.0 CFU g\({}^{-1}\) (total viable count) [4; 35]. Based on the TVC limit, indicating the shelf life acceptability of the product, and the temperature dependence of the microbial growth rates, based on Arrhenius kinetics, simple equations for MAP and ACT-MAP sea bass shelf life can be calculated using Equation (2):  
\[\text{t}_{\text{SL}}=(\text{logN}_{\text{l}}-\text{logN}_{\text{o}})/(\text{k} _{\text{ref}}\exp((-\text{E}_{\text{a}}/\text{R})(1/\text{T}-1/\text{T}_{ \text{ref}})))+\lambda_{\text{ref}}\exp((-\text{E}_{\text{a}}/\text{R})(1/ \text{T}-1/\text{T}_{\text{ref}})) \tag{2}\]  
where t\({}_{\text{SL}}\) is the shelf life (d) of gutted sea bass, logN\({}_{\text{l}}\) is the limit TVC load (7.0 log CFU g\({}^{-1}\)), logN\({}_{\text{o}}\) is the TVC at storage time zero (0), k\({}_{\text{ref}}\) is the growth rate at the reference temperature T\({}_{\text{ref}}\) (for this study 4 \({}^{\circ}\)C), E\({}_{\text{a}}\) is the activation energy of TVC growth rate, R is the universal gas constant, and \(\lambda\) is the lag phase. The estimated shelf life of gutted sea bass at all the tested storage and packaging conditions, which were calculated using the developed mathematical model, is presented in Table 3. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Arrhenius Model Parameters for** & **Arrhenius Model Parameters for** \\  & **the Microbial Growth Rate** & **the Lag Phase** \\ \hline \multicolumn{3}{c}{_Pseudomonas_ spp.} \\ \hline MAP & & \\ E\({}_{\text{a,k }}\) (kJ mol\({}^{-1}\)) & 47.8 & - \\ k\({}_{\text{ref}}\) (d\({}^{-1}\)) & 0.252 & - \\ R\({}^{2}\) & 0.754 & \\ \hline ACT-MAP & & \\ E\({}_{\text{a,k }}\) (kJ mol\({}^{-1}\)) & 36.7 & - \\ k\({}_{\text{ref}}\) (d\({}^{-1}\)) & 0.131 & \\ R\({}^{2}\) & 0.951 & \\ \hline \multicolumn{3}{c}{_Enterobacteriaceae_ spp.} \\ \hline MAP & & \\ E\({}_{\text{a,k }}\) (kJ mol\({}^{-1}\)) & 60.0 & - \\ k\({}_{\text{ref}}\) (d\({}^{-1}\)) & 0.342 & \\ R\({}^{2}\) & 0.966 & \\ \hline ACT-MAP & & \\ E\({}_{\text{a,k }}\) (kJ mol\({}^{-1}\)) & 39.7 & - \\ k\({}_{\text{ref}}\) (d\({}^{-1}\)) & 0.266 & \\ R\({}^{2}\) & 0.993 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._According to the results in Table 3, the CO\({}_{2}\) gas in the headspace of the ACT-MAP samples led to a shelf life extension of MAP gutted sea bass: 7 days at storage temperature 5 \({}^{\circ}\)C and 4 days at 0 \({}^{\circ}\)C and 10 \({}^{\circ}\)C. The use of CO\({}_{2}\) emitter in MAP significantly increased the shelf life of gutted sea bass at all the storage temperatures studied (\(p<\) 0.05). The beneficial effect of the use of CO\({}_{2}\) emitters in MAP and/or vacuum packages on the total quality and shelf life of fish products was demonstrated [19; 20; 21; 22; 36]. [PERSON] et al. [36] reported the extension of the microbial (3 d extension, for the psychrophilic bacteria to reach 6 log CFU g\({}^{-1}\)) and sensorial shelf life (4 d extension, based on the sensory criteria ammonia-like odor) of cod fillets. The vacuum + CO\({}_{2}\)-emitter packaged cod fillets were found to have 11 days of shelf life, which was more than the 7 days for the MAP + liquid absorber packaged samples based on sensory, chemical (trimethylamine), and microbial analysis (TVC and H\({}_{2}\)S-producing bacteria). [PERSON] et al. [19; 20] reported a shelf life maintenance of cod and salmon fillets (based on microbial, sensory, and texture analysis) at lower g/p ratios (e.g., 1.3-1.0/1.0 with the CO\({}_{2}\)-emitter compared to 3.9-3.0/1.0). Packaging in MAP (60% CO\({}_{2}\)-40% O\({}_{2}\)) and CO\({}_{2}\) emitter at a lower g/p ratio (1.3/1.0) or MAP at a higher g/p ratio (3.9/1.0) led to shelf life extension (14 to 21 d) of cod fillets both in terms of sensory acceptance and microbial growth compared to vacuum (7-14 d).