## 3 Methods and Materials
### Shelf Life Prediction Method
#### 3.1.2 Bacterial Growth Prediction Method
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bacteria** & **Lettuce** & **Onion** & **Carrot** & **Cabbage** \\ \hline _Aeromonas hydrophilia_ & X & X & X & X \\ _Bacillus cereus_ & X & X & X & X \\ _Listeria monocytogenes_ & X & & & \\ _Salmonella_ & X & X & X & X \\ _Shigella flexneri_ & & X & X & \\ _Staphylococcus aureus_ & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Bacteria capable of growing in each horticultural products under study [23]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Bacteria** & **Initial Dose (CFU/g)** & **Infective Dose (CFU/g)** \\ \hline _Aeromonas hydrophilia_ & \(10^{3}\) & \(10^{5}\) \\ _Bacillus cereus_ & \(10^{1}\) & \(10^{5}\) \\ _Listeria monocytogenes_ & \(10^{1}\) & \(10^{2}\) \\ _Salmonella_ & \(10^{2}\) & \(10^{5}\) \\ _Shigella flexneri_ & \(10^{0}\) & \(10^{2}\) \\ _Staphylococcus aureus_ & \(10^{1}\) & \(10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Initial and infective doses for each bacterium in study [23]. The initial physiological state was firstly introduced in the model proposed by [PERSON] and [PERSON] [9]. It is the parameter associated to the first phase of bacterial growth, i.e., the lag or latency phase and, therefore, capable of influencing it. This parameter assumes a dimensionless number comprised between 0 and 1, which expresses the physical adaptation of cells to the environment. If its value is 0, growth will not occur (latency is infinite). If its value equals 1, growth will begin immediately (there is no latency phase). The length of lag phase depends not only on the surrounding environment (temperature, water activity, pH), but also on the history of the cells. Stresses (e.g., thermal or osmotic) may significantly increase latency times. Synthetically, the initial physiological state quantifies the effect of the cell's history, which is reflected in the latency time of bacterial growth [23]. The lag time derives from initial physiological state of the cells through Equation (7). \[\text{lag}=-\text{log}\ (\text{Phys.\ State})/\text{Max.\ rate} \tag{7}\]  
where \"Phys. state\" represents initial physiological state and \"Max. Rate\" the maximum slope of the growth curve. In the proposed method, to simulate the effect of the distribution chain on bacterial growth of vegetables, the initial physiological state input will assume, in all circumstances, its maximum value, set to 1. Thus, the lag phase will be disregarded in the bacterial growth model assumed by the DSS, being associated to the time that the horticultural products in analysis take to travel through their normal distribution chain. Thus, it is considered that bacterial growth begins at moment zero of the time interval considered by the DSS, which will represent the instant when the horticultural product in study enters the retailer's warehouse, which is the last facility before being sold to the final consumer. In addition to this assumption, the DSS database, built by extracting data from [23], will be constituted for each horticultural product in the study, by:  
* Three different water activity scenarios, to simulate the effects of the relative humidity of the environment in the increasing bacterial doses. The adopted scenarios relate to the minimum, average, and maximum \(a_{w}\) values specific to each vegetable, as shown in Table 1. It is expected that the retailer, as the user of the DSS, would collect the \(a_{w}\) value that the horticultural product from a certain batch has when arriving at the final warehouse before being sold. Usually, it is impossible for the retailer to directly collect the product's \(a_{w}\) value. Assuming that equilibrium conditions are reached within a short period [26], the air relative humidity must be collected or measured, making use of the relation between \(\varphi\) and \(a_{w}\) shown in Equation (5).