## 3 Methods and Materials  
### Shelf Life Prediction Method  
#### 3.1.1 Intrinsic and Extrinsic Factors  
A food item is a complex chemical matrix. Predicting whether or how quickly microorganisms will grow in a food product is a difficult task, given that most foods contain sufficient nutrients to promote microbial growth and each microorganism develops at a different rate and under different conditions. There are several factors that promote, restrict, or prevent bacterial growth in food products, and these can be grouped into two categories: intrinsic and extrinsic factors. Intrinsic factors are the factors inherent to the food itself, which affect microbial growth, such as water activity, acidity, oxidation-reduction potential, chemical composition, or the biological structure of the food [11]. The intrinsic factors to consider in the development of the DSS are the water activity and acidity:  
* **Water activity (\(a_{\text{w}}\)):** one of the intrinsic factors of products that are likely to promote microbiological growth, given that bacteria normally grow in environments where water is available. Water activity is defined as the ratio between the vapor pressure of water (\(p_{\text{v}}\)) in the food product and the saturated vapor pressure of water (\(p_{\text{sv}}\)) at the same temperature, as shown in Equation (4) [11]. Its value ranges from 0 (dry bone) and 1 (saturated water). \[a_{\text{w}}=p_{\text{v}}/p_{\text{sv}} \tag{4}\]  
\(a_{\text{w}}\) is directly influenced by the air relative humidity, \(\varphi\). If the air in contact with a food product has lower \(\varphi\), the water migrates to the air, increasing its \(\varphi\) and reducing the moisture content of the food, until equilibrium is reached. Conversely, if a food product with low \(a_{\text{w}}\) is stored in an environment with high \(\varphi\), the \(a_{\text{w}}\) of this food will increase, promoting the multiplication of microorganisms [12]. In an isolated system, in which food products are in equilibrium with the relative humidity of the environment, the \(a_{\text{w}}\) of these foods may be defined by Equation (5). \[a_{\text{w}}=\varphi/100 \tag{5}\]  
The precise \(a_{\text{w}}\) values of each food product are difficult to be defined due to the referred dependencies of the parameters. Table 1 shows the specific water activity values according to Chirife and Fontan [13] for each of the horticultural products covered in the DSS--lettuce, onion, carrot, and cabbage--in the form of minimum, average and maximum values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Product** & **Minimum \(a_{\text{w}}\) Value** & **Average \(a_{\text{w}}\) Value** & **Maximum \(a_{\text{w}}\) Value** \\ \hline Lettuce & - & 0.996 & - \\ Onion & 0.974 & 0.982 & 0.990 \\ Carrot & 0.983 & 0.988 & 0.993 \\ Cabbage & 0.990 & 0.991 & 0.992 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Water activity intervals for each horticultural product [13]. * **Potential of Hydrogen (pH):** The level of acidity or basicity of a food product is measured by using a pH scale, defined as the inverse logarithm of the hydrogen ion activity in a solution given by Equation (6). \[\text{pH}=\text{log}_{10}(1/\text{a}_{\text{H}+})\] (6) The potential of hydrogen also plays an important part in bacterial growth. Each microorganism has an optimal pH value at which its multiplication is maximum. Both the increase and decrease in the acidity level in relation to the optimal value slows microbial growth [14]. A food's own acidity also influences microbial growth. The reduction of pH of a food product contributes to the reduction in the capacity of bacterial development and vice versa [15]. Table 2 specifies the typical pH values of the horticultural products under analysis according to [14; 16]. These values are given in the form of an interval, due to the acidity variations that each product may present among itself, but also due to the existence of several species of each of these products, knowing that each species has its own characteristics--e.g., pH.