**3. Results and discussion**

Eight different data sets of inactivation kinetics, from the collected data, were organized to compare 4 different microorganisms and 5 different types of food. The data sets were chosen to study their inactivation curves by Weibull modeling. The inactivation rate constant (*b*, min�<sup>1</sup> ) and the shape of the curve parameter *n*, as well as the theoretical decimal reduction doses (*Dv*, Jcm�<sup>2</sup> ) for one logarithmic reduction, are presented in **Table 2**.

In all cases, *n* < 1 indicates upward concave curves as can be observed in the corresponding figures. Even though the Weibull model is of empirical nature, some associations with biological effects can be made. For instance, some authors have pointed out that *n* < 1 indicates that the remaining cells have the ability to adapt to the applied stress. This indicates that the process is becoming progressively less efficient [21]. Also, the fact that all of the obtained *n* values are different from 1, indicates that for these systems, inactivation does not follow a classical first order kinetic and that, therefore a linear model is not adequate for these data sets [19].

For the analyzed systems, the inactivation rate, *b*, shows no significative difference in relation to the microorganism, nor to the type of food. However, for the calculated *Dv* value of *P. fluorescens* in mozzarella cheese, there can be observed a deviation from the


#### **Table 2.**

*Values of* b *and* n *parameters, and lethal dose value (*Dv*) obtained by Weibull modeling inactivation kinetics data sets.*

*Weibull Modeling of Microorganisms' Survival Kinetics by High Intensity Light… DOI: http://dx.doi.org/10.5772/intechopen.105162*

#### **Figure 1.**

*Inactivation curves of* P. fluorescens *on: (a) mozzarella cheese (experimental ( ) and predicted ( ) values) [15]; (b) Cheddar cheese (experimental (•) and predicted ( ) values) and (c) white American singles (experimental ( ) and predicted ( ) values) [17]. Note: Experimental values are presented as mean and s.d.*

obtained experimental data. For instance, when calculating *Dv* for the inactivation of *P. fluorescens* in mozzarella cheese (**Figure 1**) [15], the obtained value is almost five times the experimental value (10.53 J cm<sup>2</sup> ) applied to achieve the inactivation of one logarithmic cycle of *P. fluorescens*. In this case, the experimental data shows that most of the inactivated population was achieved at a small dose (equivalent to a 2 s treatment [15]) and that after this time the final population remained approximately constant (**Figure 1**). Therefore, the values of *n* and *b* are small and *Dv* calculation is inaccurate in comparison to the experimental values. This supports the relevance of choosing an adequate model that fits the data accurately. This means that even when the Weibull model has been extensively applied, this particular system might not be a good fit [13].

In cheddar cheese and American white singles (**Figure 1**), it is observed that the total inactivation as well as the inactivation rate, *b*, are higher in comparison to the ones obtained for mozzarella cheese. These results are due to the lower *Dv* values calculated for cheddar and American white singles cheese (1.24 and 0.95 J cm<sup>2</sup> respectively). This inactivation kinetics show that after one log of the microorganisms' population of inactivation was achieved on cheddar and white American cheese, the inactivation rate decreased gradually as the treatment time increased. This difference in behavior can be attributed to the higher *b* and *n* values obtained for both kinetics in comparison to the values obtained for mozzarella cheese. For instance, lower inactivation levels on the same microorganism in different food could be attributed to the noneffective access of the radiation due to the irregular surfaces. The surface of some cheeses might be rough and have pores or crevices where microorganisms are able to hide from the light which is known as the 'shadow effect' [15, 22]. The 'shadow effect' might be caused as well by the microbial cell distribution over the food surface. It is known that at higher initial contamination levels, the inactivation efficiency of pulsed light decreases, given the fact that dead microorganisms might create a protective layer to other microbial cells; making it difficult for the light beams to reach these sheltered cells [22]. Other surface characteristics affect the inactivation efficacy, such as the inoculation of microorganisms in very smooth surfaces, as the mozzarella cheese surface, which might lead to cell clustering and therefore shadowing [1].

Differences in inactivation levels could also be related to the location of the microorganisms and the presence of protective substances in some cases. Therefore, the composition also plays an important role, given the fact that some components might have protective effects vs. other types of foods [13].

In addition, it is also important to consider other possible sources of variation in the inactivation kinetics such as errors during the experimental assay. It is noticeable that in mozzarella cheese (**Figure 1**) after a dose equivalent to 14.04 J cm<sup>2</sup> , total inactivation decreases as the standard deviation seems to increase. Therefore, it is important to consider the repeatability of each experiment in an aim to reduce nonprecise data. Moreover, environmental conditions, such as pH, temperature, salt or sugar concentration, water activity, among others, should be carefully controlled since they play an important role in growth kinetics [14].

The inactivation of *L. innocua* on spinach leaves, cheddar cheese and American singles cheese, is presented in **Figure 2**; where it is shown that, at similar irradiation doses (12–13 J cm<sup>2</sup> ), slightly higher total inactivation levels were achieved on cheddar cheese and white American singles (**Figure 2**, black triangles, and green rhomboids, respectively) than the one achieved on spinach surface (**Figure 2**, blue dots). However, for this microorganism, *Dv* in spinach surface is significantly lower than in cheddar cheese and American white singles. This is explained by the fact that, as it is observed in **Figure 2**, a rapid inactivation occurs at very low energy levels, achieving an inactivation of 1.5 logarithmic cycles at fluences lower than 1 J cm<sup>2</sup> . After this point, the inactivation rate decays as the slope for this portion of the graph tends to 0 with higher energy doses, achieving a final inactivation of 2.4 log cycles. This indicates that the increase in the applied energy did not produce proportional increases in the total inactivation of the microorganism [13].

In **Figure 2**, it can be observed that *L. innocua* inactivation kinetic, shows slightly different behavior for cheddar and white American cheese in the sense that initial

#### **Figure 2.**

Listeria innocua *inactivation curves on: a) spinach surface (experimental ( ) and predicted (—) values) [13]; (b) cheddar cheese (experimental (*▲*) and predicted ( ) values) and (c) white American singles (experimental ( ) and predicted ( ) values) [17]. Note: Experimental values are presented as mean and s.d.*

*Weibull Modeling of Microorganisms' Survival Kinetics by High Intensity Light… DOI: http://dx.doi.org/10.5772/intechopen.105162*

microbial inactivation occurs at higher inactivation doses, observing not only calculated *Dv* values higher than that obtained for spinach but also significantly higher *n* values, related to the less pronounced upward concavity of the curves 2.b and 2.c in comparison to 2.a. This behavior indicates that the rate of inactivation decreases as fluence increases affecting also the calculated *Dv* value [13, 19]. In fact, this behavior is noticed in all the systems analyzed in the present study, indicating that for pulsed light inactivation, linear models are not accurate. Instead, non-linear models, such as the Weibull model, should be applied [19].

In comparison to bacteria, fungi show generally higher resistance to light pulses [23]. This is shown in **Figure 3**, where it can be observed that higher energy doses were used to achieve inactivation levels of 1.4 and 1.75 log cycles for *A, carbonarius* and *A. flavus*, respectively, than the energy doses used for *P. fluorescens* and *L. innocua*. **Figure 3** shows a similar inactivation behavior for *A. carbonarius* and *A. flavus*, where a rapid inactivation is achieved at very low doses (4 and 3 J cm for *A. carbonarius* and *A. flavus,* respectively)*.* The inactivation rate, *b*, decreases as the energy doses increases, achieving a tailing effect indicating that conidia inactivation rate dramatically fell down after energy doses equivalent to 18 J cm<sup>2</sup> [16]. However, parameter *b* is significantly higher for *A. flavus* than for *A. carbonarius* because the initial microbial population decay is higher in *A. flavus.* This behavior is also related to the small *n* values (0.12) corresponding to a pronounced upward concave curve and might be the cause of the significantly higher *Dv* value obtained for *A. carbonarius* in comparison to the *Dv* value obtained for *A. flavus* since the inactivation rate for the latter one is significantly higher, as mentioned before.

The persistent residual population, tailing effect, showed for *L. innocua* inactivation on spinach surface (**Figure 2A**) and for *A. carbonarius* and *A. flavus* inactivation on malting barley (**Figure 3**) might be attributed to factors such as genotypic differences within the population providing enhanced survival in a minority of cells, the microorganisms were not inoculated homogeneously and were not evenly distributed on the surface or the light treatments were not applied homogeneously, due to the

#### **Figure 3.**

*Inactivation of (a)* A. carbonarius *(experimental ( ) and predicted ( ) values) and (b)* A. flavus *(experimental ( ) and predicted ( ) values) in low moisture malting barley [16]. Note: Experimental values are presented as mean and s.d.*

shape of the food causing the sample to receive the light only on one side (which is likely the case for barley seeds). It should also be taken into account that some microorganisms might grow to deepen into the food tissue, thus being inaccessible to light radiation [16, 24].
