Optimal experimental design for discriminating between microbial growth models as function of suboptimal temperature.

In the field of predictive microbiology, mathematical models play an important role for describing microbial growth, survival and inactivation. Often different models are available for describing the microbial dynamics in a similar way. However, the model that describes the system in the best way is desired. Optimal experimental design for model discrimination (OED-MD) is an efficient tool for discriminating among rival models. In this work the T12-criterion proposed by Atkinson and Fedorov (1975) [1] and applied efficiently by Ucinski and Bogacka (2005) [2] and the Schwaab-approach proposed by Schwaab et al. (2008) [3] and Donckels et al. (2009) [4] will be applied for discriminating among rival models for the microbial growth rate as a function of temperature. The two methods will be tested in silico and their performances will be compared. Results from a simulation study indicate that it is possible to validate the case that one of the proposed models is more accurate for describing the temperature effect on the microbial growth rate. Both methods are able to design inputs with a sufficient discrimination potential. However, it has been observed that the Schwaab-approach provides inputs with a higher discrimination potential in combination with more accurate parameter estimates.

Quantitative dietary exposure assessment of the Catalonian population (Spain) to the mycotoxin deoxynivalenol.

The mycotoxin deoxynivalenol (DON) is one of the most common contaminants of cereals worldwide, and its occurrence has been widely reported in raw foods and foodstuffs, around the European region, including Catalonia. In the present work, a stochastic methodology has been applied to accurately assess the exposure of the Catalonian population (Spain) to DON through food consumption. Raw contamination data was provided by a large survey conducted in this region, in addition to the raw consumption data from a nutritional study specifically designed to assess the dietary intake of the main foodstuffs related to DON contamination for all population age groups. Contamination and consumption data were combined by simulation using an essentially parametric (P-P) method. The P-P method draws sampling values from distribution functions fitted to consumption and contamination data sets. Moreover, to quantify the accuracy and reliability of the statistics estimates, we built the related confidence intervals using a pseudo-parametric bootstrap method. Considering the results drawn from the P-P simulation method, the Catalonian population should be expected to be exposed at moderated levels of deoxynivalenol, the infants and individuals with ethnic dietary patterns being the most exposed population groups.

Use of global sensitivity analysis in quantitative microbial risk assessment: application to the evaluation of a biological time temperature integrator as a quality and safety indicator for cold smoked salmon.

The aim of this study was to apply a global sensitivity analysis (SA) method in model simplification and to evaluate (eO)®, a biological Time Temperature Integrator (TTI) as a quality and safety indicator for cold smoked salmon (CSS). Models were thus developed to predict the evolutions of Listeria monocytogenes and the indigenous food flora in CSS and to predict TTIs endpoint. A global SA was then applied on the three models to identify the less important factors and simplify the models accordingly. Results showed that the subset of the most important factors of the three models was mainly composed of the durations and temperatures of two chill chain links, out of the control of the manufacturers: the domestic refrigerator and the retail/cabinet links. Then, the simplified versions of the three models were run with 10(4) time temperature profiles representing the variability associated to the microbial behavior, to the TTIs evolution and to the French chill chain characteristics. The results were used to assess the distributions of the microbial contaminations obtained at the TTI endpoint and at the end of the simulated profiles and proved that, in the case of poor storage conditions, the TTI use could reduce the number of unacceptable foods by 50%.

Sensitivity analysis for high quantiles of ochratoxin A exposure distribution.

Using available data from a consumption survey and contamination data on ochratoxin A (OA) in food, a sensitivity analysis (SA) for high quantiles (95th and 99th quantiles) of OA exposure distribution was carried out, obtained by a Monte Carlo simulation in French children. Exposure assessment for food contaminants is important to control the risk of foodborne diseases. Risk assessors are interested in high quantiles of contaminant exposure distributions. As these exposure distributions are generally very asymmetrical, it is difficult to obtain relevant and stable high quantiles in such a context. Determining OA exposure distribution is complex because it is based on the sum of elementary exposure distributions (eight foodstuffs are analysed here), and each one of these is the product of a consumption distribution and a contamination distribution. The SA enables us to quantify the influences of the parameter variability of the consumption and contamination probability density functions (pdf) which have been fitted to the data, our simulation model inputs, on the 95th and 99th quantiles of the output exposure distribution. After some preliminary trials, we have postulated a quadratic polynomial regression model for the quantiles of OA exposure distribution in view of undertaking this SA. This regression model comprises 32 main factors, their 496 two-factor interactions and their 32 quadratic terms. The 32 factors are the parameters of the fitted pdf: 16 parameters of Gamma distributions relative to the eight consumed foods and 16 parameters of Gamma distributions relative to the eight food OA contaminations. For an optimal parameter estimation of such a large model, we used an experimental design approach depending on a resolution-V fractional factorial design of 6561 experiments. The factor ranges are established by a preliminary study of bootstrap sampling. From the bootstrap samples, the factor ranges are obtained taking into account the correlation between the two parameters of the fitted Gamma pdf. A full exposure distribution is simulated for each of the 6561 experiments. The consumption dependencies are taken into account by the Iman and Conover method. On the basis of this analysis, validated and useful models for each desired quantile are obtained showing a major influence of the parameters of "Cereals" (consumption and contamination) and slightly less so for parameter of "Pork" consumption in the sensitivity of the quantiles.