Shelf life of modified atmosphere packed cooked meat products: addition of Na-lactate as a fourth shelf life determinative factor in a model and product validation.

Cooked meat products are often post-contaminated because of a packaging and/or slicing step after the pasteurisation process. The shelf life is therefore limited and can be extended by adding Na-lactate. A previously developed model for the spoilage of gas packed cooked meat products, including temperature, water activity and dissolved CO2 as independent variables, was extended with a fourth factor: the Na-lactate concentration in the aqueous phase of the meat product. Models were developed for the maximum specific growth rate mu(max) and the lag phase lambda of the specific spoilage organism Lactobacillus sake subsp. carnosum. Quadratic response surface equations were compared with extended Ratkowsky models. In general, response surface equations fitted the experimental data best but in the case of mu(max) the response surface model predicted illogical growth behaviour at low water activities and high Na-lactate concentrations. A extensive product validation of the mathematical models was performed by means of inoculated as well as naturally contaminated industrially prepared cooked meat products. The deviations of the experimentally determined versus predicted growth parameters in inoculated cooked meat products were in general small. Both types of models were also able to predict the shelf life of naturally contaminated cooked meat products, except for pâté where an under-estimation of the shelf life was predicted by the response surface equations. The validation studies revealed higher accuracy of the extended Ratkowsky models in comparison to the response surface equations. A significant shelf life extending effect of Na-lactate was predicted, which was more pronounced at low refrigerated temperatures. A synergistic effect has also been noticed between Na-lactate and carbon dioxide which, at least partly, could be explained by the pH-decreasing effect of CO2.

On the design of optimal dynamic experiments for parameter estimation of a Ratkowsky-type growth kinetics at suboptimal temperatures.

It is generally known that accurate model building, i.e., proper model structure selection and reliable parameter estimation, constitutes an essential matter in the field of predictive microbiology, in particular, when integrating these predictive models in food safety systems. In this context, Versyck et al. (1999) have introduced the methodology of optimal experimental design techniques for parameter estimation within the field. Optimal experimental design focuses on the development of optimal input profiles such that the resulting rich (i.e., highly informative) experimental data enable unique model parameter estimation. As a case study, Versyck et al. (1999) [Versyck, K., Bernaerts, K., Geeraerd, A.H., Van Impe, J.F., 1999. Introducing optimal experimental design in predictive modeling: a motivating example. Int. J. Food Microbiol., 51(1), 39-51] have elaborated the estimation of Bigelow inactivation kinetics parameters (in a numerical way). Opposed to the classic (static) experimental approach in predictive modelling, an optimal dynamic experimental setup is presented. In this paper, the methodology of optimal experimental design or parameter estimation is applied to obtain uncorrelated estimates of the square root model parameters [Ratkowsky, D.A., Olley, J., McMeekin, T.A., Ball, A., 1982. Relationship between temperature and growth rate of bacterial cultures. J. Bacteriol. 149, 1-5] describing the effect of suboptimal growth temperatures on the maximum specific growth rate of microorganisms. These estimates are the direct result of fitting a primary growth model to cell density measurements as a function of time. Apart from the design of an optimal time-varying temperature profile based on a sensitivity study of the model output, an important contribution of this publication is a first experimental validation of this innovative dynamic experimental approach for uncorrelated parameter identification. An optimal step temperature profile, within the range of model validity and practical feasibility, is developed for Escherichia coli K12 and successfully applied in practice. The presented experimental validation result illustrates the large potential of the dynamic experimental approach in the context of uncorrelated parameter estimation. Based on the experimental validation result, additional remarks are formulated related to future research in the field of optimal experimental design.

Introducing optimal experimental design in predictive modeling: a motivating example.

Predictive microbiology emerges more and more as a rational quantitative framework for predicting and understanding microbial evolution in food products. During the mathematical modeling of microbial growth and/or inactivation, great, but not always efficient, effort is spent on the determination of the model parameters from experimental data. In order to optimize experimental conditions with respect to parameter estimation, experimental design has been extensively studied since the 1980s in the field of bioreactor engineering. The so-called methodology of optimal experimental design established in this research area enabled the reliable estimation of model parameters from data collected in well-designed fed-batch reactor experiments. In this paper, we introduce the optimal experimental design methodology for parameter estimation in the field of predictive microbiology. This study points out that optimal design of dynamic input signals is necessary to maximize the information content contained within the resulting experimental data. It is shown that from few dynamic experiments, more pertinent information can be extracted than from the classical static experiments. By introducing optimal experimental design into the field of predictive microbiology, a new promising frame for maximization of the information content of experimental data with respect to parameter estimation is provided. As a case study, the design of an optimal temperature profile for estimation of the parameters D(ref) and z of an Arrhenius-type model for the maximum inactivation rate kmax as a function of the temperature, T, was considered. Microbial inactivation by heating is described using the model of Geeraerd et al. (1999). The need for dynamic temperature profiles in experiments aimed at the simultaneous estimation of the model parameters from measurements of the microbial population density is clearly illustrated by analytical elaboration of the mathematical expressions involved on the one hand, and by numerical simulations on the other.