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- Application of optimal experimental design concept to improve the estimation of model parameters in microbial thermal inactivation kineticsPublication . Gil, Maria M.; Miller, Fátima A.; Silva, Cristina L.M.; Brandão, Teresa R. S.The estimation of model parameters with high precision is of major importance in mathematical predictions. If a mathematical model is properly chosen and if the primary objective is to improve parameter estimation, underlying statistical theories can be applied. Precision increases with the number of experimental points. However, and in many situations,maximum precision is attained when sampling consists of replicates of specific experimental points. Experimental conditions can be optimized using the Doptimal design concept based on minimization of the generalized variance of the parameter estimates. The objective of this work was to use this methodology for the design of experiments for microbial inactivation processes described by a Gompertz-based model under isothermal and non-isothermal conditions. The application of D-optimal design concept considerably improved parameters precision, when compared to the commonly used heuristic designs.
- On the use of the gompertz model to predict microbial thermal inactivation under isothermal and non-isothermal conditionsPublication . Gil, Maria M.; Miller, Fátima A.; Brandão, Teresa R. S.; Silva, Cristina L. M.Food processes should be designed to provide an adequate margin of safety against microbiological risk of food poisoning and food spoilage throughout shelf life. In this field, the use of mathematical models that describe the microorganisms’ kinetics in such conditions is an important tool for convenient design, control and optimization of efficient processes. If those models are accurate and precise, one can extract the best aiming at predictive purposes. The Gompertz equation is commonly applied to describe sigmoidal kinetics. Besides the proven adequacy of the model in those kinetics descriptions, most of the reported works do not use Gompertz equation in the most convenient form, and insightful information could be obtained with re-parameterized forms. This work aims at reviewing the use of the Gompertz model to describe inactivation, as well as re-parameterized forms that include parameters related to the survival curve features. Microbial survival often presents a shoulder prior to inactivation, followed by a linear phase (corresponding to a maximum inactivation rate) and a tail residual population. The versatility of the Gompertz model in describing kinetics with different shapes, varying from a log-linear tendency till a complete sigmoidal shape, makes it attractive for predictive purposes, both under static and dynamic temperature conditions. Drawbacks and critical features of the model, when it is applied to microbial responses, will be overview.