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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.
- Combined effects of temperature, pH and water activity on predictive ability of microbial kinetic inactivation modelPublication . Gil, Maria M.; Miller, Fátima A.; Brandão, Teresa R. S.; Silva, Cristina L. M.It is well known that temperature is the key factor controlling the microbial survival/inactivation. However, the interactive effects of further stressing environmental conditions may influence microbial inactivation behaviour. The objective of this work was to include, in the inactivation model, temperature, pH and water activity effects using a black box polynomial model, aiming at accurate prediction. Experimental data of Listeria innocua obtained within the temperature range of 52.5 and 65.0 °C, pH of 4.5, 6.0 and 7.5, and water activity of 0.95 and 0.99 were used for model assessment. A Gompertz-inspired model for microbial inactivation was used, with shoulder period, maximum inactivation rate and tail as parameters. The relations of such parameters with temperature, water activity and pH were purely empirical and assumed to be polynomials. When these mathematical relationships were included in the primary kinetic model, accurate predictions of the inactivation data were attained, thus validating the predictive ability of the model expressed in terms of the stressing environmental factors studied. © 2015 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Department of Food Science, Faculty of Food Engineering, University of Campinas.
- Combined effects of temperature, pH and water activity on predictive ability of microbial kinetic Inactivation modelPublication . Gil, Maria M.; Miller, Fátima A.; Brandão, Teresa R. S.; Silva, Cristina L.M.It is well known that temperature is the key factor controlling the microbial survival/inactivation. However, the interactive effects of further stressing environmental conditions may influence microbial behaviour. The objective of this work was to include, in the inactivation model, temperature, pH and aw effects using a black box polynomial model, aiming at accurate prediction. Data of Listeria innocua obtained within the temperature range of 52.5 and 65.0 °C, pH of 4.5, 6.0 and 7.5, and aw of 0.95 and 0.99 were used for model assessment. The relations of such parameters with temperature, aw and pH were assumed to be polynomials.
- Mathematical models for prediction of temperature effects on kinetic parameters of microorganisms’ inactivation: tools for model comparison and adequacy in data fittingPublication . Gil, Maria M.; Miller, Fátima A.; Brandão, Teresa R. S.; Silva, Cristina L. M.Microbial inactivation often follows a sigmoidal kinetic behaviour, with an initial lag phase, followed by a maximum inactivation rate period and tending to a final asymptotic value. Mathematically, such tendencies may be described by using primary kinetic models (Gompertz based model is one example) that describe microbial survival throughout processing time when stressing conditions are applied. The parameters of kinetic models are directly affected by temperature. Despite the number of mathematical equations used to describe the dependence of the kinetic parameters on temperature (so-called secondary models), there is a lack of studies regarding model comparison and adequacy in data fitting. This work provides a review of mathematical models that describe the temperature dependence of kinetic parameters related to microbial thermal inactivation. Regression analysis schemes and tests seeking model comparison are presented. A case study is included to provide guidance for the assessment of secondary model adequacy and regression analyses procedures. When modelling temperature effects on sigmoidal inactivation kinetics of microorganisms, one should be aware about the regression methodology applied. The most adequate models according to the two-step regression methodology may not be the best selection if a global fit is applied.