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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.
- 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.
- Influences of physicochemical stresses on injury and inactivation behaviour of Listeria innocuaPublication . Miller, Fátima A.; Ramos, Bárbara; Gil, Maria M.; Brandão, Teresa R. S.; Teixeira, Paula; Silva, Cristina L. M.Many minimally processed foods depend on a combination of inhibitory factors to reduce the hazard of foodborne illness. Therefore, inactivation of Listeria innocua was studied according to a 24 factorial experiment designed to draw conclusions about temperature (52.5 °C and 65.0 °C), pH (4.5 and 7.5), water activity (aw=0.95 and 0.99) and solute type (NaCl and glycerol) effects. Three different recovery media were used to assess injured cells. Survival data were fitted with a Gompertz-based model and kinetic parameters (shoulder, maximum inactivation rate – kmax, and tail) were estimated. Results showed that shoulder was affected by temperature, pH and combined effects; kmax was influenced by all factors and their combinations; and tail was affected by aw, temperature and aw/pH combination. Results demonstrated the potential occurrence of microbial cross-protection survival techniques between the various stresses, e.g. heat and osmolarity. Indeed, this work clearly established that, to avoid hazards, Listeria inactivation must be evaluated with a maximum of environmental factors that undergo alterations. Only thus, appropriate food preservation treatments can be developed and consequently, the safety of food products can be assured.
- 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.
- Dynamic approach to assessing food quality and safety characteristics: the case of processed foodsPublication . Brandão, Teresa R. S.; Gil, Maria M.; Miller, Fátima A.; Gonçalves, Elsa M.; Silva, Cristina L. M.Consumers expect that food products will be safe and convenient to use and still have all the qualities of a fresh product. Foods often undergo processing, which has three major aims: to make food safe while providing products with the highest quality attributes, to transform food into forms that are more convenient or more appealing, and to extend shelf-life. Food processes such as thermally based ones (i.e. pasteurization and drying) or frozen storage occur in time-varying temperature conditions. Mathematical models that describe/predict changes in processed food characteristics with accuracy and precision in realistic, dynamic conditions are important tools in the development of new products and control systems. In this chapter, mathematical models that include time-varying temperature conditions (i.e. dynamic approach) will be presented for two relevant situations in the domain of processed foods: the case of microbial thermal inactivation and the case of food quality alterations under frozen storage.
- Heat inactivation of Listeria innocua in broth and food products under non-isothermal conditionsPublication . Miller, Fátima A.; Ramos, Bárbara F.; Gil, Maria M.; Brandão, Teresa R. S.; Teixeira, Paula; Silva, C. L. M.The objective of this work was to study the effect of three linear temperature profiles (heating rates of 1.5, 1.8 and 2.6 °C/min, from 20 to 65 °C) on Listeria innocua inactivation in liquid medium. The inactivation was also analyzed in artificially contaminated parsley (heating rate of 1.8 °C/min) and throughout a frying process, using a pre-cooked frozen food as case study. Inactivation showed a sigmoidal behaviour and all data was fitted with a Gompertz-inspired model. Results demonstrated that, in liquid media, Listeria inactivation is influenced by the temperature profile used. As heating rate increases, the shoulder decreases and the tail effect disappears. If Listeria was in parsley, its heat resistance increased (for identical experimental conditions in broth). Besides model adequacy was proven in all studied situations, the heating rate affected parameters’ precision.
- Predictions of microbial thermal inactivation in solid foods: isothermal and non-isothermal conditionsPublication . Gil, Maria M.; Miller, Fátima A.; Brandão, Teresa R. S.; Silva, Cristina L. M.This work focuses on the use of the Gompertz-inspired model to predict the thermal inactivation behaviour of microorganisms obtained in solid food products, validated for isothermal and non-isothermal conditions. Experiments were carried out in parsley, artificially inoculated with Listeria innocua. For the isothermal conditions tested, the predictive ability of the model was confined. The higher the temperature, the higher deviations observed (i.e. the model underestimates the inactivation behaviour). However, for the non-isothermal condition tested, the model predicted the microbial response accurately.
- Predictions of microbial thermal inactivation in solid foods: isothermal and non-isothermal conditionsPublication . Gil, Maria M.; Miller, Fátima A.; Brandão, Teresa R. S.; Silva, Cristina L. M.