Kinetics of heat-induced changes in foods: A workflow proposal

Abstract

The goal of kinetic modeling is twofold: i) to increase scientific understanding of the process under study, and ii) to predict product properties in product and process design and shelf life. Reviewing food science literature shows that classical two-step kinetic analysis is most common, by first deriving rate constants for an assumed order of reaction (possibly after linearization to make linear regression possible) and then deriving Arrhenius parameters via linear regression, again after log-linearization. This two-step approach is not without problems and this article proposes an alternative general workflow on the untransformed data using nonlinear, global regression. The basic elements consist of: i) a full statistical analysis of the order of the reaction per temperature, ii) a global analysis of all data simultaneously to estimate Arrhenius parameters while characterizing a possibly varying order via multilevel modeling, iii) evaluation of the resulting model and parameters in terms of fitting and, even more importantly, predictive capacity. The proposed workflow is illustrated with a case study on thermal degradation of carnitin (described in literature as a first-order reaction). A Bayesian approach was used to obtain probability distributions of parameters rather than point estimates, but the common standard frequentist approach can also be applied. Kinetic analysis of the carnitin data for each temperature separately showed that the order varied with temperature between 0.9 and 1.6. Multilevel modeling on all data simultaneously was used to better characterize this variation along with the common Arrhenius parameters. Due to the nature of the Arrhenius equation, reparameterization and rescaling is necessary to avoid strong parameter correlation and numerical difficulties during nonlinear regression. Multilevel modeling of all data showed that the variation of the order with temperature was not that strong as suggested from the separate analyses but it did show that the global order was higher than one. The outcome of the suggested workflow was compared to that of the classical two-step kinetic analysis and showed considerable differences in Arrhenius parameters; this appeared to be due to linearization by taking logarithms of concentration data, at least for this case study. Furthermore, it is illustrated that Bayesian regression leads to better insight into behaviour of parameters and models than least-squares regression in terms of density distributions, parameter correlations and joint confidence intervals. Even more importantly, testing of predictive capacity of kinetic models can be done much more rigorously using the Bayesian approach. • Estimation of uncertainty in reaction order from kinetic data gives insight in reactions. • Multilevel modeling allows variation of reaction order per temperature. • Global regression leads to less uncertainty in model predictions. • Bayesian estimation gives more insight in regression parameters than least-squares. • Logarithmic transformation in Arrhenius regression leads to biased estimates.