Optimal strategies for estimating the parameters of the Baranyi-Ratkowsky model: from (optimal) experiment design to model fitting methods

The Baranyi growth model combined with the Ratkowsky secondary model (Baranyi-Ratkowsky hereafter) has demonstrated their reliability for describing microbial growth as a function of temperature. However, these models are based on empirical parameters that must be estimated from data, so robustness depends on the experimental design and the model fitting approach. This study applies a rigorous statistical analysis based on Information Theory and numerical simulations to provide clear guidelines on the best model fitting approaches and experimental designs for the Baranyi-Ratkowsky model. First, the study concludes that one-step fitting approaches result in lower parameter dispersion than two-steps approaches (for the simulated conditions: 44 %, 85 % and 96 % lower for b, logC₀ and T_min, respectively, no reduction for logN_max and logN₀). Numerical simulations demonstrate that, unlike for two-steps methods, the error of regression from the one-step approach is a realistic estimate of parameter uncertainty/variability, strengthening the case for this method. This motivates restricting the calculation of Optimal Experiment Designs (OEDs) for this approach only. The study clearly demonstrates that the experimental design has a clear impact on parameter dispersion. However, OEDs tend to be impractical, as they focus on conditions that require long experimental runs. Accordingly, a penalty term is introduced in OED definition, resulting in two strategies: to lower the number of experiments at lower temperatures, and to terminate the experiments at lower temperatures before reaching stationary phase. Based on this result, we propose a staggered experimental design that is updated recursively (storage temperature and position of time points) until convergence. Considering that isothermal experiments are still the gold standard in the field, future studies could greatly benefit from these suggestions by minimizing the experimental effort needed to obtain robust estimates for the Baranyi-Ratkowsky model.