Estimating the parameters of the Baranyi model for bacterial growth

The identifiability properties of the Baranyi model for bacterial growth were investigated, both structurally and applied to real-life data. Using the Taylor-series approach, it was formally proven that the model is structurally identifiable, i.e. it is now ascertained that it is certainly possible to give unique values to ail parameters of the model provided the bacterial growth data are of sufficiently good quality. The model also has acceptable practical identifiability properties in the presence of realistic data, which means that the confidence intervals on the parameter values are reasonable. However, there was a relatively high correlation between the maximum specific growth rate mu(max) and the suitability indicator ho. An optimal experimental design to improve parameter estimation uncertainty was worked out, using the sampling times of the microbial growth curve as experimental degree of freedom. Using a D-optimal design criterion, it could be shown that the optimal sampling times were concentrated in four time periods (initial, start and end of exponential growth, end of experiment), each providing maximum information on a particular parameter. Because the optimal experimental design requires a priori estimates of the parameters, the propagation of the parameter uncertainty into the experimental design was assessed with a Monte Carlo simulation. in this way, 95% confidence intervals could be established around the optimal sampling times to be used in the optimal experiment. Based on these intervals, a design was proposed and experimentally validated. The error on the parameter estimates was more than halved, their correlation diminished and the nonlinearity of the result improved. (C) 1999 Academic Press.