OPTIMAL DYNAMIC EXPERIMENT FOR MODELLING THE MAXIMUM SPECIFIC GROWTH RATE AT SUBOPTIMAL GROWTH TEMPERATURES
The currently used identification procedure for modelling bacterial growth as function of one or more influencing factors consists of two steps. First, a set of growth curves is generated under a variety of static (i.e., non-varying) environmental conditions. Secondly, the growth parameters (e.g., maximum specific growth rate) estimated from these curves, are modelled by a secondary model. Increasing the accuracy of parameter estimation implies increasing the quantity of data.
In this paper the large potential of optimal experimental design techniques to cope with the problem of unique practical parameter identification of predictive models is illustrated. Optimal experimental design has already proved to be a useful tool for the practical identification of the parameters of unstructured growth kinetics in bioreactors. Munack (1989,1991) and Versyck et al. (1997,1998) established the design of optimal fed-batch experiments for unique estimation of the parameters of Monod-and Haldane-type kinetics.
The objective of optimal experimental design is to increase the quality (information content) of the data in such a way that unique parameter estimation based on experimental data is possible. In the proposed case study, optimal experimental design will not only result in a significant improvement in accuracy of the parameter estimates, but also in a substantial reduction of experimental work by using dynamic (i.e., time-varying) experimental conditions.
During the production, storage and distribution of many food products temperature is a major factor determining the specific growth rate of micro-organisms (Zwietering et al. 1991). Very often this temperature lies well below the optimal growth temperature of the micro-organisms of concern. As a case study, an optimal experiment to estimate the parameters of the square root model of Ratkowsky (Ratkowksy et al. 1982) describing the dependence of the maximum specific growth rate on suboptimal growth temperatures is designed. First, the theoretical parameter identifiability (i.e., based on perfect, noise-free data) is proved by using the power series expansion of the measured output (Pohjanpalo 1978).
The paper is organised as follows. In the first section the principles of optimal experimental design are explained. Next, an introduction to the case study considered in