ON THE DESIGN OF DYNAMIC EXPERIMENTS FOR PARAMETER ESTIMATION OF MICROBIAL THERMAL INACTIVATION KINETICS
In this paper we focus on parameter estimation for a Bigelow type model which describes the maximum inactivation rate kmax as function of the temperature T [Bigelow 1921]. In the common classical approach the two parameters (D and z-value) in the model are obtained from population density data collected in series of labour-intensive and time-consuming thermal inactivation experiments at several constant temperatures, e.g., [Stumbo 1973][Juneja et al. 1997].
An optimal experiment design frame for parameter estimation of unstructured growth kinetics, such as the Monod kinetics, has been established recently in the field of bioreactor engineering. In fed-batch bioreactors the influent substrate feed rate is used as a control input which is optimised with respect to the quality of the parameter estimation. Promising results of this experiment design methodology have been reported in literature [Munack 1989] [Versyck et al. 1997a].
The main contribution of this paper is to introduce the methodology of (dynamic) optimal experiment design into the field of predictive microbiology. As a case study, we provide a useful tool for optimisation of the information content contained within the measurements of the population density by optimising the time-varying temperature profile applied during inactivation experiments. These so-called dynamic inactivation experiments are very favourable from different points of view. First, the model can be tested on its validity during (realistic) time varying temperature conditions. Second, the micro-organisms are excited and, as such, are forced to reveal the influence of the temperature history on the inactivation rate. However, in spite of their important advantages, such dynamic experiments at inactivation temperatures are not common practice in predictive microbiology.
The paper is organised as follows. First, the primary and the secondary model for microbial inactivation under study in this paper are presented. The main concepts of optimal experiment design are summarised in the subsequent section. By using these definitions, analytical expressions are obtained for the quantification of the information content in this particular case study. Simulation results -obtained by parametric optimisation of static and dynamic temperature profiles with respect to information content of the data- are discussed. The conclusions and some final remarks are stated in the last section.