On the unicity of optimal experimental design solutions for parameter estimation of microbial kinetics

In this paper, optimal experimental design for parameter estimation of unstructured microbial growth models during growth of biomass on a single limiting substrate in a fed-batch bioreactor is considered. The ratio Λ(F) of the largest to the smallest eigenvalue of the Fisher information matrix F (i.e. the modified E-criterion for optimal experimental design) is used to evaluate the information content of several simulation experiments, each with a different volumetric feed rate profile. The optimal value for this criterion (namely. Λ(F) = 1) is obtained for several feed rate profiles with different structures, after optimization of their corresponding degrees of freedom with respect to the information content of the experiment. Therefore, the solution to the problem of optimal experimental design is not unique, which means that additional specifications can be taken into account.