Development of a novel approach for secondary modelling in predictive microbiology: incorporation of microbiological knowledge in black box polynomial modelling

This research deals with the development of a novel secondary modelling procedure within the framework of predictive microbiology. The procedure consists of three steps: (i) careful formulation of the available microbiological information, both from literature and from the experimental case study at hand, (ii) translation of these requirements in mathematical terms under the form of partial derivatives throughout the complete interpolation region of the experimental design, and (iii) determination of parameter values with suitable optimisation techniques for a flexible black box modelling approach, e.g., a polynomial model or an artificial neural network model. As a vehicle for this procedure, the description of the maximum specific growth rate of Lactobacillus sakei in modified BHI-broth as influenced by suboptimal temperature, water activity, sodium lactate and dissolved carbon dioxide concentration is under study. The procedure results in a constrained polynomial model with excellent descriptive and interpolating features in comparison with an extended Ratkowsky-type model and classical polynomial model, by combining specific properties of both model types. The developed procedure is illustrated on the description of the lag phase as well. It is stressed how the confrontation with experimental data is very important to appreciate the descriptive and interpolating capacities of new or existing models, which is nowadays not always carefully performed. Alternatively, the first two steps of the novel procedure can be used as a tool to demonstrate clearly (possible) interpolative shortcomings of an existing model with straightforward spreadsheet calculations.