Modelling the effect of combined antimicrobials: A base model for multiple-hurdles

- Basic reference models for combined antimicrobials are not generally valid.
- Mock experiments against two pathogens invalidate the Bliss model.
- Mock experiments are compatible with the Loewe reference model (LRM).
- The LRM is only valid if all components have identical concentration exponents.
- A model which generalises the LRM allows for mixed concentration exponents.

Combining antimicrobials to reduce microbial growth and to combat the potential impact of antimicrobial resistance is an important subject both in foods and in pharmaceutics. Modelling of combined treatments designed to reduce or eliminate microbial contamination in foods (microbiological predictive modelling) has become commonplace. Two main reference models are used to analyse mixtures: the Bliss Independence and the Loewe reference models (LRM).By using optical density to analyse the growth of Aeromonas hydrophila, Cronobacter sakazakii and Escherichia coli in combined NaCl/NaCl (a mock combination experiment) and combined NaCl/KCl experiments, previous models for combined antimicrobials in foods, based on the Bliss approach, were shown to be inconsistent and that models based on the LRM more applicable.The LRM was shown, however, to be valid only in the specific cases where the concentration exponents of all components in a mixture were identical. This is assured for a mock combination experiment but not for a true mixture. This, essentially, invalidates the LRM as a general reference model. A new model, based on the LRM but allowing for mixed exponents, was used to analyse the combined inhibition data, and concluded that the NaCl/KCl system gave the additive effect expected from literature studies. This study suggests the need to revise current models used to analyse combined effects.