Parameterization of Inoculum Effect Via Mathematical Modeling: Aminoglycosides Against Staphylococcus aureus and Escherichia coli

Abstract

Inoculum effect describes the inoculum size dependent changes in minimum inhibitory concentrations (MIC) exhibited by antibiotic-bacterium combinations demonstrating such effect. Traditionally, inoculum effect has been loosely defined based on the extent of increase in the MIC with respect to the increase in inoculum size. In most studies, assessment of MIC data has relied on the arbitrary selection of a point of reference for both baseline MIC and inoculum size. More importantly, this conventional method of assessment does not permit information conveyed in a complete MIC versus inoculum size profile to be fully explored. To undertake these issues, a mathematical model was developed for the description of the entire inoculum effect profile. With the employment of three key parameter estimates, i.e., the baseline MIC, the threshold inoculum size at which the increase in MIC commences, and the rate of increase in MIC with respect to inoculum size, both the shape and location of the profile could be adequately defined. To verify the application of this model, a series of four aminoglycosides were tested against standard strains of E. coli and S. aureus. Results showed a good degree of organism specificity and antibioticclass dependency of the inoculum effect profiles. Analysis of the parameter estimates obtained provided further support for these observations. In conclusion, the mathematical model developed in the present study adequately described the inoculum effect exhibited by the various aminoglycoside-bacterium combinations tested. The parameter estimates generated by the modeling approach allowed comparison and quantitative analysis of the inoculum effect profiles with minimal difficulties.