Mathematical modeling to characterize the inoculum effect.

Killing by beta-lactams is well known to be reduced against a dense bacterial population, commonly known as the inoculum effect. However, the underlying mechanism of this phenomenon is not well understood. We proposed a semi-mechanistic mathematical model to account for the reduced in vitro killing observed. Time-kill studies were performed with 4 baseline inocula (ranging from approximately 1 × 10(5) to 1 × 10(8) CFU/ml) of Escherichia coli ATCC 25922 (MIC, 2 mg/liter). Constant but escalating piperacillin concentrations used ranged from 0.25× to 256× MIC. Serial samples were taken over 24 h to quantify viable bacterial burden, and all the killing profiles were mathematically modeled. The inoculum effect was attributed to a reduction of effective drug concentration available for bacterial killing, which was expressed as a function of the baseline inoculum. Biomasses associated with different inocula were examined using a colorimetric method. Despite identical drug-pathogen combinations, the baseline inoculum had a significant impact on bacterial killing. Our proposed mathematical model was unbiased and reasonable in capturing all 28 killing profiles collectively (r(2) = 0.88). Biomass was found to be significantly more after 24 h with a baseline inoculum of 1 × 10(8) CFU/ml, compared to one where the initial inoculum was 1 × 10(5) CFU/ml (P = 0.002). Our results corroborated previous observations that in vitro killing by piperacillin was significantly reduced against a dense bacterial inoculum. This phenomenon can be reasonably captured by our proposed mathematical model, and it may improve prediction of bacterial response to various drug exposures in future investigations.