Modelling time–kill studies to discern the pharmacodynamics of meropenem

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Abstract
Objectives: Time–kill studies are commonly used in investigations of new antimicrobial agents. However, they typically provide descriptive information on pharmacodynamics. We developed a mathematical model to capture the relationship between microbial burden and antimicrobial agent concentrations. Methods: Time–kill studies were performed with 108 cfu/mL of Pseudomonas aeruginosa at baseline. Meropenem at 0, 0.25, 1, 4, 16 and 64 × MIC was used (MIC = 1 mg/L). Serial samples were obtained to quantify bacterial burden over 24 h. The data were analysed by a population analysis using the non-parametric adaptive grid program. The rate of change of bacteria over time was expressed as the difference between linear bacterial growth rate and sigmoidal kill rate. Regrowth was attributed to adaptation, which was explicitly modelled as increase in C50k (concentration to achieve 50% maximal kill rate), using a saturable function of selective pressure (both meropenem concentration and time). Results: The best-fit model consisted of eight parameters and the fit to the data was satisfactory. The r2 of maximum a-posteriori probability Bayesian predictions based on the mean parameter estimates was 0.984. Maximal killing rate at baseline was found to be 4.7 h−1; C90k was achieved with meropenem at 5.0 mg/L. The model was validated by time–kill studies using 2× and 32× MIC of meropenem. Conclusions: Our model reasonably described and predicted the time course of P. aeruginosa in time–kill studies, and provided quantitative information on the pharmacodynamics of meropenem. The structural model appeared robust and could be used to provide a realistic expectation of the killing performance of antimicrobial agents.

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