Pharmacokinetic/Pharmacodynamic Modelling of Antibacterials In Vitro and In Vivo Using Bacterial Growth and Kill Kinetics

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Abstract
The minimum inhibitory concentration (MIC) is the in vitro reference value to describe the activity of an antibacterial against micro-organisms. It does not represent the dynamic effect of the antimicrobial at any point in time, but rather the total antimicrobial effect over the incubation period at a fixed concentration. To explore the concentration-effect relationship of antimicrobial concentrations against micro-organisms in relation to the MIC. Time-kill curves were generated for ceftazidime, meropenem and tobramycin against Pseudomonas aeruginosa. The Hill equation with variable slope was fit to the time-kill data, and mathematical models of growth and kill were explored with reference to the MIC. With declining concentrations, bacterial killing will decrease until a specific threshold concentration is reached. This concentration, at which bacteria are neither killed nor able to grow, is named the stationary concentration (SC) and is not equal to the MIC. Pharmacokinetic/pharmacodynamic simulations over a range of kill rates, growth rates and slope factors showed that for β-lactam antibacterials, the SC is close to the MIC value, which may explain why concentrations in vivo need to be above the MIC, while regrowth of bacteria occurs when concentrations decline below the MIC. For concentration-dependent antibacterials, such as aminoglycosides and quinolones, the SC is shown to be markedly different from the MIC and, in general, is much lower. The MIC is not a good pharmacodynamic parameter to characterise the concentration effect relationship of a given antimicrobial. For ‘concentration independent’ antimicrobials the SC is likely to be close to the MIC, but may be much lower for ‘concentration dependent’ antimicrobials, and may explain sub-MIC effects.