Mathematical corrections for bacterial loss in pharmacodynamic in vitro dilution models

Abstract

In vitro dilution models are used to simulate in vivo drug concentration-time profiles and thus to study the effects of various antibiotic concentrations on the bacteria investigated. The major disadvantage of these models is permanent dilution of the bacterial culture, which falsifies the resulting kill curves. Known equations, which usually correct bacterial loss by simple first-order kinetics, do not take into account special test conditions, such as variable elimination rate constants, exceptionally long periods of investigation, or formation of biofilms. In the present investigation, we examined the validity of these equations with regard to the test conditions mentioned. We simulated the concentration-time curves resulting from continuous infusion of 1,000 mg of meropenem with steady-state levels of 2.5, 5.0, and 7.5 micrograms/ml in an in vitro dilution model. The resulting kill curves were compared with the kill curves obtained from incubation of bacteria in an undiluted system with meropenem at constant concentrations corresponding to the above-mentioned steady-state levels. Comparison of the matching kill curves showed that the common corrections, which do not consider the formation of biofilms in the compartments, partly overestimated the effect of bacterial dilution. We defined a factor, f, as an extension to the known equations which compensates for the effect of biofilms. Another extension was developed to allow the investigation of variable elimination rate constants. With the help of these extended mathematical corrections, we were able to fit the kill curves resulting from the in vitro dilution model exactly to the kill curves given by an undiluted system.