Parameters of bacterial killing and regrowth kinetics and antimicrobial effect examined in terms of area under the concentration-time curve relationships: action of ciprofloxacin against Escherichia coli in an in vitro dynamic model

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Abstract
Although many parameters have been described to quantitate the killing and regrowth of bacteria, substantial shortcomings are inherent in most of them, such as low sensitivity to pharmacokinetic determinants of the antimicrobial effect, an inability to predict a total effect, insufficient robustness, and uncertain interrelations between the parameters that prevent an ultimate determination of the effect. To examine different parameters, the kinetics of killing and regrowth of Escherichia coli (MIC, 0.013 microg/ml) were studied in vitro by simulating a series of ciprofloxacin monoexponential pharmacokinetic profiles. Initial ciprofloxacin concentrations varied from 0.02 to 19.2 microg/ml, whereas the half-life of 4 h was the same in all experiments. The following parameters were calculated and estimated: the time to reduce the initial inoculum (N0) 10-, 100-, and 1,000-fold (T90%, T99%, and T99.9%, respectively), the rate constant of bacterial elimination (k(elb)), the nadir level (Nmin) in the viable count (N)-versus-time (t) curve, the time to reach Nmin (t(min)), the numbers of bacteria that survived (Ntau) by the end of the observation period (tau), the area under the bacterial killing and regrowth curve (log N(A)-t curve) from the zero point (time zero) to tau (AUBC), the area above this curve (AAC), the area between the control growth curve (log N(C)-t curve) and the bacterial killing and regrowth curve (log N(A)-t curve) from the zero point to tau (ABBC) or to the time point when log N(A) reaches the maximal values observed in the log N(C)-t curve (I(E); intensity of the effect), and the time shift between the control growth and regrowth curves (T(E); duration of the effect). Being highly sensitive to the AUC, I(E), and T(E) showed the most regular AUC relationships: the effect expressed by I(E) or T(E) increased systematically when the AUC or initial concentration of ciprofloxacin rose. Other parameters, especially T90%, T99%, T99.9%, t(min), and log N0 - log Nmin = delta log Nmin, related to the AUC less regularly and were poorly sensitive to the AUC. T(E) proved to be the best predictor and t(min) proved to be the worst predictor of the total antimicrobial effect reflected by I(E). Distinct feedback relationships between the effect determination and the experimental design were demonstrated. It was shown that unjustified shortening of the observation period, i.e., cutting off the log N(A)-t curves, may lead to the degeneration of the AUC-response relationships, as expressed by log N0 - log Ntau = delta log Ntau, AUBC, AAC, or ABBC, to a point where it gives rise to the false idea of an AUC- or concentration-independent effect. Thus, use of I(E) and T(E) provides the most unbiased, robust, and comprehensive means of determining the antimicrobial effect.

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