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

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.

Use of modeling techniques to aid in antibiotic selection

“…Minimum bacterial numbers expressed by ⌬ log N min (but not t min ) related better to the AUC/MIC ratio; moreover, this endpoint varied over a larger, 6-fold, range. Although ⌬ log N appeared to be even more sensitive to the AUC/MIC ratio, an AUC/MICassociated increase in ⌬ log N was less systematic [7].…”

“…Unlike the endpoints T 90% , T 99% , T 99.9% , k elb and N min , the endpoints T E , N (or the difference between logarithms of N 0 and N, or ⌬ log N ), AUBC, AAC, and I E better reflected the total antimicrobial effect. This is because all the events occurring from the moment of initial deflection of the time-kill curve away from the control growth curve to the moment of subsequent rapprochement of these curves (at the end of the regrowth phase, when bacterial regrowth predominates over killing) were attributed to the antimicrobial effect [7].…”

“…In a recent study, the predictive value of 12 currently relevant endpoint parameters was investigated, using time-kill curves with Escherichia coli exposed to ciprofloxacin over a 1000-fold range of the area under the curve (AUC)/MIC ratio [7]. The endpoints studied included ( Figure 1) the times to 10-fold, 100-fold and 1000-fold reductions of the initial inoculum (N 0 ), ie, T 90% [8], T 99% [9], and T 99.9% , respectively [10]; the slope of time-dependent changes in the difference between logarithms of viable counts with antibiotic (N A ) and without antibiotic (N C -control growth), ie, the "elimination-rate constant" of bacteria (k elb ) [11]; the minimal number of bacteria resulting from exposure to antibiotic (N min ) [12] and the time to reach this nadir (t min ) [12]; the time shift between control growth and the regrowth curves after antibiotic exposure ie, the duration of the effect (T E ) [13]; the viable bacteria count (N ) at the end of the observation period that mimics the usual dosing interval () [14]; the area under log N A -time curve (AUBC) [15,16]; the area above this curve and under the baseline drawn at the level of N A = N 0 (AAC) [17] that is the algebraic sum of the areas around the N 0 level; the area between the control-growth and bacterial killing/regrowth curves (ABBC) [18,19] over the dosing interval, ; and ABBC, determined to the end of the regrowth phase, which is also referred to as the intensity of the antimicrobial effect (I E ) [20].…”

“…Unlike these three endpoints, T E and I E varied over 20-and 30-fold ranges, respectively, and both increased systematically with increasing AUC/MIC ratios. Based both on the ability to provide a reasonable relationship to the AUC/MIC ratio and the sensitivity to changing AUC/MICs, I E can be considered the optimal endpoint of the total antimicrobial effect [7].…”

“…Indeed, visual description of time-kill curves or the use of inappropriate endpoints may or may not accompany sophisticated pharmacokinetic simulations. Without the most appropriate endpoint to describe the antimicrobial effect, accurate quantitative analysis of concentration-response or doseresponse relationships is impossible [7].…”