Inter- and Intraquinolone Predictors of Antimicrobial Effect in an In Vitro Dynamic Model: New Insight into a Widely Used Concept

Abstract

Earlier efforts to search for pharmacokinetic and bacteriological predictors of fluoroquinolone antimicrobial effects (AMEs) have resulted in conflicting findings. To elucidate whether these conflicts are real or apparent, several predictors of the AMEs of two pharmacokinetically different antibiotics, trovafloxacin (TRO) and ciprofloxacin (CIP), as well as different dosing regimens of CIP were examined. The AMEs of TRO given once daily (q.d.) and CIP given q.d. and twice daily (b.i.d.) against Escherichia coli, Pseudomonas aeruginosa, and Klebsiella pneumoniae were studied in an in vitro dynamic model. Different monoexponential pharmacokinetic profiles were simulated with a TRO half-life of 9.2 h and a CIP half-life of 4.0 h to provide similar eightfold ranges of the area under the concentration-time curve (AUC)-to-MIC ratios, from 54 to 432 and from 59 to 473 (μg · h/ml)/(μg/ml), respectively. In each case the observation periods were designed to incorporate full-term regrowth phases in the time-kill curves, and the AME was expressed by its intensity (I_E; the area between the control growth and time-kill and regrowth curves up to the point at which the viable counts of regrowing bacteria are close to the maximum values observed without drug). Species-independent linear relationships were established between I_E and log AUC/MIC, log AUC above MIC (log AUC_eff), and time above the MIC (T_eff). Specific and nonsuperimposed I_E versus log AUC/MIC or log AUC_eff relationships were inherent in each of the treatments: TRO given q.d. (r² = 0.97 and 0.96), CIP given q.d. (r² = 0.98 and 0.96), and CIP given b.i.d. (r² = 0.95 and 0.93). This suggests that in order to combine data sets obtained with individual quinolones to examine potential predictors, one must be sure that these sets may be combined. Unlike AUC/MIC and AUC_eff, the I_E-T_eff relationships plotted for the different quinolones and dosing regimens were nonspecific and virtually superimposed (r² = 0.95). Hence, AUC/MIC, AUC_eff, and T_eff were equally good predictors of the AME of each of the quinolones and each dosing regimen taken separately, whereas T_eff was also a good predictor of the AMEs of the quinolones and their regimens taken together. However, neither the quinolones nor the dosing regimens could be distinguished solely on the basis of T_eff, whereas they could be distinguished on the basis of AUC/MIC or AUC_eff. Thus, two types of predictors of the quinolone AME may be identified: intraquinolone and/or intraregimen predictors (AUC/MIC, AUC_eff and T_eff) and an interquinolone and interregimen predictor (T_eff). T_eff may be able to accurately predict the AME of one quinolone on the basis of the data obtained for another quinolone.

The concept of pharmacokinetic and bacteriological predictors of the antimicrobial effect has been offered as an alternative to the traditional concentration-response relationships usually exploited in pharmacology. Unlike many pharmacological effects, the antimicrobial effect depends not only on the drug concentration but also on the exposure time. Furthermore, the use of combined pharmacokinetic and bacteriological predictors enhances their actual predictive potential, assuming that the predictor-response relationships are bacterial species independent. Evaluation of a predictor(s) of the antimicrobial effect and/or clinical outcome has generally been accepted as a useful tool in the design of optimal dosing regimens (4). For example, if the ratio of the peak antibiotic concentration (C_max) to MIC (C_max/MIC) were shown to be the best predictor, then intermittent drug administration at relatively high doses and relatively long intervals might be superior to drug administration at lower doses and shorter intervals. On the other hand, if the antimicrobial effect correlates better with the time at which the antibiotic concentration exceeds the MIC (time above the MIC [T_eff]), the opposite dosing strategy would be preferable.

During the past decade the predictive potentials of parameters such as C_max/MIC, T_eff, the area under the concentration-time curve (AUC) related to the MIC (AUC/MIC) or the portion of AUC/MIC that reflects only the time at which the concentrations are above the MIC (AUIC) (18), and the AUC above the MIC (AUC_eff) have been examined for various antimicrobial agents (5, 16, 17, 20). Due to considerable covariance among these widely used predictors, the search for a single optimal predictor was often futile, since one was usually required to choose among equally good predictors, especially for pharmacokinetically similar drugs (8).

This covariance has also been noted in in vitro and in vivo studies with fluoroquinolones (2, 6). In this regard, the use of only one predictor, for example, C_max/MIC for enoxacin (2) or AUIC for ciprofloxacin and ofloxacin (14), does not necessarily exclude the appropriate selection of alternative predictors. Similarly, the preference for AUC/MIC measured within 24 h (AUC/MIC₂₄) over C_max/MIC as a potential predictor of the effects of ciprofloxacin and ofloxacin (15), without examination of AUC_eff or T_eff, might not be strictly appropriate, since AUC/MIC₂₄ represents the sum of AUCs produced by the administration of repeated doses of the drug, while C_max/MIC reflects only the impact of the first dose administered in the dynamic model. The infrequent attempts to directly compare several potential predictors of quinolone antimicrobial effects have led to conflicting results. For example, no differences were reported among C_max/MIC, AUC/MIC, and T_eff as predictors of the efficacy of lomefloxacin against Pseudomonas sepsis in rats: the predictive potential of each of these predictors was equally high (r² = 0.98 to 0.99) (6). In another study, C_max/MIC, AUC/MIC, and T_eff did not predict the in vitro and in vivo effects produced by seven antibiotics including ciprofloxacin and fleroxacin (3). Similarly, AUIC did not predict the effects of four quinolones in an in vitro dynamic model studied by Wiedemann et al. (25), in contrast to the data presented by Madaras-Kelly et al. (14).

To elucidate whether these contradictions can be rectified, several predictors of the antimicrobial effects of pharmacokinetically different quinolones, trovafloxacin and ciprofloxacin, as well as those of two dosing regimens of ciprofloxacin were examined on the basis of time-kill data obtained in an in vitro dynamic model.

MATERIALS AND METHODS

Antimicrobial agents.

Trovafloxacin mesylate and ciprofloxacin lactate powders, kindly provided by Roerig, a division of Pfizer, and by Bayer AG, respectively, were used in the study. Stock solutions of the quinolones were prepared in sterile distilled water.

Bacterial strains.

The clinical isolates Escherichia coli 224, Pseudomonas aeruginosa 48, and Klebsiella pneumoniae 121 were used in the study. Susceptibility testing was performed in triplicate at 24 h postexposure with organisms grown in Ca²⁺- and Mg²⁺-supplemented Mueller-Hinton broth; the inoculum size was 10⁶ CFU/ml. The MICs of trovafloxacin for E. coli, P. aeruginosa, and K. pneumoniae (0.25, 0.3, and 0.25 μg/ml, respectively) were found to be comparable to those of ciprofloxacin (0.12, 0.15, and 0.12 μg/ml, respectively).

Simulated pharmacokinetic profiles.

A series of monoexponential profiles for trovafloxacin and ciprofloxacin were simulated. The simulated half-lives (t_1/2 s; 9.25 h for trovafloxacin and 4.0 h for ciprofloxacin) were consistent with the values reported in humans: 7.2 to 9.9 h (19, 27) and 3.2 to 5.0 h (1, 13, 26), respectively. Regimens of trovafloxacin given once daily (q.d.) and ciprofloxacin given q.d. and twice daily (b.i.d.) were used in experiments with both E. coli and P. aeruginosa. For studies with K. pneumoniae only regimens of trovafloxacin given q.d. and ciprofloxacin given b.i.d. were simulated. Regardless of the antibiotic or bacterial strain, the simulated AUCs and the respective amounts of the drugs actually administered in the model were chosen to provide similar eightfold ranges of the AUC/MIC. These ratios averaged from 54 to 432 (μg · h/ml)/(μg/ml) for trovafloxacin and from 59 to 473 (μg · h/ml)/(μg/ml) for ciprofloxacin. For regimens of ciprofloxacin given b.i.d., the AUC/MICs presented reflect the sum of two AUC/MICs provided by the two doses of the quinolone administered at 12-h intervals but with the residual concentrations at the end of the first interval taken into account. The simulated time courses of the trovafloxacin and ciprofloxacin concentrations related to the MIC are presented in Fig. 1.

FIG. 1.

In vitro simulated pharmacokinetic profiles of trovafloxacin (curves labeled 1) and ciprofloxacin given q.d. (curves labeled 2) and b.i.d. (curves labeled 3). The numbers in the upper right corner of each plot are the average values of the simulated AUC/MICs [in (μg · h/ml)/(μg/ml)] of trovafloxacin/simulated AUC/MICs of ciprofloxacin.

In vitro dynamic model and operating procedure.

A previously described dynamic model (11) was used in the study. Briefly, the model consisted of two connected flasks, one containing fresh Mueller-Hinton broth and the other, the central unit, containing the same type of broth plus a bacterial culture (control growth experiments) or a bacterial culture plus antibiotic (killing and regrowth experiments). The central unit was incubated at 37°C in a shaking water bath. Peristaltic pumps (Minipuls 2; Gilson) circulated fresh nutrient medium to the bacterium- or bacterium- and antibiotic-containing medium from the central 40-ml unit at a flow rate of 3 or 7 ml/h to simulate trovafloxacin or ciprofloxacin pharmacokinetics, respectively. Hence, the clearances provided by the designed flow rates plus the volume of the central unit ensure the monoexponential elimination of both trovafloxacin or ciprofloxacin and bacteria from the system, with elimination rate constants of 0.075 h⁻¹ (t_1/2 = 9.25 h) and 0.170 h⁻¹ (t_1/2 = 4.0 h), respectively. Accurate simulations of the desired pharmacokinetic profiles are provided by maintaining constant flow rates and a constant volume in the central unit.

The system is filled with sterile Mueller-Hinton broth and is placed in a temperature-regulated incubator at 37°C. The central unit was inoculated with 18-h cultures of E. coli, P. aeruginosa, or K. pneumoniae, and after a further 2 h of incubation, trovafloxacin or ciprofloxacin was injected into the central unit. The resulting counts of the organisms in the exponentially growing cultures approached approximately 10⁶ CFU/ml. The duration of the experiments was defined in each case as the time until the antibiotic-exposed bacteria (N_A) reached the maximum numbers observed in the absence of antibiotic (control growth [N_C]), i.e., the time when N_A becomes equal to N_C. In all cases the experiments were stopped when N_A reached ≥10¹¹ CFU/ml. Since the experiments that simulated low AUC/MIC ratios met this requirement earlier than those that simulated high AUC/MIC ratios, the duration of the former experiments was shorter than that of the latter experiments. As illustrated in Fig. 1, the lower the AUC/MIC ratio, the shorter the requisite observation period.

Validation of the model.

To validate the dynamic model, trovafloxacin or ciprofloxacin concentrations in samples of Mueller-Hinton broth withdrawn from the central unit were determined in duplicate by high-performance liquid chromatography (HPLC). To precipitate the proteins from the broth, 200 μl of acetonitrile (in the presence of trovafloxacin) or methanol (with ciprofloxacin) was added to a 100-μl sample. The mixture was vortexed and centrifuged at 2,000 × g for 10 min. A total of 25 μl of the upper aqueous layer was injected into the HPLC system. Chromatography was carried out on a reversed-phase column (Silasorb C₈; 5 μm; 250 by 4.6 mm [internal diameter]). The mobile phase consisted of acetonitrile and 0.02 M KH₂PO₄ solution (30:70 [vol/vol]) for trovafloxacin and an acetonitrile, ethyl alcohol, and 0.02 M KH₂PO₄ solution (10:20:70 [vol/vol]) for ciprofloxacin; the mobile phase was delivered through a Waters chromatographic pump (model 501) at flow rates of 1.7 and 1.3 ml/min, respectively.

Trovafloxacin was detected with a Waters Lambda-Max model 481 absorbance detector at 275 nm, and ciprofloxacin was detected with a Waters model 420-AC fluorescence detector; the excitation wavelength was set at 274 nm, and the emission wavelength was set at 418 nm. The detection limit was 0.1 μg/ml for trovafloxacin and 0.05 μg/ml for ciprofloxacin, and the linearity ranged from 0.25 to 10 and from 0.1 to 4 μg/ml, respectively. The interday coefficient of variation was close to 8% for fluoroquinolone concentrations of both 2 and 0.5 μg/ml. The trovafloxacin and ciprofloxacin concentrations in the central compartment of the model determined by the HPLC method were close to the designed values, with no systematic deviation from the expected values (Fig. 2). Hence, the model provided reasonably accurate simulations of the pharmacokinetic profiles.

FIG. 2.

Observed (open symbols) and designed (lines) concentrations of trovafloxacin and ciprofloxacin in the central compartment of the dynamic model when simulating the same initial concentrations (2.35 μg/ml) but different t_1/2 (9.25 and 4.0 h, respectively).

Quantitation of bacterial growth and killing.

In each experiment 0.1-ml samples were withdrawn from the bacterium-containing medium in the central unit throughout the observation period, at first every 30 min, later hourly, then every 3 h, and during the last 6 to 7 h, again hourly. These samples were subjected to serial 10-fold dilutions with chilled, sterile 0.9% NaCl and were plated in duplicate onto Mueller-Hinton agar. Antibiotic carryover at low counts was avoided by washing the bacteria with 0.9% NaCl. After overnight incubation at 37°C the resulting bacterial colonies were counted, and the numbers of CFU per milliliter were calculated. The limit of detection was 2 × 10² CFU/ml.

Preliminary experiments performed in duplicate showed good within-day and day-by-day reproducibilities of the results. The respective pairs of representative time-kill curves observed in repeated experiments with E. coli exposed to trovafloxacin are shown in Fig. 3. As seen in Fig. 3, the data obtained from each of the paired runs were virtually superimposed.

FIG. 3.

Time courses of killing and regrowth of E. coli exposed to trovafloxacin observed in parallel runs performed on the same day [AUC/MIC = 43 (μg · h/ml)/(μg/ml) (A)] and on different days [AUC/MIC = 92 (μg · h/ml)/(μg/ml) (B)]. The data obtained in the respective paired experiments are indicated by different symbols.

To reveal possible changes in susceptibility, the quinolone concentrations corresponding to the time when the numbers of surviving organisms in the regrowth curves reached the level of the initial inoculum (C_regrowth) were determined for each run (10). No AUC/MIC-induced systematic differences in the C_regrowths were documented for any of the regimens; moreover, the appearance of bacterial regrowth was associated with values of unity for ratios of quinolone concentrations to MICs.

Quantitative evaluation of the antimicrobial effect and comparison of its predictors.

The antimicrobial effect was expressed by the intensity I_E, which describes the area between the control growth and bacterial killing and regrowth curves from time zero (the moment of drug input into the model) to the time when viable counts on the regrowth curve are close to the maximum values observed without drug (9). The upper limit of bacterial numbers, i.e., the cutoff level in the regrowth and control growth curves, used to determine the I_E was 10¹¹ CFU/ml (Fig. 4).

FIG. 4.

Schematic presentation of the I_E determination applied to the kinetics of killing and regrowth of K. pneumoniae when mimicking twice-daily ciprofloxacin administration [AUC/MIC = 59 (μg · h/ml)/(μg/ml)]. I_E describes the dashed area between the control growth (empty triangles) and the killing and regrowth (filled triangles) curves at a cutoff level of 10¹¹ CFU/ml.

To compare the predictive potentials of AUC/MIC, AUC_eff, and T_eff, the antimicrobial effects expressed by I_E were related to each predictor for each of the treatment regimens, i.e., trovafloxacin given q.d. and ciprofloxacin given q.d. and b.i.d. Correlation and regression analyses of the relationships between I_E and log AUC/MIC, log AUC_eff, or T_eff were performed by using STATISTICA software (version 4.3; StatSoft, Inc.). Statistical comparison of the regressions was performed at P < 0.05, as described elsewhere (22).

RESULTS

The time courses of viable counts that reflect killing and regrowth of E. coli, P. aeruginosa, and K. pneumoniae exposed to monoexponentially decreasing concentrations of trovafloxacin given q.d. and ciprofloxacin given q.d. and b.i.d. and the respective control growth curves are presented in Fig. 5 to 7. As seen in Fig. 5 to 7, at all the AUC/MIC ratios studied, regrowth occurred following a considerable reduction in bacterial numbers. Unlike the rate of killing or the minimum bacterial numbers achieved, the time shift of the regrowth phase to the right along the time axis was distinctly dependent on the simulated AUC/MIC: the higher the AUC/MIC, the later the regrowth. Furthermore, at every simulated AUC/MIC the time-kill curves observed for each of the quinolones and regimens were similar for the different bacteria, whereas quinolone-induced and regimen-induced (q.d. versus b.i.d. for ciprofloxacin) differences in the appearance of bacterial regrowth were evident. For all three bacterial species exposed to trovafloxacin, at each AUC/MIC, regrowth was observed later than that with the regimens of ciprofloxacin given b.i.d. and especially ciprofloxacin given q.d. Since no substantial species-dependent effects were established, subsequent comparison of the predictors allows the data obtained with different microorganisms in each of the experiments with a given quinolone or regimen to be combined.

FIG. 5.

The kinetics of killing and regrowth of gram-negative bacteria when mimicking trovafloxacin administration q.d. for E. coli (▴), P. aeruginosa (▪), and K. pneumoniae (•) with (filled symbols) and without (empty symbols) quinolones. The numbers in the bottom right corner of each plot are the simulated AUC/MICs [in (μg · h/ml)/(μg/ml)].

FIG. 7.

The kinetics of killing and regrowth of gram-negative bacteria when mimicking ciprofloxacin administration b.i.d. for E. coli (▴), P. aeruginosa (▪), and K. pneumoniae (•) with (filled symbols) and without (empty symbols) quinolones. The numbers in the bottom right corner of each plot are the simulated AUC/MICs [in (μg · h/ml)/(μg/ml)].

The plots of I_E versus log AUC/MIC, log AUC_eff, and T_eff are presented in Fig. 8. As seen in Fig. 8, a specific linear relationship between I_E and log AUC/MIC is inherent for each of the three treatments. Moreover, the correlation coefficients have similar high values (r² = 0.95 to 0.98), although the slopes of the I_E-log AUC/MIC plots differed (Table 1). The slope for trovafloxacin [276 log (CFU/ml) · h] is 1.8-fold higher than that for ciprofloxacin given b.i.d. [151 log (CFU/ml) · h], which is in turn 2.4-fold higher than that for ciprofloxacin given q.d. [113 log (CFU/ml) · h] (P < 0.05).

FIG. 8.

Antimicrobial effects of trovafloxacin given q.d. (——) and ciprofloxacin given b.i.d. (– – –) and q.d. (… .) related to the different predictors. The three points that departed from linear I_E-T_eff plot are enclosed in a circle (for more detailed discussion, see the text). ________, all treatments.

TABLE 1.

Slopes of the regressions of I_E on the predictors and the correlation coefficients

Antibiotic and regimen	AUC/MIC		AUCeff		Teff
	Slope [log (CFU/ ml) · h]	r2	Slope [log (CFU/ ml) · h]	r2	Slope (log CFU/ml)	r2
Trovafloxacin q.d.	276a	0.97	250a	0.96	9.0	0.96
Ciprofloxacin q.d.	151b	0.95	141b	0.93	9.7	0.94
Ciprofloxacin b.i.d.	113	0.98	108	0.96	8.6	0.98

^aStatistically significant difference between the drugs. 

^bStatistically significant difference between the regimens of ciprofloxacin. 

Similar considerations apply to a comparison of the relationships between I_E and AUC_eff. As seen in Fig. 8, the I_E-log AUC_eff plots obtained for trovafloxacin and ciprofloxacin given q.d. and b.i.d. differed. The slopes of the trovafloxacin plot [250 log (CFU/ml) · h] are 1.8- and 2.3-fold higher than those for the plots of ciprofloxacin given b.i.d. and q.d. [141 and 108 log (CFU/ml) · h, respectively], (P < 0.05). Again, these three plots cannot be superimposed, although I_E is highly correlated with log AUC_eff for each treatment (r² = 0.96, 0.96, and 0.93, respectively; Table 1).

The plots of I_E versus T_eff for trovafloxacin and for both ciprofloxacin regimens are linear with the single exception of the regimen of ciprofloxacin given b.i.d., in which the points corresponding to the lowest T_eff departed from the straight line that fits the points corresponding to the three higher values of T_eff. For this reason, only the linear portion of the I_E-versus-T_eff plots for ciprofloxacin given b.i.d. was used for further analysis. The I_E-T_eff plots for the two quinolones and the two ciprofloxacin dosing regimens are practically superimposed and the respective slopes are similar, with no statistically significant differences (Table 1). As seen in Fig. 8, the I_E-T_eff sets combined for all three treatments showed a very good correlation between the effect and its predictor (r² = 0.95) that is comparable to the respective correlations found for the regimens of trovafloxacin and ciprofloxacin given q.d. and b.i.d. taken separately (r² = 0.96, 0.98, and 0.94, respectively; Table 1).

DISCUSSION

This study suggests that the antimicrobial effect of an individual quinolone (trovafloxacin or ciprofloxacin) or a dosing regimen (ciprofloxacin given q.d. or b.i.d.) as expressed by its intensity (I_E) correlates equally well with each of the three predictors (AUC/MIC, AUC_eff, and T_eff). Thus, no preferences for any of them may be supported by these data. This is consistent with the reported similar predictive potentials of AUC/MIC and T_eff applied to a single quinolone (6, 21) and is quite expected, since each of the three predictors examined in our study covaried strongly (r² > 0.98 for each treatment). Similar covariance was reported previously in studies with enoxacin (2) and lomefloxacin (6).

Although all three predictors could be accurately related to the effect in a similar bacterial species-independent fashion, the log AUC/MIC-response and log AUC_eff-response relationships were specific for each drug (trovafloxacin and ciprofloxacin) and for each of the ciprofloxacin dosing regimens. This circumstance allows quantitative comparisons of the effects of the quinolones, as reported recently (7, 12). Unlike AUC/MIC and AUC_eff, the I_E-T_eff plots obtained with trovafloxacin given q.d. and ciprofloxacin given q.d. and b.i.d. were virtually superimposed and therefore are not specific. This means that the effect of one quinolone may be predicted by the I_E-T_eff relationship established for another quinolone. Thus, unlike AUC/MIC and AUC_eff, which may be referred to as intraquinolone and intraregimen predictors only, T_eff may also be considered the best interquinolone and interregimen predictor of the antimicrobial effect. However, the I_E-T_eff relationships do not reveal obvious differences between the quinolones and/or dosing regimens of ciprofloxacin, whereas the I_E-AUC/MIC and I_E-AUC_eff relationships do reveal such differences.

As already mentioned, a specific I_E-log AUC/MIC or I_E-log AUC_eff relationship was inherent for each of the treatments. Since these plots were not superimposed and the data could not be considered a homogeneous set, combining them would be incorrect. For example, if the I_E-AUC/MIC data from the regimens of trovafloxacin given q.d. and ciprofloxacin given q.d. and b.i.d. were combined, only a loose correlation between the effect and its predictor would be established (r² = 0.46). Therefore, neither AUC/MIC nor AUC_eff may be considered quinolone- or regimen-independent predictors of the antimicrobial effect produced by trovafloxacin and ciprofloxacin.

This conclusion is consistent with the lack of predictability of the effects of different quinolones taken together by using AUIC (25) or of the effects of different antibiotics including ciprofloxacin and fleroxacin by using AUC/MIC (3). At the same time, our data do not support recent reports of successful prediction of the effects of two different quinolones by AUIC (14) or the statement that AUC/MIC or AUC/MIC₂₄ were general predictors of antimicrobial effects of the fluoroquinolones (15). At least in part, these contradictions are probably less than they appear, because neither AUIC (14) nor AUC/MIC (15) was compared to alternative predictors such as AUC_eff and T_eff. Moreover, this statement was based on a scattered AUC/MIC₂₄-response curve (r² = 0.58) obtained with combined data for ciprofloxacin and ofloxacin as well as different dosing regimens. Perhaps these data (15) should be converted into a family of more accurate plots for each drug and regimen taken separately.

The comparative single-dose study of Wiedemann et al. (25), which has been performed with four gram-positive and gram-negative bacteria exposed to biexponentially decreasing concentrations of ciprofloxacin, sparfloxacin, fleroxacin, and ofloxacin, indirectly supports this hypothesis. Those investigators stated “no clear-cut relationship between AUIC and killing activity” was found when data for four different quinolones were combined. However, the differences between the logarithm of the initial inoculum and the logarithm of the minimum bacterial numbers achieved (Δlog N_min) could be related to AUIC if the data for the drugs were considered separately. For example, Δlog N_min correlates with the AUIC of fleroxacin and ofloxacin taken separately (Fig. 9), although the log AUIC-response plots associated with the individual quinolones are quite different and these data do not belong to the same homogeneous set. Thus, the conclusion that similar effects are produced by the same AUC/MICs of different fluoroquinolones (15) was not confirmed by our current findings or by the results reported by Wiedemann et al. (25). This analysis also suggests that before data sets obtained with pharmacokinetically different drugs and different dosing regimens may be combined, it is necessary to test whether these sets are homogeneous.

FIG. 9.

AUIC-dependent antimicrobial effects of two fluoroquinolones against different bacterial strains as expressed by Δlog N_min. The figure is reconstructed from Wiedemann et al. (25).

One more reason for apparently conflicting results from studies of different predictors of the antimicrobial effect is the use of different parameters to quantitate the effect. The parameters ln 1/AUEC (AUEC may be referred to as the antilogarithm of the area under the bacterial count-time curve [AUBC] [23]), the area above the time-kill curve (AAC [24]), and Δlog N_min used in the previously cited studies (15, 25) were shown to be insufficiently sensitive to the AUC/MIC of ciprofloxacin (11). Moreover, the use of AUBC and AAC might result in degenerative AUC-response relationships. These reasons also might contribute to the scattered plot relating ln 1/AUEC and AUC/MIC referred to above (15) and to the uncertain relationships between AAC and AUIC which were reconstructed for individual quinolones with data from Wiedemann et al. (25) (data not shown). In the present study an integral parameter of the antimicrobial effect, its intensity (I_E), was related to AUC/MIC, AUC_eff, and T_eff, and logical relationships between each of them and I_E were established. By its very definition, I_E includes the evaluation of full-term killing and regrowth curves from the onset to the end of the antimicrobial effect (9). The impact of recording the entire regrowth phase on the evaluation of the antimicrobial effects of quinolones has been reported recently (11).

This study, performed with bacterial strains with similar susceptibilities, allowed the selection of the best interquinolone predictor of the antimicrobial effect (T_eff), but it did not support the choice of the best intraquinolone predictor among AUC/MIC, AUC_eff, and T_eff. Recently, such a selection was proven to be possible on the basis of data obtained with one quinolone (ciprofloxacin) for organisms with different susceptibilities (21). A specific I_E-log AUC_eff plot was inherent for each of four strains of gram-negative and gram-positive bacteria (MICs, 0.013 to 0.60 μg/ml), whereas the respective I_E-log AUC/MIC and I_E-T_eff relationships were bacterial species independent. From this point of view, AUC/MIC and T_eff may be preferred to AUC_eff as intraquinolone predictors.

Overall, these and other recently published (21) data suggest that the optimal interquinolone predictors of the antimicrobial effect may be selected from studies with pharmacokinetically different drugs, and intraquinolone predictors might be selected from studies with bacteria with different susceptibilities. The concept of inter- and intraquinolone predictors might be useful for the in vitro evaluation of future quinolone compounds. Additional studies with other fluoroquinolones are needed to further support this concept.

FIG. 6.

The kinetics of killing and regrowth of gram-negative bacteria when mimicking ciprofloxacin administration q.d. for E. coli (▴), P. aeruginosa (▪), and K. pneumoniae (•) with (filled symbols) and without (empty symbols) quinolones. The numbers in the bottom right corner of each plot are the simulated AUC/MICs [in (μg · h/ml)/(μg/ml)].