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Antimicrobial Agents and Chemotherapy, March 1999, p. 498-502, Vol. 43, No. 3
0066-4804/99/$04.00+0
Copyright © 1999, American Society for Microbiology. All rights reserved.
Prediction of the Effects of Inoculum Size on the
Antimicrobial Action of Trovafloxacin and Ciprofloxacin against
Staphylococcus aureus and Escherichia coli in
an In Vitro Dynamic Model
Alexander A.
Firsov,1,*
Sergey N.
Vostrov,1
Olga V.
Kononenko,1
Stephen H.
Zinner,2 and
Yury A.
Portnoy1
Department of Pharmacokinetics, Center for
Science and Technology LekBioTech, Moscow 117246, Russia,1 and Division of Infectious
Diseases, Roger Williams Medical Center, Rhode Island Hospital, Brown
University, Providence, Rhode Island2
Received 6 March 1998/Returned for modification 30 September
1998/Accepted 17 December 1998
 |
ABSTRACT |
The effect of inoculum size (N0) on
antimicrobial action has not been extensively studied in in vitro
dynamic models. To investigate this effect and its predictability,
killing and regrowth kinetics of Staphylococcus aureus and
Escherichia coli exposed to monoexponentially decreasing
concentrations of trovafloxacin (as a single dose) and ciprofloxacin
(two doses at a 12-h interval) were compared at
N0 = 106 and 109 CFU/ml
(S. aureus) and at N0 = 106, 107, and 109 CFU/ml (E. coli). A series of pharmacokinetic profiles of trovafloxacin and
ciprofloxacin with respective half-lives of 9.2 and 4 h were simulated at different ratios of area under the concentration-time curve (AUC) to MIC (in [micrograms × hours/milliliter]/[micrograms/milliliter]): 58 to 466 with
trovafloxacin and 116 to 932 with ciprofloxacin for S. aureus and 58 to 233 and 116 to 466 for E. coli,
respectively. Although the effect of N0 was
more pronounced for E. coli than for S. aureus,
only a minor increase in minimum numbers of surviving bacteria and an
almost negligible delay in their regrowth were associated with an
increase of the N0 for both organisms. The N0-induced reductions of the intensity of the
antimicrobial effect (IE, area between control
growth and the killing-regrowth curves) were also relatively small.
However, the N0 effect could not be eliminated
either by simple shifting of the time-kill curves obtained at higher
N0s by the difference between the higher and
lowest N0 or by operating with
IEs determined within the
N0-adopted upper limits of bacterial numbers
(IE's). By using multivariate correlation and
regression analyses, linear relationships between
IE and log AUC/MIC and log
N0 related to the respective mean values [(log AUC/MIC)average and (log
N0)average] were established for
both trovafloxacin and ciprofloxacin against each of the strains
(r2 = 0.97 to 0.99). The antimicrobial effect
may be accurately predicted at a given AUC/MIC of trovafloxacin or
ciprofloxacin and at a given N0 based on the
relationship IE = a + b [(log
AUC/MIC)/(log AUC/MIC)average] 
c [(log
N0)/(log
N0)average]. Moreover, the relative impacts of AUC/MIC and N0 on
IE may be evaluated. Since the c/b
ratios for trovafloxacin and ciprofloxacin against E. coli
were much lower (0.3 to 0.4) than that for ampicillin-sulbactam as
examined previously (1.9), the inoculum effect with the quinolones may
be much less pronounced than with the 
-lactams. The described approach to the analysis of the inoculum effect in in vitro dynamic models might be useful in studies with other antibiotic classes.
| |
INTRODUCTION |
The inoculum effect with its
expected reduction of antimicrobial action at higher starting inocula
has not been extensively studied in in vitro dynamic models (2, 4,
5, 10, 11). Only two of these studies quantified the
inoculum-induced changes in the time-kill curves by calculating either
the areas under the bacterial count-time curves (AUBC
[5]) or the areas between the control growth and the
killing and regrowth curves (IE
[4]). Moreover, only one study was aimed at both
ascertainment of the inoculum effect and also examination of its
predictability (5). Due to the similar slopes of the AUBC
versus logarithm of inoculum size (log N0)
plots, which were established with five strains of Escherichia
coli exposed to the same dose of ampicillin-sulbactam, AUBC was
shown to be quite predictable at a given N0
(5). Furthermore, the time-kill curves observed at a higher
N0 (N02) might be
superimposed on those at a lower N0
(N01) simply by shifting the former curves to
account for the difference between log N01 and
log N02. This allowed the conclusion that an
increase of the starting inoculum does not induce any qualitative (or
unpredictable) reductions in the antimicrobial action of
ampicillin-sulbactam (5).
The present study was designed to examine the above approach to
inoculum effects on the antimicrobial action of trovafloxacin and
ciprofloxacin against Staphylococcus aureus and E. coli in an in vitro dynamic model.
| |
MATERIALS AND METHODS |
Antimicrobial agents and bacterial strains.
Trovafloxacin
mesylate and ciprofloxacin lactate powders were kindly provided by
Roerig, a division of Pfizer, and by Bayer AG, respectively, and
clinical isolates of S. aureus and E. coli were
used in the study. Susceptibility testing was performed in duplicate in
Ca2+- and Mg2+-supplemented Mueller-Hinton
broth at an inoculum size of 106 CFU/ml at 24 h
postexposure. The respective MICs of trovafloxacin for S. aureus and E. coli were 0.15 and 0.25 µg/ml and those
of ciprofloxacin were 0.3 and 0.12 µg/ml.
In vitro dynamic model, simulated pharmacokinetic profiles, and
starting inocula.
A previously described dynamic model
(8) was used in the study. The operation procedure,
reliability of simulations of the quinolone pharmacokinetic profiles,
and high reproducibility of the time-kill curves provided by the model
have been reported elsewhere (7).
A series of monoexponential profiles that mimic single-dose
administration of trovafloxacin and two doses of ciprofloxacin administered with a 12-hour interval were simulated. The simulated half-lives (9.25 h for trovafloxacin and 4.0 h for ciprofloxacin) were consistent with values reported for humans: 7.2 to 9.9 h (12, 14) and 3.2 to 5.0 h (1, 9, 13),
respectively. In experiments with S. aureus the simulated
areas under the concentration-time curve (AUC)/MIC ratios for
trovafloxacin and ciprofloxacin were 58, 116, 233, and 466, and 116, 233, 466, and 932 (µg · h/ml)/(µg/ml), respectively. In
experiments with E. coli the respective AUC/MICs were 58, 116, and 233, and 116, 233, and 466 (µg · h/ml)/(µg/ml). Two
different inoculum sizes that approached approximately 106
and 109 CFU/ml were designed for S. aureus, and
three inoculum sizes, 106, 107, and
109 CFU/ml, were designed for E. coli. With
ciprofloxacin, the designed AUC/MICs reflect the sum of two AUC/MICs
provided by the two doses of the quinolone administered at 12-h
intervals taking into account the residual concentrations at the end of
the first interval.
Duration of the experiments and quantitation of bacterial growth
and killing.
The duration of the experiments was defined in each
case as the time until antibiotic-exposed bacteria reached the maximum numbers observed in the absence of antibiotic (control growth). In all
cases experiments were stopped when bacteria exposed to the quinolones
reached numbers 
1011 CFU/ml. Since the experiments that
simulated low AUC/MIC ratios met this requirement earlier than those
simulating a high AUC/MIC ratio, the duration of the former experiments
was shorter than the latter: the lower the AUC/MIC ratio, the shorter
the observation period.
In each experiment 0.1-ml samples were withdrawn from
bacteria-containing media in the central unit throughout the
observation
period, at first every 30 min, later hourly, then every 3 hours,
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 on Mueller-Hinton agar. After
overnight incubation at 37°C the resulting bacterial colonies
were
counted, and the numbers of CFUs/milliliter were calculated.
The limit
of detection was 10
2 CFU/ml (
7).
Quantitative evaluation of the antimicrobial effect.
The
antimicrobial effect was expressed by its intensity
(IE) as described by the area between control
growth and bacterial killing-regrowth curves from the zero point, the
moment of drug input into the model, up to the time when viable counts
on the regrowth curve are close to maximum values observed without drug (3). The upper limit of bacterial numbers, i.e., the cutoff level in the regrowth and control growth curves used to determine the
IE was 1011 CFU/ml (Fig.
1).
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FIG. 1.
Schematic presentation of the IE
and IE' determinations applied to the kinetics
of killing and regrowth of E. coli exposed to trovafloxacin
(AUC/MIC = 58 [µg · h/ml]/[µg/ml]).
IE (or IE') describes the
dashed area between the control growth (thin lines) and killing and
regrowth (bolded lines) curves at the same cutoff level of
1011 CFU/ml (IE determination) or at
different cutoff levels (IE' determination).
|
|
Since the microorganisms are able to grow up to the same numbers
(10
11 to 10
12 CFU/ml), regardless of the
N0, the ranges of possible increase
in bacterial
numbers at different
N0s are deliberately
unequal:
the higher
N0, the more narrow the
range. For example, at
N0 =
10
9
CFU/ml the microorganisms are allowed to grow by 2 to 3 logs
only,
whereas at
N0 = 10
6 they are able to
grow by 5 to 6 logs. To account for this circumstance,
the control
growth and time-kill curves observed at
N0 = 10
6, 10
7, and 10
7 CFU/ml were
limited from above by levels of 10
8, 10
9, and
10
11 CFU/ml, respectively, and the respective fragments of
IE (
IE')
were determined
within a specific range for each
N0 (Fig.
1).
To reveal the possible net effect of inoculum size, i.e., to examine
whether qualitative changes in the time-kill curves occur
at high
N0s, these curves were shifted by the
differences between
N0 = 10
7 and
10
9 CFU/ml and the minimal
N0
(10
6 CFU/ml). The respective difference in
N0 was subtracted from
each point on the
time-kill curves obtained at the higher inocula
(
5).
Linear regression analysis of the relationships between log
N0 and
IE related to the
respective mean value for each microorganism
and each AUC/MIC was
performed by using STATISTICA software (version
4.3; StatSoft, Inc.).
The same software was used for multivariate
correlation and regression
analyses of the relationships between
IE and log
AUC/MIC and log
N0 normalized by the respective
mean
values for each paired quinolone-bacterial strain. To evaluate
the
relative impacts of
N0 and AUC/MIC on the
observed antimicrobial
effect, coefficients
c and
b were compared at the respective members
of the multiple
regression
|
(1)
|
where
Y is
IE, and
X1 and
X2 are log AUC/MIC
and log
N0 related to their mean values [(log
AUC/MIC)
average and (log
N0)
average],
respectively.
Previously reported data on the antimicrobial effects of
ampicillin-sulbactam on different strains of
E. coli
(
5) were
reassessed in a similar manner. To make the results
comparable,
the areas between the control growth and the time-kill and
regrowth
curves (ABBC) (
6) were calculated within the 8-h
observation
period designed in the earlier study. The ABBC estimates
were
used as the endpoints for multiple correlation and regression
analyses.
| |
RESULTS |
The time courses of viable counts that reflect killing and
regrowth of S. aureus and E. coli exposed to
monoexponentially decreasing concentrations of trovafloxacin and
ciprofloxacin as well as the respective control growth curves are shown
in Fig. 2. As seen in the figure, at all
the AUC/MIC ratios studied an increase of the starting inoculum
resulted in higher absolute numbers of surviving microorganisms. With
both strains, the effect of the inoculum was relatively weak, although
the inoculum-induced changes in killing of E. coli were more
noticeable than those for S. aureus.
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FIG. 2.
The kinetics of killing and regrowth of S. aureus and E. coli exposed to two quinolones at
N0 = 106 and 109 CFU/ml
(S. aureus) and at N0 = 106, 107, and 109 CFU/ml
(E. coli). The number in the right corner of each plot
indicates the simulated AUC/MIC (in [micrograms × hours/milliliters]/[micrograms/milliliters]).
|
|
These minor changes are illustrated by the IE
versus log N0 plots presented in Fig.
3. As seen in the figure, all the plots slope gently, with slightly smaller slopes for S. aureus
than those for E. coli and which in turn are dependent on
the AUC/MIC ratios. Since a specific plot was inherent in each of the
simulated AUC/MIC ratios, a direct comparison of the inoculum effects
for the two microorganisms and the two antibiotics is difficult. To suppress the AUC/MIC-induced differences in the position of the IE-log N0 plots, the
IEs determined at each AUC/MIC were related to
the respective mean values of IE. For example,
being AUC/MIC independent, the relationships between normalized
IEs of trovafloxacin and log
N0 are distinctly different for S. aureus and E. coli (Fig.
4). As seen in the figure, the effect of
the inoculum is more noticeable in the latter case. Similar
AUC/MIC-independent relationships were established with ciprofloxacin
(r2 = 0.90 and 0.96, respectively), although the
differences between the strains were less pronounced (data not shown).
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FIG. 3.
Inoculum-dependent changes in the quinolone
antimicrobial effects expressed by IEs. The
number at each plot indicates the simulated AUC/MIC (in
[micrograms × hours/milliliter]/[micrograms/milliliter]).
|
|
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FIG. 4.
Inoculum-dependent changes in the antimicrobial action
of trovafloxacin against S. aureus and E. coli as
expressed by the normalized IEs.
|
|
To examine qualitative changes in the time-kill curves at higher
N0s, a procedure of superimposing those curves
observed at N0 = 107 and
109 CFU/ml was applied. Figure
5 shows both original and the
N0-adjusted time-kill curves reflecting
trovafloxacin effects on E. coli at different AUC/MICs. As
seen in the figure, the subtraction of the differences in
N0 from each point on the time-kill curves obtained at N0 = 107 and
109 CFU/ml provides only a weak reduction in the area
between the upper and the lower curves, especially at higher AUC/MICs.
In no case did the use of the curve-shifting procedure provide
superimposed time-kill curves. Similar results were obtained with
ciprofloxacin and E. coli (data not shown). This is
consistent with the results of the IE and
IE' determination (Fig.
6). As seen in the figure, unlike
IE, which reflects a systematic reduction in the
antimicrobial effect at higher N0s, the
IE' (a fragment of IE
within the upper limit corrected by the N0)
shows even more pronounced effects at N0 = 107 and 109 CFU/ml than those at
N0 = 106 CFU/ml. Similar findings
were also obtained when comparing the IE's of
ciprofloxacin. Thus, the two examined procedures provide a
misinterpretation of the net effects of inoculum with the quinolones.
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FIG. 5.
An attempt to superimpose the time-kill curves of
E. coli exposed to trovafloxacin by shifting them to account
for the difference in the starting inocula. The number in the right
corner of each plot indicates the simulated AUC/MIC (in
[micrograms × hours/milliliter]/[micrograms/milliliter]).
|
|
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FIG. 6.
Comparison of the inoculum-induced changes in
IE and IE' reflecting the
antimicrobial action of trovafloxacin against E. coli at
different N0s and AUC/MICs.
|
|
To predict the antimicrobial effects at different inocula and AUC/MICs,
the IEs of trovafloxacin and ciprofloxacin
against both S. aureus and E. coli as well as the
ABBCs reflecting the antimicrobial action of ampicillin-sulbactam
against different strains of E. coli were subjected to
multivariate correlation and regression analyses. High correlation
coefficients were established in each case (Table
1), demonstrating a good correspondence
between the observed IEs (or ABBCs) and their
estimates calculated by using equation 1 (see Materials and Methods).
Such an equation allows not only the accurate prediction of the
antimicrobial effect at a given AUC/MIC and a given
N0 but also the establishment of the relative
impact of these two contributors as expressed by the c/b
ratio on the observed effect. These ratios for trovafloxacin and
ciprofloxacin against S. aureus (0.2 to 0.3) and E. coli (0.3 to 0.4) are much less than that for ampicillin-sulbactam
(1.9). Thus, the effect of inoculum on the antimicrobial action of
these quinolones is relatively less pronounced than that for the
-lactam antibiotic studied.
| |
DISCUSSION |
This study suggests that the inoculum effect on the antimicrobial
action of trovafloxacin and ciprofloxacin is relatively weak, and it is
less pronounced than that of ampicillin-sulbactam against E. coli. Unlike the -lactams (5), a simple procedure of
shifting the time-kill curves obtained at higher inoculum sizes by the
difference in the starting inocula did not provide superimposed curves
and, in fact, overestimates the net effect of inoculum. The same
applies to operating with the inoculum-corrected upper limits for the
IE determination (IE's):
rather than remaining constant, the IE's rise
systematically with increasing N0. Similar paradoxical results were obtained by using the differences between log
N0 and the logarithm of minimal numbers of
bacteria after exposure to the quinolones (
log
Nmin; data not shown).
Like the AUBC versus log N0 plots for E. coli strains with different susceptibilities exposed to the same
AUC of ampicillin-sulbactam, i.e., at different AUC/MIC ratios, the
IE-log N0 plots
established with trovafloxacin and ciprofloxacin were also distinctly
dependent on the simulated AUC/MIC (Fig. 3). To simultaneously account
for the impact of inoculum size and AUC/MIC ratio on the antimicrobial effect, multiple regressions were established relating the
IE (with the quinolones) or ABBC (with the
-lactams) to both log AUC/MIC and log N0 by
using multivariate correlation and regression analyses. These
regressions may be useful not only to accurately predict the
antimicrobial effect at a given AUC/MIC and a given N0 but also to evaluate the relative
contributions of these two factors. By comparing the coefficients at
the AUC/MIC and N0 terms in the regression
equation, the relative impact of the inoculum size on the effects of
trovafloxacin and ciprofloxacin against E. coli was shown to
be much less substantial than with ampicillin-sulbactam. The described
approach to the evaluation of competitive influences of antibiotic
concentration (AUC or dose) and inoculum on the antimicrobial effect
might be useful for other antimicrobials and microorganisms.
| |
ACKNOWLEDGMENT |
This study was supported by Roerig, a division of Pfizer.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Department of
Pharmacokinetics, Center for Science and Technology
LekBioTech, 8 Nauchny proezd, Moscow 117246, Russia. Phone:
011-7-095-332-3435. Fax: 011-7-095-331-4116. E-mail:
firsov{at}dol.ru.
| |
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Antimicrobial Agents and Chemotherapy, March 1999, p. 498-502, Vol. 43, No. 3
0066-4804/99/$04.00+0
Copyright © 1999, American Society for Microbiology. All rights reserved.
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Top
Abstract
Introduction
