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Antimicrobial Agents and Chemotherapy, March 2001, p. 927-931, Vol. 45, No. 3
0066-4804/01/$04.00+0 DOI: 10.1128/AAC.45.3.927-931.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
Relationships of the Area under the Curve/MIC Ratio to Different
Integral Endpoints of the Antimicrobial Effect: Gemifloxacin
Pharmacodynamics in an In Vitro Dynamic Model
Alexander A.
Firsov,1,*
Irene Y.
Lubenko,1
Yury A.
Portnoy,1
Stephen H.
Zinner,2 and
Sergey N.
Vostrov1
Department of Pharmacokinetics, Centre of
Science & Technology LekBioTech, Moscow,
Russia,1 and Mount Auburn Hospital,
Harvard Medical School, Cambridge, Massachusetts2
Received 26 April 2000/Returned for modification 21 October
2000/Accepted 26 December 2000
 |
ABSTRACT |
Most integral endpoints of the antimicrobial effect are determined
over an arbitrarily chosen time period, such as the dosing interval
(
), regardless of the actual effect duration. Unlike the -related
endpoints, the intensity of the antimicrobial effect (IE) does consider its duration
from time zero
to the time when bacterial counts on the regrowth curve achieve the
same maximal numbers as in the absence of the antimicrobial. To examine
the possible impact of this fundamental difference on the relationships of the antimicrobial effect to the ratio of the area under the concentration-time curve (AUC) to the MIC, a clinical isolate of
Staphylococcus aureus was exposed to simulated gemifloxacin pharmacokinetics over a 40-fold range of AUC/MIC ratios, from 11 to
466 h. In each run, IE and four
-related endpoints, including the area under the time-kill curve
(AUBC), the area above the curve (AAC), the area between the control
growth and time-kill curves (ABBC), and the ABBC related to the area
under the control growth curve (AUGC), were calculated for = 24 h. Unlike the IE, which displayed
pseudolinear relationships with the AUC/MIC ratio; each -related
endpoint showed a distinct saturation at potentially therapeutic
AUC/MIC ratios (116 to 466 h) when the antimicrobial effect
persisted longer than . This saturation results from the
underestimation of the true effect and may be eliminated if ABBC, AAC,
and AUBC (but not AUGC) are modified and determined in the same manner
as the IE to consider the actual effect
duration. These data suggest a marginal value of the -related endpoints as indices of the total antimicrobial effect. Since all of
them respond to AUC/MIC ratio changes less than the
IE, the latter is preferable in
comparative pharmacodynamic studies.
| |
INTRODUCTION |
Different integral endpoints
(Fig. 1), including the area under the
time-kill curve (AUBC, sometimes abbreviated AUBKC [9]) (12; S. M. Navashin, I. P. Fomina, V. M. Chernykh, A. D. Nazarov, and A. A. Firsov,
Abstr. 9th Int. Congr. Infect. Parasitic Dis., abstr. 1394, 1986), the
area above the curve (AAC) (13), the algebraic sum of the
areas around the level of the initial inoculum, the area between
the control growth and time-kill curves (ABBC) (4), and
the ABBC related to area under the control growth curve (AUGC)
(J. Bosso, C. Bonapace, R. White, L. Friedrich, D. Cappeletty,
R. Mercier, H. Houlihan, J. Aeschliman, and M. Rybak, Abstr.
38th Intersci. Conf. Antimicrob. Agents Chemother.,
abstr. 134, 1998), have been described and applied in
pharmacodynamic studies using in vitro models. All of these endpoints
are determined over an arbitrarily chosen time period, such as the
dosing interval (), regardless of the actual effect duration. Unlike
the -related endpoints, the intensity of the antimicrobial effect
(IE) does consider its duration, from time zero
to the time when bacterial counts on the regrowth curve achieve the
same maximal numbers as in the absence of the antimicrobial (3,
7).
This study was designed to examine the possible impact of the
fundamental difference between the IE and the
-related endpoint ABBC, AAC, AUGC, or AUBC on the area under the
concentration-time curve (AUC)/MIC-response relationships, with
special emphasis on AUC/MIC ratios in the therapeutic range, 100 to 500 h (10, 11), and the possibility of
improving the -related endpoints with the use of specific
modifications. To compare the different endpoints of the effect,
simulated gemifloxacin pharmacodynamics with Staphylococcus
aureus were studied over a wide range of AUC/MIC ratios using an
in vitro dynamic model.
| |
MATERIALS AND METHODS |
Antimicrobial agent and bacterial strain.
Gemifloxacin
mesylate powder, kindly provided by SmithKline Beecham Pharmaceuticals,
and a clinical isolate of methicillin-resistant S. aureus
were used in this study. The MIC of gemifloxacin, determined as
described elsewhere (5), was 0.01 µg/ml.
In vitro dynamic model and simulated pharmacokinetic
profiles.
A previously described dynamic model (7)
was used in this study. The operation procedure, reliability of
simulations of quinolone pharmacokinetic profiles, and the high
reproducibility of the time-kill curves provided by the model have been
reported elsewhere (5).
A series of monoexponential profiles that mimic single-dose
administration of gemifloxacin was simulated. The simulated half-life
(7.4 h) represented weighted medians of values reported for humans:
5.88 to 8.77 h (
1,
2). The simulated AUC/MIC ratios
and
the peak concentration-to-MIC ratios varied from 11 to 466 h
and
from 1 to 44,
respectively.
Quantitation of time-kill curves and antimicrobial effect.
In each experiment, multiple sampling of bacterium-containing medium
from the central compartment was performed throughout the observation
period. In each case, the duration of the experiments was defined
as the time until antibiotic-exposed bacteria reached the maximum
numbers observed in the absence of the antimicrobial (
1010 CFU/ml). The procedure used to quantitate viable
counts has been reported elsewhere (5). The lower limit of
accurate detection was 5 × 102 CFU/ml.
Based on time-kill data, four
-related endpoints of the
antimicrobial effect, i.e., the ABBC, AAC, AUGC, and AUBC at
=
24 h, as well as the
-independent
IE,
were determined in each
run. The upper limit of bacterial numbers,
i.e., the cutoff level
on the regrowth and control growth curves used
to determine the
ABBC, AAC, AUGC, AUBC, and
IE
was 10
9 CFU/ml.
Relationships of antimicrobial effect to the AUC/MIC ratio.
Each integral endpoint of the antimicrobial effect was related to the
log AUC/MIC of gemifloxacin. The -related endpoint-log AUC/MIC ratio
data sets were fitted by sigmoidal models. For the ABBC and AUGC, the
following equation was used:
![<UP>ABBC or AUGC = </UP>E<SUB><UP>max</UP></SUB>x<SUP><UP>s</UP></SUP><UP>/</UP>[(x<SUB><UP>50</UP></SUB>)<SUP><UP>s</UP></SUP><UP> + </UP>x<SUP><UP>s</UP></SUP>]](/content/vol45/issue3/fulltext/927/img001.gif)
|
(1)
|
For the AUBC and AAC; the following equation was used:
![<UP>AAC or AUBC = </UP>E<SUB><UP>max</UP></SUB><UP> + </UP>(E<SUB><UP>min</UP></SUB><UP> − </UP>E<SUB><UP>max</UP></SUB>)<UP>/</UP>{<UP>1 + exp </UP>[(x − x<SUB><UP>50</UP></SUB>)<UP>/dx</UP>]}](/content/vol45/issue3/fulltext/927/img002.gif)
|
(2)
|
where
x is the log AUC/MIC ratio,
Emax and
Emin are the
maximal and minimal values of the antimicrobial effect,
x50 is
x corresponding to
Emax/2, and
dx and
s are
parameters reflecting
width and sigmoidicity, respectively. Equation
1
was also used
to described the AUC/MIC relationships of the modified
AUGC (AUGC
E;
see
Results).
As for most AUC/MIC ratio ranges,
IES were linearly related to the log
AUC/MIC ratio; the
IE-log AUC/MIC ratio
data,
except for the
IE value corresponding to the
minimal AUC/MIC
ratio of 11 h, were fitted by the linear equation
|
(3)
|
where
a and
b are parameters. The
same equation was also applied to the modified AAC (AAC
E)
and AUBC (AUBC
E).
| |
RESULTS |
The time-kill curves of S. aureus exposed to
different AUC/MIC ratios of gemifloxacin are shown in Fig.
2, which shows that gemifloxacin rapidly
killed bacteria during the first 3 to 4 h at AUC/MIC ratios of
21 h. At the lowest AUC/MIC ratio of 11 h, a reduction in viable
counts was observed only over the first hour. The minimal numbers of
surviving bacteria differed substantially when the simulated AUC/MIC
ratio increased from 11 to 58 h. Further increases in the AUC/MIC
ratio were accompanied only by a small decrease in minimal counts,
although the AUC/MIC ratio increase-induced differences in this
endpoint were still seen. Unlike the minimal counts, the times to
regrowth were much more dependent on the AUC/MIC ratio: the higher the
AUC/MIC ratio, the later the regrowth.
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FIG. 2.
Killing and regrowth kinetics of S. aureus
exposed to different AUC/MIC ratios (indicated in hours above each
curve) of gemifloxacin.
|
|
Figure 3 reflects the areas that are
exploited by the IE, ABBC, AAC, and AUBC. As
seen in Fig. 3, only the areas associated with the
IE systematically increase in the AUC/MIC ratio,
including potentially therapeutic values of 116 to 466 h. Unlike
the IE, the ABBC and AAC increased up to an
AUC/MIC ratio of 116 h, with minimal further increases in these
endpoints at AUC/MIC ratios of 233 and 466 h. Similarly, the AUBC
decreased up to an AUC/MIC ratio of 116 h, with a minimal further
decrease at the higher AUC/MIC ratios. As seen in the three bottom rows
of Fig. 3, the inability of the ABBC, AAC, and AUBC to adequately
reflect the apparently greater effects of gemifloxacin at AUC/MIC
ratios of 233 and 466 h is because these -related endpoints
exploit the truncated areas that ignore substantial portions of the
actual effect. Neither the ABBC, the AAC, nor the AUBC considers the persisting effect at times of >, and therefore, they underestimate the true antimicrobial effect of a single dose at therapeutic AUC/MIC
ratios. This also applies to the AUGC. Moreover, because of their
-related nature, the AAC and AUBC (but not the ABBC) underestimate
the effect at lower AUC/MIC ratios (e.g., the three upper rows of Fig.
3). Indeed, the respective areas cover the zones where the effect has
vanished. This results in even more negative values of the AAC and the
overestimated AUBC.
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FIG. 3.
Areas exploited by the IE, ABBC,
AAC, and AUBC
( )
including the zones of vanished effect
( ) and
excluding the zones of persisting effect
( ).
|
|
These shortcomings of the -related endpoints are reflected in the
specific patterns of the AUC/MIC-response curves that contain something
like a plateau at therapeutic AUC/MIC ratios (Fig.
4). For example, only a 10% increase in
the ABBC and AAC, a 6% increase in the AUGC, and a 10% decrease in
the AUBC accompany a 300% increase in the AUC/MIC ratio from 116 to
466 h (Fig. 5). The modest sensitivity of
these -related endpoints to the AUC/MIC ratio, i.e., the saturation of the effect expressed by the ABBC, AUGC, AAC, and AUBC, is the result
of their underestimating the effect. No such saturation is seen with
the IE, an endpoint that considers the effect
duration-dependent areas rather than the truncated areas. This results
in an 80% increase in the IE associated with
the same 300% increase in the AUC/MIC ratio (Fig. 5).
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FIG. 4.
AUC/MIC ratio-dependent endpoints of the
antimicrobial effect of gemifloxacin fitted by equations 1 (ABBC,
AUGC, and AUGCE), 2 (AUBC and AAC), and 3 (IE  ABBCE, AACE; and
AUBCE). IE ABBCE,
a =  187 and b = 164; ABBC;
Emax = 137, x50 = 1.54, and s = 8.38; AUGC,
Emax = 65, x50 = 1.55, and s = 8.36; AUGCE;
Emax = 59, x50 = 1.25, and s = 7.05; AAC,
Emax = 71, Emin = 77, x50 = 1.51, and dx = 0.2; AACE, a = 93 and b = 79; AUBC, Emax = 219, Emin = 76, x50 = 1.53, and dx = 0.2; AUBCE,
a = 50 and b = 78. The therapeutic
range of AUC/MIC ratios is indicated by the shaded area.
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FIG. 5.
AUC/MIC ratio increase-induced changes ( ) in the
integral endpoints over the therapeutic range of AUC/MIC ratios (116 to
466 h).
|
|
| |
DISCUSSION |
Although each of the five integral endpoints, ABBC,
AUGC, AAC, AUBC, and IE, is purported to
be a measure of the total antimicrobial effect observed in in vitro
pharmacodynamic studies, they reflect it differently. In contrast to
IE, which considers the actual effect duration,
the -related ABBC, AUGC, AAC, and AUBC underestimate the effect when
its duration exceeds . In addition, the AAC and AUBC underestimate
the effect if its duration is less than (Fig. 3). As a result,
the respective ABBC-, AUGC-, AAC-, and AUBC-log AUC/MIC curves
were saturable whereas no saturation was seen in the
IE-log AUC/MIC plots (Fig. 4). Although much
less pronounced than with -related endpoints, a slight saturation
may be seen in the IE-log AUC/MIC ratio plots as
reported in studies with ciprofloxacin (6) and
levofloxacin (8). In this light, the patterns of the
IE-log AUC/MIC ratio plots shown in Fig. 4 can be considered pseudolinear.
The observed saturation of the -related endpoints, i.e., small, if
any, changes in the ABBC, AAC, and AUBC at AUC/MIC ratios of
approximately 50 to 1,000 h, was reported previously in a
pharmacodynamic study with ciprofloxacin (7) and
that of the AUBC at AUC/MIC ratios of 100 to 500 h in a
study with gemifloxacin (A. P. MacGowan, A. Janowska,
R. S. Hillman, H. A. Holt, and K. E. Bowker, Abstr. 39th
Intersci. Conf. Antimicrob. Agents Chemother., abstr. 21, 1999).
Moreover, the extent of the saturation of the ABBC-, AAC-, and AUBC-log AUC/MIC ratio curves was less noticeable with the longer
(7). In fact, with the prolonged observation periods that cover more of the time-kill curves, the limitations of the -related endpoints became less dramatic and the -related
endpoints correlated better with the IE, which
is free of these limitations. So, the saturable patterns of the ABBC-,
AUGC-, AAC-, and AUBC-log AUC/MIC ratio curves may not be identified
with saturation of the antimicrobial effect as such.
It is interesting that if the ABBC and AAC were determined in the same
manner as the IE, i.e., by considering the
effect duration, both endpoints (ABBCE and
AACE) should be much more sensitive to increases in the
AUC/MIC ratio (Fig. 4). In this case, the 300% increase in the AUC/MIC
ratio would give an 80% increase in the ABBCE (that is
identical to the IE) and a 100% increase in the
AACE and there would be no more saturation of the effect at
the higher AUC/MIC ratios. In addition, at the lower AUC/MIC ratios,
the contribution of the negative areas in the AACE is less
substantial than the AAC and the respective
AACES are less negative than the AACs. A
similarly modified AUBC (AUBCE) responds to the AUC/MIC
ratio changes better than the AUBC (a 30% increase in the
AUBCE versus a 10% decrease in the AUBC). Moreover, unlike
the AUBC, which is a reverse measure of the antimicrobial effect, being
a direct measure of the effect duration, the AUBCE systematically increases with an increase in the AUC/MIC ratio. As seen
in Fig. 4, in contrast to the unmodified endpoints ABBC, AAC, and AUBC,
the respective modified endpoints ABBCE
(IE), AACE, and AUBCE
exhibit plateau-free AUC/MIC ratio relationships at potentially
therapeutic AUC/MIC ratios. Unlike the ABBCE, the AACE, and the AUBCE, a modified AUGC
(AUGCE) shows a plateau that is similar to that of the
AUGC: a 10% increase in the AUGCE appears to be comparable
to a 6% increase in the AUGC that is associated with the 300%
increase in the AUC/MIC ratio.
In conclusion, this and a previous study (7) suggest that
an optimal endpoint of the total antimicrobial effect may not be
independent of its duration. In its turn, the duration of the effect is
directly related to the definition of the effect. If it is defined as
the difference between logarithms of a number of antimicrobial-exposed
and -unexposed organisms (7), the initial reduction of
viable counts may be attributed to killing that predominates over their
growth, whereas regrowth results from bacterial growth that
predominates over killing. In this light, all of the events that occur
from the moment of initial deflection of the time-kill curve from the
control growth curve to the moment of subsequent rapprochement of these
curves (at the end of the regrowth phase) may be attributed to the
antimicrobial effect. As the IE reflects these
events most comprehensively, it may be considered a preferable endpoint
of the total antimicrobial effect in an in vitro setting.
| |
ACKNOWLEDGMENT |
This study was supported by SmithKline Beecham Pharmaceuticals.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Department of
Pharmacokinetics, Centre for Science & Technology LekBioTech, 8 Nauchny Proezd, Moscow 117246, Russia. Phone: 7 (095) 332-3435. Fax: 7 (095)
332-6307. E-mail: firsov{at}dol.ru.
| |
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Antimicrobial Agents and Chemotherapy, March 2001, p. 927-931, Vol. 45, No. 3
0066-4804/01/$04.00+0 DOI: 10.1128/AAC.45.3.927-931.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
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Abstract
Introduction
