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Antimicrobial Agents and Chemotherapy, September 2001, p. 2436-2440, Vol. 45, No. 9
0066-4804/01/$04.00+0 DOI: 10.1128/AAC.45.9.2436-2440.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
Pharmacokinetic and Pharmacodynamic Parameters for Antimicrobial
Effects of Cefotaxime and Amoxicillin in an In Vitro Kinetic
Model
I.
Gustafsson,1,*
E.
Löwdin,2
I.
Odenholt,2 and
O.
Cars2
Departments of Clinical
Bacteriology1 and Infectious
Diseases,2 University Hospital, Uppsala, Sweden
Received 25 September 2000/Returned for modification 25 February
2001/Accepted 5 June 2001
 |
ABSTRACT |
An in vitro kinetic model was used to study the relation between
pharmacokinetic and pharmacodynamic (PK-PD) parameters for antimicrobial effect, e.g., the time above MIC (T>MIC), maximum concentration in serum (Cmax), and area under
the concentration-time curve (AUC). Streptococcus
pyogenes and Escherichia coli were exposed to
cefotaxime, and the activity of amoxicillin against four strains of
Streptococcus pneumoniae with different susceptibilities to
penicillin was studied. The drug elimination rate varied so that the
T>MIC ranged from 20 to 100% during 24 h, while the AUC and/or the initial concentration (Cmax) were
kept constant. For S. pyogenes and E. coli, the
maximal antimicrobial effect (Emax) at 24 h occurred when the antimicrobial concentration exceeded the MIC for 50 and 80% of the strains tested, respectively. The penicillin-susceptible pneumococci (MIC, 0.03 mg/liter) and the penicillin-intermediate strain (MIC, 0.25 mg/liter) showed maximal killing by amoxicillin at a T>MIC of 50%. For a strain for
which the MIC was 2 mg/liter, Cmax needed to be
increased to achieve the Emax. Under the
condition that Cmax was 10 times the MIC, Emax was obtained at a T>MIC of 60%,
indicating that Cmax, in addition to
T>MIC, may be an important parameter for antimicrobial effect on
moderately penicillin-resistant pneumococci. For the strain for which
the MIC was 4 mg/liter, the reduction of bacteria varied from 
0.4 to
3.6 log10 CFU/ml at a T>MIC of 100%, despite an
initial antimicrobial concentration of 10 times the MIC. Our studies
have shown that the in vitro kinetic model is a useful complement to
animal models for studying the PK-PD relationship for antimicrobial
effect of antibiotics.
| |
INTRODUCTION |
The optimal dosing regimen for
antibiotics is still not fully understood. Obtaining clinical and
microbiological efficacy is essential, but dosing regimens must also be
tailored to minimize the risk for emergence of antibiotic-resistant
strains. The prevailing method for determination of bacterial
susceptibility, the MIC, is only a rough measure of antimicrobial
activity. It gives no information about the time course or whether the
bactericidal effect is dependent on drug concentration. Many additional
factors need to be studied in order to increase knowledge about optimal dosing regimens, e.g., the relation between pharmacokinetic and pharmacodynamic parameters (PK-PD), interactions with the immune system
of the host, and pharmacological determinants for selection of
resistance at the site of infection and in the normal flora.
A number of reasons, e.g., economical and ethical, limit the
possibilities for dose finding in clinical studies in which the PK-PD
relationship can be defined for optimal efficacy. Another problem
is that the pharmacokinetic parameters are interdependent; i.e.,
an increased dose leads to a higher maximum concentration (Cmax) and a larger area under the
concentration-time curve (AUC), as a well as a longer time above the
MIC (T>MIC) (7, 8, 13). Studies of animal and in
vitro models give the possibility to minimize the interdependence
between parameters. The aim of this study was to evaluate the
usefulness of an in vitro kinetic model for defining the
pharmacokinetic parameters that correlate to efficacy for 
-lactam
antibiotics. For this purpose, we studied the effect of
cefotaxime against Streptococcus pyogenes and
Escherichia coli. The AUC was kept constant, whereas
the T>MIC and Cmax varied. To investigate
if the parameters of efficacy were similar in strains with and without
acquired resistance mechanisms, we studied the activity of amoxicillin
against four strains of Streptococcus pneumoniae with
different susceptibilities to penicillin.
| |
MATERIALS AND METHODS |
Bacteria and media.
The included strains were S. pyogenes M12 NCTC P1800; E. coli ATCC 25922; a
penicillin-sensitive pneumococcus (PSP), S. pneumoniae ATCC
6306; two clinical isolates of penicillin-resistant pneumococcus (PRP),
508-1046 and 40932; and a penicillin-intermediate pneumococcus (PIP),
9506.07-126. Strain 508-1046 derives from the University Hospital,
Uppsala, Sweden, and strain 40932 was obtained from the Centre
Hospitalier Intercommunal, Créteil, France. The PIP 9506.07-126 was a clinical isolate from Reykjavik, Iceland. In addition to
penicillin resistance, the PIP and the PRP 40932 were also resistant to
trimethoprim-sulfamethoxazole. The PRP 508-1046 carried multidrug
resistance to chloramphenicol, trimethoprim-sulfamethoxazole, and
tetracycline but was sensitive to the
macrolide-lincosamide-streptogramin B group. The gram-positive
strains were cultured in Todd-Hewitt broth saturated with
CO2. E. coli was cultured in Mueller-Hinton broth, supplemented with Ca2+ (50 mg/l) and
Mg2+ (50 mg/l).
Antibiotics.
Cefotaxime (Claforan; Aventis) was dissolved in
sterile distilled water to a concentration of 10 mg/ml. Amoxicillin
trihydrate (Astra, Södertälje, Sweden) was dissolved in
an equal volume of 0.1 M NaOH and phosphate-buffered
saline, pH 7.2, to 10 mg/ml. The stock solutions were prepared before
each experiment and diluted in broth to the desired concentration.
MIC determination.
MICs were determined by the macrodilution
technique, at an inoculum of 1 × 105 to 2 × 105 CFU/ml, according to NCCLS standards (17).
The MIC was defined as the lowest concentration inhibiting visible
growth after 20 h. The MIC determinations were made in triplicate
on separate occasions.
Determination of antibiotic concentrations.
The
microbiological agar diffusion method was used with 1.5% nutrient agar
(Difco Laboratories, Detroit Mich.). Plates were seeded with a
standardized inoculum of Providencia rettgeri P66 (Swedish
Institute for Infectious Disease Control, Solna, Sweden) for the
determination of cefotaxime concentration (18) and a spore
suspension of Bacillus stearothermophilus ATCC 3032 for the
determination of amoxicillin concentration (5). Antibiotic standards and the samples were applied to agar wells. All assays were
made in triplicate, and the plates were incubated overnight at 35 and
56°C, respectively. The limit of detection was 0.062 mg/liter for
cefotaxime and 0.031 mg/liter for amoxicillin. The correlation
coefficient for the standard curves was always >0.99.
The antibiotics were investigated for their stability under the
experimental conditions. Dilutions of cefotaxime (10 mg/liter) and
amoxicillin (1 mg/liter) in broth were incubated at 35°C for 24 h.
Samples were collected after 0, 6, 20, and 24 h, and the concentrations were determined as described above. Degradation of
cefotaxime was not taken into account (18% ± 6% at 24 h),
whereas amoxicillin was degraded by 50% ± 1%. This implies a
half-life (t1/2) of 24 h, giving a
k of 0.0289 (see formula below). In the results with PSP,
the T>MIC was recalculated to include the degradation in the
graph. In the experiments with PIP and PRP strains, the degradation was
included in the flow rate. The initial concentrations (C0) were determined in all experiments.
Amoxicillin concentrations at 24 h were also determined to confirm
the expected values.
In vitro kinetic model.
The in vitro kinetic model has
previously been described (15). It consists of a spinner
flask (110 ml) with an open bottom that was specially constructed to
fit into a new holder that has an outlet connected to a pump (P-500;
Pharmacia Biotech, Uppsala, Sweden). A filter membrane with a
pore size of 0.45 µm, lying on a perforated metal support, was placed
between the flask and the holder, impeding the elimination of bacteria.
A magnetic stirrer ensured homogenous mixing and prevented membrane
pore blockage. In one of the side arms, a silicone membrane enabled
repeated sampling. A thin plastic tubing from a vessel containing fresh medium was connected to the other arm. The medium was drawn from the
flask at a constant rate by the pump, while fresh sterile medium was
sucked into the flask at the same rate by the negative pressure built
up inside. The antibiotic was diluted according to first-order
kinetics: C = C0 × e
kt,
where C is the achieved concentration after a constant
elimination rate (k) of the C0 during
the course of time (t). The AUC at 24 h
(AUC24) was calculated as follows: AUC = C0/k C24/k, where C24 is the concentration after 24 h,
depending upon the elimination constant k, determined from
k = ln2/t1/2.
Experiments.
The intention during the experiments was to
keep the AUC constant over 24 h, while the T>MIC and the
Cmax varied (Fig.
1). Different T>MIC, ranging from 20 to 100% of 24 h, were investigated. The flask was prepared with
appropriate broth and the desired initial antibiotic concentration and
was installed in the thermostatic room (35°C). Bacteria from a 6- to
7-h broth culture were added, at an inoculum of 105 CFU/ml
for S. pyogenes and S. pneumoniae and at
104 CFU/ml for E. coli. The flow rate of the
pump was set to obtain the different t1/2s of
the drugs (Table 1).
C0, T>MIC, AUC, and the inoculum sizes for
the different experiments are presented in Table
2.
Samples for viable counts were withdrawn at 0, 3, 6, 12, and 24 h.
Appropriate dilutions were plated (0.1 and 0.01 ml) on
Columbia agar
(Acumedia Manufacturers, Inc., Baltimore, Md.) with
5% horse blood and
incubated overnight, and viable counts were
determined. The sensitivity
of the viable count was estimated
at 50 CFU/ml.
S. pyogenes was exposed to a single dose of cefotaxime in a
series of experiments. The T>MIC varied from 20 to 100%. The AUC
was kept constant at 1.4 mg/liter · h. A similar series was
performed
with
E. coli. The AUC was kept constant at 4.8 mg/liter · h, though
it was increased to 5.5 mg/L · h for
experiments with 100% T>MIC.
The activity of amoxicillin was
studied against four
S. pneumoniae isolates with
different susceptibilities to penicillin (Table
2). All experiments
were performed in
triplicate.
| |
RESULTS |
MICs.
The MICs are presented in Table 2.
Pharmacodynamics of cefotaxime.
Figure
2 shows the killing of S. pyogenes as the difference between the initial inoculum and the
number of bacteria at 24 h (change in log10 CFU per
milliliter). There was a clear difference in killing when the
T>MIC increased from 40 to 50%, although some regrowth occurred
in single experiments at T>MIC of 50, 60, and 70%. The mean
maximal antimicrobial effect (Emax) was achieved when the cefotaxime level exceeded the MIC for 50% of 24 h.
Cmax continuously decreased at higher T>MIC
(Fig. 1), indicating that Cmax was not the main
parameter for efficacy.
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|
FIG. 2.
S. pyogenes exposed to cefotaxime. Values are
presented as the change in the number of CFU per milliliter at
24 h with a constant AUC of 1.4 mg/liter · h and different
T>MIC. Error bars, standard deviation.
|
|
For
E. coli exposed to cefotaxime, a T>MIC of 80% was
needed to get a complete killing (Fig.
3). However, the lowest
C0 (2.4
times the MIC) giving 100%
T>MIC gave regrowth (data not shown).
When the
C0 and AUC were increased to three times the MIC
and
5.5 mg/liter · h, respectively (Table
2), complete killing
occurred.
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FIG. 3.
E. coli exposed to cefotaxime. Values are
presented as the change in the number of CFU per milliliter at 24 h with a constant AUC of 4.8 mg/liter · h ± standard
deviation/error bars. At 100% T>MIC, Cmax
was three times the MIC, giving an AUC of 5.5 mg/liter · h.
|
|
Pharmacodynamics of amoxicillin.
Emax
was seen for the PSP and PIP strains with a T>MIC of approximately
50% (Fig. 4 A and B). When the PRP
strain for which the MIC was 2 mg/liter was exposed to the same
conditions as PSP and PIP, with a low initial dose for 100%
T>MIC, regrowth occurred after 12 h in some experiments. The
Cmax was therefore increased to a constant
initial dose of 10 times the MIC. These conditions gave an
Emax at 60% T>MIC (Fig. 4C).
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|
FIG. 4.
The effect of amoxicillin at different T>MIC
against S. pneumoniae. (A) PSP; (B) PIP; (C) PRP (MIC, 2 mg/liter), with an initial Cmax of 10 times the
MIC and 3 times the MIC at 90 and 100%, respectively; (D) PRP (MIC, 4 mg/liter), with an initial Cmax of 10 times the
MIC. Each dot represents an experiment, and the mean is shown as a
line. The graphs illustrate change in number of bacterial CFU per
milliliter at 24 h compared with the initial inoculum. Error bars,
standard deviation.
|
|
The PRP for which the MIC was 4 mg/liter gave ambiguous results.
In a series of experiments with the T>MIC ranging from 28
to 80%
and the
Cmax ranging from 2.4 to 12 times the
MIC, the
pattern was not clear. In all experiments an initial reduction
of 2 to 3 log
10 was noted during the first 6 h. Then,
regrowth
occurred irregularly, and the reduction of bacteria varied
from
1 to 3.9 log
10 at 100% T>MIC. The design of the
experiments was
therefore adjusted to see whether an increased
Cmax would sustain
the killing process. The
initial concentration was set to 10 times
the MIC, and the T>MIC
was 36 to 100%. The results exhibited a
similar pattern, shown in Fig.
4D. A predictable killing effect
was not seen for this strain even with
100% T>MIC and an initial
C0 of 20 times
the MIC (not shown in Fig.
4). When bacteria, isolated
at 24 h,
were replicated onto plates containing amoxicillin at
4, 8, and 20 mg/liter there was no growth. Further studies on
this strain showed an
MIC/minimum bactericidal concentration ratio
of 2, and lysis during
4 h did not fulfil the criteria for tolerance
defined by Henriques
Normark et al. (
12).
| |
DISCUSSION |
The main objectives of this study were to evaluate the usefulness
of an in vitro kinetic model in defining the PK-PD parameter for
antimicrobial effect and to relate our results to those of other in
vitro studies and animal models. Several animal models, in particular
the thigh infection mice model, have been used for characterization of
PK-PD relationships. Since the animals have a fixed elimination rate,
different dosing regimens are used to achieve a variation in AUC and
T>MIC. In the in vitro kinetic model, both the dose and the
elimination rate can be varied, which makes it possible to minimize the
interdependency of the different parameters for antimicrobial effect.
Our results showed an Emax of 50% T>MIC of
-lactam antibiotics for S. pyogenes, PSP, and PIP. For
E. coli a longer time of exposure, 80% T>MIC, was
needed. Vogelman et al. showed, using the thigh infection mouse model, that the number of E. coli cells exposed to cefazolin was
reduced when the concentration in serum exceeded the MIC for at least 60% of 24 h. To obtain Emax, 100%
T>MIC was needed (21). A possible explanation of why
E. coli requires a longer T>MIC for maximal killing is
that -lactam antibiotics give a pronounced effect at subinhibitory
concentrations in the postantibiotic phase for gram-positive bacteria
but not for gram-negative bacteria (6). However, the
absolute figures on the T>MIC needed for maximal efficacy must be
interpreted cautiously since the MIC may vary according to methodology,
inoclum size, etc. For example, when tested with the E-test method (AB
Biodisk, Solna, Sweden), the MIC for PRP strain 508-1046 was lower
(MIC, 1.5 mg/liter) than that obtained by the macrodilution technique
(4 mg/liter). An Emax achieved at 50%
T>MIC with the MIC of 4 mg/liter would then correspond to 80% if
a MIC of 1.5 were used instead.
In vivo studies of amoxicillin against pneumococci, in different animal
models, have reported an Emax at 44 to 60%
T>MIC for PSP and PIP (1, 2). Barry et al.
demonstrated that amoxicillin was able to clear the infection of two
resistant pneumococci (MICs 1 and 2 mg/liter) if the dose was increased
(3). However, in a mouse pneumonia model, significant
bactericidal effect was not achieved on PRP strains for which the MIC
was 
2 mg/liter, even with a dose/MIC ratio of 200 (2).
The reason for these contradictory results is unclear but could be
attributed to tolerance (2) or to the low growth rate of
pneumococci in the pneumonia model (10). Experiments in
vitro have also reported the need for high peak concentrations and
repeated dosing for PRP (14, 19). Clinical studies of
acute otitis media caused by pneumococci are difficult to evaluate and
use for comparison, since self-limiting factors are involved
(4). An extensive clinical study by Dagan et al. concluded
that penicillin and amoxicillin-clavulanate susceptibilities of
S. pneumoniae were not related to the
bacteriological outcome in acute otitis media (9).
In their study, the MIC of amoxicillin-clavulanate was >0.5 mg/liter
for 24% of the strains, and among these only for a few strains was the
MIC >2 mg/liter.
Penicillin resistance in S. pneumoniae is due to an altered
configuration of the penicillin binding proteins in the bacterial cell
wall that causes a lower affinity to the drug (11, 16, 20). Our results with the PRP for which the MIC was 2 mg/liter yielded the same Emax at 50 to 60% T>MIC
under the condition that Cmax was increased to
10 times the MIC. The other PRP strain (MIC, 4 mg/liter) did not follow
this pattern. The latter strain exhibited a killing of 2 to 3 log10 within the first 6 h, independent of Cmax ranging from 2 to 20 times the MIC.
Regrowth occurred after 12 h in a majority of the experiments.
Thus, an increased Cmax and larger AUC was not
sufficient to achieve a predictable killing for this strain. Although
the strain did not show tolerance, genetic alterations in the pathways
that regulates autolysin activity or penicillin binding protein
production may be reasons for this adaptation to the antibiotic
environment. Additional highly resistant pneumococci strains need to be
studied to seek an explanation for this phenomenon and determine its prevalence.
The in vitro kinetic model gave results comparable to those of
different animal models for susceptible strains. It offers a
cost-effective alternative as a screening model of the PK-PD parameters
for the efficacies of new antibiotics. It has the advantages that the
drug elimination rate and other pharmacokinetic parameters can be
varied and also that bactericidal effect can be monitored continuously.
| |
ACKNOWLEDGMENTS |
We thank Marie Sandström at the Department of Pharmacy,
Uppsala University, for her helpful assistance in the pharmacokinetics calculations and Birgitta Henriques-Normark at the Swedish Institute for Infection Disease Control, for valuable discussion.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Department of
Clinical Bacteriology, Box 552, SE-751 22 Uppsala, Sweden. Phone: 46 (18) 611 39 11. Fax: 46 (18) 55 73 01. E-mail:
ingegerd.gustafsson{at}medsci.uu.se.
| |
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Antimicrobial Agents and Chemotherapy, September 2001, p. 2436-2440, Vol. 45, No. 9
0066-4804/01/$04.00+0 DOI: 10.1128/AAC.45.9.2436-2440.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
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Abstract
Introduction
