Issues in pharmacokinetics and pharmacodynamics of anti-infective agents: kill curves versus MIC

Future In Vitro and Animal Studies: Development of Pharmacokinetic and Pharmacodynamic Efficacy Predictors for Tissue-Based Antibiotics

For antibiotics to exert their action on bacteria, both the bacteria and the drug need to be in the same place at the same time. The pharmacodynamics of antibiotics, measured as the ratio of area under the concentration-time curve:minimum inhibitory concentration (AUC:MIC), the ratio of plasma concentration:MIC, or time above MIC, indexes the pharmacokinetic properties of an antibiotic (in vivo) to a measure of microbiologic (antimicrobial) activity. Antimicrobial activity is measured as the MIC, and the pharmacokinetics generally used are those in the blood. However, if the infection is not in the blood but in some peripheral tissue such as the lung, it is the concentration of the drug in the lung that the pathogen sees, and thus the concentration in the blood (serum or plasma) is not important. Both in vitro and in vivo studies can aid in the development of pharmacodynamic parameters that characterize the drug-pathogen interaction, resulting in the determination of a dose or dosage regimen capable of curing an infection clinically.

Bicompartmental kinetics of tobramycin analysed with a wide range of covariates

The pharmacokinetics of tobramycin was studied in adult patients (N = 151) admitted either for initial suspicion of Gram-negative infection or for prophylaxis. In addition to age, weight, height and creatinine clearance (CrCL), a range of other covariates were also analysed, including type of pathology, co-medication, fever, sex and ethnicity (Basque or not). All patients received 100mg tobramycin every 8 h and samples were collected at three time points after the first dose and at two time points after the fourth dose and assayed with a fluorescence polarisation immunoassay. The population mixed effects bicompartmental parameters were obtained from 725 concentration measurements using NONMEM, FOCE method, and were: systemic clearance, CL = 6.03 L/h (between-subject coefficient of variation (CV) %, 29.4%); volume of distribution, V = 15.04 L (7.3%); and intercompartmental constants, k(12) = 0.192 h(-1) (56%) and k(21) = 0.55 h(-1) (no CV% determined). Covariate modelling was performed within NONMEM. Two alternative significant covariate models (Models 1 and 2) are proposed, with functions of CrCL and/or sex (Model 2). However, for clinical purposes, differentiation by sex is insignificant. Model 1 is for CL = 3.1 + 0.05.CrCLL/h (17.3%); V = 14.6 L (12%); k(12) = 0.224 h(-1) (63%) and k(21) = 0.468 h(-1). Stochastic simulation was used to predict the expected concentration 95th percentiles after the recommended 7 mg/kg dose and for minimum inhibitory concentration (MIC) = 1 mg/L, as well as alternative once-daily dosing regimens for MIC = 2 mg/L. It is seen that once-daily high-dose tobramycin is an appropriate strategy with respect to pharmacodynamic indices, C(peak)/MIC or AUC/MIC (where C(peak) is the peak plasma concentration and AUC is the area under the concentration-time curve).

A New Modeling Approach to the Effect of Antimicrobial Agents on Heterogeneous Microbial Populations

We develop a mathematical framework to model the dynamics of the effect of antimicrobial agents on heterogeneous microbial populations of distributed antimicrobial resistance. Our framework uses the concept of cumulants of a distribution. Simplifications that result in easily usable approximation tools are presented. A case study on experimental data exemplifies shortcomings of standard methods and the usefulness of the proposed approach. Suggestions for future development are made.

Phenotypic tolerance: antibiotic enrichment of noninherited resistance in bacterial populations

When growing bacteria are exposed to bactericidal concentrations of antibiotics, the sensitivity of the bacteria to the antibiotic commonly decreases with time, and substantial fractions of the bacteria survive. Using Escherichia coli CAB1 and antibiotics of five different classes (ampicillin, ciprofloxacin, rifampin, streptomycin, and tetracycline), we examine the details of this phenomenon and, with the aid of mathematical models, develop and explore the properties and predictions of three hypotheses that can account for this phenomenon: (i) antibiotic decay, (ii) inherited resistance, and (iii) phenotypic tolerance. Our experiments cause us to reject the first two hypotheses and provide evidence that this phenomenon can be accounted for by the antibiotic-mediated enrichment of subpopulations physiologically tolerant to but genetically susceptible to these antibiotics, phenotypic tolerance. We demonstrate that tolerant subpopulations generated by exposure to one concentration of an antibiotic are also tolerant to higher concentrations of the same antibiotic and can be tolerant to antibiotics of the other four types. Using a mathematical model, we explore the effects of phenotypic tolerance to the microbiological outcome of antibiotic treatment and demonstrate, a priori, that it can have a profound effect on the rate of clearance of the bacteria and under some conditions can prevent clearance that would be achieved in the absence of tolerance.

In vitro activity of tebipenem, a new oral carbapenem antibiotic, against penicillin-nonsusceptible Streptococcus pneumoniae

The in vitro activity of tebipenem (TBM), a new oral carbapenem antibiotic, against Streptococcus pneumoniae clinical isolates (n = 202) was compared with those of 15 reference agents. The isolates were classified into five genotypic classes after PCR identification of abnormal pbp1a, pbp2x, and pbp2b genes: (i) penicillin-susceptible S. pneumoniae (PSSP) isolates with no abnormal pbp genes (n = 34; 16.8%), (ii) genotypic penicillin-intermediate S. pneumoniae (gPISP) isolates with only an abnormal pbp2x gene [gPISP (2x)] (n = 48; 23.8%), (iii) gPISP isolates with abnormal pbp1a and pbp2x genes (n = 32; 15.8%), (iv) gPISP isolates with abnormal pbp2x and pbp2b genes (n = 16; 7.9%), and (v) genotypic penicillin-resistant S. pneumoniae (gPRSP) isolates with three abnormal pbp genes (n = 72; 35.6%). The majority of the strains tested had mefA (n = 59; 29.2%) or ermB (n = 91; 45%) gene-mediating macrolide resistance. For these isolates the MIC at which 90% of isolates are inhibited was significantly lower for TBM than for the reference oral antibiotics, as follows: 0.002 microg/ml for PSSP, 0.004 mug/ml for gPISP (2x), 0.016 microg/ml for gPISP (isolates with abnormal pbp1a and pbp2x genes and isolates with abnormal pbp2x and pbp2b genes), and 0.063 microg/ml for gPRSP. In addition, TBM showed excellent bactericidal activity against gPRSP isolates, which exhibited a 3-log(10) decrease within 2 h when they were incubated with a concentration greater than or equal to the MIC. Inhibition of cell wall synthesis toward the long axis and subsequent cell lysis were observed by scanning electron microscopy after a short-term exposure to TBM, unlike the effects seen with cephalosporins. These data suggest that TBM has potent activity against multidrug-resistant S. pneumoniae, the causative pathogen of community-acquired respiratory tract infections.

Modelling time–kill studies to discern the pharmacodynamics of meropenem

OBJECTIVES

Time-kill studies are commonly used in investigations of new antimicrobial agents. However, they typically provide descriptive information on pharmacodynamics. We developed a mathematical model to capture the relationship between microbial burden and antimicrobial agent concentrations.

METHODS

Time-kill studies were performed with 10(8) cfu/mL of Pseudomonas aeruginosa at baseline. Meropenem at 0, 0.25, 1, 4, 16 and 64 x MIC was used (MIC = 1 mg/L). Serial samples were obtained to quantify bacterial burden over 24 h. The data were analysed by a population analysis using the non-parametric adaptive grid program. The rate of change of bacteria over time was expressed as the difference between linear bacterial growth rate and sigmoidal kill rate. Regrowth was attributed to adaptation, which was explicitly modelled as increase in C(50k) (concentration to achieve 50% maximal kill rate), using a saturable function of selective pressure (both meropenem concentration and time).

RESULTS

The best-fit model consisted of eight parameters and the fit to the data was satisfactory. The r2 of maximum a-posteriori probability Bayesian predictions based on the mean parameter estimates was 0.984. Maximal killing rate at baseline was found to be 4.7 h(-1); C(90k) was achieved with meropenem at 5.0 mg/L. The model was validated by time-kill studies using 2x and 32x MIC of meropenem.

CONCLUSIONS

Our model reasonably described and predicted the time course of P. aeruginosa in time-kill studies, and provided quantitative information on the pharmacodynamics of meropenem. The structural model appeared robust and could be used to provide a realistic expectation of the killing performance of antimicrobial agents.

Pharmacokinetics and pharmacodynamics of cefpirome in subcutaneous adipose tissue of septic patients

The objective of the present study was to evaluate whether cefpirome, a member of the latest class of broad-spectrum cephalosporins, sufficiently penetrates subcutaneous adipose tissue in septic patients. After the administration of the drug at 2 g, tissue cefpirome concentrations in septic patients (n = 11) and healthy controls (n = 7) were determined over a period of 4 h by means of microdialysis. To assess the antibacterial effect of cefpirome at the target site, the measured pharmacokinetic profiles were simulated in vitro with select strains of Staphylococcus aureus and Pseudomonas aeruginosa. The tissue penetration of cefpirome was significantly impaired in septic patients compared with that in healthy subjects. For subcutaneous adipose tissue, the area under the concentration-versus-time curve values from 0 to 240 min were 13.11 +/- 5.20 g . min/liter in healthy subjects and 6.90 +/- 2.56 g . min/liter in septic patients (P < 0.05). Effective bacterial growth inhibition was observed in all in vitro simulations. This was attributed to the significantly prolonged half-life in tissue (P < 0.05), which kept the tissue cefpirome levels above the MICs for relevant pathogens for extended periods in the septic group. By consideration of a dosing interval of 8 h, the values for the time above MIC (T > MIC) in tissue were greater than 60% for pathogens for which the MIC was Collapse

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MESH Headings

• Adipose Tissue/metabolism
• Adult
• Area Under Curve
• Cephalosporins/adverse effects
• Cephalosporins/pharmacokinetics
• Chromatography, Micellar Electrokinetic Capillary
• Colony Count, Microbial
• Female
• Humans
• Male
• Microbial Sensitivity Tests
• Microdialysis
• Pseudomonas aeruginosa/drug effects
• Sepsis/metabolism
• Staphylococcus aureus/drug effects
• Cefpirome

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Affiliation(s)

Robert Sauermann Department of Clinical Pharmacology, Division of Clinical Pharmacokinetics, Medical University of Vienna, Waehringer Guertel 18-20, 1090 Vienna, Austria
Georg Delle-Karth
Claudia Marsik
Ilka Steiner
Markus Zeitlinger
Bernhard X Mayer-Helm
Apostolos Georgopoulos
Markus Müller
Christian Joukhadar

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Pharmacodynamic functions: a multiparameter approach to the design of antibiotic treatment regimens

There is a complex quantitative relationship between the concentrations of antibiotics and the growth and death rates of bacteria. Despite this complexity, in most cases only a single pharmacodynamic parameter, the MIC of the drug, is employed for the rational development of antibiotic treatment regimens. In this report, we use a mathematical model based on a Hill function-which we call the pharmacodynamic function and which is related to previously published E(max) models-to describe the relationship between the bacterial net growth rates and the concentrations of antibiotics of five different classes: ampicillin, ciprofloxacin, tetracycline, streptomycin, and rifampin. Using Escherichia coli O18:K1:H7, we illustrate how precise estimates of the four parameters of the pharmacodynamic function can be obtained from in vitro time-kill data. We show that, in addition to their respective MICs, these antibiotics differ in the values of the other pharmacodynamic parameters. Using a computer simulation of antibiotic treatment in vivo, we demonstrate that, as a consequence of differences in pharmacodynamic parameters, such as the steepness of the Hill function and the minimum bacterial net growth rate attained at high antibiotic concentrations, there can be profound differences in the microbiological efficacy of antibiotics with identical MICs. We discuss the clinical implications and limitations of these results.

Impact of plasma protein binding on antimicrobial activity using time–killing curves

OBJECTIVES

Plasma protein binding (PPB) is known to impair the antimicrobial activity of beta-lactams, but its impact on the activity of other classes of antimicrobials such as fluoroquinolones is controversial. This study was undertaken to investigate the effect of PPB on bacterial killing by selected antibiotics and moxifloxacin, which served as a model compound for the class of fluoroquinolones.

METHODS

Bacterial time-killing curves were employed in the absence and presence of physiological albumin concentrations (40 g/L). Moxifloxacin, ampicillin and oxacillin were investigated. Fosfomycin, a non-protein bound antibiotic was used for comparison. Simulations were carried out by employing concentrations of antibiotics of one-fourth of the minimal inhibitory concentration (MIC), equal to the MIC and four-fold the MIC of one select bacterial strain (Staphylococcus aureus ATCC 29213). To correlate bacterial killing to the extent of PPB, bacterial time-killing curves were plotted using the calculated free and the total drug concentration.

RESULTS

Bacterial killing by fosfomycin was not affected by the addition of albumin. The antimicrobial activity of oxacillin and ampicillin was reduced in the presence of albumin as expected by the calculation of the free fraction of these antibiotics. Adding albumin to moxifloxacin resulted in a significant decrease in bacterial killing of more than 1 log10 cfu/mL after a period of 8 h when the moxifloxacin concentration was equal to the respective MIC.

CONCLUSIONS

Our data confirm the view that albumin substantially impairs the antimicrobial activity of antibiotics including moxifloxacin, a member of the class of fluoroquinolones.

Bactericidal activity of amoxicillin against non-susceptible Streptococcus pneumoniae in an in vitro pharmacodynamic model simulating the concentrations obtained with the 2000/125 mg sustained-release co-amoxiclav formulation

OBJECTIVES

To investigate the bactericidal activity against Streptococcus pneumoniae of simulated amoxicillin serum concentrations obtained in humans after 2000/125 mg sustained-release (SR) and 875/125 mg co-amoxiclav administered twice and three times a day, respectively.

METHODS

An in vitro computerized pharmacodynamic simulation was carried out and colony counts were determined over 24 h. Ten strains non-susceptible to amoxicillin (four of them exhibiting an MIC of 4 mg/L, five strains with an MIC of 8 mg/L and one strain with an MIC of 16 mg/L) were used.

RESULTS

With amoxicillin 2000 mg, an initial inoculum reduction >99.99% was obtained for strains with an MIC of 4 mg/L, > or =99% for strains with an MIC of 8 mg/L and 70.6% for the strain with an MIC of 16 mg/L at 24 h sampling time. At this sampling time, no reduction of initial inocula was obtained with amoxicillin 875 mg/8 h for two of the four strains with an MIC of 4 mg/L, three of the five strains with an MIC of 8 mg/L or for the strain with an MIC of 16 mg/L.

CONCLUSIONS

The new co-amoxiclav 2000/125 mg SR formulation appears to offer advantages versus previous formulations with respect to bactericidal activity against current amoxicillin non-susceptible strains.

Enhancement of the enterocin CRL35 activity by a synthetic peptide derived from the NH2-terminal sequence

The enterocin CRL35 biosynthetic gene cluster was cloned and sequenced. The sequence was revealed to be highly identical to that of the mundticin KS gene cluster (S. Kawamoto, J. Shima, R. Sato, T. Eguchi, S. Ohmomo, J. Shibato, N. Horikoshi, K. Takeshita, and T. Sameshima, Appl. Environ. Microbiol. 68:3830-3840, 2002). Short synthetic peptides were designed based on the bacteriocin sequence and were evaluated in antimicrobial competitive assays. The peptide KYYGNGVSCNKKGCS produced an enhancement of enterocin CRL35 antimicrobial activity in a buffer system.