Pharmacokinetic/pharmacodynamic modeling of in vitro activity of azithromycin against four different bacterial strains

Pharmacokinetic/Pharmacodynamic Modeling and Application in Antibacterial and Antifungal Pharmacotherapy: A Narrative Review

Pharmacokinetics and pharmacodynamics are areas in pharmacology related to different themes in the pharmaceutical sciences, including therapeutic drug monitoring and different stages of drug development. Although the knowledge of these disciplines is essential, they have historically been treated separately. While pharmacokinetics was limited to describing the time course of plasma concentrations after administering a drug-dose, pharmacodynamics describes the intensity of the response to these concentrations. In the last decades, the concept of pharmacokinetic/pharmacodynamic modeling (PK/PD) emerged, which seeks to establish mathematical models to describe the complete time course of the dose-response relationship. The integration of these two fields has had applications in optimizing dose regimens in treating antibacterial and antifungals. The anti-infective PK/PD models predict the relationship between different dosing regimens and their pharmacological activity. The reviewed studies show that PK/PD modeling is an essential and efficient tool for a better understanding of the pharmacological activity of antibacterial and antifungal agents.

Effects of Growth Medium and Inoculum Size on Pharmacodynamics Activity of Marbofloxacin against Staphylococcus aureus Isolated from Caprine Clinical Mastitis

Staphylococcus aureus (S. aureus) is an important pathogen that causes clinical mastitis in goats and produces infections difficult to cure. Different antimicrobials as fluoroquinolones have been used against S. aureus. However, the studies developed to evaluate the bacterial drug interaction only have used the MIC as a single reference point with artificial growth media. The aims of this study were to describe the effect of marbofloxacin on S. aureus isolated from mastitis goats' milk by different approaches as the minimum inhibitory and bactericidal concentrations (MIC and MBC) in cation adjusted Mueller-Hinton broth (CAMHB), serum and milk of goats at two inoculum sizes of 10⁵ and 10⁸ CFU/mL, the determination and analysis of the time kill curves (TKC) by non-linear mixed effect models in each growth medium and inoculum size, as well as the estimation of their pharmacokinetics/pharmacodynamics (PK/PD) cutoff values. The results obtained indicate that MIC values were higher and increases 2,4-fold in serum and 3,6-fold in milk at high inoculum, as well as the EC₅₀ values determined by each pharmacodynamics model. Finally, the PK/PD cutoff values defined as fAUC₂₄/MIC ratios to achieve clinical efficacy were highly dependent on inoculum and growth medium, with median values of 60-180, especially at high inoculum in milk, suggesting that further studies are necessary to evaluate and optimize the best therapeutic strategies for treating S. aureus in lactating goats.

In vitro pharmacokinetics/pharmacodynamics modeling and efficacy against systemic candidiasis in Drosophila melanogaster of a bisaryloxypropanamine derivative

The number of deaths due to systemic fungal infections is increasing alarmingly, which is aggravated by the limitations of traditional treatments and multidrug resistance. Therefore, the research and development of new therapeutic options against pathogenic fungi is an urgent need. To evaluate the fungicidal activity of a synthetic compound, 1,3-bis-(3,4-dichlorophenoxy)propan-2-aminium chloride (2j), through time-kill studies and pharmacokinetics/pharmacodynamics (PK/PD) modeling. The protective effect of the compound was also evaluated using the Drosophila melanogaster minihost model of candidiasis. Mathematical modeling of time-kill data of compound 2j was performed to obtain PD characteristics. Additionally, Toll-deficient D. melanogaster flies were infected with a Candida albicans strain and treated with 2j. We observed that compound 2j demonstrated a time- and dose-dependent fungicidal effect against Candida spp. and dermatophytes, even at low concentrations, and rapidly achieved kill rates reaching the maximum effect in less than one hour. The efficacy of the compound against systemic candidiasis in D. melanogaster flies was comparable to that achieved by fluconazole. These results support the potential of compound 2j as a systemic antifungal agent candidate and serve as a starting point for further studies involving mammalian animal models.

Time-kill curves of daptomycin and Monte Carlo simulation for the treatment of bacteraemia caused by Enterococcus faecium

OBJECTIVES

The aim of this study was to investigate the effect of daptomycin against vancomycin-resistant Enterococcus faecium bacteraemia using computer modelling.

METHODS

Data obtained in vitro from time-kill curves were evaluated by PK/PD modelling and Monte Carlo simulations to determine the logarithmic reduction in the number of colony-forming units (CFU)/mL over 18 days of daptomycin treatment at 6, 8, and 10 mg/kg doses every 24 or 48 h and with variations in creatinine clearance (CL_CR) of 15-29, 30-49, and 50-100 mL/min/1.73 m². Monte Carlo simulations were performed to evaluate the probability of target attainment (PTA) for an area under the unbound drug concentration-time curve/minimum inhibitory concentration (fAUC/MIC) > 36 at the same doses and CL_CR.

RESULTS

Static time-kill model was employed to investigate the antibacterial efficacy of constant daptomycin concentrations. The time-kill curve analysis was performed using mathematical modelling based on a Hill coefficient factor. There was an expressive reduction (> 2 Log CFU/mL) over 18 days of daptomycin treatment in 75th percentile of individuals with CL_CR of 15-100 mL/min/1.73 m²) with daptomycin 6-10 mg/kg/day, except for daptomycin every 48 h. Using fAUC/MIC > 36, PTA was > 90% at MICs ≤ 2 μg/mL.

CONCLUSIONS

Higher daptomycin doses were associated with higher mortality in time-kill curves. The simulations indicated that independent of the CL_CR the therapeutic responses of VRE occur with doses of daptomycin ≥ 6 mg/kg/day and daptomycin every 48 h is insufficient to treat enterococcal bacteraemia.

In vitro activities of carbapenems in combination with amikacin, colistin, or fosfomycin against carbapenem-resistant Acinetobacter baumannii clinical isolates

Carbapenem-resistant Acinetobacter baumannii clinical isolates (n=23) were investigated for carbapenem resistance mechanisms and in vitro activities of carbapenems in combination with amikacin, colistin, or fosfomycin. Major carbapenem resistance mechanism was OXA-23 production. The vast majority of these isolates were OXA-23-producing A. baumannii ST195 and ST542, followed by novel STs, ST1417, and ST1423. The interuption of carO by a novel insertion sequence, ISAba40, was found in two isolates. The combinations of imipenem and fosfomycin, meropenem and amikacin, imipenem and amikacin, and imipenem and colistin were synergistic against carbapenem-resistant A. baumannii by 65.2%, 46.2%, 30.8%, and 17.4%, respectively. Surprisingly, the combination of imipenem and fosfomycin was the most effective in this study against A. baumannii, which is intrinsically resistant to fosfomycin. Imipenem and fosfomycin inhibit cell wall synthesis; therefore, fosfomycin may be an adjuvant and enhance the inhibition of cell wall synthesis of carbapenem-resistant A. baumannii when combined with imipenem.

Defining the Active Fraction of Daptomycin against Methicillin-Resistant Staphylococcus aureus (MRSA) Using a Pharmacokinetic and Pharmacodynamic Approach

Our objective was to study the pharmacodynamics of daptomycin in the presence of varying concentrations of human serum (HS) in vitro to quantify the fraction of daptomycin that is ‘active’. Time kill experiments were performed with daptomycin (0 to 256 mg/L) against two MRSA strains at log-phase growth, in the presence of HS (0%, 10%, 30%, 50%, 70%) combined with Mueller-Hinton broth. Daptomycin ≥ 2 mg/L achieved 99.9% kill within 8 h at all HS concentrations; early killing activity was slightly attenuated at higher HS concentrations. After 1 h, bacterial reduction of USA300 upon exposure to daptomycin 4 mg/L ranged from -3.1 to -0.5 log₁₀CFU/mL in the presence of 0% to 70% HS, respectively. Bactericidal activity was achieved against both strains at daptomycin ≥ 4 mg/L for all fractions of HS exposure. A mechanism-based mathematical model (MBM) was developed to estimate the active daptomycin fraction at each %HS, comprising 3 bacterial subpopulations differing in daptomycin susceptibility. Time-kill data were fit with this MBM with excellent precision (r² >0.95). The active fraction of daptomycin was estimated to range from 34.6% to 25.2% at HS fractions of 10% to 70%, respectively. Despite the reported low unbound fraction of daptomycin, the impact of protein binding on the activity of daptomycin was modest. The active fraction approach can be utilized to design in vitro experiments and to optimize therapeutic regimens of daptomycin in humans.

The PK/PD Interactions of Doxycycline against Mycoplasma gallisepticum

Mycoplasma gallisepticum is one of the most important pathogens that cause chronic respiratory disease in chicken. This study investigated the antibacterial activity of doxycycline against M. gallisepticum strain S6. In static time–killing studies with constant antibiotic concentrations [0–64 minimum inhibitory concentration (MIC)], M. gallisepticum colonies were quantified and kill rates were calculated to estimate the drug effect. The half-life of doxycycline in chicken was 6.51 ± 0.63 h. An in vitro dynamic model (the drug concentrations are fluctuant) was also established and two half-lives of 6.51 and 12 h were simulated. The samples were collected for drug concentration determination and viable counting of M. gallisepticum. In static time–killing studies, doxycycline produced a maximum antimycoplasmal effect of 5.62log₁₀ (CFU/mL) reduction and the maximum kill rate was 0.11 h⁻¹. In the in vitro dynamic model, doxycycline had a mycoplasmacidal activity in the two regimens, and the maximum antimycoplasmal effects were 4.1 and 4.75log₁₀ (CFU/mL) reduction, respectively. Furthermore, the cumulative percentage of time over a 48-h period that the drug concentration exceeds the MIC (%T > MIC) was the pharmacokinetic–pharmacodynamic index that best correlated with antimicrobial efficacy (R² = 0.986, compared with 0.897 for the peak level divided by the MIC and 0.953 for the area under the concentration–time curve over 48 h divided by the MIC). The estimated %T > MIC values for 0log₁₀ (CFU/mL) reduction, 2log10 (CFU/mL) reduction and 3log₁₀ (CFU/mL) reduction were 32.48, 45.68, and 54.36%, respectively, during 48 h treatment period of doxycycline. In conclusion, doxycycline shows excellent effectiveness and time-dependent characteristics against M. gallisepticum strain S6 in vitro. Additionally, these results will guide optimal dosing strategies of doxycycline in M. gallisepticum infection.

Distinguishing Antimicrobial Models with Different Resistance Mechanisms via Population Pharmacodynamic Modeling

Semi-mechanistic pharmacokinetic-pharmacodynamic (PK-PD) modeling is increasingly used for antimicrobial drug development and optimization of dosage regimens, but systematic simulation-estimation studies to distinguish between competing PD models are lacking. This study compared the ability of static and dynamic in vitro infection models to distinguish between models with different resistance mechanisms and support accurate and precise parameter estimation. Monte Carlo simulations (MCS) were performed for models with one susceptible bacterial population without (M1) or with a resting stage (M2), a one population model with adaptive resistance (M5), models with pre-existing susceptible and resistant populations without (M3) or with (M4) inter-conversion, and a model with two pre-existing populations with adaptive resistance (M6). For each model, 200 datasets of the total bacterial population were simulated over 24h using static antibiotic concentrations (256-fold concentration range) or over 48h under dynamic conditions (dosing every 12h; elimination half-life: 1h). Twelve-hundred random datasets (each containing 20 curves for static or four curves for dynamic conditions) were generated by bootstrapping. Each dataset was estimated by all six models via population PD modeling to compare bias and precision. For M1 and M3, most parameter estimates were unbiased (<10%) and had good imprecision (<30%). However, parameters for adaptive resistance and inter-conversion for M2, M4, M5 and M6 had poor bias and large imprecision under static and dynamic conditions. For datasets that only contained viable counts of the total population, common statistical criteria and diagnostic plots did not support sound identification of the true resistance mechanism. Therefore, it seems advisable to quantify resistant bacteria and characterize their MICs and resistance mechanisms to support extended simulations and translate from in vitro experiments to animal infection models and ultimately patients.

Mathematical models are increasingly used for analysis and interpretation of in vitro efficacy results of antimicrobial drugs. Various models are employed in the scientific literature and it seems that they are equally able to describe the observed data. The aim of the present study was to compare different models in various experimental designs and with different resistance mechanisms of bacteria. For that purpose we have generated experimental data through Monte-Carlo simulations and then used six different mathematical models to analyze these results. We showed that statistical comparison of models did not allow determining which was the true mechanism of resistance, i.e. the one used for the simulation step. Moreover mathematical parameters for bacterial resistance were estimated with bias and with a low precision except for the simpler cases. This suggests that the choice of the mathematical model for data analysis should be guided by experimental characterization of the bacterial mechanism of resistance.

Gentamicin dosing strategy in patients with end-stage renal disease receiving haemodialysis: evaluation using a semi-mechanistic pharmacokinetic/pharmacodynamic model

OBJECTIVES

Gentamicin is widely used in end-stage renal disease (ESRD) patients for the treatment of infections. The goal of this study was to find the most reasonable dosing regimen for gentamicin in ESRD patients receiving haemodialysis.

METHODS

The in vitro antimicrobial activity of gentamicin was evaluated by static and dynamic time-kill experiments against three bacterial strains of MSSA, MRSA and Pseudomonas aeruginosa. A semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model was established afterwards, allowing the characterization of the antibacterial effect of gentamicin in the human body. The model was utilized to assess dosing regimens of gentamicin in ESRD patients receiving haemodialysis, taking both efficacy and safety into account.

RESULTS

The PK/PD model was capable of describing the bacterial response to gentamicin exposure in all three strains. Simulation based on the PK/PD model showed that pre-dialysis and post-dialysis dosing would bring comparable benefit to the ESRD patient regardless of whether the PK/PD target (fCmax/MIC >8-fold) was achieved, while the post-dialysis dosing resulted in a significantly lower trough concentration. The result of simulated dose fractionation demonstrated that both fCmax/MIC and fAUC(0-24)/MIC are strong predictors of drug effectiveness, but the PK/PD model would provide a more precise prediction of antibacterial activity as well as valuable information on dose selection in ESRD patients receiving haemodialysis.

CONCLUSIONS

Our study supports the original FDA label with regard to the dosing regimen of gentamicin in ESRD patients, which offers adequate clinical benefit as well as an acceptable safety profile.

How fitness reduced, antimicrobial resistant bacteria survive and spread: a multiple pig-multiple bacterial strain model

More than 30% of E. coli strains sampled from pig farms in Denmark over the last five years were resistant to the commonly used antimicrobial tetracycline. This raises a number of questions: How is this high level sustained if resistant bacteria have reduced growth rates? Given that there are multiple susceptible and resistant bacterial strains in the pig intestines, how can we describe their coexistence? To what extent does the composition of these multiple strains in individual pigs influence the total bacterial population of the pig pen? What happens to a complex population when antimicrobials are used? To investigate these questions, we created a model where multiple strains of bacteria coexist in the intestines of pigs sharing a pen, and explored the parameter limits of a stable system; both with and without an antimicrobial treatment. The approach taken is a deterministic bacterial population model with stochastic elements of bacterial distributions and transmission. The rates that govern the model are process-oriented to represent growth, excretion, and uptake from environment, independent of herd and meta-population structures. Furthermore, an entry barrier and elimination process for the individual strains in each pig were implemented. We demonstrate how competitive growth between multiple bacterial strains in individual pigs, and the transmission between pigs in a pen allow for strains of antimicrobial resistant bacteria to persist in a pig population to different extents, and how quickly they can become dominant if antimicrobial treatment is initiated. The level of spread depends in a non-linear way of the parameters that govern excretion and uptake. Furthermore, the sampling of initial distributions of strains and stochastic transmission events give rise to large variation in how homogenous and how resistant the bacterial population becomes. Most important: resistant bacteria are demonstrated to survive with a disadvantage in growth rate of well over 10%.

Application of pharmacokinetic/pharmacodynamic modelling and simulation for the prediction of target attainment of ceftobiprole against meticillin-resistant Staphylococcus aureus using minimum inhibitory concentration and time-kill curve based approaches

The purpose of this report was to compare two different methods for dose optimisation of antimicrobials. The probability of target attainment (PTA) was calculated using Monte Carlo simulation to predict the PK/PD target of fT>MIC or modelling and simulation of time-kill curve data. Ceftobiprole, the paradigm compound, activity against two MRSA strains was determined, ATCC 33591 (MIC=2mg/L) and a clinical isolate (MIC=1mg/L). A two-subpopulation model accounting for drug degradation during the experiment adequately fit the time-kill curve data (concentration range 0.25-16× MIC). The PTA was calculated for plasma, skeletal muscle and subcutaneous adipose tissue based on data from a microdialysis study in healthy volunteers. A two-compartment model with distribution factors to account for differences between free serum and tissue interstitial space fluid concentration appropriately fit the pharmacokinetic data. Pharmacodynamic endpoints of fT>MIC of 30% or 40% and 1- or 2-log kill were used. The PTA was >90% in all tissues based on the PK/PD endpoint of fT>MIC >40%. The PTAs based on a 1- or 2-log kill from the time-kill experiments were lower than those calculated based on fT>MIC. The PTA of a 1-log kill was >90% for both MRSA isolates for plasma and skeletal muscle but was slightly below 90% for subcutaneous adipose tissue (both isolates ca. 88%). The results support a dosing regimen of 500mg three times daily as a 2-h intravenous infusion. This dose should be confirmed as additional pharmacokinetic data from various patient populations become available.

Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs

Pharmacokinetic-pharmacodynamic (PKPD) modeling and simulation has evolved as an important tool for rational drug development and drug use, where developed models characterize both the typical trends in the data and quantify the variability in relationships between dose, concentration, and desired effects and side effects. In parallel, rapid emergence of antibiotic-resistant bacteria imposes new challenges on modern health care. Models that can characterize bacterial growth, bacterial killing by antibiotics and immune system, and selection of resistance can provide valuable information on the interactions between antibiotics, bacteria, and host. Simulations from developed models allow for outcome predictions of untested scenarios, improved study designs, and optimized dosing regimens. Today, much quantitative information on antibiotic PKPD is thrown away by summarizing data into variables with limited possibilities for extrapolation to different dosing regimens and study populations. In vitro studies allow for flexible study designs and valuable information on time courses of antibiotic drug action. Such experiments have formed the basis for development of a variety of PKPD models that primarily differ in how antibiotic drug exposure induces amplification of resistant bacteria. The models have shown promise for efficacy predictions in patients, but few PKPD models describe time courses of antibiotic drug effects in animals and patients. We promote more extensive use of modeling and simulation to speed up development of new antibiotics and promising antibiotic drug combinations. This review summarizes the value of PKPD modeling and provides an overview of the characteristics of available PKPD models of antibiotics based on in vitro, animal, and patient data.

Pharmacokinetic/pharmacodynamic (PK/PD) indices of antibiotics predicted by a semimechanistic PKPD model: a step toward model-based dose optimization

A pharmacokinetic-pharmacodynamic (PKPD) model that characterizes the full time course of in vitro time-kill curve experiments of antibacterial drugs was here evaluated in its capacity to predict the previously determined PK/PD indices. Six drugs (benzylpenicillin, cefuroxime, erythromycin, gentamicin, moxifloxacin, and vancomycin), representing a broad selection of mechanisms of action and PK and PD characteristics, were investigated. For each drug, a dose fractionation study was simulated, using a wide range of total daily doses given as intermittent doses (dosing intervals of 4, 8, 12, or 24 h) or as a constant drug exposure. The time course of the drug concentration (PK model) as well as the bacterial response to drug exposure (in vitro PKPD model) was predicted. Nonlinear least-squares regression analyses determined the PK/PD index (the maximal unbound drug concentration [fC(max)]/MIC, the area under the unbound drug concentration-time curve [fAUC]/MIC, or the percentage of a 24-h time period that the unbound drug concentration exceeds the MIC [fT(>MIC)]) that was most predictive of the effect. The in silico predictions based on the in vitro PKPD model identified the previously determined PK/PD indices, with fT(>MIC) being the best predictor of the effect for β-lactams and fAUC/MIC being the best predictor for the four remaining evaluated drugs. The selection and magnitude of the PK/PD index were, however, shown to be sensitive to differences in PK in subpopulations, uncertainty in MICs, and investigated dosing intervals. In comparison with the use of the PK/PD indices, a model-based approach, where the full time course of effect can be predicted, has a lower sensitivity to study design and allows for PK differences in subpopulations to be considered directly. This study supports the use of PKPD models built from in vitro time-kill curves in the development of optimal dosing regimens for antibacterial drugs.

Pharmacodynamic modeling of in vitro activity of marbofloxacin against Escherichia coli strains

A mathematical pharmacodynamic model was developed to describe the bactericidal activity of marbofloxacin against Escherichia coli strains with reduced susceptibility levels (determined using MICs) under optimal and intestinal growth conditions. Model parameters were estimated using nonlinear least-square curve-fitting procedures for each E. coli strain. Parameters related to bactericidal activity were subsequently analyzed using a maximum-effect (E(max)) model adapted to account for a direct and a delayed effect. While net growth rates did not vary significantly with strain susceptibility, culture medium had a major effect. The bactericidal activity of marbofloxacin was closely associated with the concentration and the duration of exposure of the bacteria to the antimicrobial agent. The value of the concentration inducing a half-maximum effect (C(50)) was highly correlated with MIC values (R(2) = 0.87 and R(2) = 0.94 under intestinal and optimal conditions, respectively). Our model reproduced the time-kill kinetics with good accuracy (R(2) of >0.90) and helped explain observed regrowth.

Attenuation of colistin bactericidal activity by high inoculum of Pseudomonas aeruginosa characterized by a new mechanism-based population pharmacodynamic model

Colistin is increasingly being utilized against Gram-negative pathogens, including Pseudomonas aeruginosa, resistant to all other antibiotics. Since limited data exist regarding killing by colistin at different initial inocula (CFUo), we evaluated killing of Pseudomonas aeruginosa by colistin at several CFUo and developed a mechanism-based mathematical model accommodating a range of CFUo. In vitro time-kill experiments were performed using >or=8 concentrations up to 64 x the MIC of colistin against P. aeruginosa PAO1 and two clinical P. aeruginosa isolates at CFUo of 10(6), 10(8), and 10(9) CFU/ml. Serial samples up to 24 h were simultaneously modeled in the NONMEM VI (results shown) and S-ADAPT software programs. The mathematical model was prospectively "validated" by additional time-kill studies assessing the effect of Ca(2+) and Mg(2+) on killing of PAO1 by colistin. Against PAO1, killing of the susceptible population was 23-fold slower at the 10(9) CFUo and 6-fold slower at the 10(8) CFUo than at the 10(6) CFUo. The model comprised three populations with different second-order killing rate constants (5.72, 0.369, and 0.00210 liters/h/mg). Bacteria were assumed to release signal molecules stimulating a phenotypic change that inhibits killing. The proposed mechanism-based model had a good predictive performance, could describe killing by colistin for all three studied strains and for two literature studies, and performed well in a prospective validation with various concentrations of Ca(2+) and Mg(2+). The extent and rate of killing of P. aeruginosa by colistin were markedly decreased at high CFUo compared to those at low CFUo. This was well described by a mechanism-based mathematical model, which should be further validated using dynamic in vitro models.

Prevalence, resistance mechanisms, and susceptibility of multidrug-resistant bloodstream isolates of Pseudomonas aeruginosa

Pseudomonas aeruginosa is an important pathogen commonly implicated in nosocomial infections. The occurrence of multidrug-resistant (MDR) P. aeruginosa strains is increasing worldwide and limiting our therapeutic options. The MDR phenotype can be mediated by a variety of resistance mechanisms, and the corresponding relative biofitness is not well established. We examined the prevalence, resistance mechanisms, and susceptibility of MDR P. aeruginosa isolates (resistant to > or =3 classes of antipseudomonal agents [penicillins/cephalosporins, carbapenems, quinolones, and aminoglycosides]) obtained from a large, university-affiliated hospital. Among 235 nonrepeat bloodstream isolates screened between 2005 and 2007, 33 isolates (from 20 unique patients) were found to be MDR (crude prevalence rate, 14%). All isolates were resistant to carbapenems and quinolones, 91% were resistant to penicillins/cephalosporins, and 21% were resistant to the aminoglycosides. By using the first available isolate for each bacteremia episode (n = 18), 13 distinct clones were revealed by repetitive-element-based PCR. Western blotting revealed eight isolates (44%) to have MexB overexpression. Production of a carbapenemase (VIM-2) was found in one isolate, and mutations in gyrA (T83I) and parC (S87L) were commonly found. Growth rates of most MDR isolates were similar to that of the wild type, and two isolates (11%) were found to be hypermutable. All available isolates were susceptible to polymyxin B, and only one isolate was nonsusceptible to colistin (MIC, 3 mg/liter), but all isolates were nonsusceptible to doripenem (MIC, >2 mg/liter). Understanding and continuous monitoring of the prevalence and resistance mechanisms of MDR P. aeruginosa would enable us to formulate rational treatment strategies to combat nosocomial infections.

In vitro pharmacodynamic models to determine the effect of antibacterial drugs

In vitro pharmacodynamic (PD) models are used to obtain useful quantitative information on the effect of either single drugs or drug combinations against bacteria. This review provides an overview of in vitro PD models and their experimental implementation. Models are categorized on the basis of whether the drug concentration remains constant or changes and whether there is a loss of bacteria from the system. Further subdifferentiation is based on whether bacterial loss involves dilution of the medium or is associated with dialysis or diffusion. For comprehension of the underlying principles, experimental settings are simplified and schematically illustrated, including the simulations of various in vivo routes of administration. The different model types are categorized and their (dis)advantages discussed. The application of in vitro models to special organs, infections and pathogens is comprehensively presented. Finally, the relevance and perspectives of in vitro investigations in drug discovery and clinical research are elucidated and discussed.

Pharmacokinetic-pharmacodynamic modeling of the in vitro activities of oxazolidinone antimicrobial agents against methicillin-resistant Staphylococcus aureus

Linezolid is the first FDA-approved oxazolidinone with activity against clinically important gram-positive pathogens, including methicillin (meticillin)-resistant Staphylococcus aureus (MRSA). RWJ-416457 is a new oxazolidinone with an antimicrobial spectrum similar to that of linezolid. The goal of the present study was to develop a general pharmacokinetic (PK)-pharmacodynamic (PD) model that allows the characterization and comparison of the in vitro activities of oxazolidinones, determined in time-kill curve experiments, against MRSA. The in vitro activities of RWJ-416457 and the first-in-class representative, linezolid, against MRSA OC2878 were determined in static and dynamic time-kill curve experiments over a wide range of concentrations: 0.125 to 8 microg/ml (MIC, 0.5 microg/ml) and 0.25 to 16 microg/ml (MIC, 1 microg/ml), respectively. After correction for drug degradation during the time-kill curve experiments, a two-subpopulation model was simultaneously fitted to all data in the NONMEM VI program. The robustness of the model and the precision of the parameter estimates were evaluated by internal model validation by nonparametric bootstrap analysis. A two-subpopulation model, consisting of a self-replicating, oxazolidinone-susceptible and a persistent, oxazolidinone-insusceptible pool of bacteria was appropriate for the characterization of the time-kill curve data. The PK-PD model identified was capable of accounting for saturation in growth, delays in the onsets of growth and drug-induced killing, as well as naturally occurring bacterial death. The simultaneous fit of the proposed indirect-response, maximum-effect model to the data resulted in concentrations that produced a half-maximum killing effect that were significantly (P < 0.05) lower for RWJ-416457 (0.41 microg/ml) than for linezolid (1.39 microg/ml). In combination with the appropriate PK data, the susceptibility-based two-subpopulation model identified may provide valuable guidance for the selection of oxazolidinone doses or dose regimens for use in clinical studies.

Pharmacodynamics of vancomycin at simulated epithelial lining fluid concentrations against methicillin-resistant Staphylococcus aureus (MRSA): implications for dosing in MRSA pneumonia

Little is known regarding killing activity of vancomycin against methicillin (meticillin)-resistant Staphylococcus aureus (MRSA) in pneumonia since the extent of vancomycin penetration into epithelial lining fluid (ELF) has not been definitively established. We evaluated the impact of the extent of ELF penetration on bacterial killing and resistance by simulating a range of vancomycin exposures (24-h free drug area under the concentration-time curve [fAUC24]/MIC) using an in vitro pharmacodynamic model and population-based mathematical modeling. A high-dose, 1.5-g-every-12-h vancomycin regimen according to American Thoracic Society/Infectious Diseases Society of America guidelines (trough concentration, 15 mg/liter) with simulated ELF/plasma penetration of 0, 20, 40, 60, 80, or 100% (fAUC24/MIC of 0, 70, 140, 210, 280, or 350) was evaluated against two agr-functional, group II MRSA clinical isolates obtained from patients with a bloodstream infection (MIC = 1.0 mg/liter) at a high inoculum of 10(8) CFU/ml. Despite high vancomycin exposures and 100% penetration, all regimens up to a fAUC24/MIC of 350 did not achieve bactericidal activity. At regimens of < or = 60% penetration (fAUC24/MIC < or = 210), stasis and regrowth occurred, amplifying the development of intermediately resistant subpopulations. Regimens simulating > or = 80% penetration (fAUC24/MIC > or = 280) suppressed development of resistance. Resistant mutants amplified by suboptimal vancomycin exposure displayed reduced rates of autolysis (Triton X-100) at 72 h. Bacterial growth and death were well characterized by a Hill-type model (r2 > or = 0.984) and a population pharmacodynamic model with a resistant and susceptible subpopulation (r2 > or = 0.965). Due to the emergence of vancomycin-intermediate resistance at a fAUC24/MIC of < or = 210, exceeding this exposure breakpoint in ELF may help to guide optimal dosage regimens in the treatment of MRSA pneumonia.

Pharmacokinetics and pharmacodynamics of antimicrobial drugs

BACKGROUND

Antimicrobial drugs exhibit different characteristics in their correlation between antimicrobial drug concentrations and effects on microorganisms. These correlations have been studied using different approaches including in vitro analyses with constant and fluctuating concentrations and in vivo analyses involving animals and humans. Mathematical analysis includes correlation of pharmacokinetic-pharmacodynamic (PK-PD) indices to an outcome parameter. Further insight can be gained by mechanism-based modelling of antimicrobial drug effects.

METHODS AND RESULTS

This review aims to provide an overview on the various approaches used to analyse antimicrobial pharmacodynamics, to discuss the limitations of these approaches, to indicate recent developments and to summarise the current knowledge on PK-PD target values as derived from human studies.

CONCLUSION

It is expected that PK-PD analysis of antimicrobial drug effects will lead to a more efficient and possibly also less toxic antimicrobial drug therapy.

Development and qualification of a pharmacodynamic model for the pronounced inoculum effect of ceftazidime against Pseudomonas aeruginosa

Evidence is mounting in support of the inoculum effect (i.e., slow killing at large initial inocula [CFUo]) for numerous antimicrobials against a variety of pathogens. Our objectives were to (i) determine the impact of the CFUo of Pseudomonas aeruginosa on ceftazidime activity and (ii) to develop and validate a pharmacokinetic/pharmacodynamic (PKPD) mathematical model accommodating a range of CFUo. Time-kill experiments using ceftazidime at seven concentrations up to 128 mg/liter (MIC, 2 mg/liter) were performed in duplicate against P. aeruginosa PAO1 at five CFUo from 10(5) to 10(9) CFU/ml. Samples were collected over 24 h and fit by candidate models in NONMEM VI and S-ADAPT 1.55 (all data were comodeled). External model qualification integrated data from eight previously published studies. Ceftazidime displayed approximately 3 to 4 log(10) CFU/ml net killing at 10(6.2) CFUo and concentrations of 4 mg/liter (or higher), less than 1.6 log(10) CFU/ml killing at 10(7.3) CFUo, and no killing at 10(8.0) CFUo for concentrations up to 128 mg/liter. The proposed mechanism-based model successfully described the inoculum effect and the concentration-independent lag time of killing. The mean generation time was 28.3 min. The effect of an autolysin was assumed to inhibit successful replication. Ceftazidime concentrations of 0.294 mg/liter stimulated the autolysin effect by 50%. The model was predictive in the internal cross-validation and had excellent in silico predictive performance for published studies of P. aeruginosa ATCC 27853 for various CFUo. The proposed PKPD model successfully described and predicted the pronounced inoculum effect of ceftazidime in vitro and integrated data from eight literature studies to support translation from time-kill experiments to in vitro infection models.

Effect of protein binding on the pharmacological activity of highly bound antibiotics

During antibiotic drug development, media are frequently spiked with either serum/plasma or protein supplements to evaluate the effect of protein binding. Usually, previously reported serum or plasma protein binding values are applied in the analysis. The aim of this study was to evaluate this approach by experimentally measuring free, unbound concentrations for antibiotics with reportedly high protein binding and their corresponding antimicrobial activities in media containing commonly used protein supplements. Free, unbound ceftriaxone and ertapenem concentrations were determined in bacterial growth medium with and without bovine/human serum albumin, as well as adult bovine serum and human plasma using in vitro microdialysis. The corresponding antimicrobial activity was determined in MIC and time-kill curve experiments using Escherichia coli ATCC 25922 and Streptococcus pneumoniae ATCC 6303 as test strains. A semimechanistic maximum effect model was simultaneously fitted to the data and respective EC(50) (concentration at half-maximum effect) values compared. Protein binding differed significantly for ceftriaxone (P < 0.05) between human plasma (76.8 +/- 11.0%) and commercially available bovine (20.2 +/- 8.3%) or human serum albumin (56.9 +/- 16.6%). Similar results were obtained for ertapenem (human plasma, 73.8 +/- 11.6%; bovine serum albumin, 12.4 +/- 4.8%; human serum albumin, 17.8 +/- 11.5%). The MICs and EC(50)s of both strains were significantly increased (P < 0.05) for ceftriaxone when comparing human and bovine serum albumin, whereas the EC(50)s were not significantly different for ertapenem. Free, unbound antibiotic concentrations differed substantially between plasma and protein supplements and correlated well with antimicrobial efficacy. Therefore, free, active concentrations should be measured in the test system instead of correcting for literature protein binding values.

A pharmacokinetic/pharmacodynamic mathematical model accurately describes the activity of voriconazole against Candida spp. in vitro

We developed a pharmacokinetic/pharmacodynamic (PK/PD) mathematical model that fits voriconazole time-kill data against Candida isolates in vitro and used the model to simulate the expected kill curves for typical intravenous and oral dosing regimens. A series of Emax mathematical models were used to fit time-kill data for two isolates each of Candida albicans, Candida glabrata and Candida parapsilosis. PK parameters extracted from human data sets were used in the model to simulate kill curves for each isolate. Time-kill data were best fit by using an adapted sigmoidal Emax model that corrected for delays in candidal growth and the onset of voriconazole activity, saturation of the number of Candida and the steepness of the concentration-response curve. The rates of maximal killing by voriconazole (kmax) were highly correlated with the growth rates (ks) of the isolates (Pearson's correlation coefficient=0.9861). Simulations using PK parameters derived from the human data sets showed fungistatic effects against each of the isolates. In conclusion, we demonstrated that the activity of voriconazole against Candida isolates can be accurately described using a mathematical model. In the future, it might be possible to devise optimal dosing regimens of voriconazole using the model and PK data collected in vivo.

Mechanism-based pharmacokinetic–pharmacodynamic modeling of antimicrobial drug effects

Mathematical modeling of drug effects maximizes the information gained from an experiment, provides further insight into the mechanisms of drug effects, and allows for simulations in order to design studies or even to derive clinical treatment strategies. We reviewed modeling of antimicrobial drug effects and show that most of the published mathematical models can be derived from one common mechanism-based PK-PD model premised on cell growth and cell killing processes. The general sigmoid Emax model applies to cell killing and the various parameters can be related to common pharmacodynamics, which enabled us to synthesize and compare the different parameter estimates for a total of 24 antimicrobial drugs from published literature. Furthermore, the common model allows the parameters of these models to be related to the MIC and to a common set of PK-PD indices. Theoretically, a high Hill coefficient and a low maximum kill rate indicate so-called time-dependent antimicrobial effects, whereas a low Hill coefficient and a high maximum kill rate indicate so-called concentration-dependent effects, as illustrated in the garenoxacin and meropenem examples. Finally, a new equation predicting the time to microorganism eradication after repeated drug doses was derived that is based on the area under the kill-rate curve.