Pharmacokinetic-pharmacodynamic modelling of antibacterial activity of cefpodoxime and cefixime in in vitro kinetic models

PK-PD integration of enrofloxacin and cefquinome alone and in combination against Klebsiella pneumoniae using an in vitro dynamic model

Introduction: Klebsiella pneumoniae is classified as a critical pathogen in both animals and humans and infections can be fatal in chickens resulting in substantial economic losses. However, the misuse of antibiotics can also lead to drug resistance and a potential transmission chain between animals and humans. Three K. pneumoniae strains with different susceptibility phenotypes were chosen to study the pharmacokinetic/pharmacodynamic (PK/PD) integration of enrofloxacin (ENR) and cefquinome (CEQ) alone and in combination. Results: Checkerboard assay results indicated that the combination treatment for type strain ATCC 700603 was synergistic effect with a fractional inhibitory concentration index (FICI) of ≤0.5. The other two clinical strains demonstrated an additive effect (FICI >0.5 to ≤1). Furthermore, static time-kill curves indicated that enrofloxacin and cefquinome added singly were effective in killing K. pneumoniae at concentrations of >2 MIC and ≥1 MIC, respectively. Additionally, the combination of enrofloxacin and cefquinome led to an enhanced antibacterial activity of cefquinome. The dynamic time-kill curves indicated that enrofloxacin and cefquinome had bactericidal and bacteriostatic activities, respectively at ≥1.5 mg/L (single-dose) and 4 mg/L (8 h split-dose) causing a decrease in bacterial counts of ≥4.45 and >2 log10 CFU/mL. Enrofloxacin possessed no bacteriostatic effects against K. pneumoniae at a constant concentration of 1× MIC. Cefquinome used in combination with 1× MIC enrofloxacin exhibited bactericidal activity at ≥4 mg/L (12 h split-dose) with reductions of ≥3.65 log10 CFU/mL. The PK/PD parameters were also analyzed to determine the concentration and duration of the drugs needed to reduce bacteria by 3 log10 CFU/mL. For enrofloxacin alone, the AUC24h/MIC was 23.29 h and the Cmax/MIC was 3.18. For cefquinome alone, the %T > MIC was 48.66 and when used in combination with enrofloxacin was 18.04. The combined use of cefquinome and enrofloxacin can increase the antibacterial activity of cefquinome against K. pneumoniae under a 12-h split-dose regimen regardless of individual drug susceptibility. Discussion: The static and dynamic time-kill curves indicated that enrofloxacin exhibited concentration-dependent activity, while cefquinome exhibited time-dependent activity. In the in vitro dynamic model, enrofloxacin alone exhibited better antimicrobial effects against K. pneumoniae compared to cefquinome alone. However, the antibacterial effect of cefquinome can be enhanced by combining it with enrofloxacin. These findings suggest a potentially effective approach for combating K. pneumoniae infections.

Kinetics of Bacterial Adaptation, Growth, and Death at Didecyldimethylammonium Chloride sub-MIC Concentrations

Minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) are standard indexes for determining disinfection effectiveness. Nevertheless, they are static values disregarding the kinetics at sub-MIC concentrations where adaptation, growth, stationary, and death phases can be observed. The understanding of these dynamic mechanisms is crucial to designing effective disinfection strategies. In this study, we studied the 48 h kinetics of Bacillus cereus and Escherichia coli cells exposed to sub-MIC concentrations of didecyldimethylammonium chloride (DDAC). Two mathematical models were employed to reproduce the experiments: the only-growth classical logistic model and a mechanistic model including growth and death dynamics. Although both models reproduce the lag, exponential and stationary phases, only the mechanistic model is able to reproduce the death phase and reveals the concentration dependence of the bactericidal/bacteriostatic activity of DDAC. This model could potentially be extended to study other antimicrobials and reproduce changes in optical density (OD) and colony-forming units (CFUs) with the same parameters and mechanisms of action.

Pharmacodynamic Parameters of Pharmacokinetic/Pharmacodynamic (PK/PD) Integration Models

Pharmacokinetic/pharmacodynamic (PK/PD) integration models are used to investigate the antimicrobial activity characteristics of drugs targeting pathogenic bacteria through comprehensive analysis of the interactions between PK and PD parameters. PK/PD models have been widely applied in the development of new drugs, optimization of the dosage regimen, and prevention and treatment of drug-resistant bacteria. In PK/PD analysis, minimal inhibitory concentration (MIC) is the most commonly applied PD parameter. However, accurately determining MIC is challenging and this can influence the therapeutic effect. Therefore, it is necessary to optimize PD indices to generate more rational results. Researchers have attempted to optimize PD parameters using mutant prevention concentration (MPC)-based PK/PD models, multiple PD parameter-based PK/PD models, kill rate-based PK/PD models, and others. In this review, we discuss progress on PD parameters for PK/PD models to provide a valuable reference for drug development, determining the dosage regimen, and preventing drug-resistant mutations.

FDA-Approved Oximes and Their Significance in Medicinal Chemistry

Despite the scientific advancements, organophosphate (OP) poisoning continues to be a major threat to humans, accounting for nearly one million poisoning cases every year leading to at least 20,000 deaths worldwide. Oximes represent the most important class in medicinal chemistry, renowned for their widespread applications as OP antidotes, drugs and intermediates for the synthesis of several pharmacological derivatives. Common oxime based reactivators or nerve antidotes include pralidoxime, obidoxime, HI-6, trimedoxime and methoxime, among which pralidoxime is the only FDA-approved drug. Cephalosporins are β-lactam based antibiotics and serve as widely acclaimed tools in fighting bacterial infections. Oxime based cephalosporins have emerged as an important class of drugs with improved efficacy and a broad spectrum of anti-microbial activity against Gram-positive and Gram-negative pathogens. Among the several oxime based derivatives, cefuroxime, ceftizoxime, cefpodoxime and cefmenoxime are the FDA approved oxime-based antibiotics. Given the pharmacological significance of oximes, in the present paper, we put together all the FDA-approved oximes and discuss their mechanism of action, pharmacokinetics and synthesis.

Predicting Antimicrobial Activity at the Target Site: Pharmacokinetic/Pharmacodynamic Indices versus Time-Kill Approaches

Antibiotic dosing strategies are generally based on systemic drug concentrations. However, drug concentrations at the infection site drive antimicrobial effect, and efficacy predictions and dosing strategies should be based on these concentrations. We set out to review different translational pharmacokinetic-pharmacodynamic (PK/PD) approaches from a target site perspective. The most common approach involves calculating the probability of attaining animal-derived PK/PD index targets, which link PK parameters to antimicrobial susceptibility measures. This approach is time efficient but ignores some aspects of the shape of the PK profile and inter-species differences in drug clearance and distribution, and provides no information on the PD time-course. Time–kill curves, in contrast, depict bacterial response over time. In vitro dynamic time–kill setups allow for the evaluation of bacterial response to clinical PK profiles, but are not representative of the infection site environment. The translational value of in vivo time–kill experiments, conversely, is limited from a PK perspective. Computational PK/PD models, especially when developed using both in vitro and in vivo data and coupled to target site PK models, can bridge translational gaps in both PK and PD. Ultimately, clinical PK and experimental and computational tools should be combined to tailor antibiotic treatment strategies to the site of infection.

Synergistic Antibacterial Potential and Cell Surface Topology Study of Carbon Nanodots and Tetracycline Against E. coli

Increasing drugs and antibiotic resistance against pathogenic bacteria create the necessity to explore novel biocompatible antibacterial materials. This study investigated the antibacterial effect of carbon dot (C-dot) against E. coli and suggested an effective synergistic dose of tetracycline with C-dot, using mathematical modeling of antibacterial data. Colony count and growth curve studies clearly show an enhanced antibacterial activity against E. coli synergistically treated with C-dot and tetracycline, even at a concentration ten times lower than the minimum inhibitory concentration (MIC). The Richards model-fit of growth curve clearly showed an increase in doubling time, reduction in growth rate, and early stationary phase in the synergistic treatment with 42% reduction in the growth rate (μ_m) compared to the control. Morphological studies of E. coli synergistically treated with C-dot + tetracycline showed cell damage and deposition of C-dots on the bacterial cell membrane in scanning electron microscopy imaging. We further validated the topological changes, cell surface roughness, and significant changes in the height profile (ΔZ) with the control and treated E. coli cells viewed under an atomic force microscope. We confirmed that the effective antibacterial doses of C-dot and tetracycline were much lower than the MIC in a synergistic treatment.

Soup with or without meatballs: Impact of nutritional factors on the MIC, kill-rates and growth-rates

BACKGROUND

The Minimum Inhibitory Concentration (MIC) is a reference value for susceptibility testing of bacteria. However, the MIC is a net result of growth and killing after a certain duration of exposure under standardized favourable in vitro conditions. Killing and growth characteristics of a drug may yield more information on its activity and help to explain discrepancies between efficacy observed in vitro and in vivo.

METHODS

The MIC of meropenem was determined for P. aeruginosa ATCC 27853 both by microdilution and the E-test in dilutions of Mueller Hinton (MH) broth from 100% to 1%. Time-kill curves were obtained for twofold dilutions of meropenem. Growth rates and kill rates at each concentration and dilution were obtained by linear regression. The Hill equation was fit to the kill rates vs concentrations.

RESULTS

Growths rates decreased log linearly from 0.63/h at 100% to 0.29/h at 6% MH. Over the 100-6% MH dilution range, there was a log-linear decrease of the MIC of meropenem of both the E-test and microdilution. The EC50s decreased from 0.29 mg/L to 0.07 mg/L, which is in agreement with the MIC results. There was a log-linear relationship between MIC and EC50 for the various dilutions MH.

CONCLUSIONS

The availability of nutritional factors is related to the MIC, and a lower availability is related to both a lower growth rate and higher kill rate. Since nutritional factors are less abundantly available in vivo as compared to in vitro, this should be taken into account when translating in vitro to in vivo pharmacodynamics.

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.

Pharmacokinetic and pharmacodynamic implications in inhalable antimicrobial therapy

Inhaled antimicrobials provide a promising alternative to the systemically delivered drugs for the treatment of acute and chronic lung infections. The delivery of antimicrobials via inhalation route decreases the systemic exposure while increasing the local concentration in the lungs, enabling the use of antimicrobials with severe systemic side effects. The inhalation route of administration has several challenges in pharmacokinetic (PK) and pharmacodynamic (PD) assessments. This review discusses various issues that need to be considered during study, data analysis, and interpretation of PK and PD of inhaled antimicrobials. Advancements overcoming the challenges are also discussed.

Comparison of intrapulmonary and systemic pharmacokinetics of colistin methanesulfonate (CMS) and colistin after aerosol delivery and intravenous administration of CMS in critically ill patients

Colistin is an old antibiotic that has recently gained a considerable renewal of interest for the treatment of pulmonary infections due to multidrug-resistant Gram-negative bacteria. Nebulization seems to be a promising form of administration, but colistin is administered as an inactive prodrug, colistin methanesulfonate (CMS); however, differences between the intrapulmonary concentrations of the active moiety as a function of the route of administration in critically ill patients have not been precisely documented. In this study, CMS and colistin concentrations were measured on two separate occasions within the plasma and epithelial lining fluid (ELF) of critically ill patients (n = 12) who had received 2 million international units (MIU) of CMS by aerosol delivery and then intravenous administration. The pharmacokinetic analysis was conducted using a population approach and completed by pharmacokinetic-pharmacodynamic (PK-PD) modeling and simulations. The ELF colistin concentrations varied considerably (9.53 to 1,137 mg/liter), but they were much higher than those in plasma (0.15 to 0.73 mg/liter) after aerosol delivery but not after intravenous administration of CMS. Following CMS aerosol delivery, typically, 9% of the CMS dose reached the ELF, and only 1.4% was presystemically converted into colistin. PK-PD analysis concluded that there was much higher antimicrobial efficacy after CMS aerosol delivery than after intravenous administration. These new data seem to support the use of aerosol delivery of CMS for the treatment of pulmonary infections in critical care patients.

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.

In vivo pharmacokinetics and in vitro antifungal activity of iodiconazole, a new triazole, determined by microdialysis sampling

In this study, the distribution of a new triazole drug, iodiconazole, in rat dermal interstitial fluid and blood was investigated by double-site microdialysis following dermal administration. It was demonstrated that well-calibrated microdialysis sampling in rats could be used to assess the percutaneous penetration kinetics of iodiconazole cream. Iodiconazole penetrated rapidly and cleared slowly from the dermis. The ratio of area under the concentration-time curve in dermis (AUC(dermis)) to that in blood (AUC(blood)) was close to 20, which meant that the free iodiconazole concentration had a higher distribution in the target tissue. Subsequently, the in vitro antifungal activities of iodiconazole were evaluated and were compared with those of fluconazole, itraconazole, ketoconazole, miconazole and terbinafine. Iodiconazole exhibited broad spectrum and potent activity against 12 kinds of clinically pathogenic fungi. The drug concentration percentage inhibition curves versus time of iodiconazole against the tested fungi elucidated the two-dimensional relationship (concentration-effect) following drug administration, indicating that the percentage inhibition (%) of iodiconazole compared with the drug-free control in dermal dialysate were all >90% in the 900-min sampling time following dermal administration. Moreover, integration of in vivo pharmacokinetic data with the in vitro minimum inhibitory concentration (MIC) provided iodiconazole AUC/MIC ratios in rat dermis and blood of 347.7h and 18.8h, respectively, with an iodiconazole cream (2%) dosage of 0.033 g/cm² (3 cm×5 cm). These findings show a reservoir effect in the skin following topical application. Iodiconazole topical cream may be a future alternative for treatment of dermatophytosis in humans.

Evaluation of pharmacokinetic/pharmacodynamic relationships of PD-0162819, a biotin carboxylase inhibitor representing a new class of antibacterial compounds, using in vitro infection models

The present study investigated the pharmacokinetic/pharmacodynamic (PK/PD) relationships of a prototype biotin carboxylase (BC) inhibitor, PD-0162819, against Haemophilus influenzae 3113 in static concentration time-kill (SCTK) and one-compartment chemostat in vitro infection models. H. influenzae 3113 was exposed to PD-0162819 concentrations of 0.5 to 16× the MIC (MIC = 0.125 μg/ml) and area-under-the-curve (AUC)/MIC ratios of 1 to 1,100 in SCTK and chemostat experiments, respectively. Serial samples were collected over 24 h. For efficacy driver analysis, a sigmoid maximum-effect (E(max)) model was fitted to the relationship between bacterial density changes over 24 h and corresponding PK/PD indices. A semimechanistic PK/PD model describing the time course of bacterial growth and death was developed. The AUC/MIC ratio best explained efficacy (r(2) = 0.95) compared to the peak drug concentration (C(max))/MIC ratio (r(2) = 0.76) and time above the MIC (T>MIC) (r(2) = 0.88). Static effects and 99.9% killing were achieved at AUC/MIC values of 500 and 600, respectively. For time course analysis, the net bacterial growth rate constant, maximum bacterial density, and maximum kill rate constant were similar in SCTK and chemostat studies, but PD-0162819 was more potent in SCTK than in the chemostat (50% effective concentration [EC(50)] = 0.046 versus 0.34 μg/ml). In conclusion, basic PK/PD relationships for PD-0162819 were established using in vitro dynamic systems. Although the bacterial growth parameters and maximum drug effects were similar in SCTK and the chemostat system, PD-0162819 appeared to be more potent in SCTK, illustrating the importance of understanding the differences in preclinical models. Additional studies are needed to determine the in vivo relevance of these results.

Predicting in vitro antibacterial efficacy across experimental designs with a semimechanistic pharmacokinetic-pharmacodynamic model

We have previously described a general semimechanistic pharmacokinetic-pharmacodynamic (PKPD) model that successfully characterized the time course of antibacterial effects seen in bacterial cultures when exposed to static concentrations of five antibacterial agents of different classes. In this PKPD model, the total bacterial population was divided into two subpopulations, one growing drug-susceptible population and one resting drug-insensitive population. The drug effect was included as an increase in the killing rate of the drug-susceptible bacteria with a maximum-effect (E(max)) model. The aim of the present study was to evaluate the ability of this PKPD model to describe and predict data from in vitro experiments with dynamic concentration-time profiles. Dynamic time-kill curve experiments were performed by using an in vitro kinetic system, where cultures of Streptococcus pyogenes were exposed to benzylpenicillin, cefuroxime, erythromycin, moxifloxacin, or vancomycin using different starting concentrations (2 and 16 times the MIC) and elimination conditions (human half-life, reduced half-life, and constant concentrations). The PKPD model was applied, and the observations for the static as well as dynamic experiments were compared to model predictions based on parameter estimation using (i) static data, (ii) dynamic data, and (iii) combined static and dynamic data. Differences in experimental settings between static and dynamic experiments did not affect the growth kinetics of the bacteria significantly. With parameter reestimation, the structure of our previously proposed PKPD model could well characterize the bacterial growth and killing kinetics when exposed to dynamic concentrations with different elimination rates of all five investigated antibiotics. Furthermore, the model with parameter estimates based on data from only the static time-kill curve experiments could predict the majority of the time-kill curves from the dynamic experiments reasonably well. Adding data from dynamic experiments in the estimation improved the model fit for cefuroxime and vancomycin, indicating some differences in sensitivity to experimental conditions among the antibiotics studied.

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.

Antimicrobial chemotherapy and lung microdialysis: a review

Pneumonia is a form of lung infection that may be caused by various micro-organisms. The predominant site of infection in pneumonia is debatable. Advances in the fields of diagnostic and therapeutic medicine have had a less than optimal effect on the outcome of pneumonia and one of the many causes is likely to be inadequate antimicrobial concentrations at the site of infection in lung tissue. Traditional antimicrobial therapy guidelines are based on indirect modelling from blood antimicrobial levels. However, studies both in humans and animals have shown the fallacy of this concept in various tissues. Many different methods have been employed to study lung tissue antimicrobial levels with limited success, and each has limitations that diminish their utility. An emerging technique being used to study the pharmacokinetics of antimicrobial agents in lung tissue is microdialysis. Development of microdialysis catheters, along with improvement in analytical techniques, has improved the accuracy of the data. Unfortunately, very few studies have reported the use of microdialysis in lung tissue, and even fewer antimicrobial classes have been studied. These studies generally suggest that this technique is a safe and effective way of assessing the pharmacokinetics of antimicrobial agents in lung tissue. Further descriptive studies need to be conducted to study the pharmacokinetics and pharmacodynamics of different antimicrobial classes in lung tissue. Data emanating from these studies could inform decisions for appropriate dosing schedules of antimicrobial agents in pneumonia.

Mathematical modeling to characterize the inoculum effect

Killing by beta-lactams is well known to be reduced against a dense bacterial population, commonly known as the inoculum effect. However, the underlying mechanism of this phenomenon is not well understood. We proposed a semi-mechanistic mathematical model to account for the reduced in vitro killing observed. Time-kill studies were performed with 4 baseline inocula (ranging from approximately 1 × 10(5) to 1 × 10(8) CFU/ml) of Escherichia coli ATCC 25922 (MIC, 2 mg/liter). Constant but escalating piperacillin concentrations used ranged from 0.25× to 256× MIC. Serial samples were taken over 24 h to quantify viable bacterial burden, and all the killing profiles were mathematically modeled. The inoculum effect was attributed to a reduction of effective drug concentration available for bacterial killing, which was expressed as a function of the baseline inoculum. Biomasses associated with different inocula were examined using a colorimetric method. Despite identical drug-pathogen combinations, the baseline inoculum had a significant impact on bacterial killing. Our proposed mathematical model was unbiased and reasonable in capturing all 28 killing profiles collectively (r(2) = 0.88). Biomass was found to be significantly more after 24 h with a baseline inoculum of 1 × 10(8) CFU/ml, compared to one where the initial inoculum was 1 × 10(5) CFU/ml (P = 0.002). Our results corroborated previous observations that in vitro killing by piperacillin was significantly reduced against a dense bacterial inoculum. This phenomenon can be reasonably captured by our proposed mathematical model, and it may improve prediction of bacterial response to various drug exposures in future investigations.

A simple in vitro PK/PD model system to determine time-kill curves of drugs against Mycobacteria

In vivo tuberculosis is exposed to continually changing drug concentrations for which static minimum inhibitory concentration (MIC) testing may be a poor surrogate. While in vitro approaches to determine time-kill curves for antibiotics have been widely applied in assessing antimicrobial activity against fast growing microorganisms, their availability and application for slow-growing microorganisms including Mycobacterium tuberculosis has so far been scarce. Thus, we developed a novel simple in vitro pharmacokinetic/pharmacodynamic (PK/PD) model for establishing time-kill curves and applied it for evaluating the antimicrobial activity of different dosing regimens of isoniazid (INH) against Mycobacterium bovis BCG as a surrogate for virulent M. tuberculosis. In the in vitro model M. bovis BCG was exposed to INH concentration-time profiles as usually encountered during multiple dose therapy with 25, 100 and 300mg/day in humans who are fast or slow INH metabolizers. Bacterial killing was followed over time by determining viable counts and the resulting time-kill data was analyzed using a semi-mechanistic PK/PD model with an adaptive IC(50) function to describe the emergence of insensitive populations of bacteria over the course of treatment. In agreement with previous studies, the time-kill data suggest that AUC(0-24)/MIC is the PK/PD index that is the most explanatory of the antimicrobial effect of INH. The presented in vitro PK/PD model and associated modeling approach were able to characterize the time-kill kinetics of INH in M. bovis BCG, and may in general serve as a potentially valuable, low cost tool for the assessment of antibacterial activity in slow-growing organisms in drug development and applied pharmacotherapy.

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.

Pharmacokinetic-pharmacodynamic modeling and simulation for bactericidal effect in an in vitro dynamic model

A pharmacokinetic (PK)/pharmacodynamic (PD) modeling strategy to explain the data from an in vitro dynamic model is proposed. Two carbapenem antibiotics, doripenem and meropenem, and three Pseudomonas aeruginosa strains were used as example drugs and strains. The PD model we originally developed to explain the in vitro time-kill data was modified by incorporating bactericidal activities and simulated in vivo PK profiles of the drugs. By employing only one parameter regarding the bactericidal activity from the data at a certain dosage regimen, the bacterial profiles at various dosage regimens could be well simulated for both antibiotics by the PK/PD model. Moreover, simulated bacterial counts for various dosage regimens correlated with time above minimum inhibitory concentration derived from free drug concentrations (fT > MIC) for doripenem. The predicted fT > MIC values to achieve PK/PD endpoints for three strains (static effect: 25.0%, 23.9%, and 39.8%, 2-log killing effect: 28.1%, 29.5%, and 49.6%, 90% maximum killing effect: 36.5%, 46.8%, and 80.7%) were similar to those estimated from free drug concentrations in animal infection models. The proposed in vitro PK/PD model would be useful for simulating bactericidal kinetics in the dynamic model and predicting the human therapeutic target for PK/PD indices estimated from animal infection models.

Pharmacokinetic–Pharmacodynamic Modeling and Simulation for in Vivo Bactericidal Effect in Murine Infection Model

A pharmacokinetic (PK)/pharmacodynamic (PD) modeling strategy to simulate in vivo bactericidal effects for three carbapenem antibiotics, doripenem (DRPM), meropenem (MEPM)/cilastatin (CS), and imipenem (IPM)/CS, against a Pseudomonas aeruginosa (P. aeruginosa) strain is proposed. The PD model we have already developed to explain in vitro time-kill profiles was modified to incorporate the growth rate, bactericidal activities, and PK profiles in murine lung infection models. Plasma concentration data and bacterial time-kill data for each antibiotic consist of six and eight time points, respectively, at one dose regimen (four or five mouse/point). In vivo time-kill curves could be well simulated for each antibiotic by the PK/PD model. Simulated bacterial counts at 24 h and PK/PD indices derived from total drug concentrations (time above the minimum inhibitory concentration (MIC) (T > MIC), C(max)/MIC, and AUC/MIC) for various dose regimens were examined for MEPM/CS and IPM/CS. Simulated bacterial counts correlated only with T > MIC (correlation coefficient: 0.951 for MEPM/CS, 0.982 for IPM/CS) and T > MIC values to achieve a bacteriostatic effect and a 2-log killing effect for both antibiotics were estimated to be approximately 15 and 20%, respectively, which are similar to previously reported results. These findings suggested that the proposed PK/PD model is a good tool for predicting in vivo bactericidal effects.

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 models of in vitro fungistatic and fungicidal effects against Candida albicans

Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) models describing the fungistatic activity of fluconazole and the fungicidal activity of caspofungin were developed using dynamic in vitro models. Antifungal-drug pharmacokinetics was simulated in vitro, assuming a one-compartment model with an elimination half-life of 3 h and using a wide (1 to 10,000) range of initial concentrations. The number of CFUs over time was determined for up to 31 h and used for PK-PD modeling. A model incorporating first-order natural growth and natural death, plus a maximum number of viable Candida cells, was used to characterize Candida growth in the absence of a drug. Fluconazole was considered to inhibit Candida growth and caspofungin to stimulate Candida death according to an Emax pharmacodynamic model. The data were analyzed with Nonmem, using a population approach. A good fit of the data was obtained with satisfactory estimates of PK-PD parameters, especially with drug concentrations producing 50% of the maximal effect: 50% inhibitory concentrations for fluconazole growth inhibition and 50% effective concentrations for caspofungin death stimulation. In conclusion, mechanistic PK-PD models were successfully developed to describe, respectively, the fungistatic and fungicidal activities of fluconazole and caspofungin in vitro. These models provide much better information on the drug effects over time than the traditional PK-PD index based on MICs. However, they need to be further characterized.

Integrated pharmacokinetics and pharmacodynamics in drug development

Drug development is a complex, lengthy and expensive process. Pharmaceutical companies and regulatory authorities have recognised that the drug development process needs optimisation for efficiency in view of the return on investments. Pharmacokinetics and pharmacodynamics are the two main principles determining the relationship between dose and response. This article provides an update on integrated approaches towards drug development by linking pharmacokinetics, pharmacodynamics and disease aspects into mathematical models. Gradually, a transition is taking place from a rather empirical approach towards a modelling- and simulation-based approach to drug development. The main learning phases should be phases 0, I and II, whereas phase III studies should merely have a confirmatory purpose. In model-based drug development, mechanism-based mathematical models, which are iteratively refined along the path of development, incorporate the accumulating knowledge of the investigational drug, the disease and their mutual interference in different subsets of the target population. These models facilitate the design of the next study and improve the probability of achieving the projected efficacy and safety endpoints. In this article, several theoretical and practical aspects of an integrated approach towards drug development are discussed, together with some case studies from different therapeutic areas illustrating the application of pharmacokinetic/pharmacodynamic disease models at different stages of drug development.

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.

Antimicrobial resistance in Haemophilus influenzae

Haemophilus influenzae is a major community-acquired pathogen causing significant morbidity and mortality worldwide. Meningitis and bacteremia due to type b strains occur in areas where the protein-conjugated type b vaccine is not in use, whereas nontypeable strains are major causes of otitis media, sinusitis, acute exacerbations of chronic bronchitis, and pneumonia. Antibiotic resistance in this organism is more diverse and widespread than is commonly appreciated. Intrinsic efflux resistance mechanisms limit the activity of the macrolides, azalides, and ketolides. beta-Lactamase production is highly prevalent worldwide and is associated with resistance to ampicillin and amoxicillin. Strains with alterations in penicillin binding proteins, particularly PBP3 (beta-lactamase negative ampicillin resistant and beta-lactamase positive amoxicillin-clavulanate resistant), are increasing in prevalence, particularly in Japan, with increasing resistance to ampicillin, amoxicillin, amoxicillin-clavulanate, and many cephalosporins, limiting the efficacy of expanded-spectrum cephalosporins against meningitis and of many oral cephalosporins against other diseases. Most strains remain susceptible to the carbapenems, which are not affected by penicillin binding protein changes, and the quinolones. The activity of many oral agents is limited by pharmacokinetics achieved with administration by this route, and the susceptibility of isolates based on pharmacokinetic and pharmacodynamic parameters is reviewed.

Semimechanistic pharmacokinetic/pharmacodynamic model for assessment of activity of antibacterial agents from time-kill curve experiments

Dosing of antibacterial agents is generally based on point estimates of the effect, even though bacteria exposed to antibiotics show complex kinetic behaviors. The use of the whole time course of the observed effects would be more advantageous. The aim of the present study was to develop a semimechanistic pharmacokinetic (PK)/pharmacodynamic (PD) model characterizing the events seen in a bacterial system when it is exposed to antibacterial agents with different mechanisms of action. Time-kill curve experiments were performed with a strain of Streptococcus pyogenes exposed to a wide range of concentrations of the following antibiotics: benzylpenicillin, cefuroxime, erythromycin, moxifloxacin, and vancomycin. Bacterial counts were monitored with frequent sampling during the experiment. A simultaneous fit of all data was accomplished. The degradation of the drugs was monitored and corrected for in the model, and a link model was used to account for an effect delay. In the final PK/PD model, the total bacterial population was divided into two subpopulations: one growing drug-susceptible population and one resting insusceptible population. The drug effect was included as an increase of the killing rate of bacteria in the susceptible state, according to a maximum-effect (E(max)) model. An internal model validation showed that the model was robust and had good predictability. In conclusion, for all drugs, the final PK/PD model successfully described bacterial growth and killing kinetics when the bacteria were exposed to different antibiotic concentrations. The semimechanistic model that was developed might, after further refinement, serve as a tool for the development of optimal dosing strategies for antibacterial agents.

Use of in vitro critical inhibitory concentration, a novel approach to predict in vivo synergistic bactericidal effect of combined amikacin and piperacillin against Pseudomonas aeruginosa in a systemic rat infection model

PURPOSE

This study was undertaken to explore the use of in vitro critical inhibitory concentration (CIC) as a surrogate marker relating the pharmacokinetic (PK) parameters to in vivo bactericidal synergistic effect [pharmacodynamic (PD)] of amikacin + piperacillin combination against Pseudomonas aeruginosa in a systemic rat infection model.

METHODS

The in vitro antibacterial activities of amikacin and piperacillin, alone and in combinations at various ratios of the concentrations, were tested against a standard [5 x 10(5) colony-forming units (CFU)/ml] and a large (1.5 x 10(8) CFU/ml) inoculum of P. aeruginosa ATCC 9027 using a modified survival-time method. The CIC of each individual antibiotic for the different combinations was determined using a cup-plate method. In vivo studies were performed on Sprague-Dawley rats using a systemic model of infection with P. aeruginosa ATCC 9027. PK profiles and in vivo killing effects of the combination at different dosing ratios were studied.

RESULTS

An inoculum effect was observed with the antibiotics studied. Synergy was seen against both the inocula at the following concentration ratios: 70% C(ami) + 30% C(pip) and 75% C(ami) + 25% C(pip), where C(ami) and C(pip) are the concentrations of amikacin and piperacillin to produce a 1000-fold decrease in bacterial population over 5 h, respectively. The CIC values determined corroborated with the order of in vitro bacterial killing observed for the antibiotic combinations. The dosing ratio of 12.6 mg/kg amikacin + 36 mg/kg piperacillin (a 70:30 ratio of the individual doses) exhibited the greatest killing in vivo when compared to the other ratios. The PK-PD relationships were described by simple, linear regression equations using the area under the in vivo killing curve as a PD marker and the AUCIC(ami)/CIC(ami) + AUCIC(pip)/CIC(pip), AUC(ami)/CIC(ami) + AUC(pip)/CIC(pip), C(max,ami)/CIC(ami) + C(max,pip)/CIC(pip), and AUCIC(ami)/MIC(ami) + AUCIC(pip)/MIC(pip) as PK markers for the amikacin + piperacillin combination.

CONCLUSION

The combination of amikacin and piperacillin exhibited synergistic killing effect on P. aeruginosa that could be modeled using CIC as a surrogate marker relating the PK parameters to in vivo bactericidal effect.