Comparisons between antimicrobial pharmacodynamic indices and bacterial killing as described by using the Zhi model

Antimicrobial polymer-siRNA polyplexes as a dual-mode platform for the treatment of wound biofilm infections

Treatment of wound biofilm infections faces challenges from both pathogens and uncontrolled host immune response. Treating both issues through a single vector would provide enhanced wound healing. Here, we report the use of a potent cationic antimicrobial polymer to generate siRNA polyplexes for dual-mode treatment of wound biofilms in vivo. These polyplexes act both as an antibiofilm agent and a delivery vehicle for siRNA for the knockdown of biofilm-associated pro-inflammatory MMP9 in host macrophages. The resulting polyplexes were effective in vitro, eradicating MRSA biofilms and efficiently delivering siRNA to macrophages in vitro with concomitant knockdown of MMP9. These polyplexes were likewise effective in an in vivo murine wound biofilm model, significantly reducing bacterial load in the wound (∼99% bacterial clearance) and reducing MMP9 expression by 80% (qRT-PCR). This combination therapeutic strategy dramatically reduced wound purulence and significantly expedited wound healing. Taken together, these polyplexes provide an effective and translatable strategy for managing biofilm-infected wounds.

Optimizing Antimicrobial Treatment Schedules: Some Fundamental Analytical Results

This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC), which is equivalent to minimizing the cumulative dosage. We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the ideal concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the 'ideal' concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the 'ideal' concentration profile, using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the 'ideal' concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.

The pharmacokinetic-pharmacodynamic modelling framework as a tool to predict drug resistance evolution

Pharmacokinetic-pharmacodynamic (PKPD) models, which describe how drug concentrations change over time and how that affects pathogen growth, have proven highly valuable in designing optimal drug treatments aimed at bacterial eradication. However, the fast rise of antimicrobial resistance calls for increased focus on an additional treatment optimization criterion: avoidance of resistance evolution. We demonstrate here how coupling PKPD and population genetics models can be used to determine treatment regimens that minimize the potential for antimicrobial resistance evolution. Importantly, the resulting modelling framework enables the assessment of resistance evolution in response to dynamic selection pressures, including changes in antimicrobial concentration and the emergence of adaptive phenotypes. Using antibiotics and antimicrobial peptides as an example, we discuss the empirical evidence and intuition behind individual model parameters. We further suggest several extensions of this framework that allow a more comprehensive and realistic prediction of bacterial escape from antimicrobials through various phenotypic and genetic mechanisms.

Mathematical Modeling for an MTT Assay in Fluorine-Containing Graphene Quantum Dots

The paper reports on a new mathematical model, starting with the original Hill equation which is derived to describe cell viability (V) while testing nanomaterials (NMs). Key information on the sample's morphology, such as mean size (⟨s⟩) and size dispersity (σ) is included in the new model via the lognormal distribution function. The new Hill-inspired equation is successfully used to fit MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) data from assays performed with the HepG2 cell line challenged by fluorine-containing graphene quantum dots (F:GQDs) under light (400-700 nm wavelength) and dark conditions. The extracted "biological polydispersity" (light: ⟨sMTT⟩=1.77±0.02 nm and σMTT=0.21±0.02); dark: ⟨sMTT⟩=1.87±0.02 nm and σMTT=0.22±0.01) is compared with the "morphological polydispersity" (⟨sTEM⟩=1.98±0.06 nm and σTEM=0.19±0.03), the latter obtained from TEM (transmission electron microscopy). The fitted data are then used to simulate a series of V responses. Two aspects are emphasized in the simulations: (i) fixing σ, one simulates V versus ⟨s⟩ and (ii) fixing ⟨s⟩, one simulates V versus σ. Trends observed in the simulations are supported by a phenomenological model picture describing the monotonic reduction in V as ⟨s⟩ increases (V~pa/(s)p-a; p and a are fitting parameters) and accounting for two opposite trends of V versus σ: under light (V~σ) and under dark (V~1/σ).

Formulation of Antimicrobial Tobramycin Loaded PLGA Nanoparticles via Complexation with AOT

Tobramycin is a potent antimicrobial aminoglycoside and its effective delivery by encapsulation within nanoparticle carriers could increase its activity against infections through a combination of sustained release and enhanced uptake. Effective antimicrobial therapy against a clinically relevant model bacteria (Pseudomonas aeruginosa) requires sufficient levels of therapeutic drug to maintain a drug concentration above the microbial inhibitory concentration (MIC) of the bacteria. Previous studies have shown that loading of aminoglycoside drugs in poly(lactic-co-glycolic) acid (PLGA)-based delivery systems is generally poor due to weak interactions between the drug and the polymer. The formation of complexes of tobramycin with dioctylsulfosuccinate (AOT) allows the effective loading of the drug in PLGA-nanoparticles and such nanoparticles can effectively deliver the antimicrobial aminoglycoside with retention of tobramycin antibacterial function.

Predicting drug resistance evolution: insights from antimicrobial peptides and antibiotics

Antibiotic resistance constitutes one of the most pressing public health concerns. Antimicrobial peptides (AMPs) of multicellular organisms are considered part of a solution to this problem, and AMPs produced by bacteria such as colistin are last-resort drugs. Importantly, AMPs differ from many antibiotics in their pharmacodynamic characteristics. Here we implement these differences within a theoretical framework to predict the evolution of resistance against AMPs and compare it to antibiotic resistance. Our analysis of resistance evolution finds that pharmacodynamic differences all combine to produce a much lower probability that resistance will evolve against AMPs. The finding can be generalized to all drugs with pharmacodynamics similar to AMPs. Pharmacodynamic concepts are familiar to most practitioners of medical microbiology, and data can be easily obtained for any drug or drug combination. Our theoretical and conceptual framework is, therefore, widely applicable and can help avoid resistance evolution if implemented in antibiotic stewardship schemes or the rational choice of new drug candidates.

En Route towards European Clinical Breakpoints for Veterinary Antimicrobial Susceptibility Testing: A Position Paper Explaining the VetCAST Approach

VetCAST is the EUCAST sub-committee for Veterinary Antimicrobial Susceptibility Testing. Its remit is to define clinical breakpoints (CBPs) for antimicrobial drugs (AMDs) used in veterinary medicine in Europe. This position paper outlines the procedures and reviews scientific options to solve challenges for the determination of specific CBPs for animal species, drug substances and disease conditions. VetCAST will adopt EUCAST approaches: the initial step will be data assessment; then procedures for decisions on the CBP; and finally the release of recommendations for CBP implementation. The principal challenges anticipated by VetCAST are those associated with the differing modalities of AMD administration, including mass medication, specific long-acting product formulations or local administration. Specific challenges comprise mastitis treatment in dairy cattle, the range of species and within species breed considerations and several other variable factors not relevant to human medicine. Each CBP will be based on consideration of: (i) an epidemiological cut-off value (ECOFF) - the highest MIC that defines the upper end of the wild-type MIC distribution; (ii) a PK/PD breakpoint obtained from pre-clinical pharmacokinetic data [this PK/PD break-point is the highest possible MIC for which a given percentage of animals in the target population achieves a critical value for the selected PK/PD index (fAUC/MIC or fT > MIC)] and (iii) when possible, a clinical cut-off, that is the relationship between MIC and clinical cure. For the latter, VetCAST acknowledges the paucity of such data in veterinary medicine. When a CBP cannot be established, VetCAST will recommend use of ECOFF as surrogate. For decision steps, VetCAST will follow EUCAST procedures involving transparency, consensus and independence. VetCAST will ensure freely available dissemination of information, concerning standards, guidelines, ECOFF, PK/PD breakpoints, CBPs and other relevant information for AST implementation. Finally, after establishing a CBP, VetCAST will promulgate expert comments and/or recommendations associated with CBPs to facilitate their sound implementation in a clinical setting.

Application of PK/PD Modeling in Veterinary Field: Dose Optimization and Drug Resistance Prediction

Among veterinary drugs, antibiotics are frequently used. The true mean of antibiotic treatment is to administer dose of drug that will have enough high possibility of attaining the preferred curative effect, with adequately low chance of concentration associated toxicity. Rising of antibacterial resistance and lack of novel antibiotic is a global crisis; therefore there is an urgent need to overcome this problem. Inappropriate antibiotic selection, group treatment, and suboptimal dosing are mostly responsible for the mentioned problem. One approach to minimizing the antibacterial resistance is to optimize the dosage regimen. PK/PD model is important realm to be used for that purpose from several years. PK/PD model describes the relationship between drug potency, microorganism exposed to drug, and the effect observed. Proper use of the most modern PK/PD modeling approaches in veterinary medicine can optimize the dosage for patient, which in turn reduce toxicity and reduce the emergence of resistance. The aim of this review is to look at the existing state and application of PK/PD in veterinary medicine based on in vitro, in vivo, healthy, and disease model.

Two mechanisms of killing of Pseudomonas aeruginosa by tobramycin assessed at multiple inocula via mechanism-based modeling

Bacterial resistance is among the most serious threats to human health globally, and many bacterial isolates have emerged that are resistant to all antibiotics in monotherapy. Aminoglycosides are often used in combination therapies against severe infections by multidrug-resistant bacteria. However, models quantifying different antibacterial effects of aminoglycosides are lacking. While the mode of aminoglycoside action on protein synthesis has often been studied, their disruptive action on the outer membrane of Gram-negative bacteria remains poorly characterized. Here, we developed a novel quantitative model for these two mechanisms of aminoglycoside action, phenotypic tolerance at high bacterial densities, and adaptive bacterial resistance in response to an aminoglycoside (tobramycin) against three Pseudomonas aeruginosa strains. At low-intermediate tobramycin concentrations (<4 mg/liter), bacterial killing due to the effect on protein synthesis was most important, whereas disruption of the outer membrane was the predominant killing mechanism at higher tobramycin concentrations (≥8 mg/liter). The extent of killing was comparable across all inocula; however, the rate of bacterial killing and growth was substantially lower at the 10(8.9) CFU/ml inoculum than that at the lower inocula. At 1 to 4 mg/liter tobramycin for strain PAO1-RH, there was a 0.5- to 6-h lag time of killing that was modeled via the time to synthesize hypothetical lethal protein(s). Disruption of the outer bacterial membrane by tobramycin may be critical to enhance the target site penetration of antibiotics used in synergistic combinations with aminoglycosides and thereby combat multidrug-resistant bacteria. The two mechanisms of aminoglycoside action and the new quantitative model hold great promise to rationally design novel, synergistic aminoglycoside combination dosage regimens.

In vitro evaluation of synergistic activity between ciprofloxacin and broad snouted caiman serum against Escherichia coli

The in vitro synergistic activity between ciprofloxacin and serum of broad snouted caiman on Escherichia coli was studied. The estimated MIC value of ciprofloxacin was 0.0188 µg/ml, and two assays of kill curve during 5 hours were performed: the first one in a standard culture medium and the second one in the presence of caiman serum. Different concentrations of ciprofloxacin were tested. Ciprofloxacin showed higher values of bacterial elimination rate in the presence of caiman serum in all concentrations tested. The combined activity of sub-inhibitory concentrations of ciprofloxacin and the humoral immune factors present in caiman serum determined an increase in the bacterial elimination observed in this assay. We suggest that the antibacterial activity of complement and natural antibodies present in caiman serum, which can bind to both Gram-negative and Gram-positive bacteria and acting through the classical complement pathway, can inhibit bacterial growth of Escherichia coli by lysis.

Exploring the collaboration between antibiotics and the immune response in the treatment of acute, self-limiting infections

The successful treatment of bacterial infections is the product of a collaboration between antibiotics and the host's immune defenses. Nevertheless, in the design of antibiotic treatment regimens, few studies have explored the combined action of antibiotics and the immune response to clearing infections. Here, we use mathematical models to examine the collective contribution of antibiotics and the immune response to the treatment of acute, self-limiting bacterial infections. Our models incorporate the pharmacokinetics and pharmacodynamics of the antibiotics, the innate and adaptive immune responses, and the population and evolutionary dynamics of the target bacteria. We consider two extremes for the antibiotic-immune relationship: one in which the efficacy of the immune response in clearing infections is directly proportional to the density of the pathogen; the other in which its action is largely independent of this density. We explore the effect of antibiotic dose, dosing frequency, and term of treatment on the time before clearance of the infection and the likelihood of antibiotic-resistant bacteria emerging and ascending. Our results suggest that, under most conditions, high dose, full-term therapy is more effective than more moderate dosing in promoting the clearance of the infection and decreasing the likelihood of emergence of antibiotic resistance. Our results also indicate that the clinical and evolutionary benefits of increasing antibiotic dose are not indefinite. We discuss the current status of data in support of and in opposition to the predictions of this study, consider those elements that require additional testing, and suggest how they can be tested.

Interpreting culture and susceptibility data in critical care: perks and pitfalls

PROBLEM

The need for immediate, effective antimicrobial therapy in the critical care patient must be tempered by approaches which simultaneously minimize emergence of antimicrobial resistance. Ideally, therapy will successfully resolve clinical signs of infection, while eradicating infecting pathogens such that the risk of resistance is avoided. Increasing limitations associated with empirical antimicrobial choices direct the need for culture and susceptibility data as a basis of therapy. Even so, such in vitro data should be utilized within its limitations.

OBJECTIVES

To demonstrate the attributes and limitations of patient and population culture and susceptibility (pharmacodynamic) data in the selection of antimicrobial drugs and to demonstrate the design of individualized dosing regimens based on integration of pharmacodynamic (PD) and pharmacokinetic (PK) data.

DIAGNOSIS

Limitations in culture and susceptibility testing begin with sample collection and continue through drug selection and dose design. Among the challenges in interpretation is discrimination between pathogens and commensals. Properly collected samples are critical for generation of data relevant to the patient's infection. Data are presented as minimum inhibitory concentrations (MICs). The MIC facilitate selection of the most appropriate drug, particularly when considered in the context of antimicrobial concentrations achieved in the patient at a chosen dose. Integration of MIC data with key PK data yields the C(max):MIC important to efficacy of concentration-dependent drugs and T>MIC, which guides use of time-dependent drugs. These indices are then used to design dosing regimens that are more likely to kill all infecting pathogens. In the absence of patient MIC data, population data (eg, MIC(90)) may serve as a reasonable surrogate.

CONCLUSIONS

Properly collected, performed, and interpreted culture and susceptibility data are increasingly important in the selection of and design of dosing regimens for antimicrobial drugs. Integration of PK and PD data as modified by host and microbial factors supports a hit hard, exit fast approach to therapy that will facilitate efficacy while minimizing resistance.

Antimicrobial breakpoint estimation accounting for variability in pharmacokinetics

Background

Pharmacokinetic and pharmacodynamic (PK/PD) indices are increasingly being used in the microbiological field to assess the efficacy of a dosing regimen. In contrast to methods using MIC, PK/PD-based methods reflect in vivo conditions and are more predictive of efficacy. Unfortunately, they entail the use of one PK-derived value such as AUC or Cmax and may thus lead to biased efficiency information when the variability is large. The aim of the present work was to evaluate the efficacy of a treatment by adjusting classical breakpoint estimation methods to the situation of variable PK profiles.

Methods and results

We propose a logical generalisation of the usual AUC methods by introducing the concept of "efficiency" for a PK profile, which involves the efficacy function as a weight. We formulated these methods for both classes of concentration- and time-dependent antibiotics. Using drug models and in silico approaches, we provide a theoretical basis for characterizing the efficiency of a PK profile under in vivo conditions. We also used the particular case of variable drug intake to assess the effect of the variable PK profiles generated and to analyse the implications for breakpoint estimation.

Conclusion

Compared to traditional methods, our weighted AUC approach gives a more powerful PK/PD link and reveals, through examples, interesting issues about the uniqueness of therapeutic outcome indices and antibiotic resistance problems.

Modeling the mechanism of postantibiotic effect and determining implications for dosing regimens

A stochastic model is proposed to explain one possible underlying mechanism of the postantibiotic effect (PAE). This phenomenon, of continued inhibition of bacterial growth after removal of the antibiotic drug, is of high relevance in the context of optimizing dosing regimens. One clinical implication of long PAE lies in the possibility of increasing intervals between drug administrations. The model describes the dynamics of synthesis, saturation and removal of penicillin binding proteins (PBPs). High fractions of saturated PBPs are in the model associated with a lower growth capacity of bacteria. An analytical solution for the bivariate probability of saturated and unsaturated PBPs is used as a basis to explore optimal antibiotic dosing regimens. Our finding that longer PAEs do not necessarily promote for increased intervals between doses, might help for our understanding of data provided from earlier PAE studies and for the determination of the clinical relevance of PAE in future studies.

Effects of age on the pharmacokinetics of single dose sulfamethazine after intravenous administration in cattle

Sulphonamides are still being used widely, influenced by the low cost and the efficacy against many common bacterial infections, since they present a broad spectrum of activity. The aim of this study was to determine the effect of age on the pharmacokinetic/pharmacodynamics (PK/PD) integration of intravenous sulfamethazine (60 mg/kgbw) in cattle, and the possible therapeutic outcomes. Six healthy female calves, at the age of one, three, seven and fifteen weeks were used. Normality analysis was assessed with the Shapiro-Wilk test. Non-parametric tests for paired data were used. Plasma concentrations were quantified using HPLC/uv. Differences were found between one-three-weeks-old calves and seven-fifteen-weeks-old calves, in pharmacokinetic parameters (clearance, area under the concentration-time curve and elimination half-life) and in the PK/PD integration. The ratios obtained in PK/PD integration (T>MIC, WAUC) confirm that it is necessary to apply twice the dose of sulfamethazine in > or = 7 weeks-old cattle to reach a satisfactory dosage regimen (MIC > or = 32 microg/mL).

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.

Pharmacokinetics of enrofloxacin in turkeys

The pharmacokinetics of enrofloxacin (EFL) and its active metabolite ciprofloxacin (CIP) was investigated in 7-8 month old turkeys (6 birds per sex). EFL was administered intravenously (i.v.) and orally (p.o.) at a dose 10 mg kg(-1) body weight. Blood was taken prior to and at 0.17, 0.33, 0.5, 1, 2, 3, 4, 6, 8, 10 and 24 h following drug administration. The concentrations of EFL and CIP in blood serum were determined by high-performance liquid chromatography (HPLC). Serum concentrations versus time were analysed by a noncompartmental analysis. The elimination half-live and the mean residence time of EFL after i.v. injection for the serum were after oral administration 6.64+/-0.90 h, 8.96+/-1.18 h and 6.92+/-0.97 h, 11.91+/-1.87 h, respectively. After single p.o. administration, EFL was absorbed slowly (MAT=2.76+/-0.48 h) with time to reach maximum serum concentrations of 6.33+/-2.54 h. Maximum serum concentrations was 1.23+/-0.30 microg mL(-1). Oral bioavailability for for EFL after oral administration was found to be 69.20+/-1.49%. The ratios C(max)/MIC and AUC(0 --> 24)/MIC were respectively from 161.23+/-5.9 h to 12.90+/-0.5 h for the pharmacodynamic predictor C(max)/MIC, and from 2153.44+/-66.6 h to 137.82+/-4.27 h for AUC(0 --> 24)/MIC, for the different clinically significant microorganisms, whose values for MIC varies from 0.008 microg L(-1) to 0.125 microg mL(-1).

Pharmacodynamics of non-replicating viruses, bacteriocins and lysins

The pharmacodynamics of antibiotics and many other chemotherapeutic agents is often governed by a 'multi-hit' kinetics, which requires the binding of several molecules of the therapeutic agent for the killing of their targets. In contrast, the pharmacodynamics of novel alternative therapeutic agents, such as phages and bacteriocins against bacterial infections or viruses engineered to target tumour cells, is governed by a 'single-hit' kinetics according to which the agent will kill once it is bound to its target. In addition to requiring only a single molecule for killing, these agents bind irreversibly to their targets. Here, we explore the pharmacodynamics of such 'irreversible, single-hit inhibitors' using mathematical models. We focus on agents that do not replicate, i.e. in the case of phage therapy, we deal only with non-lytic phages and in the case of cancer treatment, we restrict our analysis to replication of incompetent viruses. We study the impact of adsorption on dead cells, heterogeneity in adsorption rates and spatial compartmentalization.

Principles of Antimicrobial Therapy

The most compelling reason for practicing judicious antimicrobial use is to facilitate therapeutic success. The definition of therapeutic success has changed in recent years, however; not only does success include eradication of infection, but it must now include avoidance of resistance. If the goal of antimicrobial therapy is to achieve sufficient concentrations at the site of infection such that the infecting organism is killed, therapy should be successful.

Pharmacodynamic model to describe the concentration-dependent selection of cefotaxime-resistant Escherichia coli

Antibiotic dosing regimens may vary in their capacity to select mutants. Our hypothesis was that selection of a more resistant bacterial subpopulation would increase with the time within a selective window (SW), i.e., when drug concentrations fall between the MICs of two strains. An in vitro kinetic model was used to study the selection of two Escherichia coli strains with different susceptibilities to cefotaxime. The bacterial mixtures were exposed to cefotaxime for 24 h and SWs of 1, 2, 4, 8, and 12 h. A mathematical model was developed that described the selection of preexisting and newborn mutants and the post-MIC effect (PME) as functions of pharmacokinetic parameters. Our main conclusions were as follows: (i) the selection between preexisting mutants increased with the time within the SW; (ii) the emergence and selection of newborn mutants increased with the time within the SW (with a short time, only 4% of the preexisting mutants were replaced by newborn mutants, compared to the longest times, where 100% were replaced); and (iii) PME increased with the area under the concentration-time curve (AUC) and was slightly more pronounced with a long elimination half-life (T(1/2)) than with a short T(1/2) situation, when AUC is fixed. We showed that, in a dynamic competition between strains with different levels of resistance, the appearance of newborn high-level resistant mutants from the parental strains and the PME can strongly affect the outcome of the selection and that pharmacodynamic models can be used to predict the outcome of resistance development.

Pharmacokinetic/pharmacodynamic relationships of antimicrobial drugs used in veterinary medicine

The rise in incidence of antimicrobial resistance, consumer demands and improved understanding of antimicrobial action has encouraged international agencies to review the use of antimicrobial drugs. More detailed understanding of relationships between the pharmacokinetics (PK) of antimicrobial drugs in target animal species and their action on target pathogens [pharmacodynamics (PD)] has led to greater sophistication in design of dosage schedules which improve the activity and reduce the selection pressure for resistance in antimicrobial therapy. This, in turn, may be informative in the pharmaceutical development of antimicrobial drugs and in their selection and clinical utility. PK/PD relationships between area under the concentration time curve from zero to 24 h (AUC(0-24)) and minimum inhibitory concentration (MIC), maximum plasma concentration (C(max)) and MIC and time during which plasma concentrations exceed the MIC have been particularly useful in optimizing efficacy and minimizing resistance. Antimicrobial drugs have been classified as concentration-dependent where increasing concentrations at the locus of infection improve bacterial kill, or time-dependent where exceeding the MIC for a prolonged percentage of the inter-dosing interval correlates with improved efficacy. For the latter group increasing the absolute concentration obtained above a threshold does not improve efficacy. The PK/PD relationship for each group of antimicrobial drugs is 'bug and drug' specific, although ratios of 125 for AUC(0-24):MIC and 10 for C(max):MIC have been recommended to achieve high efficacy for concentration-dependent antimicrobial drugs, and exceeding MIC by 1-5 multiples for between 40 and 100% of the inter-dosing interval is appropriate for most time-dependent agents. Fluoroquinolones, aminoglycosides and metronidazole are concentration-dependent and beta-lactams, macrolides, lincosamides and glycopeptides are time-dependent. For drugs of other classes there is limited and conflicting information on their classification. Resistance selection may be reduced for concentration-dependent antimicrobials by achieving an AUC(0-24):MIC ratio of greater than 100 or a C(max):MIC ratio of greater than 8. The relationships between time greater than MIC and resistance selection for time-dependent antimicrobials have not been well characterized.

Relationship between pharmacokinetics and pharmacodynamics of beta-lactams and outcome

The in-vitro susceptibility of an organism and the pharmacokinetics of an antimicrobial agent are two basic factors on which the choice of standardised treatment regimens is based. However, the inter-individual variability of these factors, which modifies the exposure of bacteria to an antibiotic in terms of time and quantity, is not usually taken into account. In 87 patients treated with beta-lactams (ceftriaxone, cefepime or piperacillin), the probability of failure was greater when the infectious process was located in tissues with barriers to the distribution of beta-lactams. Mean MICs of piperacillin and cefepime, but not ceftriaxone, were below the breakpoints in cases of both recovery and failure, but organisms isolated from patients with a poor outcome had higher MICs. Therefore, the use of breakpoints to determine the susceptibility of microorganisms was not satisfactory in predicting the outcome for a large number of patients. If MICs are determined and plasma concentrations are monitored, dosages can be adjusted according to these parameters, thereby allowing antibiotic treatment to be individualised.

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.

Aminoglycoside nephrotoxicity: modeling, simulation, and control

The main constraints on the administration of aminoglycosides are the risks of nephrotoxicity and ototoxicity, which can lead to acute, renal, vestibular, and auditory toxicities. In the present study we focused on nephrotoxicity. No reliable predictor of nephrotoxicity has been found to date. We have developed a deterministic model which describes the pharmacokinetic behavior of aminoglycosides (with a two-compartment model), the kinetics of aminoglycoside accumulation in the renal cortex, the effects of aminoglycosides on renal cells, the resulting effects on renal function by tubuloglomerular feedback, and the resulting effects on serum creatinine concentrations. The pharmacokinetic parameter values were estimated by use of the NPEM program. The estimated pharmacodynamic parameter values were obtained after minimization of the least-squares objective function between the measured and the calculated serum creatinine concentrations. A simulation program assessed the influences of the dosage regimens on the occurrence of nephrotoxicity. We have also demonstrated the relevancy of modeling of the circadian rhythm of the renal function. We have shown the ability of the model to fit with 49 observed serum creatinine concentrations for a group of eight patients treated for endocarditis by comparison with 49 calculated serum creatinine concentrations (r(2) = 0.988; P < 0.001). We have found that for the same daily dose, the nephrotoxicity observed with a thrice-daily administration schedule appears more rapidly, induces a greater decrease in renal function, and is more prolonged than those that occur with less frequent administration schedules (for example, once-daily administration). Moreover, for once-daily administration, we have demonstrated that the time of day of administration can influence the incidence of aminoglycoside nephrotoxicity. The lowest level of nephrotoxicity was observed when aminoglycosides were administered at 1:30 p.m. Clinical application of this model might make it possible to adjust aminoglycoside dosage regimens by taking into account both the efficacies and toxicities of the drugs.

Analogy between temperature-dependent and concentration-dependent bacterial killing

In this article an analogy between temperature-dependent and concentration-dependent bacterial killing is described. The validation process of autoclaves uses parameters such as reduction rate constant k, decimal reduction time D and resistance coefficient z from an imaginary microorganism to describe the sterilization process. Total lethality of the process is calculated as the integral of the lethality (a function of the temperature) over time. In the case of concentration-dependent killing-i.e. using antibiotic drugs-the k-value is not necessarily a constant; it is the difference between growth and killing of the microorganism. Equations are derived for the decimal reduction time D and resistance coefficient z. Pharmacodynamic models of tobramycin, ciprofloxacin and ceftazidime are used to demonstrate that there is an optimal concentration for all three drugs: C(opt-tobra)=3.20 MICmg/l, C(opt-cipro)=3.45 MICmg/l and C(opt-cefta)=1.35 MICmg/l.

The pharmacokinetic-pharmacodynamic approach to a rational dosage regimen for antibiotics

Pharmacokinetic-pharmacodynamic (PK/PD) surrogate indices (AUIC, AUC/MIC, C(max)/MIC, T>MIC) for measuring antibiotic efficacy are presented and reviewed. As clinical trials are not sufficiently sensitive to establish a dosage regimen which guarantees total bacteriological cure (Pollyanna phenomenon), PK/PD indexes have been proposed from in vitro, ex vivo, and in vivo infection models and subsequently validated in retrospective or prospective human clinical trials. The target value for time-dependent antibiotics (beta-lactams, macrolides) is a time above the MIC (T>MIC) of 50-80% of the dosage interval, while for concentration-dependent antibiotics (quinolones and aminoglycosides), the area under the inhibitory curve (AUIC, or more simply AUC/MIC of about 125h) is the best surrogate indicator of activity. Using the latter drugs, high concentrations achieved early during therapy are desirable to prevent the development of resistance. A C(max)/MIC ratio greater than 10-12 seems to be an appropriate target for aminoglycosides.

In vitro models, in vivo models, and pharmacokinetics: what can we learn from in vitro models?

In vitro pharmacokinetic models of infection can make an important contribution to the study of the pharmacodynamic properties of an antibacterial agent. In conjunction with animal and human pharmacodynamic evaluations, they provide data to allow for the optimization of drug dosing regimens. In vitro models can be used simply to describe the effect of a drug on a bacterial population as well as to provide data for more-analytical studies, including hypothesis testing. Analytical study designs provide information on the pharmacodynamic parameter best related to the chosen outcome, as well as its magnitude. Factors such as the characteristics of the model (method of drug removal, inoculum density, and growth phase), doses simulated, species and susceptibility range of bacteria, and methods and analytical tools used to measure antibacterial effect will have an effect on the conclusions drawn. In vitro models have an important future role in ensuring antibiotic efficacy and in reducing the risks of resistance.

Exploration of the in-vitro pharmacodynamic activity of moxifloxacin for Staphylococcus aureus and Streptococci of lancefield groups A and G

The serum concentrations associated with the oral administration of 400 mg moxifloxacin every 24 h over 48 h in man were simulated in an in-vitro dilutional, continuous bacterial culture model of infection. The initial inoculum was 5 x 10(7)-5 x 10(8) cfu/mL and all strains were tested on at least three occasions. Two strains of Staphylococcus aureus (one methicillin susceptible, the other resistant) with moxifloxacin MICs 0.14 mg/L and 0.06 mg/L and two strains of beta-haemolytic streptococci, Lancefield Group A, MIC 0. 16 mg/L and Group G, MIC 0.4 mg/L were used. In addition, two laboratory-generated mutants with raised moxifloxacin MICs were also employed: methicillin-sensitive S. aureus (MSSA) MIC 1.0 mg/L and Group A streptococcus MIC 1.8 mg/L. The antibacterial effect of moxifloxacin was judged by changes in viable count over time, and the area under the bacterial-kill curve (AUBKC) after 24 and 48 h. For S. aureus MIC 0.14 mg/L the AUBKC(24) (log cfu/mL.h) was 77.8 +/- 4.6 and AUBKC(48) 92.0 +/- 6.9. For its mutant, moxifloxacin MIC 1.0 mg/L, the AUBKC(24) was 116.1 +/- 15.6 and AUBKC(48) 211.9 +/- 23.1, indicating decreased killing. AUBKC(24) and AUBKC(48) values of 110.7 +/- 10.3 and 130.9 +/- 21.3, respectively, were noted for the MRSA strain. The Group A streptococcus, MIC 0.16 mg/L, had an AUBKC(24) of 91.4 +/- 19.4 and AUBKC(48) of 157.0 +/- 70.9. The mutant, MIC 1.8 mg/L, had an AUBKC(24) of 127.0 +/- 1.9 and AUBKC(48) of 205.1 +/- 6.4. Despite a lower MIC (0.4 mg/L) the single strain of Group G streptococcus tested was killed poorly, AUBKC(24) 139.9 +/- 3.6 and AUBKC(48) 252.3 +/- 18.6. The pharmacodynamic parameters AUC/MIC, T > MIC, (AUC > MIC)/MIC (AUC = area under the curve, T = time) and WAUC ((AUC/MIC) (T > MIC/100)) (WAUC = weighted area under the curve) were related to AUBKC(24) and AUBKC(48) using an inhibitory sigmoid E(max) model. T > MIC was poorly related to AUBKC (r = 0.36) while AUC/MIC, (AUC > MIC)/MIC and WAUC were strongly related to AUBKC(24) (r = 0.75-0.79) and AUBKC(48) (r = 0.78-0.84). The maximum antibacterial effect was achieved with an AUC/MIC ratio of 150-200. AUC-related pharmacodynamic parameters predicted antibacterial effect better than T > MIC.

Some international approaches to aminoglycoside monitoring in the extended dosing interval era

Aminoglycosides have rightly remained a cost-effective anti-microbial strategy for the treatment of gram-positive infections for some 25 years. However, in recent years there has been a review of the traditional thrice-daily administration regimen in favor of an extended dosing interval strategy that takes into account the individual patient's renal function. The general recommendations that have been provided to date have been adopted in various ways internationally. These approaches were a matter of discussion for the Clinical Pharmacokinetics Committee of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology at its congress (Vancouver, Canada; November 1997), and will again be a workshop issue at the Cairns (Australia) congress of the Association (September 1999). The present report provides examples of how these practices have been applied at a group of centers from Canada (2 centers), The Netherlands, Egypt, and Australia. These reports demonstrate a variety of approaches and highlight the need for further research for assessing clinical outcomes from different dosing strategies.