The use of in vitro pharmacodynamic models of infection to optimize fluoroquinolone dosing regimens

In vitro pharmacodynamic models of infection are widely used to assess the likely efficacy of various antibacterial dosing regimens against relevant common pathogens. A significant body of data has been accumulated on the pharmacodynamics of fluoroquinolones using such systems, but there are conflicts with data from other in vitro models and with animal and human findings. To ensure clarity in the development of dosing with fluoroquinolones, and to ensure that regimens are optimized in terms of antibacterial effect and/or preventing emergence of resistance, it is important to seek explanations for these divergent findings. In this review we will discuss the methodological and analytical factors involved in pharmacodynamic analyses using in vitro models of infection and how these may affect the conclusions drawn. The simplest type of experiment using in vitro pharmacodynamic models tests the simulated serum pharmacokinetic profile of a drug at a defined dose against a range of pathogens likely to be encountered in clinical trials and subsequent clinical use. Efficacy is judged by bacterial killing over the time of study.1–3 For example, many studies have recently been published on the effects of ciprofloxacin, levofloxacin, moxifloxacin, ofloxacin, sparfloxacin and trovafloxacin against Streptococcus pneumoniae.4–9 Variations on this basic design include the simulation of increasing doses at the same frequency (dose escalation studies); studying the emergence of antibacterial resistance during drug exposure; and using resistant isogenic or other mutants with increased drug MICs.10–12 Aside from these descriptive studies, in vitro models are also used to examine which pharmacodynamic factors are associated with maximizing antibacterial effects or minimizing the emergence of resistance. This process is inherently more complex than simply describing antibacterial effects. The following factors may affect the conclusions of these experiments: (i) Design of the dosing schedules to be simulated. Both dose escalation and dose fractionation can be performed using the same strain. In dose fractionation designs, the same total dose is given over a defined time as a single dose or split into two, three, four, etc., doses. Dose escalation is the use of larger and larger doses given at the same dose interval. In practice dose escalation studies are rarely performed but similar data to those obtained from such studies can be obtained by using strains with different MICs. In addition, simulations should resemble concentration ranges observed in human pharmacokinetic studies. However, such approaches do not always produce a sufficient range in pharmacodynamic parameters, such as AUC/MIC, to allow the subsequent studies on their relationship with antibacterial effect to be explored fully. (ii) Type of model systems used. Pharmacodynamic models simulate the elimination phase of a drug's pharmacokinetics by drug dilution, diffusion or dialysis to simulate drug clearance from the body.13 All these approaches produce a smooth exponential decline in drug concentration usually as a monoexponential decay curve. Biphasic decay curves can also be simulated and occasionally stepwise declining concentrations are simulated without the use of chemostats.4,14 Different bacterial inocula are often used and organisms may be in different growth phases, introducing further variability. (iii) Bacterial species or strains used. There are data from some models suggesting that different bacterial species or strains of the same species may behave in different ways;15,16 however, many authors group different species together.17 Recently it has been postulated that the pharmacodynamic predictors of outcome for fluoroquinolones in Gram-negative infection may not apply to Gram-positive bacteria such as Staphylococcus aureus or S. pneumoniae.18,19 The same situation may apply with Bacterioides fragilis.20 However, definitive data are lacking. Use of bacteria with differing mechanisms of resistance may help in the evaluation of these mechanisms in determining antibacterial effects or emergence of resistance. (iv) Measures of antibacterial effect. Many different measures of antibacterial effect are used. Some depend on a reduction in viable count of bacteria after a defined time, or the time taken to kill a predetermined proportion of the initial inoculum, while others are related to the area around the bacterial time–kill curve or slope of the time–kill curve line. Emergence of resistance is a further endpoint and can be defined by a change in MIC or in the proportion of bacteria recovered from the model able to grow on antibiotic-containing medium.11,17 (v) Pharmacodynamic parameters. A number of pharmacodynamic parameters have been employed and these parameters are fundamentally pharmacokinetic/bacteriological hybrids that may predict antimicrobial effect. There are three that are commonly used: the time for which the simulated drug concentrations remain above the MIC (t > MIC), the maximum drug concentration to MIC ratio (Cmax/MIC) and the area under the simulated serum time curve to MIC ratio (AUC/MIC) (Figure 1). Other parameters such as the area under the simulated serum concentration–time curve (AUC) above the MIC (AUC > MIC) or weighted AUC (AUC/MIC•t > MIC) have been suggested.21 (vi) Methods of relating pharmacodynamic factors to measures of antibacterial effect. Descriptive analysis is the simplest but, perhaps, least informative approach, so mathematical models have been developed to relate pharmacodynamic factors to measures of antibacterial effect. The simplest is the linear model, but such models do not adequately describe most drug–bacteria relationships, as most are intrinsically non-linear in nature except for effects that fall in the middle of the range of responses. Other models used include the simple Emax model and sigmoid Emax model, which more closely describe these biological relationships.22–26 In some cases multivariate analyses have been performed.25,26 Dose escalation and fractionation studies enable the relative antibacterial effects of t > MIC, Cmax/MIC or AUC/ MIC to be untangled. If such studies are not performed it may be very difficult to perform meaningful analysis because of the strong co-variance of most pharmacodynamic parameters. This is important as the three parameters are closely related to one another, but the implications of the different parameters for dosing vary considerably. If t > MIC is the dominant predictor of outcome, then a slow-release formulation, frequent dosing or continuous infusion therapy is likely to be of benefit. If Cmax/MIC predicts outcome, then infrequent large doses are likely to be of benefit, whereas if the AUC/MIC ratio determines outcome, then any drug regimen that produces the same AUC/MIC ratio will be equally effective. It may be that, for quinolones, the predictors of outcome vary across a range of simulated serum concentrations or MICs, so that AUC/MIC is dominant for some concentrations, while Cmax/MIC is important for others.27,28 Furthermore, some pharmacodynamic parameters may be more important in early dosing and others later on.29 There have been very few systematic studies of the reproducibility and predictive value of the various measures of antibacterial effect used in in vitro models. The simplest parameters depend on a single bacterial count or change in bacterial count from the inoculum, measured in cfu/mL. The time after exposure for these observations is often related to the dosing interval, 24 h or 48 h of the dosing simulation, or the time to reach the minimum bacterial count. While these approaches are widely used3,14,17,30–32 there is little consistency as to the times during the simulation at which changes in viable counts are calculated. Another measure of killing commonly used is the time taken for the drug to kill 99.9% of the initial inoculum,16,18–20,33 but this measure of killing is arbitrary: times to 90%, 99% or 99.99% kill, are all equally valid. In addition, it is unclear if the time taken to kill 99.9% of the initial inoculum (▵99.9) is a reliable measure of drug activity. For example, using ▵99.9 to measure antibacterial effect, it was not possible to relate the activity of trovafloxacin, clinafloxacin, ciprofloxacin, sparfloxacin or levofloxacin against S. aureus to AUC/MIC, Cmax/MIC or t > MIC.18 Similarly, the antibacterial effects of ciprofloxacin, levofloxacin and trovafloxacin against S. pneumoniae were assessed using ▵99.9 and no relationship between AUC/ MIC, Cmax/MIC or t > MIC was found.19 In contrast, a descriptive analysis of ▵99.9 at different AUC/MIC ratios of trovafloxacin, ofloxacin and ciprofloxacin against S. pneumoniae seemed to indicate a relationship between AUC/MIC and ▵99.9.34 The failure of some workers to detect a relationship between ▵99.9 and pharmacodynamic parameters may be related to the undetected emergence of resistance in these simulations, which will obscure the true ▵99.9 value. Areas related to the time–kill curve have also been used to describe killing, but again there is no agreement as to which area measure is most appropriate. Rustige & Wiedemann35 used a measure termed the area above the curve (AAC), measured in cfu (log difference from inoculum)/ mL•h. A negative AAC value is associated with bacterial growth and a positive one with killing; increasing values of AAC are related to increasing kill (Figure 2).36 The area under the bacterial time–kill curve (AUBKC) has also been used, sometimes excluding bacterial regrowth, but usually including it. AUBKC is usually standardized to take account of variation in initial inoculum.25,33,37 The AUBKC is inversely related to killing: as killing increases, AUBKC decreases. AUBKC has been shown to be a reproducible and robust measure of bacterial killing in systems using fixed antibiotic concentrations and in in vitro models.38,39 It also varies across a wide range of MICs, unlike the log change in viable count (which has a maximum response once bacterial counts are reduced below the minimum level of detection) and time taken to kill 99.9% of the inoculum (which may never occur when testing strains with high MICs as killing is of insufficient magnitude).40 Other measures of antibacterial effect have also been studied using an in vitro model to simulate a monoexponential decline in ciprofloxacin concentrations from maximum simulated concentrations of 0.019–19.2 mg/L, and with a half-life of 4 h.23 In this work, several different measures of area were studied including AAC, AUBKC and the intensity of the effect (IE) in log cfu/mL•h. The latter parameter defines the difference between the growth profile over time of controls (no antibiotic) and that of bacteria exposed to antibiotic up to the time taken for the time–kill profile of bacteria exposed to antibiotic and that of the control bacteria to reach the same density (Figure 2). More traditional measures of antibacterial effect, such as time taken to kill 99.9, 99 or 90% of the inoculum and log changes in viable count at various times during the simulation, were also studied. The antibacterial effect measures were compared with the area under the drug concentration curve (AUC) over a range of concentrations from 0.1 to 100 (mg/L•h), equivalent to an AUC/MIC ratio of 7.6–7690 for the Escherichia coli strain tested (MIC 0.013 mg/L). Parameters such as the time taken to kill 90% or 99% of the inoculum and changes in viable count at various times during the simulation correlated poorly with each other (r2 generally <0.6), while the various area parameters (AAC, AUBKC and IE) correlated well with each other (r2 = 0.74–0.99). Parameters dependent on calculation of areas or slope were thought to be more robust measures of antibacterial effect than other parameters, probably because they require multiple time points on the time–kill curve for their calculation and are therefore less subject to variation in individual sampling points. IE was favoured as the most unbiased, robust and comprehensive means of determining antimicrobial effect.23 However, the reproducibility of the measure was not studied and it is not clear how bias was assessed. IE showed a linear relationship to log AUC/MIC over the appropriate range (7.0–8000) while AAC had a simple Emax relationship to AUC/MIC and AUBKC and an inhibitory effect Emax relationship to AUC/MIC. However, it is more likely that, over a greater AUC/MIC range, IE will show an increasing exponential relationship as, at a certain AUC/MIC ratio, no regrowth will occur and hence IE will be infinitely large. There may be other problems associated with use of this measure, which is mainly determined by the time to bacterial regrowth, rather than initial killing. It is likely that, in human infection, initial killing of bacteria is an important factor in outcome;41 regrowth, as defined by relapsed infection in clinical studies, is undesirable. In addition, quinolone pharmacodynamic data from studies on humans indicate that the relationship between clinical cure or bacterial eradication and log AUC/MIC follows a sigmoidal relationship over a range of 10–10000 (unlike IE, which is linear).42,43 In this respect, AUBKC or AAC, which show a simple Emax or inhibitory Emax relationship to AUC, may be more relevant to the clinical situation. A further variation on area as a measure of antibacterial effect is the use of the ratio of the area under the bacterial growth control curve (AUBGC) to area under the bacterial killing curve (AUBKC) to define outcome.44 Measures of area such as AAC, IE or AUBGC/ AUBKC have, as yet, only been used by their originators; in contrast, AUBKC has been used by several researchers. Methodologies used for the detection of resistance are less variable, with many using direct culture from the in vitro model on to a range of plates with increasing quinolone concentrations.11,16,17 Less commonly, MICs are determined before and after exposure.14,25 In our view, the three main pharmacodynamic parameters (t > MIC, Cmax/MIC and AUC/MIC) should all be related to measures of antibacterial effect and/or emergence of resistance. The value of other parameters, such as weighted AUC or AUC > MIC, awaits further evaluation.15,21 However, in many studies only one or two pharmacodynamic parameters are related to outcome (Table). For example, Madaras-Kelly et al.33 and MacGowan et al.8 explored only the relationship between AUC/MIC and the antibacterial effect while, in an otherwise comprehensive analysis, t > MIC appeared to be omitted.25,45 Others have omitted Cmax/MIC from their calculations.23 The number of occasions on which t > MIC, Cmax/MIC and AUC/MIC have all been included in analysis is relatively small and even then the ability of the model to describe adequately the relationship between a measure of antibacterial effect and pharmacodynamic parameters has been variable.18–20,26,31,44 The use of different measures of antibacterial effect and incomplete sets of pharmacodynamic parameters is further complicated by different methods of relating pharmacodynamic parameter to an antibacterial effect. These range from the entirely descriptive11,14,16,17,30 to linear regression analysis45 and use of simple or sigmoidal Emax models.25,32 Some authors have also used stepwise multiple regression analysis.25,26 Most multivariate analyses indicate that AUC/ MIC is predictive of antibacterial effect.22,23 How do the different approaches in terms of models used, doses simulated, endpoints measured, pharmacodynamic parameters included and analytical tools used affect conclusions about quinolone pharmacodynamics in terms of antibacterial efficacy or prevention of the emergence of resistance? Studies that have explored the relationship of three main pharmacodynamic predictors to anti bacterial effect have come to different conclusions. All three pharmacodynamic parameters were poor predictors of response in a model designed to mimic device-related infection31 and were unable to predict antibacterial effect against S. aureus, S. pneumoniae or B. fragilis when measured by the time to 99.9% kill.18,20 However, using AUBKC as the measure of antibacterial effect and multiple regression analysis, two groups have shown AUC/MIC to be the best predictor of AUBKC.25,27 Others, using AUBGC/AUBKC as the endpoint, showed that Cmax/MIC was best related to antibacterial effect.44 When IE is used as the endpoint, then t > MIC best predicts the outcome for data from different quinolones or from the same quinolone given in different dosing regimens.45 This is because IE is dependent on the time it takes for bacteria to start regrowing and this will be determined by t > MIC plus any post-antibiotic effect. Hence, quinolones with long half-lives will have a greater IE for the same serum AUC and dosing twice will have a greater IE than dosing once if the half-life and AUC are constant.45 In a further set of experiments, Firsov et al.45 explored the relationships of AUC/ MIC, t > MIC and AUC > MIC to IE using data generated from simulations of trovafloxacin and ciprofloxacin administration. t > MIC and AUC/MIC had a linear relationship to IE that was not species specific. However, only AUC/ MIC enabled comparisons to be made between the two quinolones. The reason for this is that, for a given t > MIC value, either quinolone produced the same IE while, for a given AUC/MIC value, trovafloxacin produced a larger IE than ciprofloxacin owing to its longer half-life. Hence, it would appear that, using this model, IE can be predicted for all quinolones on the basis of t > MIC but with AUC/MIC the IE varies with the quinolone half-life.46,47 Given the difference in factors determining IE compared with other outcome measures, some caution should be employed in interpreting these findings, at least until they are confirmed by others and related more clearly to human pharmacodynamic studies. There is more consensus (based only on descriptive analysis) that a high Cmax/MIC ratio is associated with reduced emergence of resistance.11,17,25,33,48 Some data related to bacterial killing also argue in favour of larger infrequent doses; for example, simulations of enoxacin 1 g every 24 h produced more reliable killing than 500 mg every 12 h.17 Simulations of 1200 mg ciprofloxacin as a single 24 h dose produced lower minimum bacterial counts than simulations of 600 mg given 12 hourly or 400 mg given 8 hourly, but did result in more regrowth.11 The time to 99.9% kill was shorter for some strains of S. aureus when the same daily doses of ciprofloxacin, ofloxacin or levofloxacin were simulated as a single 24 h dose rather than two 12 h doses.16,49 In contrast, using a model system dependent on stepwise declining concentrations and minimum bacterial counts as the antibacterial measure, simulations of ciprofloxacin 400 mg given 8 hourly were more bactericidal than ciprofloxacin 600 mg 12 hourly against Klebsiella pneumoniae and Pseudomonas aeruginosa.14,30 The IE model also favours two small doses of ciprofloxacin rather than one large one.45 The antibacterial measure chosen will affect the conclusion reached; for example, in a simulation of ciprofloxacin 1 g 24 hourly compared with 500 mg 12 hourly, the maximum reduction in viable count, the change in count after 12 h and the slope of initial kill all favoured 24 hourly dosing over 12 hourly dosing, but both regimens were equivalent with respect to change in count after 24 h, AUBKC and time to 99.9% kill. For none of the antibacterial effect measures could it be shown that 12 hourly dosing was superior to 24 hourly dosing.32 At present there are no direct data from in vitro models to support the suggestions based on animal and clinical data that, if Cmax/MIC is >10, then Cmax/MIC predicts outcome, while if Cmax/MIC is <10, then AUC/MIC predicts outcome.27 However, in our study simulating doses of ciprofloxacin once- and twice-daily, >50% of Cmax/MIC ratios were <10 and AUC/MIC was the best predictor of outcome.26 In contrast, work with trovafloxacin and two vancomycin-intermediate S. aureus strains indicated that Cmax/MIC was the best predictor of outcome despite Cmax/ MIC ratios being <10.44 In conclusion, there is a consensus that descriptive analysis of data from in vitro models indicates that high Cmax/MIC values are important in preventing emergence of resistance. Furthermore, dose fractionation studies (in which the AUC/MIC is the same for all doses simulated) indicate that larger, less frequent quinolone doses produce more rapid killing early in drug exposure, although regrowth often occurs. Most data suggest that AUC/MIC is the best predictor of antibacterial effect, but once the appropriate value of this ratio has been obtained, larger, less frequent doses may be more effective than smaller, more frequent ones. Pharmacodynamic studies on quinolones in in vitro models Pharmacodynamic studies on quinolones in in vitro models Pharmacodynamic parameters used in analysis. Cmax, maximum serum concentration; Cmin, minimum serum concentration; AUC, area under the curve (□) plus□); AUC > MIC, area under curve above the MIC (□); t > MIC, time for which the serum concentration is greater than the MIC. Bacterial time–kill curve showing how different antibacterial effect areas are calculated. AAC, area above the curve (□); AUBKC, area below the bacterial kill curve; IE, intensity effect.