Assessment of different antibacterial effect measures used in in vitro models of infection and subsequent use in pharmacodynamic correlations for moxifloxacin

Alasdair MacGowan*, Chris Rogers, H. Alan Holt, Mandy Wootton and Karen Bowker

Bristol Centre for Antimicrobial Research and Evaluation, North Bristol NHS Trust and University of Bristol, Department of Medical Microbiology, Southmead Hospital, Westbury-on-Trym, Bristol BS10 5NB, UK


    Abstract
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
A dilutional culture in vitro pharmacodynamic model of infection was used to assess the best measure of antibacterial effect for moxifloxacin at simulated human doses of 400 mg 24 hourly for 48 h. This was then related to two pharmacodynamic parameters, the drug area under curve: MIC ratio (AUC/MIC) and the length of time that the drug concentration remained above the MIC of the bacterium (T > MIC). Twenty-one bacterial strains (Streptococcus pneumoniae n = 6; Haemophilus influenzae n = 6; Moraxella catarrhalis n = 3; ß-haemolytic streptococci n = 3; Staphylococcus aureus n = 3; MIC range 0.06–3.6 mg/L) were tested in 69 individual simulations. The measures or parameters of antibacterial effect considered were log change in viable count in the initial inoculum at 12 h ({triangleup}12), 24 h ({triangleup}24), 36 h ({triangleup}36), 48 h ({triangleup}48), maximum reduction in count ({triangleup}max); time for bacterial counts to reduce by 100-fold from the initial density (T99) or 1,000-fold (T99.9); and area under the bacterial kill curve from 0 to 24 h (AUBKC24) or from 0 to 48 h (AUBKC48). {triangleup}12, {triangleup}24, {triangleup}36, {triangleup}48, {triangleup}max, T99, T99.9 did not vary over the complete range of MICs; at high MICs, especially with Gram-positive bacteria the T99 and T99.9 values were >48 h while at low MICs, especially with Gram-negative bacteria, bacterial counts were reduced below the limit of detection with {triangleup}12, {triangleup}24, {triangleup}36, {triangleup}48 and {triangleup}max exceeding >6.5 log reduction. AUBKC24 and AUBKC48 varied more completely over the range of MICs and more importantly had the best within-strain reproducibility (median percentage coefficient of variation <15%). The relationship between the transformed AUBKC24 and AUC/MIC could be described by a sigmoid Emax model but the relationship with T > MIC could not. Use of weighted least squares regression to examine the combined effect of AUC/MIC and T > MIC on AUBKC24 indicated that AUC/MIC provided a good fit to the data (r2 = 0.94) and adding T > MIC did not improve the model fit. Cox proportional hazards regression indicated that AUC/MIC was predictive of T99 and in a multivariate model although AUC/MIC predicted outcome after fitting AUC/MIC, T > MIC was not significant. AUBKC was thus shown to be the optimum measure of antibacterial effect to use in pharmacodynamic studies of moxifloxacin and AUC/MIC the best predictor of antibacterial effect as measured by AUBKC24 or T99. These results are in good agreement with animal data on moxifloxacin pharmacodynamics and human data for some other fluoroquinolones.


    Introduction
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
In vitro pharmacodynamic models of infection are used with increasing frequency to study antibacterial dosing regimens especially for agents in development. Together with dosing studies in animals and human clinical trials they help to inform decisions about optimal dosing. Dosing, using pharmacodynamic principles, can be optimized in terms of clinical efficacy, emergence of resistance and convenience.14 If the antibacterial effect of a particular dosing regimen is to be described using an in vitro model of infection, then which is the most appropriate measure of antibacterial effect? At present there is no consensus on which measures of antibacterial effect are the most reproducible, reliable in terms of pharmacodynamic conclusions, and correlate with the pharmacodynamic results from animal or human studies. Recently it has been proposed that a measure IE (intensity of effect) is the optimal measure.5 This measure is the difference between the area under the control bacterial growth curve and test curve when the bacteria are exposed to antibiotic, measured over the time it takes for the exposed population to regrow to the same density as the controls after the initial inhibition/ killing stage. However, other areas related to bacterial time–kill curves have been used, such as the area above the bacterial kill curve (AABKC, log cfu/mL•h),6 area under the bacterial kill curve (AUBKC, log cfu/mL•h)7,8 and ratio of the AUBKC for the control and test experiments.9 Other measures related to arbitrarily defined criteria such as the time to kill 99.9 or 99% of the initial inoculum, changes in viable count (log cfu/mL) after a fraction or multiple of the dosing interval or at 25 h or 48 h are widely used. Minimum bacterial counts have also been employed.1012 It is possible that conclusions about antibiotic efficacy and pharmacodynamic properties may be influenced by the choice of the measure of antibacterial effect used.13 In this study we used simulations of 24 h dosing with moxifloxacin and compared different measures of antibacterial effect based on time to kill 99.9 or 99% of the initial bacterial population, log changes in viable count, maximum change in count and AUBKC after one or two doses to establish which was best. We examined which measure exhibited the least variation when the same strain was tested on multiple occasions. In addition, as time to kill 99.9% of the inoculum had been used as an antibacterial measure which failed to be related to pharmacodynamic parameters, we wished to explore this further.14,15 Finally, we used the optimal measure of antibacterial effect in pharmacodynamic correlations to assess whether the predictions based on the model were in keeping with human and animal data. For this purpose we used data from a large set of experiments simulating human doses of 400 mg od moxifloxacin given for two doses (that is 48 h).1618


    Materials and methods
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
A New Brunswick Bioflo 1000 (Hatfield, UK) in vitro model was used to simulate oral administration of 400 mg moxifloxacin every 24 h over 48 h, i.e. two simulated doses. The apparatus consists of a single central culture chamber connected via aluminium and silicone tubing first to a dosing chamber, which is in turn connected to a reservoir containing broth, and secondly to a vessel collecting outflow broth from the central chamber. The dosing chamber and central culture chamber were diluted with broth using a peristaltic pump (Ismatec Bennett & C., Weston-super-Mare, UK). The temperature was maintained at 37°C. Seventy-five per cent brain–heart infusion broth (Unipath, Basingstoke, UK) supplemented with haemin, ß-nicotinamide adenine dinucleotide and l-histidine, was used for the experiments with Streptococcus pneumoniae, Haemophilus influenzae, Moraxella catarrhalis and ß-haemolytic streptococci. Six per cent Iso-Sensitest broth (Unipath) was used for Staphylococcus aureus. Preliminary experiments indicated that these broths supported a growth density of 5 x 107–5 x 108 cfu/mL 18 h after inoculation into the model.

The model and strains employed have been described previously.1618 Briefly, six strains of S. pneumoniae, moxifloxacin MIC range 0.08–3.6 mg/L, six strains of H. influenzae MICs 0.06–1.0 mg/L, three strains of M. catarrhalis MICs 0.06–1.0 mg/L, three strains of S. aureus MICs 0.06–1.0 mg/L and three ß-haemolytic streptococcal strains MICs 0.16–1.8 mg/L were used. Moxifloxacin was obtained from Bayer AG (Wuppertal, Germany) and MICs were determined by BSAC guidelines. The concentrations were to simulate serum concentration in man after an oral dose every 24 h. The area-under-the-curve (AUC) was 24.4 mg/L.

For all experiments samples were taken from the central chamber throughout the 48 h period, that is at time 0, 1, 2, 3, 4, 5, 6, 7, 10, 12, 22, 24, 25, 26, 27, 28, 29, 30, 31, 34, 36, 46 and 48 h for assessment of viable bacterial count.

The antibacterial activity of moxifloxacin was assessed by calculating the log change in viable count compared with time 0 at 12 h ({triangleup}12), 24 h ({triangleup}24), 36 h ({triangleup}36) and 48 h ({triangleup}48). In addition, the maximum reduction in viable count was recorded ({triangleup}max). The AUBKC (log cfu/mL•h) was calculated for time periods 0–24 h (AUBKC24) and 48 h (AUBKC48). The time to kill either 99% of the initial inoculum and 99.9% (T99 and T99.9, respectively) were also calculated.

The percentage coefficient of variation was calculated as %CV = [s.d. mean] x 100. To explore the relationship between AUBKC24 and AUC/MIC and between AUBKC24 and the time the concentration exceeds the MIC (T > MIC) a series of non-linear models were fitted to the means of the replicate experiments. A number of transformations of the pharmacodynamic parameter, AUBKC24, were considered and a variety of non-linear ‘Emax’ models were fitted. Akaike Information Criterion was used to compare models and plots of residuals against fitted values were used to assess the adequacy of the model fit (Win Nonlin, SCI, CA, USA). To assess the combined influence of AUC/MIC and T > MIC on the untransformed AUBKC24 weighted least squares regression was used. Again, means of the replicated experiments were analysed. Weights (proportional to the universe of the variance) were used to stabilize the variance. The sensitivity of the results to variation in the choice of weights was assessed.

Cox proportional hazards regression was used to assess whether AUC/MIC or T > MIC was predictive of T99.


    Results
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
The variation in each measure of antibacterial effect, that is, {triangleup}12, {triangleup}24, {triangleup}36, {triangleup}48, {triangleup}max, T99, T99.9, AUBKC24 and AUBKC48, was plotted against the MIC for the pathogen (this ranged from 0.06 to 3.6 mg/L moxifloxacin). For isolates with low MICs {triangleup}12, {triangleup}24, {triangleup}36, {triangleup}48 and {triangleup}max exceeded the limit of detection. The viable counts were reduced below about 2 x 102 cfu/mL, hence for an inoculum of about 1–5 x 108, all measures were >6.5 log. Figure 1Go illustrates that, for {triangleup}24, if the moxifloxacin MIC was <=0.1 mg/L, then {triangleup}24 would not increase further as the MIC reduced. Similarly for {triangleup}48 and {triangleup}max (Figures 2 and 3GoGo) all isolates with MICs of <0.5 mg/L gave reductions in viable count of >6.5 log. In contrast, T99.9 exceeded 48 h for some Gram-positive bacteria, especially S. pneumoniae with MICs of >=1.0 mg/L (Figure 4Go). AUBKC24 varied across the range of MICs tested (Figure 5Go).



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Figure 1. Variation in viable count at 24 h (one dose interval) with MIC. ({blacksquare}), S. pneumoniae; ({square}), H. influenzae and M. catarrhalis; (•), S. aureus and ß-haemolytic streptococci.

 


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Figure 2. Variation in viable count at 48 h (two dose intervals) with MIC. ({blacksquare}), S. pneumoniae; ({square}), H. influenzae and M. catarrhalis; (•}, S. aureus and ß-haemolytic streptococci.

 


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Figure 3. Variation in maximum change in viable count with MIC. ({blacksquare}), S. pneumoniae; ({square}), H. influenzae and M. catarrhalis; (•), S. aureus and ß-haemolytic streptococci.

 


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Figure 4. Variation in time to 99.9% reduction in viable count with MIC. ({blacksquare}), S. pneumoniae; ({square}), H. influenzae and M. catarrhalis; (•), S. aureus and ß-haemolytic streptococci.

 


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Figure 5. Variation in the area under the killing curve 0–24 h with MIC. ({blacksquare}), S. pneumoniae; ({square}), H. influenzae and M. catarrhalis; (•), S. aureus and ß-haemolytic streptococci.

 
To assess variability when a strain was tested on three or more occasions the %CV was calculated (TableGo) for those experiments where the pharmacodynamic parameters could be determined. Thus the coefficient of variation for {triangleup}24, {triangleup}48 and {triangleup}max was calculated for less than 12 strains. In contrast, the %CV for AUBKC24 and AUBKC48 was calculable for all experiments. This was because for some strains {triangleup}24, {triangleup}48 and {triangleup}max could not be calculated, as the bacterial counts were below the minimum detection limit. The median %CV was more than 25% for {triangleup}12, {triangleup}24, {triangleup}36 and {triangleup}48 but somewhat lower for {triangleup}max: 17%. T99.9 and T99 gave median %CV in the range 25–27%, while AUBKC24 and AUBKC48 had median %CVs of <=14%, indicating that these parameters showed least variability. As AUBKC24 had the least variation within experiments on the same strain it was the measure selected for use in the pharmacodynamic analysis.


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Table. Percentage coefficients of variation of the measures of antibacterial effect
 
Of the transformations considered, ln (1/AUBKC24) +6 was found to be the most appropriate for describing the relationship between AUBKC24 and AUC/MIC. This transformation was used previously by Madaras-Kelly et al.8 Except for a single strain, the relationship between these variables could be described by a sigmoid Emax model (estimated model parameters Emax = 2.98 (S.E. 0.61) EO = 1.30 (S.E. 0.10); {gamma} = 4.71 (S.E. 3.11); EC50 = 282.75 (S.E. 63.97), see Figure 6Go). The relationship between T > MIC and AUBKC could not be adequately described by any of the non-linear models considered.



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Figure 6. Moxifloxacin against 21 bacterial strains: relationship between AUBKC and AUC/MIC. ({circ}), observed; —, predicted.

 
A linear model describing the relationship between AUC/MIC and the untransformed AUBKC24, fitted using weighted least squares, provided a good fit to the data (r2 = 0.94). Adding T > MIC to the model did not improve the fit (P = 0.28). The results were robust to the choice of weights and the conclusions remained unchanged. Because this study did not use dose escalation or fractionation we were unable to address the comparative effect of AUC/MIC or Cmax/MIC on antibacterial effect.

Both AUC/MIC and T > MIC were predictive of T99 (P = 0.001 and P = 0.01 respectively). Cox proportional hazards regression was used to assess whether AUC/MIC and/or T > MIC was related to T99. When considered together in a multivariate model, while AUC/MIC continued to be predictive of the outcome after fitting AUC/MIC, T > MIC was no longer significant (change in model fit when adding T > MIC to a model containing AUC/MIC, –2 log L = 0.5, P = 0.48). The predictor AUC/MIC was fitted as a continuous variable. The assumption of a linear relationship between ln (hazard ratio) and AUC/MIC was assessed and there was no evidence to suggest a non-linear relationship. The proportional hazards assumption was also assessed and the statistical tests indicated that the assumption was tenable.


    Discussion
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Excepting the work of Firsov et al.,5,19 there are few data on the best measure or parameter of antibacterial effect for use in in vitro pharmacodynamic models. Firsov et al. modelled a mono-exponential curve (half-life 4 h), with ciprofloxacin to explore the relationship between drug AUC and various measures of antibacterial effect. The AUC was varied by changing the initial ciprofloxacin concentration from 0.019 to 19.2 mg/L against a single strain of Escherichia coli (MIC 0.013 mg/L). The drug concentration–time profiles modelled did not therefore correspond to any particular dosing regimen used in man. Furthermore, in human infection, the MIC for the pathogen is likely to vary more than pharmacokinetic parameters such as AUC or Cmax. A range of measures of antibacterial effect were determined, such as time to 90, 99 or 99.9% reduction in viable count, minimum bacterial count, bacterial count at various times during the simulation and the area parameters AUBKC, AABKC and IE. These parameters were compared with drug AUC. The authors found that measures of antibacterial activity which were dependent on time to kill a pre-determined proportion of the initial bacterial count or bacterial counts at various times through the simulation, produced a poorer correlation with drug AUC than the area parameters (AABKC, AUBKC and IE).

The present data confirm these broad conclusions, as non-area parameters do not vary once certain MICs are reached; that is, with high MICs in Gram-positive bacteria T99.9 or T99 are >48 h while at low MICs, especially with Gram-negative bacteria, reductions in viable count are all >6.5 log. Therefore these measures become non-discriminatory once certain MIC values are reached. In addition, and more importantly, we were able to study the within-strain reproducibility of each measure which indicated that AUBKC had the lowest %CV. Previous data using conventional time–kill curves also support this conclusion.20 IE was selected by Firsov et al.,5 in preference to AABKC or AUBKC as it showed a broadly linear relationship to drug AUC over the range 0.1—100 mg/L•h, which is equivalent to an AUC/MIC ratio of 7.7–7700. The use of IE as the primary antibacterial measure may be associated with some potential problems. First, the relationship between AUC/MIC ratio and bacteriological or clinical outcome probably follows a sigmoid Emax shape over a range 10–1000 not a linear one as for IE,1,2,8 and secondly IE critically depends on bacterial regrowth; while clinically rapid early killing may be more important. Also IE varies with the T > MIC, such that for a similar AUC/MIC ratio, two small doses of ciprofloxacin will produce a larger IE than one large one.17 Data from other in vitro models indicate that large infrequent doses have a greater or equivalent antibacterial effect to several smaller doses.10,12,14,21

Using AUBKC24 as the main measure of antibacterial effect, we were able to relate it to AUC/MIC using a sigmoid Emax model and when we modelled the combined effect of AUC/MIC and T > MIC on AUBKC24, T > MIC was not found to be predictive of AUBKC24. In addition, but unlike others,14,15 we were able to show that AUC/MIC was predictive of T99 and that in a multivariate model after fitting of AUC/MIC, T > MIC was not significant. This implies that for moxifloxacin in our model system, AUC/ MIC is the main pharmacodynamic factor. This is in agreement with animal data with moxifloxacin22 and clinical data with ciprofloxacin and grepafloxacin.1,2

In conclusion, AUBKC24 is the optimal measure of antibacterial effect in this in vitro pharmacodynamic model of infection, and the antibacterial effect of moxifloxacin is determined by the AUC/MIC ratio. AUC/MIC is also predictive of T99.


    Notes
 
* Corresponding author. Tel: +44-117-959-5652; Fax: +44-117-959-3154; E-mail: MACGOWAN_A{at}southmead.swest.nhs.uk Back


    References
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
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Received 14 June 1999; returned 13 October 1999; revised 10 January 2000; accepted 1 February 2000