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pharmacodynamic modeling of in vitro activity of azithromycin against four different bacterial strains
International Journal of Antimicrobial Agents 29 (2007) 263–270
Pharmacokinetic/pharmacodynamic modeling of in vitro activity of azithromycin against four different bacterial strains Wanchai Treyaprasert a,b , Stephan Schmidt b , Kenneth H. Rand c , Uthai Suvanakoot a , Hartmut Derendorf b,∗ a
Department of Pharmacy, Faculty of Pharmaceutical Sciences, Chulalongkorn University, Bangkok 10330, Thailand b Department of Pharmaceutics, College of Pharmacy, University of Florida, Gainesville, FL 32610, USA c Department of Pathology, Immunology and Laboratory Medicine, College of Medicine, University of Florida, Gainesville, FL 32610, USA Received 25 June 2006; accepted 25 August 2006
Abstract The bacterial time–kill curves of azithromycin against four bacterial strains (Streptococcus pneumoniae/penicillin-intermediate, S. pneumoniae/penicillin-sensitive, Haemophilus influenzae and Moraxella catarrhalis) were determined by in vitro infection models. Eighteen different pharmacokinetic/pharmacodynamic models were fitted to the time–kill data using non-linear regression and compared for best fit. A simple, widely used Emax model was not sufficient to describe the pharmacodynamic effects for the four bacterial strains. Appropriate models that gave good curve fits included additional terms for saturation of the number of bacteria (Nmax ), delay in the initial bacterial growth phase and/or the onset of anti-infective activity (1 − exp−zt ) as well as a Hill factor (h) that captures the steepness of the concentration–response profile. Azithromycin was highly effective against S. pneumoniae strains and M. catarrhalis while the efficacy against H. influenzae was poor. Applications of these pharmacokinetic/pharmacodynamic models will eventually provide a tool for rational antibiotic dosing regimen decisions. © 2006 Elsevier B.V. and the International Society of Chemotherapy. All rights reserved. Keywords: Azithromycin; In vitro activity; Modeling
1. Introduction The parameter most commonly used to quantify the antimicrobial activity of antibiotics against a certain bacterium is usually the minimum inhibitory concentration (MIC). It is defined as the lowest concentration of drug that prevents visible growth of the organism as detected by the unaided eye [1]. Although the MIC is a well-established pharmacodynamic (PD) parameter routinely determined in microbiology, this parameter has several disadvantages. For instance, the MIC does not provide information on the rate ∗ Corresponding author at: 1600 SW Archer Road, P.O. Box 100494, Gainesville, FL 32610, USA. Tel.: +1 352 846 2726; fax: +1 352 392 447. E-mail address: [email protected] (H. Derendorf).
of bacterial kill. Since the MIC determination depends on the number of bacteria at a single time-point, many different combinations of growth and kill rates can result in the same MIC. Antibacterial activity is a dynamic process whereas MIC is only a threshold value, a one-point measurement with poor precision determined in two-fold dilution steps [2]. An alternative PD approach, bacterial time–kill curves, has been proposed to offer detailed information about the antibacterial efficacy as a function of both time and antibiotic concentration [3]. Time–kill curves of many antibacterial agents have been studied in both in vitro kinetic models and animal infection models. To date, pharmacokinetic/pharmacodynamic (PK/PD) modeling has become a powerful tool to evaluate the antimicrobial effect of antibiotics. An Emax model has been
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successfully applied to describe the relationship between concentration and effect in many drug classes [4,5]. There have been some attempts to evaluate antimicrobial activity with an adapted Emax model [6]. Some parameters such as the maximum number of bacteria (Nmax ) at the end of the growth phase, adaptation rate terms (x, y, z) and Hill factor (h) have been included in a PK/PD model to optimize these models [7]. Previously, several -lactam and fluoroquinolone antibiotics have been evaluated in our group for their antibacterial activities at different dosing regimens: piperacillin [2], piperacillin–tazobactam [4], cefaclor [5], faropenem [8] and ciprofloxacin [9]. In all cases the Emax model allowed good characterization of the observed antimicrobial effects. Azithromycin, a 15-membered macrolide, is a commonly prescribed antibacterial agent used to treat respiratory tract infections [10]. The American Thoracic Society and the Infectious Diseases Society of America have recommended a macrolide as a viable first-line option for treating communityacquired pneumonia [11]. In the present study, four bacterial strains, S. pneumoniae (penicillin-intermediate), S. pneumoniae (penicillin-sensitive), H. influenzae and M. catarrhalis, the most common causes of community-acquired pneumonia, were tested. The purpose of this study was to investigate the PD effect of azithromycin by evaluating in vitro time–kill curves against four common bacterial strains and to establish a mathematical model to describe the PK/PD relationship of azithromycin.
2. Materials and methods 2.1. Drugs and bacteria Azithromycin was provided by Pfizer Inc., Groton, CT, USA. Four different bacterial strains: S. pneumoniae (penicillin-intermediate) ATCC® 49619, S. pneumoniae (penicillin-sensitive) ATCC® 6303, H. influenzae ATCC® 10211 and M. catarrhalis ATCC® 8176 were obtained from the microbiology laboratory in Shands Hospital at the University of Florida, Gainesville, FL, USA. 2.2. Broth preparation Mueller–Hinton broth (MHB; Becton Dickinson, Franklin Lakes, NJ, USA) and Todd–Hewitt broth (THB; Difco, Detroit, USA) were both prepared according to the manufacturer’s instructions and autoclaved prior to use at 121 ◦ C (15 min/1 L). Haemophilus test media (HTM; Remel Microbiology Products, Lenexa, KS, USA) broth was purchased sterile and ready to use and stored in a refrigerator at approximately 7 ◦ C. MHB was used for M. catarrhalis, THB for S. pneumoniae and HTM for H. influenzae.
2.3. Bacterial inoculation The bacterial inoculum was prepared from colonies incubated overnight on appropriate agar plates (5% sheep blood agar plates, Remel Microbiology Products, Lenexa, KS, USA, for S. pneumoniae and M. catarrhalis; chocolate agar plates, Remel Microbiology Products, Lenexa, KS, USA, for H. influenzae). The microorganisms were suspended in sterile saline solution 0.9% (Shands Hospital at the University of Florida, Gainesville, FL, USA) to a concentration equivalent to a 0.5 value in the McFarland scale (Remel Microbiology Products, Lenexa, KS, USA) with a turbidimeter (A-JUSTTM , Abbott Laboratories, North Chicago, IL, USA). This value on the McFarland scale of 0.5 is equivalent to a number of 1 × 108 viable colony forming units (CFU)/mL. Further dilution steps to reach a final working inoculum of approximately 5 × 105 CFU/mL were done in broth. 2.4. Determination of MIC The MICs for all strains were determined by serial twofold macrodilutions. Briefly, a sterile, flat-bottom 24-well plate with a lid (Corning Incorporated, NY, USA) was used for the preparation of the serial two-fold dilutions. Each plate was divided in half so that there were two replicates per plate. Broth (1 mL) was added to each of the wells, except for the first and last wells. The last well received 2 mL of broth and served as negative control. Then 2 mL of the highest azithromycin concentration of the drug in broth was added to the first well. Next, with the help of an automatic pipette (Eppendorf AG, Hamburg, Germany), 1 mL of solution from the first well was transferred to the second well and mixed. Subsequently, 1 mL was taken from the second well into the third well and mixed. This procedure was systematically repeated up to the tenth well, from which 1 mL was taken and discarded. Thus, each well held a solution of azithromycin in broth that was half the concentration of the previous one. The eleventh well did not receive azithromycin and so served as a positive (growth) control. Finally, 1 mL of the working inoculum was added to each well and the plates were incubated at 37 ◦ C and 5% CO2 (for S. pneumoniae and H. influenzae) for 18–20 h. The MIC was determined as the concentration of azithromycin that prevented visual growth of the bacteria after this incubation period. 2.5. Constant concentration time–kill curves An in vitro kinetic model was used to investigate the antibacterial efficacy of constant drug concentrations for 6 h. The model consisted of a 50 mL vented-cap tissue culture flask with a canted neck (NuncTM , Nunc A/S, Roskilde, Denmark), containing 20 mL of the appropriate broth media, incubated at 37 ◦ C and 5% CO2 (for S. pneumoniae and H. influenzae).
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An aliquot of a suspension (100 L) of the initial inoculation (1 × 108 CFU/mL) was added to the in vitro model to produce a final inoculum of approximately 5 × 105 CFU/mL. The bacteria were incubated for 2 h, which allowed them to reach the logarithmic growth phase, before adding different azithromycin concentrations. The selection of azithromycin concentrations tested in each bacterial strain was based on their MIC values. At least seven different concentrations covering the entire azithromaycin range were investigated including minimum inhibition of bacterial growth (0.25 × MIC, 0.5 × MIC, 1 × MIC), efficient bacterial killing (2 × MIC, 4 × MIC) and maximum bacterial killing (8 × MIC, 16 × MIC). A control experiment with bacteria and no drug was run simultaneously. Samples were taken at 0, 0.5, 1, 1.5, 2, 3, 4, 5 and 6 h. 2.6. Bacterial quantification Bacterial counts were determined by plating 50 L of the serial 10-fold dilutions on appropriate agar plates, using an adapted droplet-plate method. Briefly, agar plates were divided into four quadrants. With an automatic pipette, 5 × 10 L droplets of the chosen dilution were equidistantly plated onto one of the quadrants. A duplicate was plated onto the adjacent quadrant. Then, the plates were incubated at 37 ◦ C and 5% CO2 (for S. pneumoniae and H. influenzae) for 16–24 h before reading. The procedure was repeated at least three times per bacterial strain and dose. Positive controls with bacteria but no drug were run simultaneously. Following incubation, the number of CFUs was counted in each duplicate quadrant at each time-point and averaged.
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tionally, the graphs were visually inspected for goodness of fit. First, an adaptation rate constant (z) was incorporated into model 1. If the bacteria have not yet reached the logarithmic growth phase at time zero, an exponential correction factor (1 − exp−zt ) may be necessary to compensate for this delay in the onset of growth. In the resulting model 2, this delay term affects both growth and kill equally: kmax C dN = k0 − (1 − exp−zt )N (model 2) dt EC50 + C However, it is not necessarily true that both growth and kill show the same time-frame for the delay. Therefore, model 3 describes a delayed effect in growth (1 − exp−xt ) and model 4 a delay in kill (1 − exp−yt ) only. kmax C dN −xt N (model 3) = k0 (1 − exp ) − EC50 + C dt kmax C dN −yt (model 4) (1 − exp ) N = k0 − EC50 + C dt In in vitro systems, available space and nutrients are limited. The factor that accounts for the resulting saturation in growth is the maximum number of bacteria (Nmax ) shown in model 5: N kmax C dN − = k0 1 − N (model 5) dt Nmax EC50 + C Incorporation of the three adaptation rate terms from models 2–4 results in models 6–8: N kmax C dN − = k0 1 − (1 − exp−zt )N dt Nmax EC50 + C (model 6)
2.7. PK/PD modeling Time–kill curve analysis and mathematical modeling of the kill curve data were performed with the non-linear regression software program Scientist® 3.0 (Micromath, Salt Lake, UT, USA). The simplest, but commonly used, Emax model was fitted to the PD data: dN kmax C = k0 − N (model 1) dt EC50 + C Where dN/dt is the change in number of bacteria as a function of time, k0 (h−1 ) is the bacterial growth rate constant in the absence of antibiotic, kmax (h−1 ) the maximum killing rate constant (maximum effect), EC50 (g/mL) the concentration of antibiotic necessary to produce 50% of maximum effect, C (g/mL) the concentration of antibiotic at any time (t) and N (CFU/mL) the number of viable bacteria. Next, this simple Emax model was extended stepwise, fitted simultaneously to the data and the resulting models were compared for best fit. To determine the best model, the following criteria were taken into consideration: model selection criterion (MSC), coefficient of determination (R2 ) and the correlation between observed and calculated values. Addi-
dN N kmax C −xt (1 − exp ) − = k0 1 − N dt Nmax EC50 + C (model 7) dN N kmax C −yt − = k0 1 − (1 − exp ) N dt Nmax EC50 + C (model 8) In practice, saturation in growth as well as a delay in the onset of growth that is different from the onset in kill can be observed. This relatively complex scenario can be described by model 9: N dN (1 − exp−xt ) = k0 1 − dt Nmax kmax C −yt − (1 − exp ) N (model 9) EC50 + C In general, the uniform delay described by the z term can also be achieved by setting x equals y. The curve fit obtained from models 1–9 can now be further improved by adding a Hill or shape factor (h) that smooths the curve out by modifying the
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steepness of the slope. Alteration of model 1 results in model 10:
dN = k0 − dt
· Ch
kmax ECh50 + Ch
3.1. MIC values and azithromycin time–kill curve concentrations
·N
3. Results
(model 10)
Models 2–9 were modified in a similar way, resulting in a total of 18 different models. For each bacterial strain, the initial estimate for k0 was determined using positive control data. Based on the determined k0 , kmax was found by using the data from the highest azithromycin concentration. Thereafter, k0 and kmax were fixed in each model at their determined values, whereas Nmax , EC50 , x, y, z and h were fitted simultaneously to the experimental data.
The determined MIC values and azithromycin concentrations used in the time–kill curve experiments against the four bacterial strains are summarized in Table 1. Overall, the results obtained in this study were consistent with the reported MIC values [12–14]. 3.2. Comparison of the investigated models Simulated effects of the different parameters, incorporated in the modified Emax models, are shown in Fig. 1. Fig. 1A
Fig. 1. Simulations of bacterial growth ( ) and kill ( ). (A) simplest Emax model (model 1); (B) uniform delay in the onset of growth and kill (model 2); (C) delay in the onset of growth (model 3); (D) delay in the onset of kill (model 4); (E) saturation in growth (model 5); (F) saturation in growth and uniform delay in growth and kill (model 6); (G) saturation in growth plus delay in the onset of growth (model 7); (H) saturation in growth plus delay in the onset of kill (model 8); (I) saturation in growth plus delay in the onset of growth and kill (model 9).
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Fig. 1. (Continued ).
shows a simple Emax model (model 1) without any delay or saturation terms. In Fig. 1B (model 2) the onset of growth and kill are equally delayed. With increasing time the exponential term becomes larger and finally reaches infinity. However, exp−inf equals zero and so one minus zero results in one. Therefore, either growth or kill or both are not affected any longer. In contrast, at very early time-points the exponential term is close to one and so neither growth nor kill constants affect the overall behaviour. Summarizing, the effect of the delay term (1 − exp−zt ) is maximal at very early timepoints but diminishes with time. The same holds true for Fig. 1C (model 3) and 1D (model 4), where both growth and kill are delayed independently. A saturation in growth, characterized by Nmax , only affects bacterial growth (Fig. 1E),
Table 1 Azithromycin MIC values and concentrations in the time–kill curve experiments Strains
MIC (g/mL)
Tested concentrations (g/mL)
S. pneumoniae ATCC 6303
0.06
S. pneumoniae ATCC 49619
0.06
M. catarrhalis ATCC 8176
0.008
H. influenzae ATCC 10211
1
0.015, 0.03, 0.06, 0.12, 0.24, 0.48, 0.96 0.015, 0.03, 0.06, 0.12, 0.24, 0.48, 0.96 0.002, 0.004, 0.008, 0.016, 0.032, 0.064, 0.128, 0.256, 0.512, 1.024 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64
whereas both growth and kill can be delayed as mentioned above. With increasing numbers of bacteria, the Nmax term approaches zero and so bacterial growth reaches the static phase. The incorporated effect of the Nmax term on models 2–4 in addition to the delay effect is shown in Fig. 1F–H. Finally, Fig. 1I summarizes saturation in growth and delays in the onset of growth and kill that are given different values. 3.3. PK/PD analysis The fitted curves of azithromycin against four bacterial strains are shown in Fig. 2. For both penicillin-sensitive and penicillin-intermediate S. pneumoniae, the data were best explained by PK/PD model 9, which incorporates an Nmax term as well as delay terms for the onset of growth and kill. Model 1 was found appropriate to describe the data for M. catarrhalis. For H. influenzae, model 4 could not explain the data well. A better fit was reached by employing an additional Hill (h) factor. The determined PD parameters of azithromycin for each individual bacterial strain are listed in Table 2. The results indicate that the models chosen are appropriate for fitting the data. Summarizing the data, azithromycin showed high efficacy against S. pneumoniae strains (EC50 /ATCC 6303: 0.16 mg/L; EC50 /ATCC 49619: 0.05 mg/L) and M. catarrhalis (EC50 : 0.12 mg/L) but low efficacy against H. influenzae (EC50 : 18.50 mg/L).
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Fig. 2. Curve fits for four bacterial strains with the various constant concentrations (g/L): (A) azithromycin against S. pneumoniae ATCC 6303; (B) azithromycin against S. pneumoniae ATCC 49619; (C) azithromycin against M. catarrhalis ATCC 8176; (D) azithromycin against H. influenzae ATCC 10211. Table 2 Determined pharmacodynamic azithromycin parameters and goodness of fit criteria Parameters (h−1 )
k0 kmax (h−1 ) EC50 (g/mL) Nmax (108 CFU/mL) x (h−1 ) y (h−1 ) z (h−1 ) h MSC/R2
S. pneumoniae ATCC 6303
S. pneumoniae ATCC 49619
M. catarrhalis ATCC 8176
H. influenzae ATCC 10211
1.51 2.44 0.16 1.38 8.07 2.06 – – 2.09/0.91
1.21 1.69 0.05 3.79 2.31 2.10 – – 3.24/0.96
0.99 1.67 0.12 – – – – – 1.89/0.87
1.22 9.28 18.50 – – 0.53 – 1.28 2.22/0.91
4. Discussion In this study we have used two different PK/PD approaches (MIC and time–kill curve) to evaluate the antimicrobial efficacy of the second generation macrolide azithromycin [15] against four different bacterial strains. Although widely used, MICs do not provide a very detailed characterization of antimicrobial activity [16]. Therefore, the more sophisticated time–kill curve approach was used. Compared to the MIC, one of the main advantages of the kill curve approach is the PD effect can be described by at least three parameters, k0 , kmax and EC50 , derived from an Emax model instead of one single threshold value. The results indicate that a sim-
ple Emax model was not sufficient to describe the observed PD effect for the four bacterial strains investigated. For both penicillin-sensitive and penicillin-intermediate S. pneumoniae, the limitation of space and nutrients (Nmax ) had an effect on the growth rate. Therefore, the addition of a saturation term into the basic Emax model appeared to be necessary. In comparison, the growth of H. influenzae was unaltered while the onset of kill was delayed. To account for that delay, a timedependent delay term was added. A similar behaviour was observed when H. influenzae was exposed to azithromycin. However, at time-point zero of the experiment H. influenzae had not reached the logarithmic growth phase yet. In this case a delay term was necessary to account for both effects. In con-
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Fig. 3. Simulated PK/PD of azithromycin against four bacterial strains after once daily oral administration of 500 mg azithromycin, accounting for mean PK/PD parameters of free, unbound azithromycin. Bacterial growth ( ) and kill ( ).
trast to other antibiotic classes, like -lactams, no correlation was found between the delay in the onset of growth and kill due to the mechanism of action. Once these models have been established and validated, it is then possible to simulate the expected kill curves for different doses and dosing regimens of the antibiotic against the bacteria of interest by substituting the concentration term in the mathematical model by the respective concentration versus time profile of the drug [16]. However, to predict changes in the number of bacteria for common dosing regimens in humans, protein binding has to be addressed. Therefore, the overall concentration C (g/mL) has to be substituted by the free, active concentration Cf (g/mL). It was shown in clinical studies that after once-daily oral administration of 500 mg azithromycin dihydrate the average total azithromycin Cmax is 0.45 g/mL [17]. Although azithromycin shows nonlinear protein-binding properties [18], the average protein binding of about 12% was used, resulting in an average Cmaxf of 0.40 g/mL. For each individual strain, the most suitable PK/PD model was applied to describe the antimicrobial activity of azithromycin with regard to free drug levels. Simulations for 500 mg azithromycin, given orally once-daily, are
shown in Fig. 3. For S. pneumoniae (both penicillin-sensitive and penicillin-intermediate), a dose of 500 mg azithromycin shows a good bactericidal effect [19]. For H. influenzae and M. catarrhalis, the same dose does not seem to be sufficient enough to decrease bacterial counts. For H. influenzae, the unbound azithromycin peak concentration was determined to be approximately 0.32 g/mL, which is less than 1 × MIC (1 g/mL) [20]. Therefore, predicted azithromycin serum concentrations do not show a bactericidal effect on H. influenzae for that particular dosing regimen. Although free azithromycin serum concentrations do not reach MIC levels for H. influenzae, efficacy is shown in clinical data [20–24]. It may seem paradoxical that although serum concentrations are much lower than reported tissue concentrations [20,25], azithromycin is effective against extracellular H. influenzae. Therefore, it is a subject of controversy whether serum or tissue concentrations should be considered for antimicrobial efficacy [25,26]. Originally, it was suggested to use free serum concentrations as a predictor of extracellular fluid concentrations as the main determinant of efficacy against extracellular pathogens [26]. However, host-defence mechanisms themselves might have been underestimated so far. Advanced-generation macrolides, and in particular
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azithromycin, are highly concentrated in polymorphonuclear leukocytes [10,27], which gravitate by chemotactic mechanisms to sites of infection. Following phagocytosis at the infection site, they are exposed to very high, and sometimes cidal, intracellular concentrations of the antibacterial agent [20,25]. When the drug-containing lysosomes are mechanically destroyed, high concentrations of azithromycin will be released locally, making it difficult to predict accurately what the unbound concentrations are in the extracellular space. Measurement of the free, unbound concentration in the infected tissue fluid, with e.g. microdialysis [28], might help to clarify this question. However, due to its high lipophilicity [29], problems in terms of cross-membrane permeability can be expected. Summarizing, for all four pathogens tested, modified Emax models were found to be adequate to describe the observed kill curve data. Simulations based on previous clinical trials can predict clinical outcome and help to come up with dose recommendations. However, further work needs to be completed in order to fully understand the PK/PD of azithromycin.
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Pharmacokinetic/pharmacodynamic modeling of in vitro activity of azithromycin against four different bacterial strains Wanchai Treyaprasert a,b , Stephan Schmidt b , Kenneth H. Rand c , Uthai Suvanakoot a , Hartmut Derendorf b,∗ a
Department of Pharmacy, Faculty of Pharmaceutical Sciences, Chulalongkorn University, Bangkok 10330, Thailand b Department of Pharmaceutics, College of Pharmacy, University of Florida, Gainesville, FL 32610, USA c Department of Pathology, Immunology and Laboratory Medicine, College of Medicine, University of Florida, Gainesville, FL 32610, USA Received 25 June 2006; accepted 25 August 2006
Abstract The bacterial time–kill curves of azithromycin against four bacterial strains (Streptococcus pneumoniae/penicillin-intermediate, S. pneumoniae/penicillin-sensitive, Haemophilus influenzae and Moraxella catarrhalis) were determined by in vitro infection models. Eighteen different pharmacokinetic/pharmacodynamic models were fitted to the time–kill data using non-linear regression and compared for best fit. A simple, widely used Emax model was not sufficient to describe the pharmacodynamic effects for the four bacterial strains. Appropriate models that gave good curve fits included additional terms for saturation of the number of bacteria (Nmax ), delay in the initial bacterial growth phase and/or the onset of anti-infective activity (1 − exp−zt ) as well as a Hill factor (h) that captures the steepness of the concentration–response profile. Azithromycin was highly effective against S. pneumoniae strains and M. catarrhalis while the efficacy against H. influenzae was poor. Applications of these pharmacokinetic/pharmacodynamic models will eventually provide a tool for rational antibiotic dosing regimen decisions. © 2006 Elsevier B.V. and the International Society of Chemotherapy. All rights reserved. Keywords: Azithromycin; In vitro activity; Modeling
1. Introduction The parameter most commonly used to quantify the antimicrobial activity of antibiotics against a certain bacterium is usually the minimum inhibitory concentration (MIC). It is defined as the lowest concentration of drug that prevents visible growth of the organism as detected by the unaided eye [1]. Although the MIC is a well-established pharmacodynamic (PD) parameter routinely determined in microbiology, this parameter has several disadvantages. For instance, the MIC does not provide information on the rate ∗ Corresponding author at: 1600 SW Archer Road, P.O. Box 100494, Gainesville, FL 32610, USA. Tel.: +1 352 846 2726; fax: +1 352 392 447. E-mail address: [email protected] (H. Derendorf).
of bacterial kill. Since the MIC determination depends on the number of bacteria at a single time-point, many different combinations of growth and kill rates can result in the same MIC. Antibacterial activity is a dynamic process whereas MIC is only a threshold value, a one-point measurement with poor precision determined in two-fold dilution steps [2]. An alternative PD approach, bacterial time–kill curves, has been proposed to offer detailed information about the antibacterial efficacy as a function of both time and antibiotic concentration [3]. Time–kill curves of many antibacterial agents have been studied in both in vitro kinetic models and animal infection models. To date, pharmacokinetic/pharmacodynamic (PK/PD) modeling has become a powerful tool to evaluate the antimicrobial effect of antibiotics. An Emax model has been
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successfully applied to describe the relationship between concentration and effect in many drug classes [4,5]. There have been some attempts to evaluate antimicrobial activity with an adapted Emax model [6]. Some parameters such as the maximum number of bacteria (Nmax ) at the end of the growth phase, adaptation rate terms (x, y, z) and Hill factor (h) have been included in a PK/PD model to optimize these models [7]. Previously, several -lactam and fluoroquinolone antibiotics have been evaluated in our group for their antibacterial activities at different dosing regimens: piperacillin [2], piperacillin–tazobactam [4], cefaclor [5], faropenem [8] and ciprofloxacin [9]. In all cases the Emax model allowed good characterization of the observed antimicrobial effects. Azithromycin, a 15-membered macrolide, is a commonly prescribed antibacterial agent used to treat respiratory tract infections [10]. The American Thoracic Society and the Infectious Diseases Society of America have recommended a macrolide as a viable first-line option for treating communityacquired pneumonia [11]. In the present study, four bacterial strains, S. pneumoniae (penicillin-intermediate), S. pneumoniae (penicillin-sensitive), H. influenzae and M. catarrhalis, the most common causes of community-acquired pneumonia, were tested. The purpose of this study was to investigate the PD effect of azithromycin by evaluating in vitro time–kill curves against four common bacterial strains and to establish a mathematical model to describe the PK/PD relationship of azithromycin.
2. Materials and methods 2.1. Drugs and bacteria Azithromycin was provided by Pfizer Inc., Groton, CT, USA. Four different bacterial strains: S. pneumoniae (penicillin-intermediate) ATCC® 49619, S. pneumoniae (penicillin-sensitive) ATCC® 6303, H. influenzae ATCC® 10211 and M. catarrhalis ATCC® 8176 were obtained from the microbiology laboratory in Shands Hospital at the University of Florida, Gainesville, FL, USA. 2.2. Broth preparation Mueller–Hinton broth (MHB; Becton Dickinson, Franklin Lakes, NJ, USA) and Todd–Hewitt broth (THB; Difco, Detroit, USA) were both prepared according to the manufacturer’s instructions and autoclaved prior to use at 121 ◦ C (15 min/1 L). Haemophilus test media (HTM; Remel Microbiology Products, Lenexa, KS, USA) broth was purchased sterile and ready to use and stored in a refrigerator at approximately 7 ◦ C. MHB was used for M. catarrhalis, THB for S. pneumoniae and HTM for H. influenzae.
2.3. Bacterial inoculation The bacterial inoculum was prepared from colonies incubated overnight on appropriate agar plates (5% sheep blood agar plates, Remel Microbiology Products, Lenexa, KS, USA, for S. pneumoniae and M. catarrhalis; chocolate agar plates, Remel Microbiology Products, Lenexa, KS, USA, for H. influenzae). The microorganisms were suspended in sterile saline solution 0.9% (Shands Hospital at the University of Florida, Gainesville, FL, USA) to a concentration equivalent to a 0.5 value in the McFarland scale (Remel Microbiology Products, Lenexa, KS, USA) with a turbidimeter (A-JUSTTM , Abbott Laboratories, North Chicago, IL, USA). This value on the McFarland scale of 0.5 is equivalent to a number of 1 × 108 viable colony forming units (CFU)/mL. Further dilution steps to reach a final working inoculum of approximately 5 × 105 CFU/mL were done in broth. 2.4. Determination of MIC The MICs for all strains were determined by serial twofold macrodilutions. Briefly, a sterile, flat-bottom 24-well plate with a lid (Corning Incorporated, NY, USA) was used for the preparation of the serial two-fold dilutions. Each plate was divided in half so that there were two replicates per plate. Broth (1 mL) was added to each of the wells, except for the first and last wells. The last well received 2 mL of broth and served as negative control. Then 2 mL of the highest azithromycin concentration of the drug in broth was added to the first well. Next, with the help of an automatic pipette (Eppendorf AG, Hamburg, Germany), 1 mL of solution from the first well was transferred to the second well and mixed. Subsequently, 1 mL was taken from the second well into the third well and mixed. This procedure was systematically repeated up to the tenth well, from which 1 mL was taken and discarded. Thus, each well held a solution of azithromycin in broth that was half the concentration of the previous one. The eleventh well did not receive azithromycin and so served as a positive (growth) control. Finally, 1 mL of the working inoculum was added to each well and the plates were incubated at 37 ◦ C and 5% CO2 (for S. pneumoniae and H. influenzae) for 18–20 h. The MIC was determined as the concentration of azithromycin that prevented visual growth of the bacteria after this incubation period. 2.5. Constant concentration time–kill curves An in vitro kinetic model was used to investigate the antibacterial efficacy of constant drug concentrations for 6 h. The model consisted of a 50 mL vented-cap tissue culture flask with a canted neck (NuncTM , Nunc A/S, Roskilde, Denmark), containing 20 mL of the appropriate broth media, incubated at 37 ◦ C and 5% CO2 (for S. pneumoniae and H. influenzae).
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An aliquot of a suspension (100 L) of the initial inoculation (1 × 108 CFU/mL) was added to the in vitro model to produce a final inoculum of approximately 5 × 105 CFU/mL. The bacteria were incubated for 2 h, which allowed them to reach the logarithmic growth phase, before adding different azithromycin concentrations. The selection of azithromycin concentrations tested in each bacterial strain was based on their MIC values. At least seven different concentrations covering the entire azithromaycin range were investigated including minimum inhibition of bacterial growth (0.25 × MIC, 0.5 × MIC, 1 × MIC), efficient bacterial killing (2 × MIC, 4 × MIC) and maximum bacterial killing (8 × MIC, 16 × MIC). A control experiment with bacteria and no drug was run simultaneously. Samples were taken at 0, 0.5, 1, 1.5, 2, 3, 4, 5 and 6 h. 2.6. Bacterial quantification Bacterial counts were determined by plating 50 L of the serial 10-fold dilutions on appropriate agar plates, using an adapted droplet-plate method. Briefly, agar plates were divided into four quadrants. With an automatic pipette, 5 × 10 L droplets of the chosen dilution were equidistantly plated onto one of the quadrants. A duplicate was plated onto the adjacent quadrant. Then, the plates were incubated at 37 ◦ C and 5% CO2 (for S. pneumoniae and H. influenzae) for 16–24 h before reading. The procedure was repeated at least three times per bacterial strain and dose. Positive controls with bacteria but no drug were run simultaneously. Following incubation, the number of CFUs was counted in each duplicate quadrant at each time-point and averaged.
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tionally, the graphs were visually inspected for goodness of fit. First, an adaptation rate constant (z) was incorporated into model 1. If the bacteria have not yet reached the logarithmic growth phase at time zero, an exponential correction factor (1 − exp−zt ) may be necessary to compensate for this delay in the onset of growth. In the resulting model 2, this delay term affects both growth and kill equally: kmax C dN = k0 − (1 − exp−zt )N (model 2) dt EC50 + C However, it is not necessarily true that both growth and kill show the same time-frame for the delay. Therefore, model 3 describes a delayed effect in growth (1 − exp−xt ) and model 4 a delay in kill (1 − exp−yt ) only. kmax C dN −xt N (model 3) = k0 (1 − exp ) − EC50 + C dt kmax C dN −yt (model 4) (1 − exp ) N = k0 − EC50 + C dt In in vitro systems, available space and nutrients are limited. The factor that accounts for the resulting saturation in growth is the maximum number of bacteria (Nmax ) shown in model 5: N kmax C dN − = k0 1 − N (model 5) dt Nmax EC50 + C Incorporation of the three adaptation rate terms from models 2–4 results in models 6–8: N kmax C dN − = k0 1 − (1 − exp−zt )N dt Nmax EC50 + C (model 6)
2.7. PK/PD modeling Time–kill curve analysis and mathematical modeling of the kill curve data were performed with the non-linear regression software program Scientist® 3.0 (Micromath, Salt Lake, UT, USA). The simplest, but commonly used, Emax model was fitted to the PD data: dN kmax C = k0 − N (model 1) dt EC50 + C Where dN/dt is the change in number of bacteria as a function of time, k0 (h−1 ) is the bacterial growth rate constant in the absence of antibiotic, kmax (h−1 ) the maximum killing rate constant (maximum effect), EC50 (g/mL) the concentration of antibiotic necessary to produce 50% of maximum effect, C (g/mL) the concentration of antibiotic at any time (t) and N (CFU/mL) the number of viable bacteria. Next, this simple Emax model was extended stepwise, fitted simultaneously to the data and the resulting models were compared for best fit. To determine the best model, the following criteria were taken into consideration: model selection criterion (MSC), coefficient of determination (R2 ) and the correlation between observed and calculated values. Addi-
dN N kmax C −xt (1 − exp ) − = k0 1 − N dt Nmax EC50 + C (model 7) dN N kmax C −yt − = k0 1 − (1 − exp ) N dt Nmax EC50 + C (model 8) In practice, saturation in growth as well as a delay in the onset of growth that is different from the onset in kill can be observed. This relatively complex scenario can be described by model 9: N dN (1 − exp−xt ) = k0 1 − dt Nmax kmax C −yt − (1 − exp ) N (model 9) EC50 + C In general, the uniform delay described by the z term can also be achieved by setting x equals y. The curve fit obtained from models 1–9 can now be further improved by adding a Hill or shape factor (h) that smooths the curve out by modifying the
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steepness of the slope. Alteration of model 1 results in model 10:
dN = k0 − dt
· Ch
kmax ECh50 + Ch
3.1. MIC values and azithromycin time–kill curve concentrations
·N
3. Results
(model 10)
Models 2–9 were modified in a similar way, resulting in a total of 18 different models. For each bacterial strain, the initial estimate for k0 was determined using positive control data. Based on the determined k0 , kmax was found by using the data from the highest azithromycin concentration. Thereafter, k0 and kmax were fixed in each model at their determined values, whereas Nmax , EC50 , x, y, z and h were fitted simultaneously to the experimental data.
The determined MIC values and azithromycin concentrations used in the time–kill curve experiments against the four bacterial strains are summarized in Table 1. Overall, the results obtained in this study were consistent with the reported MIC values [12–14]. 3.2. Comparison of the investigated models Simulated effects of the different parameters, incorporated in the modified Emax models, are shown in Fig. 1. Fig. 1A
Fig. 1. Simulations of bacterial growth ( ) and kill ( ). (A) simplest Emax model (model 1); (B) uniform delay in the onset of growth and kill (model 2); (C) delay in the onset of growth (model 3); (D) delay in the onset of kill (model 4); (E) saturation in growth (model 5); (F) saturation in growth and uniform delay in growth and kill (model 6); (G) saturation in growth plus delay in the onset of growth (model 7); (H) saturation in growth plus delay in the onset of kill (model 8); (I) saturation in growth plus delay in the onset of growth and kill (model 9).
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Fig. 1. (Continued ).
shows a simple Emax model (model 1) without any delay or saturation terms. In Fig. 1B (model 2) the onset of growth and kill are equally delayed. With increasing time the exponential term becomes larger and finally reaches infinity. However, exp−inf equals zero and so one minus zero results in one. Therefore, either growth or kill or both are not affected any longer. In contrast, at very early time-points the exponential term is close to one and so neither growth nor kill constants affect the overall behaviour. Summarizing, the effect of the delay term (1 − exp−zt ) is maximal at very early timepoints but diminishes with time. The same holds true for Fig. 1C (model 3) and 1D (model 4), where both growth and kill are delayed independently. A saturation in growth, characterized by Nmax , only affects bacterial growth (Fig. 1E),
Table 1 Azithromycin MIC values and concentrations in the time–kill curve experiments Strains
MIC (g/mL)
Tested concentrations (g/mL)
S. pneumoniae ATCC 6303
0.06
S. pneumoniae ATCC 49619
0.06
M. catarrhalis ATCC 8176
0.008
H. influenzae ATCC 10211
1
0.015, 0.03, 0.06, 0.12, 0.24, 0.48, 0.96 0.015, 0.03, 0.06, 0.12, 0.24, 0.48, 0.96 0.002, 0.004, 0.008, 0.016, 0.032, 0.064, 0.128, 0.256, 0.512, 1.024 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64
whereas both growth and kill can be delayed as mentioned above. With increasing numbers of bacteria, the Nmax term approaches zero and so bacterial growth reaches the static phase. The incorporated effect of the Nmax term on models 2–4 in addition to the delay effect is shown in Fig. 1F–H. Finally, Fig. 1I summarizes saturation in growth and delays in the onset of growth and kill that are given different values. 3.3. PK/PD analysis The fitted curves of azithromycin against four bacterial strains are shown in Fig. 2. For both penicillin-sensitive and penicillin-intermediate S. pneumoniae, the data were best explained by PK/PD model 9, which incorporates an Nmax term as well as delay terms for the onset of growth and kill. Model 1 was found appropriate to describe the data for M. catarrhalis. For H. influenzae, model 4 could not explain the data well. A better fit was reached by employing an additional Hill (h) factor. The determined PD parameters of azithromycin for each individual bacterial strain are listed in Table 2. The results indicate that the models chosen are appropriate for fitting the data. Summarizing the data, azithromycin showed high efficacy against S. pneumoniae strains (EC50 /ATCC 6303: 0.16 mg/L; EC50 /ATCC 49619: 0.05 mg/L) and M. catarrhalis (EC50 : 0.12 mg/L) but low efficacy against H. influenzae (EC50 : 18.50 mg/L).
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Fig. 2. Curve fits for four bacterial strains with the various constant concentrations (g/L): (A) azithromycin against S. pneumoniae ATCC 6303; (B) azithromycin against S. pneumoniae ATCC 49619; (C) azithromycin against M. catarrhalis ATCC 8176; (D) azithromycin against H. influenzae ATCC 10211. Table 2 Determined pharmacodynamic azithromycin parameters and goodness of fit criteria Parameters (h−1 )
k0 kmax (h−1 ) EC50 (g/mL) Nmax (108 CFU/mL) x (h−1 ) y (h−1 ) z (h−1 ) h MSC/R2
S. pneumoniae ATCC 6303
S. pneumoniae ATCC 49619
M. catarrhalis ATCC 8176
H. influenzae ATCC 10211
1.51 2.44 0.16 1.38 8.07 2.06 – – 2.09/0.91
1.21 1.69 0.05 3.79 2.31 2.10 – – 3.24/0.96
0.99 1.67 0.12 – – – – – 1.89/0.87
1.22 9.28 18.50 – – 0.53 – 1.28 2.22/0.91
4. Discussion In this study we have used two different PK/PD approaches (MIC and time–kill curve) to evaluate the antimicrobial efficacy of the second generation macrolide azithromycin [15] against four different bacterial strains. Although widely used, MICs do not provide a very detailed characterization of antimicrobial activity [16]. Therefore, the more sophisticated time–kill curve approach was used. Compared to the MIC, one of the main advantages of the kill curve approach is the PD effect can be described by at least three parameters, k0 , kmax and EC50 , derived from an Emax model instead of one single threshold value. The results indicate that a sim-
ple Emax model was not sufficient to describe the observed PD effect for the four bacterial strains investigated. For both penicillin-sensitive and penicillin-intermediate S. pneumoniae, the limitation of space and nutrients (Nmax ) had an effect on the growth rate. Therefore, the addition of a saturation term into the basic Emax model appeared to be necessary. In comparison, the growth of H. influenzae was unaltered while the onset of kill was delayed. To account for that delay, a timedependent delay term was added. A similar behaviour was observed when H. influenzae was exposed to azithromycin. However, at time-point zero of the experiment H. influenzae had not reached the logarithmic growth phase yet. In this case a delay term was necessary to account for both effects. In con-
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Fig. 3. Simulated PK/PD of azithromycin against four bacterial strains after once daily oral administration of 500 mg azithromycin, accounting for mean PK/PD parameters of free, unbound azithromycin. Bacterial growth ( ) and kill ( ).
trast to other antibiotic classes, like -lactams, no correlation was found between the delay in the onset of growth and kill due to the mechanism of action. Once these models have been established and validated, it is then possible to simulate the expected kill curves for different doses and dosing regimens of the antibiotic against the bacteria of interest by substituting the concentration term in the mathematical model by the respective concentration versus time profile of the drug [16]. However, to predict changes in the number of bacteria for common dosing regimens in humans, protein binding has to be addressed. Therefore, the overall concentration C (g/mL) has to be substituted by the free, active concentration Cf (g/mL). It was shown in clinical studies that after once-daily oral administration of 500 mg azithromycin dihydrate the average total azithromycin Cmax is 0.45 g/mL [17]. Although azithromycin shows nonlinear protein-binding properties [18], the average protein binding of about 12% was used, resulting in an average Cmaxf of 0.40 g/mL. For each individual strain, the most suitable PK/PD model was applied to describe the antimicrobial activity of azithromycin with regard to free drug levels. Simulations for 500 mg azithromycin, given orally once-daily, are
shown in Fig. 3. For S. pneumoniae (both penicillin-sensitive and penicillin-intermediate), a dose of 500 mg azithromycin shows a good bactericidal effect [19]. For H. influenzae and M. catarrhalis, the same dose does not seem to be sufficient enough to decrease bacterial counts. For H. influenzae, the unbound azithromycin peak concentration was determined to be approximately 0.32 g/mL, which is less than 1 × MIC (1 g/mL) [20]. Therefore, predicted azithromycin serum concentrations do not show a bactericidal effect on H. influenzae for that particular dosing regimen. Although free azithromycin serum concentrations do not reach MIC levels for H. influenzae, efficacy is shown in clinical data [20–24]. It may seem paradoxical that although serum concentrations are much lower than reported tissue concentrations [20,25], azithromycin is effective against extracellular H. influenzae. Therefore, it is a subject of controversy whether serum or tissue concentrations should be considered for antimicrobial efficacy [25,26]. Originally, it was suggested to use free serum concentrations as a predictor of extracellular fluid concentrations as the main determinant of efficacy against extracellular pathogens [26]. However, host-defence mechanisms themselves might have been underestimated so far. Advanced-generation macrolides, and in particular
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azithromycin, are highly concentrated in polymorphonuclear leukocytes [10,27], which gravitate by chemotactic mechanisms to sites of infection. Following phagocytosis at the infection site, they are exposed to very high, and sometimes cidal, intracellular concentrations of the antibacterial agent [20,25]. When the drug-containing lysosomes are mechanically destroyed, high concentrations of azithromycin will be released locally, making it difficult to predict accurately what the unbound concentrations are in the extracellular space. Measurement of the free, unbound concentration in the infected tissue fluid, with e.g. microdialysis [28], might help to clarify this question. However, due to its high lipophilicity [29], problems in terms of cross-membrane permeability can be expected. Summarizing, for all four pathogens tested, modified Emax models were found to be adequate to describe the observed kill curve data. Simulations based on previous clinical trials can predict clinical outcome and help to come up with dose recommendations. However, further work needs to be completed in order to fully understand the PK/PD of azithromycin.
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