1 University of Houston College of Pharmacy, 1441 Moursund Street, Houston, TX 77030; 2 University of Houston, Department of Chemical Engineering, Houston, TX, USA
Received 13 November 2004; returned 24 January 2005; revised 31 January 2005; accepted 2 February 2005
![]() |
Abstract |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Methods: Timekill studies were performed with 108 cfu/mL of Pseudomonas aeruginosa at baseline. Meropenem at 0, 0.25, 1, 4, 16 and 64 x MIC was used (MIC = 1 mg/L). Serial samples were obtained to quantify bacterial burden over 24 h. The data were analysed by a population analysis using the non-parametric adaptive grid program. The rate of change of bacteria over time was expressed as the difference between linear bacterial growth rate and sigmoidal kill rate. Regrowth was attributed to adaptation, which was explicitly modelled as increase in C50k (concentration to achieve 50% maximal kill rate), using a saturable function of selective pressure (both meropenem concentration and time).
Results: The best-fit model consisted of eight parameters and the fit to the data was satisfactory. The r2 of maximum a-posteriori probability Bayesian predictions based on the mean parameter estimates was 0.984. Maximal killing rate at baseline was found to be 4.7 h1; C90k was achieved with meropenem at 5.0 mg/L. The model was validated by timekill studies using 2x and 32x MIC of meropenem.
Conclusions: Our model reasonably described and predicted the time course of P. aeruginosa in timekill studies, and provided quantitative information on the pharmacodynamics of meropenem. The structural model appeared robust and could be used to provide a realistic expectation of the killing performance of antimicrobial agents.
Keywords: pharmacodynamic modelling , mathematical models , Pseudomonas aeruginosa
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
An important problem often observed in timekill studies, but rarely addressed in data analysis, is microbial regrowth after initial reduction in the starting inoculum. Previous modelling/analysis techniques of the regrowth phenomenon have conceptualized a microbial population as consisting of two distinct sub-populations with different susceptibility.13 The regrowth phenomenon was attributed to the preferential killing of the susceptible sub-population, coupled with selective amplification of the resistant sub-population. However, this modelling approach is usually not informative until the entire microbial population is dominated by the resistant sub-population. Given that typical timekill studies are performed for 24 h, there may not be adequate time for the resistant sub-population to take over the entire population in the study time period. Consequently, a more flexible alternative modelling approach is necessary to describe observations in timekill studies. To facilitate further improvement in new drug development and in vitro drug interaction investigations, we developed a mathematical model to capture the relationship between the killing activity and concentration of an antimicrobial agent. In this study, such a system approach is illustrated by experimental data with Pseudomonas aeruginosa.
P. aeruginosa is an important pathogen associated with serious nosocomial infections such as pneumonia and sepsis. It is also associated with multiple mechanisms of resistance to various antimicrobial agents.4 Treatment of pseudomonal infections often represents a challenge to clinicians and combination therapy is commonly used to prevent the emergence of resistance. Some of the mechanisms of resistance are highly specific to one agent, whereas others affect a broad spectrum of antimicrobial agents, conferring different levels of resistance. Resistance to first line agents (e.g. ß-lactams, fluoroquinolones, etc.) has been reported and is becoming more prevalent.5,6 A high prevalence rate (12%) of multidrug resistance in Gram-negative bacteria has been reported in a recent surveillance study in Brooklyn, NY, USA. The prevalence of P. aeruginosa resistance to standard antimicrobial agents ranged from 1529%. The authors cautioned that in the event of an outbreak there is a risk of a return to the pre-antibiotic era.7 Another surveillance study examining fluoroquinolone resistance among Gram-negative bacilli in USA intensive care units demonstrated that P. aeruginosa resistance to ciprofloxacin has been escalating steadily from about 15% in 1994 to >30% in 2000.6 It is therefore imperative that we develop new antipseudomonal agents and/or better treatment strategies rapidly for infections caused by this bacterium.
The proposed model-based system approach is not confined to a specific antimicrobial agentpathogen combination, but is general and flexible. Consequently, it could be extrapolated to other antimicrobial agents (antibacterials, antifungals and antivirals) with different mechanisms of action, as well as to other pathogens (including human immunodeficiency virus, Mycobacterium tuberculosis and other infectious agents potentially implicated in bioterrorism) with different biological characteristics.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Meropenem powder was supplied by AstraZeneca (Wilmington, DE, USA). A stock solution of meropenem at 1024 mg/L in sterile water was prepared, aliquotted and stored at 70 °C. Prior to each susceptibility testing, an aliquot of the drug was thawed and diluted to the desired concentrations with cation-adjusted MuellerHinton II broth (Ca-MHB) (BBL, Sparks, MD, USA).
Microorganism
P. aeruginosa ATCC 27853 (American Type Culture Collection, Rockville, MD, USA) was used in the study. The bacterium was stored at 70 °C in Protect® (Key Scientific Products, Round Rock, TX, USA) storage vials. Fresh isolates were sub-cultured twice on 5% blood agar plates (Hardy Diagnostics, Santa Maria, CA, USA) for 24 h at 35 °C prior to each experiment.
Susceptibility studies
Meropenem MIC and MBC were determined for P. aeruginosa ATCC 27853 in Ca-MHB using a macrobroth dilution method as described by NCCLS.8
The final concentration of bacteria in each macrobroth dilution tube was 5 x 105 cfu/mL of Ca-MHB. Serial two-fold dilutions of meropenem were used. The MIC was defined as the lowest concentration of antimicrobial agent that resulted in no visible growth after 24 h of incubation at 35 °C in ambient air. Samples (50 µL) from clear tubes and the cloudy tube with the highest antimicrobial agent concentration were plated on MuellerHinton agar (MHA) plates (Hardy Diagnostics, Santa Maria, CA, USA). The MBC was defined as the lowest concentration of antimicrobial agent that resulted in
99.9% kill of the initial inoculum. Drug carry-over effect was assessed by visual inspection of the distribution of colonies on media plates. The studies were conducted in duplicate and repeated at least once on a separate day.
Timekill studies
Timekill studies were conducted with different and escalating meropenem concentrations. Six clinically achievable concentrations of meropenem were used, normalized to 0 (control), 0.25, 1, 4, 16 and 64 x MIC. An overnight culture of the isolate was diluted 30-fold with pre-warmed Ca-MHB and incubated further at 35 °C until reaching late log phase growth. The bacterial suspension was diluted with Ca-MHB accordingly based on absorbance at 630 nm; 15 mL of the suspension was transferred to 50 mL sterile conical flasks each containing 1 mL of an antimicrobial agent solution at 16x the target concentration. The final concentration of the bacterial suspension in each flask was 1 x 108 cfu/mL. The high inoculum used was to simulate the bacterial load in severe infection, and to allow resistant sub-population(s) to be present at baseline. The experiment was conducted for 24 h in a shaker water bath set at 35 °C.
Serial samples in duplicate were obtained from each flask over 24 h [at 0 (baseline), 2, 4, 8, 12 and 24 h] to characterize the effect of various meropenem concentrations on the total bacterial population. Prior to culturing the bacteria quantitatively, the bacterial samples (0.5 mL) were centrifuged at 10000 g for 15 min, and reconstituted with sterile normal saline to their original volumes in order to minimize drug carry-over effect. Total bacterial populations were quantified by spiral plating 10x serial dilutions of the samples (50 µL) onto MHA plates. The media plates were incubated in a humidified incubator (35 °C) for 1824 h, and the bacterial density from each sample was determined by CASBA-4 colony scanner/software (Spiral Biotech, Bethesda, MD, USA). The theoretical lower limit of detection was 400 cfu/mL.
Growth dynamics model
The time courses of bacterial burden under different drug exposures were described using a mathematical model, as shown in Figure 1. In contrast to the conventional approach in which the final observed effects are modelled, we utilized information over time to develop a dynamic model system that would capture bacterial growth/killing rates. The starting point was a mathematical model describing the time course of bacterial burden [biological response, N(t)] under the influence of various antimicrobial agent concentrations C(t). The rate of change of bacteria over time was expressed as the difference between the intrinsic bacterial growth rate and the kill rate provided by the antimicrobial agent (equation 1 of Figure 1). Based on previous studies, we adopted a linear bacterial growth rate. Additional model parameters were used to account for other physiological phenomena such as contact inhibition (using a maximum population size) and non-linear (sigmoidal) kill rate to account for target site saturation.1,9,10 Regrowth was attributed to adaptation, which was explicitly modelled as increase in the concentration necessary to achieve 50% maximal kill rate (C50k), using a saturable function of antimicrobial agent selective pressure (both meropenem concentration and time) (equation 2 of Figure 1).
|
Model validation
To examine the robustness and predicting ability of the model, final parameter estimates from the best-fit model were used to simulate bacterial behaviours under the influence of meropenem concentrations not previously investigated, using the ADAPT II program.12 The predicted bacterial burden over time associated with a meropenem concentration was first simulated with the maximum a-posteriori probability (MAP) Bayesian estimated growth dynamics parameter of the two regimens closest to the concentration used (e.g. final parameter estimates derived for both 1 x MIC and 4 x MIC were used to predict the effect associated with 2 x MIC). The final prediction was based on the mean of both sets of simulations. Timekill studies, as described above, were repeated in duplicate on different days with meropenem at 2x and 32 x MIC. The observed time courses of bacteria over time were compared with the model predictions.
To substantiate the physiological basis of our modelling approach, all samples in the validation timekill studies were also cultured quantitatively on MHA plates supplemented with meropenem at 1, 2 and 4 mg/L. The distribution of susceptibility in the bacterial population was tracked over time (susceptibility distribution analysis) under the influence of meropenem, to provide an explanation of regrowth.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The MIC and MBC of P. aeruginosa ATCC 27853 to meropenem were both found to be 1 mg/L.
Timekill studies
The time courses of bacterial burden associated with various meropenem concentrations were as shown in Figure 2(a). There was a significant ( > 2 log) drop in bacterial burden at 24 h with meropenem concentrations 4 x MIC (4 mg/L). Meropenem exhibited a partially concentration-dependent killing profile; initial killing of meropenem appeared to have been maximized at a concentration of
4 x MIC. These observations are consistent with previous in vitro studies with the ß-lactams.13
Regrowth was observed with meropenem concentrations of 0.25 x MIC and 1 x MIC between 12 and 24 h. The bacterial burden observed at 24 h was modelled using an inhibitory sigmoid Emax model (conventional approach), as shown in Figure 2(b).
|
The final best-fit model consisted of eight parameters. The final estimates of the parameters and their SDs are as shown in Table 1. The model fit to the data was satisfactory; r2 of MAP Bayesian predictions based on the mean parameter estimates was 0.984 (Figure 3). At baseline, the concentration necessary to attain 80% maximal kill rate (C80k) and 90% maximal kill rate (C90k) was achieved with meropenem at 3.8 and 5.0 mg/L, respectively (Figure 4a). As the surviving bacterial population became more resistant (adapted) over time, a higher concentration was needed to achieve the same kill rate. The rate of adaptation (increase in C50k) over time was as shown in Figure 4(b), as a function of meropenem concentration and time (selective pressure). Faster adaptation was observed with higher meropenem concentrations, as anticipated.
|
|
|
The predicted and observed time courses of the bacteria were as shown in Figure 5. The predictions correlated well with the observations, suggesting good predicting ability of the model. The r2 between predicted and mean observed bacteria burden for 2 x and 32 x MIC of meropenem were 0.83 and 0.97, respectively. Despite apparently conflicting input data (regrowth was observed with meropenem at 1 x MIC, but not with 4 x MIC), the model accurately predicted regrowth associated with meropenem at 2 x MIC. Susceptibility distribution analysis suggested that there were multiple bacterial sub-populations. The proportion of sub-populations with reduced susceptibility in the total bacterial population remained relatively constant over time in the absence of a selective pressure (placebo), as shown in Figure 6(a). Regrowth could be explained by selective amplification of sub-populations with reduced susceptibility over time in the presence of low (at 2 x MIC) meropenem exposure (Figure 6b). All sub-populations with reduced susceptibility grew, and the surviving bacterial population became increasingly resistant over time. The entire bacterial population had an MIC of >1 mg/L at 24 h, compared with 1 in 106 cfu at baseline. With an elevated (at 32 x MIC) meropenem exposure, all bacterial populations were suppressed and no regrowth was observed (Figure 6c).
|
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Conventional modelling methods of pharmacodynamic studies take a snapshot of microbial burden at the end of the observation period, and non-linear regression is used to fit the microbial load as a function of surrogate pharmacodynamic indices (Cmax/MIC, AUC/MIC, time above MIC, etc.) or drug concentration without making use of intermediate information (Figure 2b).1417 It is therefore not surprising that such approaches, although reasonable in describing such observations, are not robust enough to make good predictions, especially when the experimental conditions (multiple agents involved or fluctuating drug concentration profile over time) are different. As illustrated in Figure 7, identical bacterial burdens were observed after 24 h of exposure to either a slow bactericidal antimicrobial agent or a rapid killing agent followed by regrowth (due to emergence of resistance). It would be impossible to distinguish the two killing profiles using the conventional modelling approach shown in Figure 2(b). Consequently, such a simplistic modelling approach may not be ideal to provide a realistic expectation of the killing performance of the agent(s). The use of a fundamentally sound mass balance differential equation (equation 1 of Figure 1) has been proposed to provide quantitative information on the activity of antimicrobial agents.9,10,18
|
In this study, we modelled the entire bacterial population, which had a genetic plasticity and consisted of multiple (in principle infinite) sub-populations. We believe this approach captured more realistically the physiology of a bacterial population evolving from a predominantly susceptible population (in the absence of drug exposure) to a resistant one under antimicrobial pressure, with consequently a wider clinical application. In contrast to the abovementioned approach, we attributed regrowth to adaptation. In a dense bacterial population, many sub-populations with different susceptibilities co-exist. Constant drug exposure represents selective pressure on the bacterial populations; the more susceptible sub-populations are eradicated more readily, resulting in a more resistant mixture of bacterial sub-populations over time. The resultant bacterial population thus becomes increasingly more difficult to kill over time. C50k is directly proportional to the more commonly used MIC (the drug concentration at which growth rate equals killing rate),21 and it has been used as an overall index of susceptibility for a population of bacteria. If the starting inoculum is heterogeneous, we can reasonably expect a gradual increase in C50k of the surviving bacterial population over time, as shown in Figure 4(b). We further postulated that the rate of increase in C50k is dependent on the antimicrobial selective pressure, which was likely to be a function of both the antimicrobial agent concentration and duration of exposure.22 With higher antimicrobial agent concentrations, more sub-populations would be eradicated, leading to a more rapid increase in C50k of the surviving bacterial populations (Figure 4b). Theoretically, the observations can also be modelled as a gradual decline in the maximal kill rate (Kk),1 but we considered the former approach more rational and it was used in this study. In the validation studies, quantitative cultures were performed in antimicrobial-free MHA and media plates supplemented with various concentrations of meropenem to determine the susceptibility distribution of the bacterial population. Regrowth observed with meropenem (at 2 x MIC, Figure 6b) could be attributed to selective amplification of sub-populations with reduced susceptibility (adaptation), thus providing support for our modelling approach. Upon removal of the drug selective pressure, the susceptibility of the bacterial population is expected to reverse gradually to baseline. This phenomenon is also supported by well known clinical observations in the HIV cohorts, in which mutant viral populations reverted to wild-type after therapy was interrupted.23
Initial attempts were made to model the drug selective pressure as a simple time-dependent linear (non-saturable) function; however, this approach was thought to be non-physiological and thus was abandoned (data not shown). Instead, we used an empiric exponential (saturable) function in the final model. In view of the short duration of the study, we assumed that no spontaneous mutation occurred during antimicrobial exposure. There would ultimately be a maximal increase in C50k, corresponding to the most resistant cell (or sub-population) present at baseline (in this study a dimensionless parameter ß was used). Consequently, adaptation can be considered as the rate of evolution of the bacterial populations towards the total replacement of the bacterial population by the most resistant clone. Another model parameter was used to enhance the flexibility of the model and to facilitate the model fitting to the observations. Although the adaptation function was empiric, our results suggested that our modelling approach was reasonable in quantitatively describing and predicting bacterial burden over time under the influence of meropenem. Since the baseline MIC of the bacterial population to meropenem was performed in two-fold dilutions, the true MIC could have been between 0.511 mg/L (reported as 1 mg/L above). As shown in Figure 5(a), the model predicted regrowth and the susceptibility of the bacterial population would increase
3 times (to between 1.533 mg/L) after exposure to meropenem at 2 x MIC for 24 h (Figure 4b). Consistent with the model prediction, the validation timekill study with meropenem at 2 x MIC revealed that the MIC of the bacterial population at 24 h was between 12 mg/L (Figure 6b). The model also accurately predicted the lack of regrowth with meropenem at 32 x MIC (Figure 5b), as the kill rate was higher than the growth rates of all the bacterial sub-populations.
Since our approach is not specific to a particular antimicrobial agentpathogen combination, we expect the same approach could be adopted for other antimicrobial agents, as well as to other pathogens. As we are faced with a crisis of antimicrobial resistance in various pathogens, there is an urgent need to seek a more efficient approach to evaluate new agents and/or better treatment strategies for infections caused by these pathogens. Ideally, clinical investigations of new drugs should be optimally guided by informative pre-clinical studies. Mathematical modelling and computer simulation of microbial responses to antimicrobial agents (such as our approach) should be one of the essential components. By capturing the relationship between antimicrobial agent concentration and microbial response (pharmacodynamics), the effectiveness of a large number of compounds and treatment strategies (such as dose, dosing frequency, duration of therapy and the necessity for combination therapy) can be screened efficiently using computer simulations, but only promising agents and treatment strategies associated with high probabilities of favourable outcomes will be investigated in clinical trials. Our modelling approach may be adopted to provide quantitative expected performance of antimicrobial agents alone or in combination in in vitro investigations of pharmacodynamic drug interactions.24 By accounting for additional essential physiological processes (such as natural resistance mutation frequency and fluctuating drug concentrationtime profile), both cell kill and the emergence of resistance during therapy can also be evaluated (current work in progress), as proposed previously.19,2528 Resources could be devoted selectively to fewer agents in expensive and labour-intensive clinical testing, and the overall higher success rate would result in a lower cost of drug development. Since the treatment strategies investigated are designed to provide maximal killing and suppression of resistance emergence, the clinical lifespan of new agents approved for clinical use could also be prolonged.
We intentionally used a higher ( > 100-fold) inoculum in this study than the standard methodology. Since the mutation frequency is commonly believed to be 1 in 1078
, it was more likely to result in a heterogeneous bacterial population at baseline. As a result, the regrowth phenomenon might have been more prominent than expected. This is essential to examine the robustness and flexibility of our model. If a more homogeneous (lower burden) bacterial population is studied, the adaptation function could be easily ignored (the parameter ß is fixed as zero) for ease of estimation and simulation.
In conclusion, our model reasonably described and predicted the time course of P. aeruginosa in in vitro timekill studies, and provided quantitative information on pharmacodynamics of meropenem. The structural model appeared robust and could be used as a foundation to provide a more realistic expectation of the in vitro killing performance of antimicrobial agents.
![]() |
Acknowledgements |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
2
.
Jumbe, N., Louie, A., Leary, R. et al. (2003). Application of a mathematical model to prevent in vivo amplification of antibiotic-resistant bacterial populations during therapy. Journal of Clinical Investigation 112, 27585.
3 . Tam, V. H., Louie, A., Deziel, M. R., et al. (2001). Prevention of emergence of resistance of Pseudomonas aeruginosa (PA) through population co-modeling drug concentration, susceptible and resistant populations (P) In Programs and Abstracts of the Forty-first Interscience Conference on Antimicrobial Agents and Chemotherapy, Chicago, IL, 2001, Abstract A-2100, p. 35. American Society for Microbiology, Washington, DC, USA.
4 . Livermore, D. M. (2002). Multiple mechanisms of antimicrobial resistance in Pseudomonas aeruginosa: our worst nightmare? Clinical Infectious Diseases 34, 63440.[CrossRef][ISI][Medline]
5 . Gales, A. C., Sader, H. H. & Jones, R. N. (2002). Respiratory tract pathogens isolated from patients hospitalized with suspected pneumonia in Latin America: frequency of occurrence and antimicrobial susceptibility profile: results from the SENTRY Antimicrobial Surveillance Program (19972000). Diagnostic Microbiology and Infectious Diseases 44, 30111.[CrossRef][ISI][Medline]
6
.
Neuhauser, M. M., Weinstein, R. A., Rydman, R. et al. (2003). Antibiotic resistance among gram-negative bacilli in US intensive care units: implications for fluoroquinolone use. Journal of the American Medical Association 289, 8858.
7
.
Landman, D., Quale, J. M., Mayorga, D. et al. (2002). Citywide clonal outbreak of multiresistant Acinetobacter baumannii and Pseudomonas aeruginosa in Brooklyn, NY: the preantibiotic era has returned. Archives of Internal Medicine 162, 151520.
8 . National Committee for Clinical Laboratory Standards (2003). Methods for Dilution Antimicrobial Susceptibility Tests for Bacteria that Grow AerobicallySixth Edition M7A6 NCCLS, Villanova, PA, USA.
9 . Zhi, J., Nightingale, C. H. & Quintiliani, R. (1986). A pharmacodynamic model for the activity of antibiotics against microorganisms under nonsaturable conditions. Journal of Pharmaceutical Sciences 75, 10637.[ISI][Medline]
10 . Zhi, J. G., Nightingale, C. H. & Quintiliani, R. (1988). Microbial pharmacodynamics of piperacillin in neutropenic mice of systematic infection due to Pseudomonas aeruginosa. Journal of Pharmacokinetics and Biopharmaceutics 16, 35575.[CrossRef][ISI][Medline]
11 . Leary, R., Jelliffe, R., Schumitzky, A., et al. (2001). An adaptive grid non-parametric approach to pharmacokinetic and dynamic (PK/PD) models. In Fourteenth IEEE Symposium on Computer-Based Medical Systems, Bethesda, MD, 2001, pp. 289394. IEEE Computer Society, Washington, DC, USA.
12 . D'Argenio, D. Z. & Schumitzky, A. (1997), Biomedical simulations resource ADAPT II User's Guide: Pharmacokinetic/Pharmacodynamic Systems Analysis Software. Biomedical simulations resource, University of Southern California, Los Angeles, CA, USA.
13 . Craig, W. A. & Ebert, S. C. (1990). Killing and regrowth of bacteria in vitro: a review. Scandinavian Journal of Infectious Diseases Supplement 74, 6370.[Medline]
14
.
Miyazaki, S., Okazaki, K., Tsuji, M. et al. (2004). Pharmacodynamics of S-3578, a novel cephem, in murine lung and systemic infection models. Antimicrobial Agents and Chemotherapy 48, 37883.
15
.
Andes, D., Marchillo, K., Conklin, R. et al. (2004). Pharmacodynamics of a new triazole, posaconazole, in a murine model of disseminated candidiasis. Antimicrobial Agents and Chemotherapy 48, 13742.
16
.
Maglio, D., Ong, C., Banevicius, M. A. et al. (2004). Determination of the in vivo pharmacodynamic profile of cefepime against extended-spectrum-ß-lactamase-producing Escherichia coli at various inocula. Antimicrobial Agents and Chemotherapy 48, 19417.
17
.
Dandekar, P. K., Tessier, P. R., Williams, P. et al. (2003). Pharmacodynamic profile of daptomycin against Enterococcus species and methicillin-resistant Staphylococcus aureus in a murine thigh infection model. Journal of Antimicrobial Chemotherapy 52, 40511.
18 . Lipsitch, M. & Levin, B. R. (1997). The population dynamics of antimicrobial chemotherapy. Antimicrobial Agents and Chemotherapy 41, 36373.[Abstract]
19
.
Regoes, R. R., Wiuff, C., Zappala, R. M. et al. (2004). Pharmacodynamic functions: a multiparameter approach to the design of antibiotic treatment regimens. Antimicrobial Agents and Chemotherapy 48, 36706.
20 . Fredrickson, A. G. (1977). Behavior of mixed cultures of microorganisms. Annual Reviews of Microbiology 31, 6387.[CrossRef]
21
.
Mueller, M., de la Pena, A. & Derendorf, H. (2004). Issues in pharmacokinetics and pharmacodynamics of anti-infective agents: kill curves versus MIC. Antimicrobial Agents and Chemotherapy 48, 36977.
22 . Tam, V. H., Louie, A., Deziel, M. R., et al. (2001). AUC/MIC ratio and duration of therapy both influence the probability of emergence of resistance to a fluoroquinolone in an in vitro hollow fiber infection model (IVHFIM). In Programs and Abstracts of the Thirty-ninth Annual Meeting of the Infectious Diseases Society of America, San Francisco, CA, 2001, Abstract 473, p. 1169. Infectious Diseases Society of America, Alexandria, VA, USA.
23
.
Lawrence, J., Mayers, D. L., Hullsiek, K. H. et al. (2003). Structured treatment interruption in patients with multidrug-resistant human immunodeficiency virus. New England Journal of Medicine 349, 83746.
24
.
Tam, V. H., Schilling, A. N., Lewis, R. E. et al. (2004). Novel approach to characterization of combined pharmacodynamic effects of antimicrobial agents. Antimicrobial Agents and Chemotherapy 48, 431521.
25
.
Bonhoeffer, S., Lipsitch, M. & Levin, B. R. (1997). Evaluating treatment protocols to prevent antibiotic resistance. Proceedings of the National Academy of Sciences, USA 94, 1210611.
26 . Drusano, G. L. (2004). Antimicrobial pharmacodynamics: critical interactions of bug and drug. Nature Review Microbiology 2, 289300.[CrossRef][ISI]
27
.
Lipsitch, M., Bacon, T. H., Leary, J. J. et al. (2000). Effects of antiviral usage on transmission dynamics of herpes simplex virus type 1 and on antiviral resistance: predictions of mathematical models. Antimicrobial Agents and Chemotherapy 44, 282435.
28
.
Webb, G. F. & Blaser, M. J. (2002). Dynamics of bacterial phenotype selection in a colonized host. Proceedings of the National Academy of Sciences, USA 99, 313540.