Predicting in vitro antibacterial efficacy across experimental designs with a semimechanistic pharmacokinetic-pharmacodynamic model

Abstract

We have previously described a general semimechanistic pharmacokinetic-pharmacodynamic (PKPD) model that successfully characterized the time course of antibacterial effects seen in bacterial cultures when exposed to static concentrations of five antibacterial agents of different classes. In this PKPD model, the total bacterial population was divided into two subpopulations, one growing drug-susceptible population and one resting drug-insensitive population. The drug effect was included as an increase in the killing rate of the drug-susceptible bacteria with a maximum-effect (E(max)) model. The aim of the present study was to evaluate the ability of this PKPD model to describe and predict data from in vitro experiments with dynamic concentration-time profiles. Dynamic time-kill curve experiments were performed by using an in vitro kinetic system, where cultures of Streptococcus pyogenes were exposed to benzylpenicillin, cefuroxime, erythromycin, moxifloxacin, or vancomycin using different starting concentrations (2 and 16 times the MIC) and elimination conditions (human half-life, reduced half-life, and constant concentrations). The PKPD model was applied, and the observations for the static as well as dynamic experiments were compared to model predictions based on parameter estimation using (i) static data, (ii) dynamic data, and (iii) combined static and dynamic data. Differences in experimental settings between static and dynamic experiments did not affect the growth kinetics of the bacteria significantly. With parameter reestimation, the structure of our previously proposed PKPD model could well characterize the bacterial growth and killing kinetics when exposed to dynamic concentrations with different elimination rates of all five investigated antibiotics. Furthermore, the model with parameter estimates based on data from only the static time-kill curve experiments could predict the majority of the time-kill curves from the dynamic experiments reasonably well. Adding data from dynamic experiments in the estimation improved the model fit for cefuroxime and vancomycin, indicating some differences in sensitivity to experimental conditions among the antibiotics studied.

FIG. 1.

Semimechanistic PKPD model describing the time course of bacterial growth and killing after antibacterial treatment. C, drug compartment; Ce, drug effect compartment; S, proliferating and drug-sensitive bacteria; R, resting and drug-insensitive bacteria; k_e, drug elimination rate constant; k_deg, degradation rate constant; k_e0, rate constant for effect delay; k_growth and k_death, rate constants for multiplication and degradation of bacteria, respectively; k_SR, rate constant for transformation from the growing, sensitive stage into the resting stage.

FIG. 2.

Growth curves of S. pyogenes performed in static (gray dotted) and dynamic (black dotted) environments for starting inocula aimed at 10³ to 10⁶ CFU/ml. Included are model predicted growth curves for a start inoculum of 5 × 10⁴ CFU/ml where parameters were estimated using all data simultaneously (with and without antibiotics) from experiments run in a static (black dashed line) or in a dynamic (black solid line) setting.

FIG. 3.

Observed time-kill curves for the dynamic experiments with model predictions (as medians and 95% prediction intervals) using parameter estimates based on data from only static experiments (A), only dynamic experiments (B), or combined static and dynamic experiments (C). Bacterial counts below the LOD are plotted as 5 CFU/ml. PEN, benzylpenicillin; CXM, cefuroxime; ERY, erythromycin; MXF, moxifloxacin; VAN, vancomycin. Numbers in panel strips indicate types of PK profiles: 2:n, initial concentration 2× the MIC with simulated human half-life; 2:r, initial concentration 2× the MIC with simulated one-third of the human half-life; 16:n, initial concentration 16× the MIC with simulated human half-life; 16:c, initial concentration 16× the MIC with a constant concentration.

FIG. 4.

Observed time-kill curves of S. pyogenes exposed to repeated doses of benzylpenicillin. Included are model predictions (as medians and 95% prediction intervals) using parameter estimates based on combined data from static and dynamic experiments. PEN, benzylpenicillin. Numbers in panel strips indicate the concentrations of the antibiotic used as multiples of the MIC.

FIG. 5.

Observed time-kill curves for a selection of the static experiments with model predictions (as medians and 95% prediction intervals) using parameter estimates based on data from only static experiments (A), only dynamic experiments (B), and combined static and dynamic experiments (C). Bacterial counts below the LOD are plotted as 5 CFU/ml. PEN, benzylpenicillin; CXM, cefuroxime; ERY, erythromycin; MXF, moxifloxacin; VAN, vancomycin. Numbers in panel strips indicate the concentrations of the antibiotic used as a multiple of the MIC.

FIG. 6.

Goodness-of-fit plots with observed and model-predicted bacterial counts with all data used in the parameter estimation. (A) No separate parameters were estimated for static and dynamic experiments. (B) Results from the final model in the SCM allowing separate estimates for experimental type if statistically significant. Bacterial counts below the LOD are plotted as 5 CFU/ml. ○, static experiments; +, dynamic experiments. Included are lines of identity.