The impact of bacterial growth kinetics on predicted antibiotic efficacy under different pharmacodynamic model assumptions: An in vivo case example
Miriam Stephanie Rosemarie Happ1,2, Christin Nyhoegen1, Mara Baldry3, Charlotte Costa3, Delphine Cayet3, Wilhelm Huisinga2,4, Jean-Claude Sirard3, Charlotte Kloft1,2,5, Robin Michelet1,5
1Department of Clinical Pharmacy and Biochemistry, Institute of Pharmacy, Freie Universität Berlin, 2Graduate Research Training program PharMetrX, 3Institut Pasteur de Lille, Center for Infection and Immunity of Lille, Inserm, 4Institute of Mathematics, University of Potsdam, 5shared senior authorship
Introduction: In recent years, the translational potential of longitudinal pharmacokinetic/ pharmacodynamic (PKPD) models, describing antibiotic effects on bacterial growth, has been increasingly recognised [1,2]. Importantly, these models are able to combine knowledge from in vivo and in vitro studies [3]. To increase confidence in the translatability of such models, robust predictivity across experimental setups and bacterial strains is crucial [1,4]. For example, bacterial growth dynamics between bacterial strains of the same species [5] and between different in vitro and in vivo experimental setups [5,6,7] might vary. Here, we show how bacterial growth dynamics are a key factor in longitudinal PKPD model extrapolation. Furthermore, we demonstrate the impact of changes in growth dynamics on predicted treatment outcome under different PD model assumptions by applying stochastic simulations of three PKPD models, equally well suited to describe the data generated in context of the EU H2020 project FAIR [8]. Methods: Three candidate models were used throughout the analysis, all accounting for amoxicillin PK [9], logistic bacterial growth of Streptococcus pneumoniae D39 in a murine superinfection pneumonia model (parameterised by net growth rate constant (knet); maximum carrying capacity (Bmax)), and amoxicillin effect using a non-sigmoidal Emax model (sequential approach, NONMEM 7.5.1). Models differed in the description of antibiotic effect, implemented as either: i)a first-order killing process (kill rate constant), ii)a proportional reduction of the net growth rate constant, iii)a total reduction in the net growth rate constant. All candidate models showed an equal fit to the underlying data, indicated by visual predictive check and minor differences in OFV (<1) or parameter precision (<0.5% points RSE). Stochastic simulations of all model candidates were performed (mrgsolve 1.5.2). Changes in bacterial growth dynamics were investigated by varying related parameters of knet equivalently to varying the maximum doubling time (ln(2)/knet) by ±2 h and Bmax between 105 and 10? CFU/lung. All parameter sets were investigated simulating three different dosing scenarios: a control group receiving no antibiotic, a low-dose group receiving a single dose of 5 µg, and a high-dose group receiving a single intragastric dose of 150 µg amoxicillin. To evaluate treatment efficacy, 1000 replicates were simulated per scenario and the median and 90% confidence interval of the log10-reduction in bacterial count per lung was estimated 12 hours after treatment, compared to both bacterial count at time of treatment and bacterial count in untreated control. Results: All three candidate models showed for the high-dose group the treatment efficacy (measured as log10-reduction compared to control or time of treatment) to be dependent on knet or Bmax. Knet had a larger impact on the log10-reduction of bacterial lung count than Bmax. The absolute increase in median log10-reduction when changing Bmax from 105 to 10? was (i): 0.790, (ii) 4.06 and (iii) 1.27, respectively. Increasing knet caused a decrease in log10-reduction for two of the models (i and iii), due to faster net growth compensating bacterial killing. For the other model (ii) an increase in log10-reduction was observed, as the effect is directly dependent on knet. Observed changes in the treatment efficacy also included differences in magnitude of change in log10-reduction between the different model candidates: The log10-reduction of the high-dose group compared to the control varied from 0.0160 to 5.34, and 0.00897 to 5.42 for models (i) and (iii), respectively, while for model (ii) the log10-reduction was 1.49 to 10.99. Conclusions: While goodness-of-fit criteria did not differ between model candidates, the assumptions related to the implementation of PD effect had a high impact on extrapolation to other bacterial growth dynamics scenarios. This impact on extrapolation should be considered during model development; i.e., whether decisions on effect implementation can be solely based on mechanistical knowledge of the drug or whether further validation of the model, including data on various growth conditions or bacterial strains, is needed to gain sufficient confidence in the model and its application/translation. Funding: This project received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 847786.
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