Purpose Predicting target site drug concentration in the brain is of key importance for the successful development of drugs acting on the central nervous system. We propose a generic mathematical model to describe the pharmacokinetics in brain compartments, and apply this model to predict human brain disposition. Methods A mathematical model consisting of several physiological brain compartments in the rat was developed using rich concentration-time profiles from nine structurally diverse drugs in plasma, brain extracellular fluid, and two cerebrospinal fluid compartments. The effect of active drug transporters was also accounted for. Subsequently, the model was translated to predict human concentration-time profiles for acetaminophen and morphine, by scaling or replacing system- and drug-specific parameters in the model. Results A common model structure was identified that adequately described the rat pharmacokinetic profiles for each of the nine drugs across brain compartments, with good precision of structural model parameters (relative standard error <37.5%). The model predicted the human concentration-time profiles in different brain compartments well (symmetric mean absolute percentage error <90%). Conclusions A multi-compartmental brain pharmacokinetic model was developed and its structure could adequately describe data across nine different drugs. The model could be successfully translated to predict human brain concentrations.

Pharmacokinetic/pharmacodynamic (PKPD) models have emerged as valuable tools for the characterization and translation of antibiotic effects, and consequently for drug development and therapy. In contrast to traditional PKPD concepts for antibiotics such as minimum inhibitory concentration and PKPD indices, PKPD models enable description of the continuous, often species- or population-dependent time course of antimicrobial effects, commonly considering mechanistic pathogen- and drug-related knowledge. This review presents a comprehensive overview of previously published PKPD models describing repeated measurements of antibiotic effects. A literature review was conducted to identify PKPD models based on: (i) antibiotic compounds; (ii) Gram-positive or Gram-negative pathogens; and (iii) in-vitro or in-vivo longitudinal colony-forming unit data. In total, 132 publications were identified that were released between 1963 and 2021, including models based on exposure to single antibiotics (n=92) and drug combinations (n=40), as well as different experimental settings (e.g. static/traditional dynamic/hollow-fibre/animal time-kill models, n=90/27/32/11). An interactive, fully searchable table summarizes the details of each model, namely variants and mechanistic elements of PKPD submodels capturing observed bacterial growth, regrowth, drug effects and interactions. Furthermore, the review highlights the main purposes of PKPD model development, including the translation of preclinical PKPD to clinical settings, and the assessment of varied dosing regimens and patient characteristics for their impact on clinical antibiotic effects. In summary, this comprehensive overview of PKPD models will assist in identifying PKPD modelling strategies to describe growth, killing, regrowth and interaction patterns for pathogen-antibiotic combinations over time, and ultimately facilitate model-informed antibiotic translation, dosing and drug development.

New drugs and methods to efficiently fight carbapenem-resistant gram-negative pathogens are sorely needed. In this study, we characterized the preclinical pharmacokinetics (PK) and pharmacodynamics of the clinical stage drug candidate apramycin in time kill and mouse lung infection models. Based on in vitro and in vivo data, we developed a mathematical model to predict human efficacy. Three pneumonia-inducing gram-negative species Acinetobacter baumannii, Pseudomonas aeruginosa, and Klebsiella pneumoniae were studied. Bactericidal kinetics were evaluated with time-kill curves; in vivo PK were studied in healthy and infected mice, with sampling in plasma and epithelial lining fluid after subcutaneous administration; in vivo efficacy was measured in a neutropenic mouse pneumonia model. A pharmacokinetic-pharmacodynamic model, integrating all the data, was developed and simulations were performed. Good lung penetration of apramycin in epithelial lining fluid (ELF) was shown (area under the curve (AUC)_ELF/AUC_plasma = 88%). Plasma clearance was 48% lower in lung infected mice compared to healthy mice. For two out of five strains studied, a delay in growth (∼5 h) was observed in vivo but not in vitro. The mathematical model enabled integration of lung PK to drive mouse PK and pharmacodynamics. Simulations predicted that 30 mg/kg of apramycin once daily would result in bacteriostasis in patients. Apramycin is a candidate for treatment of carbapenem-resistant gram-negative pneumonia as demonstrated in an integrated modeling framework for three bacterial species. We show that mathematical modelling is a useful tool for simultaneous inclusion of multiple data sources, notably plasma and lung in vivo PK and simulation of expected scenarios in a clinical setting, notably lung infections.

To expand on previous reports of synergy between polymyxin B (PMB) and minocycline (MIN) against Acinetobacter baumannii; and to gain insight into the qualitative and quantitative determinants of their synergy. A semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model was developed on the basis of data from in vitro time-kill experiments with determination of resistant bacterial count to describe the effects of PMB and MIN alone and in combination. The model was enriched by complementary experiments providing information on the characteristics of the resistant subpopulation. The model successfully described the data and made possible quantification of the strength of interaction between the two drugs and formulation of hypotheses about the mechanisms of the observed interaction. The effect of the combination was driven by MIN, with PMB acting as an helper drug; simulations at clinically achievable concentrations showed that 1.5 mg/L MIN +0.2 mg/L PMB is expected to produce sustained killing over 30 hours, while 0.3 mg/L MIN +1 mg/L PMB is met by bacterial regrowth. Interaction equations showed that maximal synergy is reached for PMB concentrations ≥0.1 mg/L and MIN concentrations ≥1 mg/L. Semi-mechanistic PK/PD modelling was used to investigate the quantitative determinants of synergy between PMB and MIN on a PMB-resistant A. baumannii strain. The developed model, improving on usual study techniques, showed asymmetry in the drug interaction, as PMB acted mostly as a helper to MIN, and provided simulations as a tool for future studies.

Although polymyxin B has been in use since the late 1950s, there have been limited studies done to unravel its pharmacokinetics (PK) and pharmacodynamics (PD) index. We determined, in neutropenic infected mice, the PK, plasma protein binding and PK/PD index best correlating with efficacy for Escherichia coli and Klebsiella pneumoniae strains. The pharmacokinetic profile showed non-linear PK; dose was significantly correlated with absorption rate and clearance. The inhibitory sigmoid dose–effect model for the fC_max/MIC index of E. coli fitted best, but was only modestly higher than the R² of %fT_>MIC and fAUC/MIC (R² 0.91–0.93). For K. pneumoniae the fAUC/MIC index had the best fit, which was slightly higher than the R² of %fT_>MIC and fC_max/MIC (R² 0.85–0.91). Static targets of polymyxin B fAUC/MIC were 27.5–102.6 (median 63.5) and 5.9–60.5 (median 11.6) in E. coli and in K. pneumoniae isolates, respectively. A 1 log kill effect was only reached in two E. coli isolates and one K. pneumoniae. The PTA with the standard dosing was low for isolates with MIC >0.25 mg/L. This study confirms that fAUC/MIC can describe the exposure–response relationship for polymyxin B. The 1 log kill effect was achieved in the minority of the isolates whereas polymyxin B PK/PD targets cannot be attained for the majority of clinical isolates with the standard dosing regimen, indicating that polymyxin B may be not effective against serious infections as monotherapy.