A Model-Based PK/PD Antimicrobial Chemotherapy Drug Development Platform to Simultaneously Combat Infectious Diseases and Drug Resistance

A mathematical model-based analysis of the time-kill kinetics of ceftazidime/avibactam against Pseudomonas aeruginosa

Objectives

To characterize quantitatively the effect of avibactam in potentiating ceftazidime against MDR Pseudomonas aeruginosa by developing a mathematical model to describe the bacterial response to constant concentration time-kill information and validating it using both constant and time-varying concentration-effect data from in vitro and in vivo infection systems.

Methods

The time course of the bacterial population dynamics in the presence of static concentrations of ceftazidime and avibactam was modelled using a two-state pharmacokinetic/pharmacodynamic (PK/PD) model, consisting of active and resting states, to account for bactericidal activities, bacteria-mediated ceftazidime degradation and inhibition of degradation by avibactam. Ceftazidime's effect on the bacterial population was described as an enhancement of the death rate of the active population, with the effect of avibactam being to increase ceftazidime potency. Model validation was performed by comparing simulated time courses of bacterial responses with those from in vitro and in vivo experimental exposures of ceftazidime and avibactam that represented those predicted in an average patient dosed with 2 g/0.5 g ceftazidime/avibactam administered every 8 h as 2 h infusions.

Results

The two-state model successfully described the bacterial population dynamics, ceftazidime degradation and its inhibition by avibactam. For external validation, the model correctly predicted the bacterial response of P. aeruginosa isolates evaluated in in vitro hollow-fibre and in vivo neutropenic mouse thigh and lung infection models.

Conclusions

The PK/PD model and modelled strains successfully replicated the spread in activity when compared with a large selection of P. aeruginosa strains reported in the literature.

Importance of relating efficacy measures to unbound drug concentrations for anti-infective agents

For the optimization of dosing regimens of anti-infective agents, it is imperative to have a good understanding of pharmacokinetics (PK) and pharmacodynamics (PD). Whenever possible, drug efficacy needs to be related to unbound concentrations at the site of action. For anti-infective drugs, the infection site is typically located outside plasma, and a drug must diffuse through capillary membranes to reach its target. Disease- and drug-related factors can contribute to differential tissue distribution. As a result, the assumption that the plasma concentration of drugs represents a suitable surrogate of tissue concentrations may lead to erroneous conclusions. Quantifying drug exposure in tissues represents an opportunity to relate the pharmacologically active concentrations to an observed pharmacodynamic parameter, such as the MIC. Selection of an appropriate specimen to sample and the advantages and limitations of the available sampling techniques require careful consideration. Ultimately, the goal will be to assess the appropriateness of a drug and dosing regimen for a specific pathogen and infection.