Kill kinetics of bacteria under fluctuating concentrations of various antibiotics. I. Description of the model

In vitro pharmacodynamic models to determine the effect of antibacterial drugs

In vitro pharmacodynamic (PD) models are used to obtain useful quantitative information on the effect of either single drugs or drug combinations against bacteria. This review provides an overview of in vitro PD models and their experimental implementation. Models are categorized on the basis of whether the drug concentration remains constant or changes and whether there is a loss of bacteria from the system. Further subdifferentiation is based on whether bacterial loss involves dilution of the medium or is associated with dialysis or diffusion. For comprehension of the underlying principles, experimental settings are simplified and schematically illustrated, including the simulations of various in vivo routes of administration. The different model types are categorized and their (dis)advantages discussed. The application of in vitro models to special organs, infections and pathogens is comprehensively presented. Finally, the relevance and perspectives of in vitro investigations in drug discovery and clinical research are elucidated and discussed.

Microbial pharmacodynamics of piperacillin in neutropenic mice of systematic infection due to Pseudomonas aeruginosa

Mathematical solutions for two possible pharmacodynamic interactions (linear nonsaturable and nonlinear saturable) between antibiotics and microorganisms derived from the incorporation of clinically relevant antibiotic dosage regimens such as single bolus dosing, multiple doses, and constant infusion at steady state have been obtained. It is concluded that the saturable nonlinear interaction model between the tested antibiotic and microorganism appears appropriate. The model and its derived equations are capable of describing in vivo bacterial growth of P. aeruginosa after single bolus dosing and multiple doses of piperacillin as described by a linear one-compartment pharmacokinetic model. The activity of piperacillin against P. aeruginosa in the neutropenic mouse systemic infection model can be described by an equation with three dynamic parameters: the bacterial growth rate constant kapp, 0.02345 min-1, the bacterial killing rate constant k'kill, 0.02623 min-1, and the Michaelis-Menten type saturation constant Km, 0.05467 microgram/ml. The concept and derived equations for the optimal dosing interval and minimum critical concentration are of clinical importance for the proper selection of antibiotic dosage regimens.

A pharmacodynamic model for the activity of antibiotics against microorganisms under nonsaturable conditions

An exact mathematical solution was derived to a pharmacodynamic model which illustrates bacterial survival in the presence of antibiotics. In this report the survival of Pseudomonas aeruginosa in the medium of an initial concentration of 0.64 mM (320 mg/L) of piperacillin [(2S,5R,6R)-6-[(R)-2-(4-ethyl-2,3-dioxo-1- piperazinecarboxyamido)-2-phenylacetamido]-3,3-dimethyl-7- oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylate] was well described by the derived model for up to 24 h. The bacterial killing by the antibiotic and apparent natural growth rate constants were 2955.3 h-1 X mol-1 and 0.5698 h-1, respectively. The functional equation was also fit to the data of ampicillin against Escherichia coli under simulated in vivo conditions. The optimal multiple dosing time and the minimum critical concentration to achieve antimicrobial action can be readily calculated from the developed model. Computer simulations were made to examine the effect on microbial survival of such factors as initial antibiotic concentration (Co), elimination half-life (t1/2), kill rate constant (K) of the antibiotic, and apparent growth rate constant (Kapp) of the test organism.