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We developed and applied pharmacokinetic-pharmacodynamic (PK-PD) models to characterize in vitro bacterial rate of killing as a function of ceftazidime concentrations over time. For PK-PD modeling, data obtained during continuous and intermittent infusion of ceftazidime in Pseudomonas aeruginosa killing experiments with an in vitro pharmacokinetic model were used. The basic PK-PD model was a maximum-effect model which described the number of viable bacteria (N) as a function of the growth rate (lambda) and killing rate (epsilon) according to the equation dN/dt = [lambda - epsilon x [Cgamma(EC50gamma + Cgamma)]] N, where gamma is the Hill factor, C is the concentration of antibiotic, and EC50 is the concentration of antibiotic at which 50% of the maximum effect is obtained. Next, four different models with increasing complexity were analyzed by using the EDSIM program (MediWare, Groningen, The Netherlands). These models incorporated either an adaptation rate factor and a maximum number of bacteria (Nmax) factor or combinations of the two parameters. In addition, a two-population model was evaluated. Model discrimination was by Akaike's information criterion. The experimental data were best described by the model which included an Nmax term and a rate term for adaptation for a period up to 36 h. The absolute values for maximal growth rate and killing rate in this model were different from those in the original experiment, but net growth rates were comparable. It is concluded that the derived models can describe bacterial growth and killing in the presence of antibiotic concentrations mimicking human pharmacokinetics. Application of these models will eventually provide us with parameters which can be used for further dosage optimization.

Pharmacokinetic-pharmacodynamic modeling of activity of ceftazidime during continuous and intermittent infusion