Objectives:

The aim of the study was to develop a PK/PD model for the prediction of the effect of antibiotics on Escherichia coli. Therefore the long-term effect of constant ciprofloxacin (CIP) concentrations against E. coli was examined. Based on these experimental data, the model was developed and applied for the calculation of the effect of moxifloxacin (MOX), tobramycin (TOB) and ampicillin (AMP) on E. coli.

Methods:

The efficacy of various constant CIP, MOX, TOB and AMP (0.5- to 32-fold MIC) concentrations against E. coli [MICCIP: 0.03125 mg/L, MICMOX: 0.0625 mg/L, MICTOB: 1 mg/L, MICAMP: 2 mg/L] was studied in batch cultures over 24 h. The experimental kill curves were used to develop the PK/PD model. The simulation and fitting of the model was performed with the computer program MatLab^®.

Results:

The antibacterial activity of CIP against E. coli showed an increasing effect of CIP up to 16-fold MIC. This or higher concentrations could not effect a total killing of the cultures as some bacteria persisted despite the presence of CIP. These data were fitted to the following PK/PD model:

The model assumes that the bacterial population (Ntotal) is heterogenous, consting of the subpopulations N1 and N2. N2 are persisting cells that cannot be killed by the antibiotic. The kill rate of N1 depends on the antibiotic concentration C and incorporates the Emax model. With time, N1 adapts to the antibiotic according to e-h·t. The growth rates of both N1 and N2 depend on the antibiotic concentration. The growth of the bacterial culture cannot exceed Nmax, the maximal density of bacteria in the culture (=logistic growth).

Fitting the effect of CIP on E. coli resulted in a set of parameters, which allowed kill curve fitting of E. coli after the influence of MOX, TOB and AMP.

Conclusions:

Based on the experimentally determined kill curves the model allows excellent curve fits of the activity of CIP. Furthermore, the variation of the parameters in the model enables the prediction of the antibacterial activity of MOX, TOB and AMP on E. coli. Thus, the new PK/PD model enables the prediction of the antibacterial effect of constant concentrations of various antibiotics on E. coli.