Pharmacodynamic modeling of bacterial kinetics: β‐Lactam antibiotics against Escherichia coli

A simple pharmacodynamic model has been developed to describe the bacterial kinetics exhibited by β‐lactam antibiotics. In contrast with previous models that only characterized the early killing phase of a time‐kill curve, the present model is capable of simultaneously describing both the killing and regrowth phases. The model relied on the use of both first‐order bactericidal and resistance formation rate constants to accurately define the time‐dependent changes in the bacterial populations of an antibiotic‐treated culture. The concentration dependency of the bactericidal rate constant was further delineated using a saturable‐receptor model. Furthermore, an exponential decrease in the resistance formation rate with increasing antibiotic concentrations was demonstrated. The evolving pharmacodynamic model was also explored via computer simulations by perturbing the two governing rate constants. The model was subsequently applied to the description of time‐kill data for amoxicillin, penicillin G, and cephalexin against Escherichia coli. The description of amdinocillin's action against E. coli was not as comprehensive because of the existence of a second killing phase. However, this model can be applicable to many classes of antibiotics that display the usual killing and regrowth phases in time‐kill studies. The pharmacodynamic model can potentially improve the prediction of bacterial killing and regrowth and foster an improved understanding of complex antimicrobial pharmacodynamics.