Pharmacodynamic functions: A multiparameter approach to the design of antibiotic treatment regimens

There is a complex quantitative relationship between the concentrations of antibiotics and the growth and death rates of bacteria. Despite this complexity, in most cases only a single pharmacodynamic parameter, the MIC of the drug, is employed for the rational development of antibiotic treatment regimens. In this report, we use a mathematical model based on a Hill function-which we call the pharmacodynamic function and which is related to previously published E-max models-to describe the relationship between the bacterial net growth rates and the concentrations of antibiotics of five different classes: ampicillin, ciprofloxacin, tetracycline, streptomycin, and rifampin. Using Escherichia coli 018:K1:H7, we illustrate how precise estimates of the four parameters of the pharmacodynamic function can be obtained from in vitro time-kill data. We show that, in addition to their respective MICs, these antibiotics differ in the values of the other pharmacodynamic parameters. Using a computer simulation of antibiotic treatment in vivo, we demonstrate that, as a consequence of differences in pharmacodynamic parameters, such as the steepness of the Hill function and the minimum bacterial net growth rate attained at high antibiotic concentrations, there can be profound differences in the microbiological efficacy of antibiotics with identical MICs. We discuss the clinical implications and limitations of these results.