Application of Logistic Growth Model to Pharmacodynamic Analysis of in Vitro Bactericidal Kinetics

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Abstract
A new pharmacodynamic model for the analysis of in vitro bactericidal kinetics was developed based on the logistic growth model, with the bacterial phases divided into two compartments. The model equations are expressed as nonlinear simultaneous differential equations, and the Runge-Kutta-Gill method was adopted to numerically solve the equations in both the simulation and the least squares curve-fitting procedures. The model can describe the initial killing and the regrowth phases and can explain the nonlinear dependence of the killing rate on the drug concentration. The model can also explain the plateau in the bacterial growth curve that is often observed in in vitro experiments. The model was applied to analysis of the in vitro time-killing data of beta-lactam antibiotics, S-4661, meropenem, imipenem, cefpirome, and ceftazidim against three types of bacteria, Escherichia coli, Pseudomonas aeruginosa, and Staphylococcus aureus. The results of curve-fitting using the least squares program MULTI (Runge) showed good fits for all types of drugs and bacteria. The relationship between the characteristics of the drug-bacteria interactions and the estimated pharmacodynamic parameters is discussed.