A new model for bacterial growth & drug effects

Purpose: To develop a mathematical model for bacterial growth & PDs. Methods: 48 volunteers, documented to have nasal colonization with S aureus, were randomized (16/group) to receive PO linezolid 200, 400 or 600 mg q. 12h for either 3 or 5d. Plasma for drug assay (HPLC, CV% <5) was obtained around the first & last doses; nasal swabs were obtained at 0, 4, 8, 12, 16, 24, 48, 72, 120 & (for 5 d courses) 168 h; CFU were quantitated. All PK & PD data were comodelled (maximum likelihood, Adapt II); model discrimination was by Akaike's Information Criterion. Results: The PD model for bacterial CFU includes capacity-limited growth & first order death & is defined by the following differential equation: d(CFU)/dt=CFU(VGmax/(CFUm+CFU)-Kd); in which VGmax is the maximum rate of bacterial growth (CFU/h); CFUm is the CFU at which the rate of growth is half-maximal; & Kd, the first order death rate constant, is a function of Ce, the drug concentrations at the effect site: Kd = Kdo (1+Emax-Ce^H/[(SITm·MIC)^H+Ce^H], in which Kdo is the drug-free Kd, Emax is the maximum linezolid-induced increase in Kd, SITm·MIC is the Ce at which drug effect is half-maximal and H is Hill's constant. Fitted PD parameter values, as mean (and CV%), included: VGmax CFUm Kdo Emax SITm H 1624(55) 844(21) .12(105) .89(11) 1.0(1.6) 3.7(51) The derived mean (CV%) maximal, drug-free net rate of bacterial growth, in the log-growth phase, was 0.85 (65%) log₁₀ (CFU)/h. The model fit the data very well; there were no differences in fitted parameters by dose. Conclusions: The model enabled us to evaluate changes in S aureus titer through elaboration of rate of growth, as well as kill rates, during dosing with linezolid. An approach such as this, could be applied to other experimental models, in which bacteria can be quantified serially.