A pharmacodynamic model for the activity of antibiotics against microorganisms under nonsaturable conditions.

An exact mathematical solution was derived to a pharmacodynamic model which illustrates bacterial survival in the presence of antibiotics. In this report the survival of Pseudomonas aeruginosa in the medium of an initial concentration of 0.64 mM (320 mg/L) of piperacillin [(2S,5R,6R)-6-[(R)-2-(4-ethyl-2,3-dioxo-1- piperazinecarboxyamido)-2-phenylacetamido]-3,3-dimethyl-7- oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylate] was well described by the derived model for up to 24 h. The bacterial killing by the antibiotic and apparent natural growth rate constants were 2955.3 h-1 X mol-1 and 0.5698 h-1, respectively. The functional equation was also fit to the data of ampicillin against Escherichia coli under simulated in vivo conditions. The optimal multiple dosing time and the minimum critical concentration to achieve antimicrobial action can be readily calculated from the developed model. Computer simulations were made to examine the effect on microbial survival of such factors as initial antibiotic concentration (Co), elimination half-life (t1/2), kill rate constant (K) of the antibiotic, and apparent growth rate constant (Kapp) of the test organism.