This document presents a SimBiology model characterizing the pharmacokinetic/pharmacodynamic (PK/PD) relationship of antimicrobial agents as described in the article, "Semi-mechanistic Model for Assessment of Activity of Antibacterial Agents from Time-Kill Curve Experiments” by Nielsen et al .
In 2007, Nielson et al  proposed an integrated PK/PD model to characterize the effect of antibacterial drugs on bacterial growth kinetics in time-kill curve studies. Time-kill curve experiments involve exposing an in vitro bacterial inoculum to a fixed antibiotic dose and monitoring bacterial activity over time. The authors described the in vitro drug kinetics using a one-compartment model with linear elimination ( kdeg ) to account for drug degradation due to compound instability. The authors also included a second compartment, Biophase, to incorporate potential pharmacologic delay. Input and output to the Biophase compartment were described as a first order processes ( ke ). The dotted line indicates that the Drug in the Central compartment is both a reactant and product in the input process; this models the assumption that the presence of the Biophase compartment does not affect the mass balance.
For the bacterial growth model, it was assumed that the bacterial system is comprised of 2 subpopulations – Growing and Resting. All the processes in the bacterial dynamics model – growth (kgrowth), the reversible transformation between sub-populations (ksr and krs) and decay (kdeath) – were modeled as first-order processes. It was assumed that only the cells in the growing phase are drug-susceptible. The inhibitory effect of the antibiotic was build into the decay rate (kdeath + Effect) of the Growing population. The pharmacodynamic effect was modeled using a sigmoidal Emax model:
where Ce is the Drug concentration in the Biophase compartment, E_max represents the maximal achievable antibiotic effect, EC50 is the drug concentration that induces 50% of the maximum effect, and ? is the hill coefficient.
 Nielsen, E. I., A. Viberg, E. Lowdin, O. Cars, M. O. Karlsson, and M. Sandstrom (2007) Semimechanistic pharmacokinetic/pharmacodynamic model for assessment of activity of antibacterial agents from time-kill curve experiments. Antimicrobial Agents and Chemotherapy. 51:128-136.