Model-based assessment of erlotinib effect in vitro measured by real-time cell analysis

Real time cell analysis (RTCA) is an impedance-based technology which tracks various living cell characteristics over time, such as their number, morphology or adhesion to the extra cellular matrix. However, there is no consensus about how RTCA data should be used to quantitatively evaluate pharmacodynamic parameters which describe drug efficacy or toxicity. The purpose of this work was to determine how RTCA data can be analyzed with mathematical modeling to explore and quantify drug effect in vitro. The pharmacokinetic-pharmacodynamic erlotinib concentration profile predicted by the model and its effect on the human epidermoïd carcinoma cell line A431 in vitro was measured through RTCA output, designated as cell index. A population approach was used to estimate model parameter values, considering a plate well as the statistical unit. The model related the cell index to the number of cells by means of a proportionality factor. Cell growth was described by an exponential model. A delay between erlotinib pharmacokinetics and cell killing was described by a transit compartment model, and the effect potency, by an E max function of erlotinib concentration. The modeling analysis performed on RTCA data distinguished drug effects in vitro on cell number from other effects likely to modify the relationship between cell index and cell number. It also revealed a time-dependent decrease of erlotinib concentration over time, described by a mono-exponential pharmacokinetic model with nonspecific binding.