Using mathematical modeling to estimate time-independent cancer chemotherapy efficacy parameters

Abstract

One of the primary cancer treatment modalities is chemotherapy. Unfortunately, traditional anti-cancer drugs are often not selective and cause damage to healthy cells, leading to serious side effects for patients. For this reason more targeted therapeutics and drug delivery methods are being developed. The effectiveness of new treatments is initially determined via in vitro cell viability assays, which determine the ${\mathrm{IC}}_{50}$ of the drug. However, these assays are known to result in estimates of ${\mathrm{IC}}_{50}$ that depend on the measurement time, possibly resulting in over- or under-estimation of the ${\mathrm{IC}}_{50}$ . Here, we test the possibility of using cell growth curves and fitting of mathematical models to determine the ${\mathrm{IC}}_{50}$ as well as the maximum efficacy of a drug ( ${\epsilon }_{\max }$ ). We measured cell growth of MCF-7 and HeLa cells in the presence of different concentrations of doxorubicin and fit the data with a logistic growth model that incorporates the effect of the drug. This method leads to measurement time-independent estimates of ${\mathrm{IC}}_{50}$ and ${\epsilon }_{\max }$ , but we find that ${\epsilon }_{\max }$ is not identifiable. Further refinement of this methodology is needed to produce uniquely identifiable parameter estimates.

Keywords: Chemotherapy; Data fitting; Drug efficacy; Mathematical model; Parameter estimation.