Modelling the effect of doxorubicin on tumor cells within a dynamic model of competition between tumor cells and healthy cells

This project engages mathematical models to explore interactions between healthy cells and cancer cells. Another focus of the research is to investigate how competitive interaction among cells can be affected by the application of a chemotherapy agent in a dose-dependent manner. In the model [1] of growth dynamics and competitive interaction between these cells, differences between the cell types in metabolism and acidity lead to degradation of healthy cells that neighbor cancer cells. This aspect of the model allows us to explain the dynamics by which cancer cells can invade the healthy cells and spread. Furthermore, we are extending this model to include the effects of the chemotherapy treatment, in particular application of a DNA damaging agent (DDA), such as doxorubicin. The goal is to investigate the effects of the chemotherapy agent in order to characterize its impact. within a system that models competitive dynamics between cells. A critical first step is development of a quantitative dose response model for the effects of the chemotherapy agent [B] is the important first step.

The integration of these models allows us to examine the effects of varying doses of a chemotherapy agent, such as doxorubicin, within a dynamical system modelling the interaction between invading cancer cells and healthy tissue. In fact, this exploration directly extends our recent model [2], which quantitative represents the effects of doxorubicin on DU-145 cells as a function of concentration and duration of exposure. The analysis applies a reaction-diffusion model in the system of equations modelling tumor cells (T), healthy cells (C), and hydrogen ions (H), as given in [1] to explore how different levels of chemotherapy affects the completion between these cell populations. This aligns directly with some of our underlying goals of the development of the quantitative models of [2] to accurately represent the dose response-relationship. Among other potential applications of an accurate quantitative dose-response model, this application in a system of partial differential equations is a primary area of interest.

It is an important point that while dose-response data for chemotherapy drugs are usually collected from isolated tumor cells, real treatments happen within a much more complex biological system. This project initiates our goal of model development allowing combination of these issues, and we explore the effects of bringing these models together. We would also like to consider what else needs to be considered and other questions that need to be addressed in the development and application of these models.