Mathematical modeling of cancer systems is beginning to be used to design better treatment regimens, especially in chemotherapy and radiotherapy. The effectiveness of mathematical modeling to inform treatment decisions and identify therapy protocols, some of which are highly nonintuitive, is because it enables the exploration of a huge number of therapeutic possibilities. Considering the immense cost of laboratory research and clinical trials, these nonintuitive therapy protocols would likely never be found by experimental approaches. While much of the work to date in this area has involved high-level models, which look simply at overall tumor growth or the interaction of resistant and sensitive cell types, mechanistic models that integrate molecular biology and pharmacology can contribute greatly to the discovery of better cancer treatment regimens. These mechanistic models are better able to account for the effect of drug interactions and the dynamics of therapy. The aim of this chapter is to demonstrate the use of ordinary differential equation-based mechanistic models to describe the dynamic interactions between the molecular signaling of breast cancer cells and two key clinical drugs. In particular, we illustrate the procedure for building a model of the response of MCF-7 cells to standard therapies used in the clinic. Such mathematical models can be used to explore the vast number of potential protocols to suggest better treatment approaches.
Keywords: Breast cancer; Cdk4/6 inhibition; Endocrine therapy; MCF-7 cells; Mathematical modeling; Palbociclib.
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