Nonlinear dynamics of estrogen receptor-positive breast cancer integrating experimental data: A novel spatial modeling approach

Oncology research has focused extensively on estrogen hormones and their function in breast cancer proliferation. Mathematical modeling is essential for the analysis and simulation of breast cancers. This research presents a novel approach to examine the therapeutic and inhibitory effects of hormone and estrogen therapies on the onset of breast cancer. Our proposed mathematical model comprises a nonlinear coupled system of partial differential equations, capturing intricate interactions among estrogen, cytotoxic T lymphocytes, dormant cancer cells, and active cancer cells. The model's parameters are meticulously estimated through experimental studies, and we conduct a comprehensive global sensitivity analysis to assess the uncertainty of these parameter values. Remarkably, our findings underscore the pivotal role of hormone therapy in curtailing breast tumor growth by blocking estrogen's influence on cancer cells. Beyond this crucial insight, our proposed model offers an integrated framework to delve into the complexity of tumor progression and immune response under hormone therapy. We employ diverse experimental datasets encompassing gene expression profiles, spatial tumor morphology, and cellular interactions. Integrating multidimensional experimental data with mathematical models enhances our understanding of breast cancer dynamics and paves the way for personalized treatment strategies. Our study advances our comprehension of estrogen receptor-positive breast cancer and exemplifies a transformative approach that merges experimental data with cutting-edge mathematical modeling. This framework promises to illuminate the complexities of cancer progression and therapy, with broad implications for oncology