A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Abstract

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model

“…Cancer is among one of the most mathematically modeled diseases, some aim to answer questions about cancer as a whole system of biological and chemical interactions [ 44 – 47 ], some investigate the mechanical properties of a cancerous tissue [ 48 , 49 ], and some others focus on modeling cancer response to different treatments [ 50 – 52 ]. The most desirable features of mathematical models of cancer, including stochastic [ 53 – 55 ] and deterministic models [ 56 – 58 ], are their ability to make good predictions, testing plausible biological hypotheses or generating clinically testable hypothesis. For example, a multiscale model of prostate cancer shows that low androgen levels may increase resistance to hormonal therapy and that treatment with 5 α -reductase inhibitors may lead to more therapy-resistant cancer cells [ 59 ], and a data driven mathematical model predicts the response to FOLFIRI treatment for colon cancer patients [ 60 ].…”

Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment

“…Interleukin-2 and interleukin-12 ( ): IL-2 is mainly produced by CD4+ helper T-cells [ 58 , 72 ] and NK cells [ 57 ]. Moreover, IL-12 is secreted by helper T-cells, cytotoxic cells, dendritic cells, and macrophages [ 18 , 43 , 57 ]. As both IL-2 and IL-12 have the same functionalities, we combine them into one variable, such as .…”

“…Since vascular endothelial growth factor (VEGF) helps in angiogenesis in tumors, another study by Sharma et al studied the effectiveness of the VEGF receptor 2 (VEGFR2) inhibitor in renal cell carcinoma (RCC) patients and found that an inhibitor compound named SCHEMBL469307 is the most effective [ 15 ]. In addition, complex data-driven mathematical models of other cancers, such as breast cancer, osteosarcoma, and colon cancer, were developed by Mohammad Mirzaei et al, Kirshtein et al, and Le et al to investigate the interactions between the important immune cells and cytokines involving many key cells and molecules corresponding to the particular type of cancer and found that the interactions between the cells and molecules are important to understand the dynamics of cancer growth [ 16 , 17 , 18 ].…”

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

“…At the same time, mathematical modeling of cancer development and tumor micro-environment offers insights and can be used in discovering new treatments [ 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ]. As the complex spatial cell-to-cell interactions in the tumor micro-environment has attracted many experimental studies, a more thorough mathematical model can help scientists gain a better insight into the mechanisms of cancer growth.…”