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

Abstract

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells’ location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells’ diffusion and immune cells’ influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes’ diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

Infantile hemangioma models: is the needle in a haystack?

“…This turns on intracellular and extracellular signaling pathways, helps hemangiomas grow in mice, and mimics the way human infantile hemangiomas grow [ 68 ]. Many studies have shown that PyMT is a key player in the growth of tumors and can cause cell death in vitro, which can lead to benign and malignant tumors in organs such as the skin, salivary gland, and mammary gland of mice [ 69 , 70 ]. Xu et al [ 71 ] made an IH animal model by microinjecting the PyMT transgenic DNA of polyomavirus into fertilized embryos, transferring them to mice that looked like they were pregnant, and observing the tumors in the newborn mice’s phenotypes and histological shapes (Fig.…”

Investigating the spatial interaction of immune cells in colon cancer

“…propose a PDE model of breast cancer progression based on PyMT-MMTV mouse data. 35 Their results show that, in the regions with more immune cells interaction, cancer population is less dense, and a constant influx of immune cells controls the tumor size and cancer population. But, they do not further investigate the patterns formed in the tumor microenvironment and the pathways responsible for them.…”

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models

“…Similar approaches have been taken in the context of cancer modeling. Mohammad Mirzaei et al extends ODE models of breast cancer and colorectal cancer to reaction-diffusion-advection models coupled with mechanical growth to investigate the effect of immune cells heterogeneity on cancer progression [15,16]. Wang et al use morphoelasticity in a simple model to investigate the effect of mechanics on tumor spheroid growth [9].…”