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Interaction of Tumor with Its Micro-environment: A Mathematical Model

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Abstract

This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the tumor micro-environment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-β) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds, TGF-β induces fibroblasts to differentiate into myofibroblasts which secrete EGF at a larger rate than fibroblasts. We monitor the entire process in silico, in a setup which mimics experiments in a Tumor Chamber Invasion Assay, where a semi-permeable membrane coated by extracellular matrix (ECM) is placed between two chambers, one containing TECs and another containing fibroblasts. We develop a mathematical model, based on a system of PDEs, that includes the interaction between TECs, fibroblasts, myofibroblasts, TGF-β, and EGF, and we show how model parameters affect tumor progression. The model is used to generate several hypotheses on how to slow tumor growth and invasion. In an Appendix, it is proved that the mathematical model has a unique global in-time solution.

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  1. Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, 43210, USA

    Yangjin Kim & Avner Friedman

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Correspondence to Yangjin Kim.

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Y. Kim and A. Friedman are supported by the National Science Foundation upon agreement 112050.

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Kim, Y., Friedman, A. Interaction of Tumor with Its Micro-environment: A Mathematical Model. Bull. Math. Biol. 72, 1029–1068 (2010). https://doi.org/10.1007/s11538-009-9481-z

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