Modeling the stem cell hypothesis: Investigating the effects of cancer stem cells and TGF−β on tumor growth

Samantha L Elliott; Emek Kose; Allison L Lewis; Anna E Steinfeld; Elizabeth A Zollinger; Samantha L Elliott; Emek Kose; Allison L Lewis; Anna E Steinfeld; Elizabeth A Zollinger

doi:10.3934/mbe.2019360

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7177-7194. doi: 10.3934/mbe.2019360

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Modeling the stem cell hypothesis: Investigating the effects of cancer stem cells and TGF−β on tumor growth

1.
Department of Biology, St. Mary’s College of Maryland, 47645 College Drive, St. Mary’s City, MD 20686, USA
2.
Department of Mathematics and Computer Science, St. Mary’s College of Maryland, 47645 College Drive, St. Mary’s City, MD 20686, USA
3.
Department of Mathematics, Lafayette College, 730 High Street, Easton, PA 18042, USA
4.
National Cancer Institute, 9000 Rockville Pike Bethesda, MD 20892, USA
5.
Department of Mathematics and Computer Science, St. Joseph’s College, 245 Clinton AVE, Brooklyn, NY 11205, USA

Received: 31 March 2019 Accepted: 08 July 2019 Published: 07 August 2019

We propose a mathematical model to describe the interaction of cancer stem cells, tumor cells, and the immune system in order to better understand tumor growth in the presence of cancer stem cells. We consider the system in two scenarios: with no-treatment and with a chemotherapy treatment regimen. We develop a system of differential equations, fit the parameters to experimental data, and perform sensitivity and stability analysis. The model simulations show that the tumor cells grow as predicted with no-treatment and that with chemotherapy, which targets only the tumor cells, the cancer will eventually relapse. As chemotherapy does not target the cancer stem cells, we conclude that the tumor cells recover due to the presence of cancer stem cells.
- mathematical oncology,
- cancer stem cell,
- chemotherapy,
- transforming growth factor,
- mathematical model
Citation: Samantha L Elliott, Emek Kose, Allison L Lewis, Anna E Steinfeld, Elizabeth A Zollinger. Modeling the stem cell hypothesis: Investigating the effects of cancer stem cells and TGF−β on tumor growth[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7177-7194. doi: 10.3934/mbe.2019360

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Abstract

We propose a mathematical model to describe the interaction of cancer stem cells, tumor cells, and the immune system in order to better understand tumor growth in the presence of cancer stem cells. We consider the system in two scenarios: with no-treatment and with a chemotherapy treatment regimen. We develop a system of differential equations, fit the parameters to experimental data, and perform sensitivity and stability analysis. The model simulations show that the tumor cells grow as predicted with no-treatment and that with chemotherapy, which targets only the tumor cells, the cancer will eventually relapse. As chemotherapy does not target the cancer stem cells, we conclude that the tumor cells recover due to the presence of cancer stem cells.

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