Mathematical modeling of tumor growth: the MCF-7 breast cancer cell line

Hsiu-Chuan Wei; Hsiu-Chuan Wei

doi:10.3934/mbe.2019325

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6512-6535. doi: 10.3934/mbe.2019325

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Mathematical modeling of tumor growth: the MCF-7 breast cancer cell line

Hsiu-Chuan Wei ^,

Department of Applied Mathematics, Feng Chia University, Seatwen, Taichung 40724, Taiwan

Received: 31 December 2018 Accepted: 04 July 2019 Published: 15 July 2019

Breast cancer is the second most commonly diagnosed cancer in women worldwide. MCF-7 cell line is an extensively studied human breast cancer cell line. This cell line expresses estrogen receptors, and the growth of MCF-7 cells is hormone dependent. In this study, a mathematical model, which governs MCF-7 cell growth with interaction among tumor cells, estradiol, natural killer (NK) cells, cytotoxic T lymphocytes (CTLs) or CD8+ T cells, and white blood cells (WBCs), is proposed. Experimental data are used to determine functional forms and parameter values. Breast tumor growth is then studied using the mathematical model. The results obtained from numerical simulation are compared with those from clinical and experimental studies. The system has three coexisting stable equilibria representing the tumor free state, a microscopic tumor, and a large tumor. Numerical simulation shows that an immune system is able to eliminate or control a tumor with a restricted initial size. A healthy immune system is able to effectively eliminate a small tumor or produces long-term dormancy. An immune system with WBC count at the low parts of the normal ranges or with temporary low NK cell count is able to eliminate a smaller tumor. The cytotoxicity of CTLs plays an important role in immune surveillance. The association between the circulating estradiol level and cancer risk is not significant.
- breast cancer,
- MCF-7 cell line,
- long-term dormancy,
- mathematical modeling,
- numerical simulation
Citation: Hsiu-Chuan Wei. Mathematical modeling of tumor growth: the MCF-7 breast cancer cell line[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6512-6535. doi: 10.3934/mbe.2019325

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Abstract

Breast cancer is the second most commonly diagnosed cancer in women worldwide. MCF-7 cell line is an extensively studied human breast cancer cell line. This cell line expresses estrogen receptors, and the growth of MCF-7 cells is hormone dependent. In this study, a mathematical model, which governs MCF-7 cell growth with interaction among tumor cells, estradiol, natural killer (NK) cells, cytotoxic T lymphocytes (CTLs) or CD8+ T cells, and white blood cells (WBCs), is proposed. Experimental data are used to determine functional forms and parameter values. Breast tumor growth is then studied using the mathematical model. The results obtained from numerical simulation are compared with those from clinical and experimental studies. The system has three coexisting stable equilibria representing the tumor free state, a microscopic tumor, and a large tumor. Numerical simulation shows that an immune system is able to eliminate or control a tumor with a restricted initial size. A healthy immune system is able to effectively eliminate a small tumor or produces long-term dormancy. An immune system with WBC count at the low parts of the normal ranges or with temporary low NK cell count is able to eliminate a smaller tumor. The cytotoxicity of CTLs plays an important role in immune surveillance. The association between the circulating estradiol level and cancer risk is not significant.

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