International Journal of Systems Science and Applied Mathematics

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Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression

Received: Jan. 31, 2019    Accepted: Mar. 18, 2019    Published: Apr. 03, 2019
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Abstract

Mathematical model that allowed qualitative and quantitative description of the interactions between the host immune system, breast cancer cells, and a cancer vaccine was presented with a system of differential equations. Key immune components used in the vaccine were cytotoxic T lymphocytes (CTLs), macrophages, Natural Killer (NK) and helper T cells. The parameters of the model were based on experimental and clinical results from published articles. MATLAB software tool was used to generate data from the model and results were analyzed and discussed. Findings supported clinical studies that maximum immune activation was needed to reduce the cancer cells. Thus, for a given breast cancer growth rate, there was an optimal activation that maximized the response of the immune system. It was also observed that given a sufficiently high rate of CTLs, natural killer, or helper T cells infiltration resulted in significant tumor elimination. However, varying CTLs and Macrophages activation rates caused a chaotic behavior of the tumor. Thus, optimizing large M1:M2 ratios verses large/small numbers of tumor-infiltrating macrophages on long term patient survival were necessary in improving breast cancer therapies.

DOI 10.11648/j.ijssam.20190401.11
Published in International Journal of Systems Science and Applied Mathematics ( Volume 4, Issue 1, March 2019 )
Page(s) 1-12
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Breast Cancer, Immune System, Mathematical Model

References
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    Kodwo Annan. (2019). Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression. International Journal of Systems Science and Applied Mathematics, 4(1), 1-12. https://doi.org/10.11648/j.ijssam.20190401.11

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    Kodwo Annan. Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression. Int. J. Syst. Sci. Appl. Math. 2019, 4(1), 1-12. doi: 10.11648/j.ijssam.20190401.11

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    AMA Style

    Kodwo Annan. Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression. Int J Syst Sci Appl Math. 2019;4(1):1-12. doi: 10.11648/j.ijssam.20190401.11

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  • @article{10.11648/j.ijssam.20190401.11,
      author = {Kodwo Annan},
      title = {Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {4},
      number = {1},
      pages = {1-12},
      doi = {10.11648/j.ijssam.20190401.11},
      url = {https://doi.org/10.11648/j.ijssam.20190401.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijssam.20190401.11},
      abstract = {Mathematical model that allowed qualitative and quantitative description of the interactions between the host immune system, breast cancer cells, and a cancer vaccine was presented with a system of differential equations. Key immune components used in the vaccine were cytotoxic T lymphocytes (CTLs), macrophages, Natural Killer (NK) and helper T cells. The parameters of the model were based on experimental and clinical results from published articles. MATLAB software tool was used to generate data from the model and results were analyzed and discussed. Findings supported clinical studies that maximum immune activation was needed to reduce the cancer cells. Thus, for a given breast cancer growth rate, there was an optimal activation that maximized the response of the immune system. It was also observed that given a sufficiently high rate of CTLs, natural killer, or helper T cells infiltration resulted in significant tumor elimination. However, varying CTLs and Macrophages activation rates caused a chaotic behavior of the tumor. Thus, optimizing large M1:M2 ratios verses large/small numbers of tumor-infiltrating macrophages on long term patient survival were necessary in improving breast cancer therapies.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression
    AU  - Kodwo Annan
    Y1  - 2019/04/03
    PY  - 2019
    N1  - https://doi.org/10.11648/j.ijssam.20190401.11
    DO  - 10.11648/j.ijssam.20190401.11
    T2  - International Journal of Systems Science and Applied Mathematics
    JF  - International Journal of Systems Science and Applied Mathematics
    JO  - International Journal of Systems Science and Applied Mathematics
    SP  - 1
    EP  - 12
    PB  - Science Publishing Group
    SN  - 2575-5803
    UR  - https://doi.org/10.11648/j.ijssam.20190401.11
    AB  - Mathematical model that allowed qualitative and quantitative description of the interactions between the host immune system, breast cancer cells, and a cancer vaccine was presented with a system of differential equations. Key immune components used in the vaccine were cytotoxic T lymphocytes (CTLs), macrophages, Natural Killer (NK) and helper T cells. The parameters of the model were based on experimental and clinical results from published articles. MATLAB software tool was used to generate data from the model and results were analyzed and discussed. Findings supported clinical studies that maximum immune activation was needed to reduce the cancer cells. Thus, for a given breast cancer growth rate, there was an optimal activation that maximized the response of the immune system. It was also observed that given a sufficiently high rate of CTLs, natural killer, or helper T cells infiltration resulted in significant tumor elimination. However, varying CTLs and Macrophages activation rates caused a chaotic behavior of the tumor. Thus, optimizing large M1:M2 ratios verses large/small numbers of tumor-infiltrating macrophages on long term patient survival were necessary in improving breast cancer therapies.
    VL  - 4
    IS  - 1
    ER  - 

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  • School of Science and Technology, Georgia Gwinnett College, Lawrenceville, USA

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