Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression

Kodwo Annan

doi:doi:10.11648/j.ijssam.20190401.11

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Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression

Kodwo Annan

Published in International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 1)

Received: 31 January 2019 Accepted: 18 March 2019 Published: 3 April 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.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 1)
DOI	10.11648/j.ijssam.20190401.11
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), 2019. Published by Science Publishing Group

Keywords

Breast Cancer, Immune System, Mathematical Model

References

[1]	Siegel, RL, Miller, KD, Jemal, A. Cancer statistics, 2019. CA Cancer J Clin. 2019; 68:7–30. doi:10.3322/caac.21442.
[2]	Loi S. Tumor-infiltrating lymphocytes, breast cancer subtypes and therapeutic efficacy. Oncoimmunology. 2013; 2(7):e24720.
[3]	Heidi Dritschel, Sarah L. Waters, Andreas Roller & Helen M. Byrne (2018). A mathematical model of cytotoxic and helper T cell interactions in a tumour microenvironment, Letters in Biomathematics, 5:sup1, S36-S68, DOI: 10.1080/23737867.2018.1465863
[4]	Denkert C, Loibl S, Noske A, et al. Tumor-associated lymphocytes as an independent predictor of response to neoadjuvant chemotherapy in breast cancer. J Clin Oncol. 2010; 28(1):105-113.
[5]	Gu-Trantien C, Loi S, Garaud S, et al. CD4⁺ follicular helper T cell infiltration predicts breast cancer survival. J Clin Invest. 2013; 123(7):2873-2892.
[6]	Loi S, Sirtaine N, Piette F, et al. Prognostic and predictive value of tumor-infiltrating lymphocytes in a phase III randomized adjuvant breast cancer trial in nodepositive breast cancer comparing the addition of docetaxel to doxorubicin with doxorubicin-based chemotherapy: BIG 02-98. J Clin Oncol. 2013; 31(7):860-867.
[7]	Loi S. Tumor-infiltrating lymphocytes, breast cancer subtypes and therapeutic efficacy. Oncoimmunology. 2013; 2(7):e24720.
[8]	Quinonez J, Dasu N, Qureshi M. A Mathematical Investigation on Tumor-Immune Dynamics: The Impact of Vaccines on the Immune Response. J Cancer Sci Ther 2017 9: 675-682. doi:10.4172/1948-5956.1000491
[9]	Benedetti, R., Dell'Aversana, C., Giorgio, C., Astorri, R., & Altucci, L. (2017). Breast Cancer Vaccines: New Insights. Frontiers in endocrinology, 8, 270. doi:10.3389/fendo.2017.00270.
[10]	Baraka A, Borai M, Hesam M, Almalky M. Study of T-regulatory cells in patients with acute, idiopathic thrombocytopenic purpura. Egyptian J Haematol. 2014 39: 37.
[11]	Gu-Trantien C, Loi S, Garaud S, et al. CD4⁺ follicular helper T cell infiltration predicts breast cancer survival. J Clin Invest. 2013; 123(7):2873-2892.
[12]	Fridman WH, Galon J, Pages F, Tartour E, Sautes-Fridman C, Kroemer G. Prognostic and predictive impact of intra- and peritumoral immune infiltrates. Cancer Res. 2011; 71(17): 5601-5605.
[13]	Slichter SJ, Bolgiano D, Corson J, Jones MK, Christoffel T. Extended storage of platelet-rich plasma-prepared platelet concentrates in plasma or Plasmalyte. Transfusion. 2010; 50(10):2199-2209.
[14]	West NR, Milne K, Truong PT, Macpherson N, Nelson BH, Watson PH. Tumor-infiltrating lymphocytes predict response to anthracycline-based chemotherapy in estrogen receptor-negative breast cancer. Breast Cancer Res. 2011; 13(6):R126.
[15]	Yamaguchi R, Tanaka M, Yano A, et al. Tumor-infiltrating lymphocytes are important pathologic predictors for neoadjuvant chemotherapy in patients with breast cancer. Hum Pathol. 2012; 43(10):1688-1694.
[16]	Lee HJ, Seo J-Y, Ahn J-H, Ahn S-H, Gong G. Tumor-associated lymphocytes predict response to neoadjuvant chemotherapy in breast cancer patients. J Breast Cancer. 2013; 16(1):32-39.
[17]	Ono M, Tsuda H, Shimizu C, et al. Tumor-infiltrating lymphocytes are correlated with response to neoadjuvant chemotherapy in triple-negative breast cancer. Breast Cancer Res Treat. 2012; 132(3):793-805.
[18]	Issa-Nummer Y, Darb-Esfahani S, Loibl S, et al. Prospective validation of immunological infiltrate for prediction of response to neoadjuvant chemotherapy in HER2-negative breast cancer—a substudy of the neoadjuvant GeparQuinto trial. PLoS One. 2013; 8(12):e79775.
[19]	Salgado R, Denkert C, Demaria S, et al. The evaluation of tumor-infiltrating lymphocytes (TILs) in breast cancer: recommandations by an international TILs working group 2014. Ann Oncol. 2015; 26(2):259-271.
[20]	Ono M, Tsuda H, Shimizu C, et al. Tumor-infiltrating lymphocytes are correlated with response to neoadjuvant chemotherapy in triple-negative breast cancer. Breast Cancer Res Treat. 2012; 132(3):793-805.
[21]	Issa-Nummer Y, Darb-Esfahani S, Loibl S, et al. Prospective validation of immunological infiltrate for prediction of response to neoadjuvant chemotherapy in HER2-negative breast cancer—a substudy of the neoadjuvant GeparQuinto trial. PLoS One. 2013; 8(12):e79775.
[22]	Salgado R, Denkert C, Demaria S, et al. The evaluation of tumor-infiltrating lymphocytes (TILs) in breast cancer: recommandations by an international TILs working group 2014. Ann Oncol. 2015; 26(2):259-271.
[23]	Ladoire S, Arnould L, Apetoh L, et al. Pathologic complete response to neoadjuvant chemotherapy of breast carcinoma is associated with the disappearance of tumor-infiltrating foxp3 regulatory T cells. Clin Cancer Res. 2008; 14(8):2413-2420.
[24]	Hodi FS, O’Day SJ, McDermott DF, et al. Improved survival with ipilimumab in patients with metastatic melanoma. N Engl J Med. 2010; 363(8):711-723.
[25]	Loi S, Michiels S, Salgado R, et al. Tumor infiltrating lymphocytes are prognostic in triple negative breast cancer and predictive for trastuzumab benefit in early breast cancer: results from the FinHER trial. Ann Oncol. 2014; 25(8):1544-1550.
[26]	Adams S, Gray RJ, Demaria S, et al. Prognostic value of tumor-infiltrating lymphocytes in triple-negative breast cancers from two phase III randomized adjuvant breast cancer trials: ECOG 2197 and ECOG 1199. J Clin Oncol. 2014; 32(27):2959-2966.
[27]	Dieci MV, Criscitiello C, Goubar A, et al. Prognostic value of tumor-infiltrating lymphocytes on residual disease after primary chemotherapy for triple-negative breast cancer: a retrospective multicenter study. Ann Oncol. 2014; 25(3):611-618.
[28]	Azim HA Jr, Vingiani A, Peccatori F, Viale G, Loi S, Pruneri G. Tumour infiltrating lymphocytes (TILs) in breast cancer during pregnancy. Breast. 2015; S0960- 9776(15)00010-7.
[29]	Nagalla S, Chou JW, Willingham MC, et al. Interactions between immunity, proliferation and molecular subtype in breast cancer prognosis. Genome Biol. 2013; 14(4):R34.
[30]	Mittendorf EA, Peoples GE. Injecting hope – a review of breast cancer vaccines. Oncology (Williston Park) (2016) 30(5):475–81.
[31]	Perez EA, Thompson EA, Ballman KV, et al. Genomic analysis reveals that immune function genes are strongly linked to clinical outcome in the north central cancer treatment group n9831 adjuvant trastuzumab trial. J Clin Oncol. 2015; 33(7):701-708.
[32]	Adnan Aydiner, Systemic Treatment of HER2-Overexpressing Metastatic Breast Cancer, Breast Cancer, 10.1007/978-3-319-96947-3_23, (509-531), (2018).
[33]	Cui N, Shi J, Yang C. HER2-Based Immunotherapy for Breast Cancer. Cancer Biother Radiopharm. 2018 Jun; 33(5):169-175. Epub 2018 Jun 6.
[34]	Seliger B, Steven A: The role of immune escape and immune cell infiltration in breast cancer. Breast Care 2018; 13:DOI:10.1159/000486585.
[35]	Schütz F, Marmé F, Domschke C, Sohn C, von Au A: Immunooncology in breast cancer: active and passive vaccination strategies. Breast Care 2018; 13:DOI: 10.1159/000486330
[36]	Lehmann BD, Bauer JA, Chen X, et al. Identification of human triple-negative breast cancer subtypes and preclinical models for selection of targeted therapies. J Clin Invest. 2011; 121(7):2750-2767.
[37]	Gu-Trantien C, Loi S, Garaud S, et al. CD4⁺ follicular helper T cell infiltration predicts breast cancer survival. J Clin Invest. 2013; 123(7):2873-2892.
[38]	Hiraoka, K. , Miyamoto, M. , Cho, Y. , Suzuoki, M. , Oshikiri, T. , Nakakubo, Y. , Katoh, H. Concurrent infiltration by CD8+ T cells and CD4+ T cells is a favourable prognostic factor in non-small-cell lung carcinoma. British Journal of Cancer, 2006, 94 (2), 275–280.
[39]	Rad, F. , Ajdary, S. , Omranipour, R. , Alimohammadian, M. ,& Hassan, Z. Comparative analysis of CD4+ and CD8+ T cells in tumor tissues, Lymph nodes and the peripheral blood from patients with breast cancer. Iranian Biomedical Journal, 2015, 19 (1), 35.
[40]	Badoual, C. , Hans, S. , Rodriguez, J. , Peyrard, S. , Klein, C. , Agueznay, N. E. H. , ... Gey, A. Prognostic value of tumor-infiltrating CD4+ T-cell subpopulations in head and neck cancers. Clinical Cancer Research. 2006, 12 (2), 465–472.
[41]	Magombedze, G. , Reddy, P. , Eda, S. , & Ganusov, V. Cellular and population plasticity of helper CD4+ T cell responses. Frontiers in Physiology. 2013, 4 , 206.
[42]	Fridman, W. H. , Pages, F. , Sautes-Fridman, C. , & Galon, J. The immune contexture in human tumours: Impact on clinical outcome. Nature Reviews Cancer. 2012, 12 (4), 298–306.
[43]	Chen, D. S. , & Mellman, I.(2013). Oncology meets immunology: The cancer-immunity cycle. Immunity. 2013, 39(1), 1–10.
[44]	Magombedze, G. , Reddy, P. , Eda, S. , & Ganusov, V. (2013). Cellular and population plasticity of helper CD4+ T cell responses. Frontiers in Physiology. 2013, 4 , 206.
[45]	Cassetta, L., Cassol, E., & Poli, G. Macrophage polarisation in health and disease. TheScientificWorld JOURNAL. 2011, 11, 2391–2402.
[46]	Italiani, P., & Boraschi, D. From monocytes to M1/M2 macrophages: Phenotypical vs. functional differentiation. Frontiers in Immunology. 2014, 5, 514.
[47]	Jakeman, P. G., Hills, T. E., Fisher, K. D., & Seymour, L. W. (2015). Macrophages and their interactions with oncolytic viruses. Current Opinion in Pharmacology. 2015, 24, 23–29.
[48]	Denton, N. L., Chen, C.-Y., Scott, T. R., & Cripe, T. P. Tumour-associated macrophages in oncolytic virotherapy: Friend or foe? Biomedicines. 2016, 4, 13.
[49]	Hamilton G., Reiner A., Teleky B. et al. Natural killer cell activities of patients with breast cancer against different target cells. J Cancer Res Clin Oncol. (1988) 114:191–196.
[50]	Diefenbach A. and Raulet D. H. The innate immune response to tumors and its role in the induction of T-cell immunity, Immunological Reviews. 2002, Vol. 188 Issue1, pp 9-21.
[51]	Orange J. S. Human Natural Killer cell defiencies. Curr Opin Allergy Clin Immunol, 6:(6): (2006) 399-409.
[52]	Berrien-Elliot MM, Romee R, Fehniger TA. Improving natural killer cell cancer immunotherapy. Curr Opin Organ Transplant (2015) 20(6):671–80.10.1097/MOT.0000000000000243
[53]	Pillis L. G. and Radunskaya A. A Mathematical Tumor Model with Immune Resistance and Drug Therapy: an Optimal Control Approach. Journal of Theoretical Medicine, (2000), Vol. 3, 79-100.
[54]	Eisen M. Mathematical models in cell biology and cancer chemotherapy. Berlin: Springer -Verlag; Berlin, 1979.
[55]	Bellomo N., Preziosi L. Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Mathematical and Computer Model ling (2000) 32:41 3–52.
[56]	Coldman A. J., Goldie J. H. A stochastic model for the origin and treatment of tumors containing drug-resistant cells. Bull Math Biol. 1986; 48:27 9–92.
[57]	Eisen M. Mathematical models in cell biology and cancer chemotherapy. Berlin: Springer -Verlag; Berlin, 1979.
[58]	Bellomo N., Preziosi L. Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Mathematical and Computer Model ling (2000) 32:41 3–52.
[59]	Coldman A. J., Goldie J. H. A stochastic model for the origin and treatment of tumors containing drug-resistant cells. Bull Math Biol. 1986; 48:27 9–92.
[60]	Skipper H. E. On mathematical modeling of critical variables in cancer treatment (Goals: better understanding of the past and better planning in the future). Bull Math Biol. 1986; 48:25 3–78.
[61]	Rubinstein W. S., O'Neill S. M., Peters J. A., Rittmeyer L. J., Stadler M. P. Mathematical modeling for breast cancer risk assessment. State of the art and role in medicine. Oncology, (2002), 16(8):1082-94; discussion 1094, 1097-9.
[62]	Roe-Dale R., Isaacson D., Kupferschmid M. A Mathematical Model of Breast Cancer Treatment with CMF and Doxorubicin. Bull Math Biol. (2011) 73: 585–608
[63]	d’Onofrio A. A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235
[64]	Nagy J. D. Competition and Natural Selection in a Mathematical Model of Cancer. Bulletin of Mathematical Biology, (2004), 66, 663-687.
[65]	Thomas D. and Massague J. TGF-P directly targets cytotoxic T-cell functions during tumor evasion of immune surveillance Cancer cell 8, (2005) 369-380.
[66]	De Pillis LG, Radunskaya AE, Wiseman CL. A validated mathematical model of cell mediated immune response to tumor growth. Cancer Res 2005, 65: 7950-7958.

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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://article.sciencepublishinggroup.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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Kodwo Annan

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

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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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ACS 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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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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

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  -

Copy | Download