Numerical Experiments for Mammary Adenocarcinoma Cell Progression


We have analyzed cell culture and animal and mathematical models for the investigation of mammary carcinoma progression. The development and characterization of a progressive series of C3(1)/Tag mammary carcinoma cell lines have been described by means of integro-differential equations of Boltzmann type. The numerical approximations to the solutions of the proposed mathematical model have shown a good agreement with the laboratory data of the tumor growth rates.


Invasive Lobular Carcinoma Mammary Adenocarcinoma Normal Mammary Tissue Mammary Adenocarcinoma Cell Tumorigenic Cell Line 
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  1. [ArBeAnLa03]
    Arlotti, L., Bellomo, N., De Angelis, E., Lachowicz, M.: Generalized Kinetic Models in Applied Sciences, Series on Advances in Mathematics for Applied Sciences, 64, World Scientific Publishing Co., Inc., River Edge, NJ, xii+199 (2003). Google Scholar
  2. [ArBaClEl04]
    Arpino, G., Bardou, V.J., Clark, G.M., Elledge, R.M.: Infiltrating lobular carcinoma of the breast: tumor characteristics and clinical outcome. Breast Cancer Research, 6, 149–156 (2004). CrossRefGoogle Scholar
  3. [BeFo94]
    Bellomo, N., Forni, G.: Dynamics of tumor interaction with the host immune system. Math. Comput. Modelling, 20, 107–122 (1994). MATHCrossRefGoogle Scholar
  4. [BeBe06]
    Bellomo, N., Bellouquid, A.: On the mathematical kinetic theory of active particles with discrete states. The derivation of macroscopic equations. Math. Comput. Modelling, 44, 397–404 (2006). MathSciNetMATHCrossRefGoogle Scholar
  5. [BeSl06]
    Bellomo, N., Sleeman, B.: Preface in: Multiscale Cancer Modelling. Comput. Math. Meth. Med., (special issue) 20, 67–70 (2006). MathSciNetCrossRefGoogle Scholar
  6. [BeMa06]
    Bellomo, N., Maini, P.: Preface in: Cancer Modelling (II). Math. Models Methods Appl. Sci., (special issue) 16, n. 7b, iii–vii (2006). MathSciNetGoogle Scholar
  7. [Be07]
    Bellomo, N.: Modelling Complex Living Systems, Birkhäuser, Boston (2007). Google Scholar
  8. [BeLiMa08]
    Bellomo, N., Li, N.K., Maini, P.K.: On the foundations of cancer modelling: selected topics, speculations, and perspectives. Math. Models Methods Appl. Sci., 18, 593–646 (2008). MathSciNetMATHCrossRefGoogle Scholar
  9. [BeDe08]
    Bellomo, N., Delitala, M.: From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Physics of Life Reviews, 5, 183–206 (2008). CrossRefGoogle Scholar
  10. [BeDe06]
    Bellouquid, A., Delitala, M.: Modelling Complex Biological Systems – A Kinetic Theory Approach, Birkhäuser, Boston (2006). Google Scholar
  11. [BCF]
    Breast Cancer Facts & Figures 2009–2010. American Cancer Society, Inc., Atlanta. Google Scholar
  12. [Ca02]
    Calvo, A., Xiao, N., Kang, J., Best, C.J.M., Leiva, I., Emmert-Buck, M.R., Jorcyk, C., Green, J.E.: Alterations in gene expression profiles during prostate cancer progression: functional correlations to tumorigenicity and down-regulation of selenoprotein-P in mouse and human tumors. Cancer Research, 62, 5325–5335 (2002). Google Scholar
  13. [CoChLe94]
    Cox, L.A., Chen, G., Lee, E.Y.: Tumor suppressor genes and their roles in breast cancer. Breast Cancer Research Treat, 32, 19–38 (1994). CrossRefGoogle Scholar
  14. [AnLo08]
    De Angelis, E., Lodz, B.: On the kinetic theory for active particles: A model for tumor-immune system competition. Math. Comput. Modelling, 47, 196–209 (2008). MathSciNetMATHCrossRefGoogle Scholar
  15. [LiSaBe07]
    De Lillo, S., Salvatori, M.C., Bellomo, N.: Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity. Math. Comput. Modelling, 45, 564–578 (2007). MathSciNetMATHCrossRefGoogle Scholar
  16. [DrKoMaZu10]
    Drucis, K., Kolev, M., Majda, W., Zubik-Kowal, B.: Nonlinear modeling with mammographic evidence of carcinoma, Nonlinear Anal. Real World Appl., 11, 4326–4334 (2010). MathSciNetMATHCrossRefGoogle Scholar
  17. [DyBuWhHaH89]
    Dyson, N., Buchkovich, K., Whyte, P., Harlow, E.: The cellular 107K protein that binds to adenovirus E1A also associates with the large T antigens of SV40 and JC virus. Cell, 58, 249–255 (1989). CrossRefGoogle Scholar
  18. [Ge00]
    Green, J.E., Shibata, M., Yoshidome, K., Liu, M., Jorcyk, C.L., Anver, M.R., Wigginton, J.M., Wiltrout, R., Shibata, E., Kaczmarczyk, S., Wang, W., Liu, Z., Calvo, A., Couldrey, C.: The C3(1)/SV40 T-antigen transgenic mouse model of mammary carncer: ductal epithelial cell targeting with multistage progression to carcinoma. Oncogene, 19, 1020–1027 (2000). CrossRefGoogle Scholar
  19. [H03]
    Holzer, R.G., MacDougall, C., Cortright, G., Atwood, K., Green, J.E., Jorcyk, C.L.: Development and characterization of a progressive series of mammary adenocarcinoma cell lines derived from the C3(1)/SV40 large T-antigen transgenic mouse model. Breast Cancer Research Treat, 77, 65–76 (2003). CrossRefGoogle Scholar
  20. [Ja09]
    Jackiewicz, Z., Jorcyk, C.L., Kolev, M., Zubik-Kowal, B.: Correlation between animal and mathematical models for prostate cancer progression. Comput. Math. Methods Med., 10, 241–252 (2009). MathSciNetCrossRefGoogle Scholar
  21. [JaSe92]
    Jäger, E., Segel, L.: On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math., 52, 1442–1468 (1992). MathSciNetMATHCrossRefGoogle Scholar
  22. [Jo98]
    Jorcyk, C.L., Liu, M.L., Shibata, M.A., Maroulakou, I.G., Komschlies, K.L., McPhaul, M.J., Reseau, J.H., Green, J.E.: Development and characterization of a mouse prostate adenocarcinoma cell line: ductal formation determined by extracellular matrix. Prostate, 34, 10–22 (1998). CrossRefGoogle Scholar
  23. [Ko05]
    Kolev, M.: A mathematical model of cellular immune response to leukemia. Math. Comput. Modelling, 41, 1071–1081 (2005). MathSciNetMATHCrossRefGoogle Scholar
  24. [Ku97]
    Kuby, J.: Immunology, 3rd edition, W.H. Freeman, New York (1997). Google Scholar
  25. [LyWhFa00]
    Lydyard, P.M., Whelan, A., Fanger, M.W.: Instant Notes in Immunology, BIOS Scientific Publishers Ltd., Oxford (2000). Google Scholar
  26. [Ma94]
    Maroulakou, I.G., Anver, M., Garrett, L., Green, J.E.: Prostate and mammary adenocarcinoma in transgenic mice carrying a rat C3(1) simian virus 40 large tumor antigen fusion protein. Proc. Natl. Acad. Sci. USA, 91, 11236–11240 (1994). CrossRefGoogle Scholar
  27. [M9i2]
    Mietz, J.A., Unger, T., Huibregtse, J.M., Howly, P.M.: The transcriptional transactivation function of wild-type p53 is inhibited by SV40 large T antigen and by HPV-16 E6 oncoprotein. EMBO J., 11, 5013–5020 (1992). Google Scholar
  28. [Os91]
    Osborne, R.J., Merlo, G.R., Mitsudomi, T., Venesio, T., Liscia, D.S., Cappa, A.P., Chiba, I., Takahashi, T., Nau, M.M., Callahan, R., et al.: Mutations in the p53 gene in primary human breast cancers. Cancer Research, 51, 6194–6198 (1991). Google Scholar
  29. [Pa83]
    Parker, M.G.R., White, H., Hurst, M., Needham, M., Tilly, R.: Prostatic steroid-binding protein: isolation and characterization of C3 genes. J. Biol. Chem., 258, 12–15 (1983). Google Scholar
  30. [ScVa10]
    Schmid, M.C., Varner, J.A.: Myeloid cells in the tumor microenvironment: modulation of tumor angiogenesis and tumor inflammation. Journal of Oncology, 1–10 (2010). Google Scholar
  31. [SoshGrJo02]
    Soares, C.R., Shibata, M.A., Green, J.E., Jorcyk, C.L.: Development of PIN and prostate adenocarcinoma cell lines: a model system for multistage tumor progression. Neoplasia, 4, 112–20 (2002). CrossRefGoogle Scholar
  32. [Yo98]
    Yoshidome, K., Shibata, M., Maroulakou, I.G., Liu, M., Jorcyk, C.L., Gold, L.G., Welch, V.N., Green, J.E.: Genetic alterations in the development of mammary and prostate cancer in the C3(1)/Tag transgenic mouse model. Int. J. Oncol., 12, 449–453 (1998). Google Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Boise State UniversityBoiseUSA
  2. 2.University of Warmia and MazuryOlsztynPoland

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