The Power of the Tumor Microenvironment: A Systemic Approach for a Systemic Disease

  • Irina Kareva
  • Kathleen P. Wilkie
  • Philip HahnfeldtEmail author
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Cancer is increasingly recognized as not solely a disease of the genes and chromosomes but as a systemic disease that affects numerous components of the host including blood vessel formation, immune cell function, and nutrient recycling. This review summarizes a variety of time-dependent mathematical models that focus on the consequences of tumor growth within an evolving microenvironment, represented by a dynamic carrying capacity. Transcending the specifics of each model, their overview reveals that the key to tumor control really lies in controlling the support furnished the tumor by its microenvironment.


Tumor microenvironment Mathematical modeling Cancer systems biology Tumor-promoting inflammation Metronomic chemotherapy 


  1. 1.
    V.T. DeVita Jr., T.S. Lawrence, S.A. Rosenberg (eds.), DeVita, Hellman, and Rosenberg’s Cancer: Principles and Practice of Oncology, 9th edn. (Lippincott, Williams & Wilkins, Philadelphia, 2011)Google Scholar
  2. 2.
    I. Kareva, What can ecology teach us about cancer? Transl. Oncol. 4(5), 266–270 (2011)CrossRefGoogle Scholar
  3. 3.
    K.E. deVisser, A. Eichten, L.M. Coussens, Paradoxical roles of the immune system during cancer development. Nat. Rev. Cancer 6(1), 24–37 (2006)Google Scholar
  4. 4.
    J. Folkman, Tumor angiogenesis: therapeutic implications. New Engl. J. Med. 285(21), 1182–1186 (1971)CrossRefGoogle Scholar
  5. 5.
    M.S. O’Reilly, T. Boehm, Y. Shing, N. Fukai, G. Vasios, W.S. Lane et al., Endostatin: an endogenous inhibitor of angiogenesis and tumor growth. Cell 88, 277–285 (1997)CrossRefGoogle Scholar
  6. 6.
    P. Hahnfeldt, D. Panigraphy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59(19), 4770–4775 (1999)Google Scholar
  7. 7.
    S.I. Grivennikov, F.R. Greten, M. Karin, Immunity, inflammation, and cancer. Cell 140(6), 883–899 (2010)CrossRefGoogle Scholar
  8. 8.
    M.J. Thun, S.J. Henley, C. Patrono, Nonsteroidal anti-inflammatory drugs as anticancer agents: mechanistic, pharmacologic, and clinical issues. J. Natl. Cancer Inst. 94(4), 252–266 (2002)CrossRefGoogle Scholar
  9. 9.
    M. Boersma, J.J. Elser, Too much of a good thing: on stoichiometrically balanced diets and maximal growth. Ecology 87(5), 1325–1330 (2006)CrossRefGoogle Scholar
  10. 10.
    J. Elser, Biological stoichiometry: a chemical bridge between ecosystem ecology and evolutionary biology. Am. Nat. 168(Suppl 6), S25–S35 (2006)CrossRefGoogle Scholar
  11. 11.
    J.J. Elser, J.D. Nagy, Y. Kuang, Biological stoichiometry: an ecological perspective on tumor dynamics. Bioscience 53(11), 1112–1120 (2003)CrossRefGoogle Scholar
  12. 12.
    A.K. Laird, Dynamics of tumor growth. Br. J. Cancer 18(3), 490–502 (1964)CrossRefGoogle Scholar
  13. 13.
    C. DeLisi, A. Rescigno, Immune surveillance and neoplasia–1 a minimal mathematical model. Bull. Math. Biol. 39(2), 201–221 (1977)MathSciNetzbMATHGoogle Scholar
  14. 14.
    V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, A.S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. 56(2), 295–321 (1994)CrossRefzbMATHGoogle Scholar
  15. 15.
    D. Kirschner, J.C. Panetta, Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol. 37(3), 235–252 (1998)CrossRefzbMATHGoogle Scholar
  16. 16.
    L.G. de Pillis, A.E. Radunskaya, C.L. Wiseman, A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res. 65(17), 7950–7958 (2005)Google Scholar
  17. 17.
    A. d’Onofrio, A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Physica D 208(3–4), 220–235 (2005)Google Scholar
  18. 18.
    A. Cappuccio, M. Elishmereni, Z. Agur, Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model. Cancer Res. 66(14), 7293–7300 (2006)CrossRefGoogle Scholar
  19. 19.
    R. Eftimie, J.L. Bramson, D.J. Earn, Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull. Math. Biol. 73(1), 2–32 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    K.P. Wilkie, A review of mathematical models of cancer-immune interactions in the context of tumor dormancy. Adv. Exp. Med. Biol. 734, 201–234 (2013). doi:10.1007/978-1-4614-1445-2_10CrossRefGoogle Scholar
  21. 21.
    R. Lefever, W. Horsthemke, Bistability in fluctuating environments. implications in tumor immunology. Bull. Math. Biol. 41, 469–490 (1979)Google Scholar
  22. 22.
    A. d’Onofrio, Bounded-noise-induced transitions in a tumor-immune system interplay. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(2), 021923, 1–7 (2010)Google Scholar
  23. 23.
    A. d’Onofrio, A. Ciancio, Simple biophysical model of tumor evasion from immune system control. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 84(3), 031910 (2011). doi:10.1103/PhysRevE.84.031910Google Scholar
  24. 24.
    K.P. Wilkie, P. Hahnfeldt, Mathematical models of immune-induced cancer dormancy and the emergence of immune evasion. Interface Focus 3, 20130010 (2013)CrossRefGoogle Scholar
  25. 25.
    A. Matzavinos, M.A.J. Chaplain, V.A. Kuznetsov, Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. Math. Med. Biol. 21(1), 1–34 (2004)CrossRefzbMATHGoogle Scholar
  26. 26.
    T. Roose, S.J. Chapman, R.K. Maini Mathematical models of avascular tumor growth. SIAM Rev. 49(2), 179–208 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    H. Enderling, L. Hlatky, P. Hahnfeldt, Immunoediting: evidence of the multifaceted role of the immune system in self-metastatic tumor growth. Theor. Biol. Med. Model. 9, 31 (2012). doi:10.1186/1742-4682-9-31CrossRefGoogle Scholar
  28. 28.
    T. Takayanagi, H. Kawamura, A. Ohuchi, Cellular automaton model of a tumor tissue consisting of tumor cells, cytotoxic T lymphocytes (CTLs), and cytokine produced by CTLs. IPSJ Trans. Math. Model. Appl. 47(1),61–67 (2006). doi:10.2197/ipsjdc.2.138Google Scholar
  29. 29.
    A. d’Onofrio, A. Gandolfi, Tumor eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999). Bath Biosci. 191(2), 159–184 (2004)Google Scholar
  30. 30.
    A. d’Onofrio, A. Gandolfi, A family of models of angiogenesis and antiangiogenesis anti-cancer therapy. Math. Med. Biol. 26(1), 63–95 (2009)Google Scholar
  31. 31.
    U. Ledzewicz, H. Schättler, Antiangiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Control Optim. 46(3), 1052–1079 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    U. Ledzewicz, H. Schättler, Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. J. Theor. Biol. 252(2), 295–312 (2008)CrossRefGoogle Scholar
  33. 33.
    U. Ledzewicz, A. d’Onofrio, H. Schättler, Tumor development under combination treatments with anti-angiogenic therapies, in Mathematical Methods and Models in Biomedicine, ed. by U. Ledzewicz, H. Schättler, A. Friedman, E. Kashdan. Lecture Notes on Mathematical Modeling in the Life Sciences (Springer, Heidelberg, 2012), pp. 301–327Google Scholar
  34. 34.
    S. Benzekry, G. Chapuisat, J. Ciccolini, A. Erlinger, F. Hubert, A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology. C. R. Math. Acad. Sci. Paris 350(1–2), 23–28 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    T.L. Jackson, Vascular tumor growth and treatment: consequences of polyclonality, competition and dynamic vascular support. J. Math. Biol. 44(3), 201–226 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    S. Benzekr, Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis. J. Evol. Equat. 11(1), 187–213 (2010)Google Scholar
  37. 37.
    K.P. Wilkie, P. Hahfeldt, Tumor-immune dynamics regulated in the microenvironment inform the transient nature of immune-induced tumor dormancy. Cancer Res. 73(12), 3534–3544 (2013)CrossRefGoogle Scholar
  38. 38.
    G.N. Naumov, E. Bender, D. Zurakowski, S.Y. Kang, D. Sampson, E. Flynn et al., A model of human tumor dormancy: an angiogenic switch from the nonangiogenic phenotype. J. Natl. Cancer Inst. 98(5), 316–325 (2006)CrossRefGoogle Scholar
  39. 39.
    M. Hu, J. Yao, D.K. Carroll, S. Weremowicz, H. Chen, D. Carrasco et al., Regulation of in situ to invasive breast carcinoma transition. Cancer Cell 13(5), 394–406 (2008)CrossRefGoogle Scholar
  40. 40.
    H. Withers, Treatment-induced accelerated human tumor growth. Semin. Radiat. Oncol. 3(2), 135–143 (1993)CrossRefGoogle Scholar
  41. 41.
    S.Y. El Sharouni, H.B. Kal, J.J. Battermann, Accelerated regrowth of non-small-cell lung tumours after induction chemotherapy. Br. J. Cancer 89(12), 2184–2189 (2003)CrossRefGoogle Scholar
  42. 42.
    S. Kraus, N. Arber, Inflammation and colorectal cancer. Curr. Opin. Pharmacol. 9(4), 405–410 (2009)CrossRefGoogle Scholar
  43. 43.
    A. Mantovani, P. Romero, A.K. Palucka, F.M. Marincola, Tumour immunity: effector response to tumour and role of the microenvironment. Lancet 371(9614), 771–783 (2008)CrossRefGoogle Scholar
  44. 44.
    F.R. Balkwill, L.M. Coussens, Cancer: an inflammatory link. Nature 431(7007), 405–406 (2004)CrossRefGoogle Scholar
  45. 45.
    J. Condeelis, J.W. Pollard, Macrophages: obligate partners for tumor cell migration, invasion, and metastasis. Cell 124(2), 263–266 (2006)CrossRefGoogle Scholar
  46. 46.
    D. Nelson, R. Ganss, Tumor growth or regression: powered by inflammation. J. Leukocyte Biol. 80(4), 685–690 (2006)CrossRefGoogle Scholar
  47. 47.
    K.P. Wilkie, P. Hahnfeldt, Modeling the dichotomy of the immune response to cancer: cytotoxic effects and tumor-promoting inflammation (2013). ArXiv:1305.3634Google Scholar
  48. 48.
    J.D. Wolchok, A. Hoos, S. O’Day, J.S. Weber, O. Hamid, C. Lebbé et al., Guidelines for the evaluation of immune therapy activity in solid tumors: immune-related response criteria. Clin. Cancer Res. 15(23), 7412–7420 (2009)CrossRefGoogle Scholar
  49. 49.
    H. Jin, C. Xu, H. Lim, S. Park, J. Shin, Y. Chung et al., High dietary inorganic phosphate increases lung tumorigenesis and alters AKT signaling. Am. J. Respir. Crit. Care Med. 179(1), 59–68 (2009)CrossRefGoogle Scholar
  50. 50.
    J.J. Elser, M.M. Kyle, M.S. Smith, J.D. Nagy, Biological stoichiometry in human cancer. PLoS ONE 2(10), e1028 (2007). doi:10.1371/journal.pone.0001028CrossRefGoogle Scholar
  51. 51.
    Y. Kuang, J.D. Nagy, J.J. Elser, Biological stoichiometry of tumor dynamics: mathematical models and analysis. Discrete Contin. Dyn. B 4(1), 221–240 (2004)MathSciNetzbMATHGoogle Scholar
  52. 52.
    I. Kareva, Biological stoichiometry in tumor micro-environments. PLoS ONE 8(1), e51844 (2013)Google Scholar
  53. 53.
    S.M. Gapstur, M.J. Thun, Progress in the war on cancer. J. Am. Med. Assoc. 303(11), 1084–1085 (2010)CrossRefGoogle Scholar
  54. 54.
    J.M.L. Ebos, R.S. Kerbel, Antiangiogenic therapy: impact on invasion, disease progression, and metastasis. Nat. Rev. Clin. Oncol. 8(4), 210–221 (2011)CrossRefGoogle Scholar
  55. 55.
    L. Bello, G. Carrabba, C. Giussani, V. Lucini, F. Ceruutti, F. Scaglione et al., Low-dose chemotherapy combined with an antiangiogenic drug reduces human glioma growth in vivo. Cancer Res. 61(20), 7501–7506 (2001)Google Scholar
  56. 56.
    P. Hahnfeldt, J. Folkman, L.R. Hlatky, Minimizing long-term tumor burden: the logic for metronomic chemotherapeutic dosing and its antiangiogenic basis. J. Theor. Biol. 220, 545–554 (2003)CrossRefGoogle Scholar
  57. 57.
    J.C. Doloff, D.J. Waxman, VEGF receptor inhibitors block the ability of metronomically dosed cyclophosphamide to activate innate immunity-induced tumor regression. Cancer Res. 72(5), 1103–1115 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Irina Kareva
    • 1
  • Kathleen P. Wilkie
    • 1
  • Philip Hahnfeldt
    • 1
    Email author
  1. 1.Center of Cancer Systems Biology, GeneSys Research InstituteTufts University School of MedicineBostonUSA

Personalised recommendations