A Multistage Model for Tumor Progression

  • James L. Hargrove
Part of the Modeling Dynamic Systems book series (MDS)


Because cancer is among the leading causes of death in the United States and most developed societies, it is of great medical and scientific interest. In the clinic, one deals with screening, diagnosis, and treatment; however, the individual who has not developed the disease is most interested in risk reduction. In either case, knowledge about the ways that cancer can develop is important. Just as the research literature concerning cancer is immense, so too are there many different kinds of mathematical models of cancer. Among those of interest are models of cell cycle kinetics (Kimmel and Axelrod, 1991 ; Novak and Tyson, 1993), carcinogenicity (Ioannides et al., 1993), models based on tumor growth (Mehl, 1991), multistage models of tumor development (Moolgavkar and Knudson, 1981; Stein and Stein, 1990; Moolgavkar and Luebeck, 1992), and metastasis (spreading of a cancer from its site of origin; Tracqui, 1995), and models of treatment outcomes (Retsky et al., 1994; Duchting et al., 1996). Growth models have already been discussed. Here let us consider a multistage model of tumor development, because most tumors require mutations in three or more genes involved in growth control (cellular protooncogenes). The model used here is based on colon cancer, for this cancer affects men and women alike, and is known to be influenced by dietary and lifestyle-related factors.


Colon Cancer Multistage Model Adenomatous Polyposis Coli Growth Control Intermediate Cell 
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  1. Allan, S.M., and N.P.M. Sacks. “Colorectal cancer.” In: Horwich, A., ed. Oncology. A Multidisdplinary Textbook. London: Chapman and Hall, 1995, 513–528.Google Scholar
  2. American Cancer Society 1996 Advisory Committee on Diet, Nutrition, and Cancer Prevention. Guidelines on diet, nutrition, and cancer prevention—reducing the risk of cancer with healthy food choices and physical activity. CA-Cancer J. Clin. 46 (1996): 325–341.CrossRefGoogle Scholar
  3. Cho, K.R., and B. Vogelstein. “Genetic alterations in the adenoma-carcinoma sequence.” Cancer 70 (Suppl. 6, 1992): 1727–1731.CrossRefPubMedGoogle Scholar
  4. Duchting, W., W. Ulmer, and T. Ginsberg. “Cancer: a challenge for control theory and computer modelling.” Eur.J. Cancer 32A (1996): 1283–1292.CrossRefPubMedGoogle Scholar
  5. Fearon, E.R., and B. Vogelstein. “A genetic model for colorectal tumorigenesis.” Cell 61 (1990): 759–767.CrossRefPubMedGoogle Scholar
  6. Frazier, M. L. “Molecular basis of colon cancer.” In: Freireich, E.J., and S.A. Stass, eds. Molecular Basis of Oncology. Oxford: Blackwell Science Publishers, 1995 317–339.Google Scholar
  7. Ioannides, C., D.F. Lewis, and D.V. Parke. “Computer modelling in predicting carcinogenicity.” Eur.J. Cancer Prev. 2 (1993): 275–282.CrossRefPubMedGoogle Scholar
  8. Kimmel, M., and D.E. Axelrod. “Unequal cell division, growth regulation, and colony size of mammalian cells: a mathematical model and anlysis of experimental data.” J. Theoret. Biol. 153 (1991): 157–180.CrossRefGoogle Scholar
  9. Mehl, L.E. “A mathematical computer simulation model for the development of colonic polyps and colon cancer.” J. Surg. Oncol. 47: 243–252; 1991.CrossRefPubMedGoogle Scholar
  10. Moolgavkar, S.H., and A.G. Knudson. “Mutation and cancer: a model for human carcinogenesis.” J. Nat. Cancer Inst. 66 (1981): 1037–1052.PubMedGoogle Scholar
  11. Moolgavkar, S.H., and E.G. Luebeck. “Multistage carcinogenesis: population-based model for colon cancer.” J. Natl. Cancer Inst. 84 (1992): 610–618.CrossRefPubMedGoogle Scholar
  12. Novak, B., and J.J. Tyson. “Modeling the cell division cycle: M-phase trigger, oscillations, and size control.”J. Theor. Biol. 165 (1993): 101–134.CrossRefGoogle Scholar
  13. Retsky, M.W., D.E. Swartzendruber, P.D. Barne, and R.H. Wardwell. “Computer model challenges breast cancer treatment strategy.” Cancer Invest. 12 (1994): 559–567.CrossRefPubMedGoogle Scholar
  14. Stein, W.D., and A.D. Stein. “Testing and characterizing the two-stage model of carcinogenesis for a wide range of human cancers.” J. Theoret. Biol. 145 (1990): 95–122.CrossRefGoogle Scholar
  15. Tracqui, P. “From passive diffusion to active cellular migration in mathematical models of tumor invasion.” Acta Biotheoretica 43 (1995): 443–464.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • James L. Hargrove
    • 1
  1. 1.Department of Foods and NutritionUniversity of GeorgiaAthensUSA

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