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The early growth of cancer

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In this paper, we compare two types of stochastic models for the initial growth of cancerous tumors. In one type, the random element enters via the initial time of growth or via the initial size of the growth clone. In the other type, tumors differ from one another essentially via their growth rates. We present a simple test to distinguish between the two types when tumor size distributions are available from several time points. Size distributions are the key elements of such kinetic analysis given the limitation that an individual tumor can be measured only once, at the time of sacrifice of an experimental animal. We discuss these concepts in connection with data from particular experiments on carcinogenic growth in the livers of mice.

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  1. 1.

    Athreya, K. B., Ney, P. E.: Branching processes. Berlin, Heidelberg, New York: Springer, 1972

  2. 2.

    Atkinson, E. N., Bartozynski, R., Brown, B., Thompson, J. On estimating the growth function of tumors. Math Biosciences 67, 145–166 (1983)

  3. 3.

    Bailey, N. T. J.: The elements of stochastic processes with applications to the natural sciences. New York: Wiley, 1964

  4. 4.

    Bartlett, M. S.: An introduction to stochastic processes with special references to methods and applications, 3rd ed., Cambridge: Cambridge University Press, 1978

  5. 5.

    Harris, T. E.: The theory of branching processes. Berlin, Heidelberg, New York: Springer, 1963

  6. 6.

    Jagers, P.: Branching processes with biological applications. New York: Wiley, 1975

  7. 7.

    Kesten, H., Stigum, B. P.: Limit theorems for decomposable multi-dimensional Galton-Watson processes. J. Math. Anal, and Applns. 17, 309–338 (1967).

  8. 8.

    Pugh, T.: Reliable stereological method for estimating the number of microscopic hepatocellular foci from their transections. Cancer Research 43, 1261–1268 (1983)

  9. 9.

    Whittemore, A., Keller, J. B.: Quantitative theories of carcinogenesis. Siam Review 20, 1–30 (1978)

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Recipient of a fellowship award from NIH Training Grant 5-T32-Es 07015-07.

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Chover, J., King, J.H. The early growth of cancer. J. Math. Biology 21, 329–346 (1985). https://doi.org/10.1007/BF00276231

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Key words

  • Carcinogenesis-models
  • cancer kinetics
  • hepatocellular foci
  • scaling factors
  • estimation
  • birth and branching processes