Page 91 - 20dynamics of cancer

76 CHAPTER 4

original multistage theory, the two-stage clonal expansion theory, or the
newer hybrid models. Armitage and Doll’s (1961, p. 36) conclusions still
apply:

In summary, we doubt whether the available observational data
provide clear and consistent evidence in favor of any particular
model. Further elucidation is likely to come either from direct bi-
ological evidence of a nonquantitative nature, or from quantitative
experiments, carefully designed and reported, perhaps on a larger
scale than is usually undertaken at present.

I agree that one cannot easily choose between the main classes of
models by analyzing how well they fit the data. Most of the models
supply a set of reasonable assumptions or modifications that provide a
good fit. However, I do think that comparative tests like those originally
used by Ashley (1969a) and Knudson (1971) can be developed to dis-
criminate between the models (Frank 2005; Frank et al. 2005). I discuss
that approach in Chapter 8.

4.6 The Geometry of Cell Lineages

Two aspects of cellular reproduction influence mutation accumula-
tion. First, the rate of cell division influences the number of mutational
events per unit time, because mutations arise primarily during cell repli-
cation. Second, the shape of cellular lineages determines how a single
mutational event passes to descendant cells of a lineage. The rate at
which a second hit strikes a descendant cell depends on how many of
those descendant cells exist.
Some tissues have extensive cell division early in life and then rel-
atively little after childhood, for example, neural and bone tissue. The
relatively rare childhood cancers occur in such tissues, whereas the com-
mon adult cancers occur in continuously dividing tissues. Perhaps as
much as 90% of human cancers arise in renewing epithelial tissues, most
commonly, those of the colon, lung, breast, and prostate.
I am not certain about the historical origins of these ideas on cell
division. The early chemical carcinogenesis literature emphasized the
role of cell division rate stimulated by particular chemical agents. With
regard to childhood cancers and tissue growth, Moolgavkar and Knud-
son (1981) reviewed some prior work and then presented an extensive
mathematical framework in which to analyze the role of development