Page 189 - 20dynamics of cancer

174 CHAPTER 9

does of course increase the accumulation of mutations, but does so dif-
ferently from the mechanisms by which classical mutagens act. For ex-
ample, the potentially mutagenic chemicals in cigarette smoke diffuse
widely throughout the body, yet the carcinogenic effects concentrate
disproportionately in the lungs. To explain this discrepancy in smok-
ers between the distribution of chemical mutagens and the distribution
of tumors, Cairns argued that the carcinogenic effects of smoke arise
mostly from the irritation to the lung epithelia and the associated in-
crease in cell division.
If carcinogens sometimes act primarily by increasing cell division,
then we would need to know how mitogenic effects rise with dose. For
example, doubling the number of cigarettes smoked might not double
the rate at which epithelial stem cells divide to repair tissue damage. I
do not know of data that measure the actual relation between mitoge-
nesis and dose, but, plausibly, mitogenesis might rise with something
like the square root of dose instead of increasing linearly with dose.
A diminishing increase in transition rates with dose would explain the
observation that the exponent on dose is usually less than the exponent
on duration. That observation is often expressed with the Druckrey
equation that fits data from many studies of chemical carcinogenesis
(Figures 2.11, 9.2). The Druckrey equation can be expressed as k =
n
r
d m , where k is a constant, d is the dose level, and m is the median
duration of carcinogen exposure to onset of a particular type of tumor.
Usually, r< n, that is, the exponent on dose is less than the exponent
on duration. Peto (1977) mentioned that, for carcinomas, r/n is often
about 1/2.
Now consider a simple multistage model with n stages and equal tran-
sition rates, u, between stages. Assume a carcinogen has the same effect
on all stages, in which the transition rate is uf(d), where f(d) is a func-
n
n
tion of carcinogen dose, d. Then k = [f(d)] m , because the carcinogen
has the same multiplicative effect on all n stages.
Suppose that the rise in transition rates diminishes with dose, for
a
example, f(d) = d , with a< 1. Then the basic multistage model with
n
all n transitions affected by a carcinogen leads to k = d an m .If a = r/n,
r
n
then we have the standard Druckrey relation, k = d m , which closely
fits observations from many different experiments with a = r/n ≈ 1/2.
Alternatively, we could use the more plausible expression uf(d) =
a n
n
a
u(1 + bd ), which leads to the multistage prediction k = (1 + bd ) m .