Knowledge regarding the kinetics of metastatic tumor formation, as related to
the growth of the primary tumor, represents a fundamental issue in cancer
biology. Using an in vivo mammalian model, we show here that one can obtain
useful information from the frequency distribution of the sizes of metastatic
colonies in distant organs after serial sectioning and image reconstruction. To
explain the experimental findings, we constructed a biophysical model based on
the respective growth patterns of the primary tumor and metastases and a
stochastic process of metastatic colony formation. Heterogeneous distributions
of various biological parameters were considered. We found that the elementary
assumption of exponential forms of growth for the primary tumor and metastatic
colonies predicts a linear relation on a log-log plot of a metastatic colony
size distribution, which was consistent with the experimental results.
Furthermore, the slope of the curve signifies the ratio of growth rates of the
primary and the metastases. Non-exponential (Gompertzian and logistic) tumor
growth patterns were also incorporated into the theory to explain possible
deviation from the log-log linear relation. The observed metastasis-free
probability also supported the assumption of a time-dependent Poisson process.
With this approach, we determined the mechanistic parameters governing the
process of metastatogenesis in the lungs for two murine tumor cell lines (KHT
and MCaK). Since biological parameters specified in the model could be obtained
in the laboratory, a workable metastatic "assay" may be established for various
malignancies and in turn contribute in formulating rational treatment regimens
for subclinical metastases.Comment: 14 pages, 6 figure
