The kinetic analysis of metastatic tumor formation and its clinical relevance

Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology with significant clinical relevancy. By using an in vivo mammalian model, this work showed that one could obtain useful information from the frequency distribution of the sizes of metastatic colonies in distant organs after serial sectioning and image reconstruction. Tumor cells were implanted into the mice subcutaneously, and the subsequent presence of metastases in the lungs at various time points was assessed and their individual colony size measured. To explain the experimental finding, a quantitative model was constructed based on the growth patterns of the primary tumor and metastases and a stochastic process of metastatic colony formation. With this approach, the mechanistic parameters governing the process of metastatogenesis in the lungs for two murine tumor cell lines (KHT and MCaK) were determined. It was 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. The observed metastasis-free probability also supported the assumption of a time-dependent Poisson process of metastatic formation. More complicated tumor growth patterns, e.g. Gompertzian and logistic models, were included in the mathematical construct, with the attempt to explain possible deviation from the log-log linear relation. Heterogeneous distributions of various biological parameters were also introduced.; After showing that the biological parameters in the model could be obtained in the laboratory (thus a workable metastatic “assay”), the theoretical model was expanded to interpret some clinically assessable quantities encountered in cancer medicine. These included metastasis-free survival probability (derived by assuming certain limiting detection resolution of clinical diagnostic technology) and dose-dependent control probability by a cytotoxic agent (e.g. radiation therapy). In this way, a more rational basis in designing treatment regimens for subclinical metastases could be established. Finally, ways to improve the efficiency of the metastatic “assay” developed in this work were explored, using sampling technique and the mathematics of stereology.