Stochastic model of metastases formation.

A mathematical model is developed to describe the dynamics of the hematogenous metastatic process to the lung from a solid tumor growing in a peripheral body site. The accumulation of tumor cell clumps of various sizes in the pulmonary circulation and the formation of metastatic foci are described by a non-homogeneous, two-dimensional Markov process. An analytical solution is found for the special case of metastases produced by the intravenous injection of tumor cell clumps. The system is decoupled experimentally to determine the time-varying entrance rate of tumor cell clumps into the circulation from a growing fibrosarcoma and the number of metastatic foci produced by the intravenous injection of tumor clumps. Model validation is based on comparisons of model simulations with data for the development of metastatic foci and the probability of cure following tumor excision. The model is used to simulate hypothetical therapy to prevent tumor metastases.