Micrometastases formation: a probabilistic model.

A mathematical model of the process of metastases is formulated in which the hematogenous metastatic process from a solid tumor is considered to consist of a series of stages. A mathematical expression is obtained for the probability that no metastases will have been established by a characteristic time interval after tumor initiation. The murine T241 fibrosarcoma that rapidly and reproduceably produces pulmonary metastases was studied. Estimates of parameters required for the expression of probability of metastases formation were derived experimentally. The probability remains close to one for a characteristic time at which point it drops to zero. This indicates that at least in this experimental system there is a predictable critical time period beyond which micrometastases are virtually certain to have been formed.