A Frequency Distribution for the Number of Hematogenous Organ Metastases

The number of metastases associated with a primary tumor can be a major determinant for the chance of cure. A model is proposed here where the frequency distribution of the number of experimental organ metastases is affected by Poisson statistics, and by stochastic variations in regional blood flow. The model predicts that the mean E (X) and variance var (X) of the number of metastases per organ should relate according to a power function,var (X)= E (X)p+E (X), where and p are the constants, and that the actual distribution has a Poisson-negative binomial form. This model was found consistent with the data derived from a meta-analysis of over 47 000 murine experimental metastases. This frequency distribution (together with knowledge of the size distribution for metastases and the fraction of clonogenic cells) could permit more accurate assessments for tumor control probabilities with adjuvant therapies.