Characterization of the frequency distribution for human hematogenous metastases: evidence for clustering and a power variance function.

ABSTRACT

When groups of mice are injected with cells from a metastasizing tumor, a minority of individuals within a given group tends to sustain disproportionately larger numbers of metastases relative to the remaining group members. This clustering of metastases obeys a power function relationship, sigma2 = amub, between the variance sigma2 and the mean number of lung metastases per animal mu (a and b constant). To see whether such clustering occurs with human lung, brain, and liver metastases, a meta-analysis of clinical and pathological series was performed. Thirty-three published series were identified that provided data regarding the numbers of organ metastases sustained by 5582 people. The data were grouped according to the primary tumor, site of metastasis and method of detection of metastases. Clustering of metastases within individuals of each subgroup (similar to the murine systems) was demonstrated by variance to mean ratios greater than 1, and by a strong correlation to the variance to mean power function (a approximately 0.49, b approximately 2.24, r2 = 96%, p < 10(-6)). The cause of this clustering remains unclear, but it may in part relate to heterogeneities in regional blood flow. As a consequence of this clustering, limited metastases would be expected to occur more frequently than predicted from random chance-providing for some optimism in the management of limited metastasis. As well, the frequency distribution for metastases revealed certain scaling symmetries, likely reflective of the underlying mechanisms of metastasis, that could be of interest to both clinicians and experimentalists working with metastasis.