Fractal heterogeneity of peripheral blood flow: Implications for hematogenous metastases

Abstract

To determine how inhomogeneities in blood perfusion might affect the number of metastases that develop within an individual with cancer.Experiments with lung metastases in mice, involving 320 treatment groups and 3165 mice, were reviewed. Inhomogeneities in the distribution of metastases amongst identically treated mice were analyzed by calculating the relative dispersion and clumping index.The relative dispersion exhibited fractal self-similarity on change of scale, and paralleled the effects observed with pulmonary blood flow. Clustering of metastases was also apparent: a minority of mice developed relatively large numbers of metastases; a majority of mice developed few metastases.Clustering of lung metastases occurred within groups of identically treated mice, and could be attributed to inhomogeneous blood perfusion. Consequently, the number of metastases in any individual was highly variable and correlated only partly with malignant potential. Inhomogeneities in blood flow favored the development of relatively few metastases, such that solitary or nil metastasis should occur more frequently than expected from chance alone.