Experimental metastasis: a novel application of the variance-to-mean power function

An empiric power function relationship between a population's mean density (m) and its corresponding variance (v), written v = a.mb (a, b, constants), may be applied to the analysis of experimentally induced pulmonary metastases within syngeneic (C57BL/6 X C3H)F1 mice. The mean and variance of the numbers of resultant B16 F1 and B16 F10 melanoma metastases strongly correlated with the power function (r2 greater than 0.8). The exponent b was 1.4 +/- 0.1 and 1.6 +/- 0.2 for the F1 and F10 melanomas, respectively, indicating a clustering of metastases within certain mice. This clustering of metastases within more highly affected animals may reflect a diffusion-limited aggregation of tumor cells within the circulation and the resultant greater ability of these aggregates to form metastases.