The size distribution of human hematogenous metastases

The development of primary cancers and their subsequent metastases occur th rough a complex sequence of discrete steps. A hypothesis is proposed here w hereby the time available for the growth of metastases is normally distribu ted, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size dist ribution would be lognormal; Gompertzian growth would imply a modified (Gom pertz-normal) distribution, where larger metastases would occur less freque ntly as a consequence of a decreased growth rate. These two size distributi ons were evaluated against fs human autopsy cases where precise size measur ements had been collected from over 3900 macroscopic hematogenous organ met astases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to over-represent metastases greater than 10 mm diameter. The Gompertz-normal distribution provided more stringent agre ement, correcting for this over-representation These observations supported the hypothesis of normally distributed growth times, and qualified the uti lity of the lognormal and Gompertz-normal distributions for the size distri bution of metastases. (C) 2001 Academic Press.