Allometric Scaling Law Questions the Traditional Mechanical Model for Axillary Lymph Node Involvement in Breast Cancer

Abstract

To find a quantitative relationship between tumor size and frequency of axillary lymph node involvement. The frequency of axillary node involvement versus primary tumor volume was analyzed in 10 selected series of patients incorporating a total of 57,244 women with resectable breast cancer. The average number of events per unit volume resulting in tumor spread to axillary lymph nodes before tumor surgical removal Theta(V)/V, was estimated under simple probabilistic assumptions. The allometric scaling law Theta(V)/V = 0.0586V(-0.7457) was estimated on the data, fitting the proportion of lymph node involvement on tumor volume V (in microliters). The estimate 0.7457 (95% CI, 0.7200 to 0.7713) suggests that the true scaling exponent, under the assumed model, may be the fractional value, which characterizes scaling relationships for a wide variety of biologic variables at both the whole organism level and organ level. Results suggest that the phenomenon should be related to some internal structural trait of the tumor. The vascular network seems to be the best candidate. This result does not support a mere mechanical model of lymphatic tumor spread. A more complex biology-based model of lymphohematogenous spread is suggested, in which the axillary nodes draining the lymph from the primary tumor may become activated by factors produced by both tumor cells and tumor stroma, thus favoring cell-selective homing of otherwise circulating tumor cells. The success of fractal features related to the internal architecture brings additional support to the consideration of primary breast cancer as an organ-like structure.