Originally published as JCO Early Release 10.1200/JCO.2006.05.5988 on August 22 2006

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

Romano Demicheli, Elia Biganzoli, Patrizia Boracchi, Marco Greco, William J.M. Hrushesky, Michael W. Retsky

From the Departments of Medical Oncology, Medical Statistics and Biometry, and Breast Surgery, Istituto Nazionale Tumori; Medical Statistics and Biometry, Università di Milano, Milano, Italy; The University of South Carolina, Dorn Veteran's Administration Medical Center, Columbia, SC; and the Department of Vascular Biology, Children's Hospital and Harvard Medical School, Boston, MA

Address reprint requests to Romano Demicheli, MD, PhD, Istituto Nazionale Tumori di Milano, Via Venezian 1, 20137 Milano, Italy; e-mail: demicheli{at}istitutotumori.mi.it

PURPOSE: To find a quantitative relationship between tumor size and frequency of axillary lymph node involvement.

PATIENTS AND METHODS: 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 (V)/V, was estimated under simple probabilistic assumptions.

RESULTS: The allometric scaling law (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.

CONCLUSION: 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.

published online ahead of print at www.jco.org on August 21, 2006.

Authors' disclosures of potential conflicts of interest and author contributions are found at the end of this article.

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