Allometric law

“The relationship between resting energy expenditure (REE) (kJ/d) and body mass (M) (kg) is a cornerstone in the study of energy physiology. By expressing REE as a function of body mass observed across mammals, Kleiber (1930) formulated the now classic equation: REE = 293M0.75. “ (1). Calder (1984) (2) has shown that such a relationship holds also for organs in an adult body. The following equation describes the relationship between organ mass and tissue mass.
T = b * M^q  where b is a constant and q is a scaling exponent

This relationship  holds for mammals e.g., mouse or elephant and is  called an allometric law. It is a manifestation of an optimality principle which controls  the structure of organisms. The size of each organ depends on, and is controlled by the overall size of the body. The whole controls its parts.

Breast cancer

An important study by Demicheli et al (3) revealed that this law describes also the relationship  between a tumor of the breast and axillary lymph nodes. The graph published by the team depicts the proportion of patients with positive lymph nodes as a function of tumor volume in the adjacent breast.

The curve is derived from the following equation F[N+]  = 1 – exp(–0.0586 V 0.254)  (3)
F[N+] : proportion of positive lymph nodes
V : Tumor volume

The implications are startling.

Axillary lymph node involvement indicates tumor metastasis.  Metastatic seeding  depends on tumor size and is non linear. Actually the graph depicts also tumor evolution whose seeding rate, which is the derivative of  F[N+] or F’[N+] is depicted below.

F’[N+]. =

Metastasis rate is inversely proportional to tumor size. The bigger the tumor the slower its rate of metastasis. In other words tumor controls its metastasis rate.  More precisely  tumor and metastasis constitute one system. They are one organ that  evolves as a whole.

Metastatic seeding following surgery

Many clinical studies report a metastatic flare up following tumor surgery, like the appearance of liver metastases following the surgery of colon cancer. Surgery leads to mobilization of tumor cells into peripheral blood which is generally attributed to manual tumor handling. Yet the following study on metastasis following treatment indicates that it is triggered by the treatment.

A recent study demonstrated that “circulating epithelial cells were already present before surgery in all patients. During the first 30–60 min after surgery values did not change immediately. They started increasing during the following 3 to 4 days up to thousand fold in 85% of treated patients in spite of complete resection of the tumor with tumor free margins in all patients. “ (4)

Implication for therapy

If tumor and metastasis are indeed one organ (system)  tumor reduction will raise the rate of metastasis. Which supports the approach of this site.  As long as tumor does not impinge upon a vital function and does not cause pain or suffering it ought to be left intact. Treatment ought to preserve the tumor and alleviate its secondary manifestations.

Bi-modal hazard rate (BMH)

The above observations explain why following breast cancer surgery the hazard rate rises.
Tumor ablation raises the metastatic rate which accounts for the rising hazard.

Pernicious cachexia
Metastasis following treatment
Bi-modal hazard rate
WOB controls cancer
Allometric law and complexity

References

1 ZiMiang Wang et al.
The Reconstruction of Kleiber’s Law at the Organ-Tissue Level
J. Nutr. 131:2967-2970, November 2001
2 Calder, W. A., III (1984) Size, Function, and Life History 1984 Dover Publications New York. .
3 Romano Demicheli, Elia Biganzoli, Patrizia Boracchi, Marco Greco, William J.M. Hrushesky, Michael W. Retsky.  Allometric Scaling Law Questions the Traditional Mechanical Model for Axillary Lymph Node Involvement in Breast Cancer
Journal of Clinical Oncology, Vol 24, No 27 (September 20), 2006: pp. 4391-4396
4. Oumar Camara, Andreas Kavallaris, Helmut Nöschel, Matthias Rengsberger, Cornelia Jörke, and Katharina Pachmann
Seeding of epithelial cells into circulation during surgery for breast cancer: the fate of malignant and benign mobilized cells
World J Surg Oncol. 2006; 4: 67.