The Tree Branching Law: Correcting Misconceptions on Capillary Cross-Section Areas and Blood Speed

Abstract: The Tree Branching Law (TBL) states: The trunk of a branching tree does not give rise to branches that have cross-section areas larger than its own, meaning: The sum of all tree branches cross-section areas is less than its own trunk. The reported results demonstrate that TBL is correct. This law rule applies down the arterial tree to the terminal arterioles and capillaries, and up a green tree to its leaves. The sum of all cross-section areas of all branches at any level is less than that of the trunk. Similarly, the sum of all cross-section area of all capillaries is less than that of the aorta. The TBL thus dispels the misconceptions on cross-section areas of all capillaries are larger than the aorta and red blood cells (RBCs) speed in the capillary is very slow. It provides solid evidence with RBCs speed is fast with a speed gradient between the inlet and exit of the capillary. This allows the magnetic field-like phenomena of the G tube to cause fast capillary-ISF transfer that provide for the cell viability at rest and exercise. The physiological relevance and clinical significance of TBL are discussed.

Keywords: Hydrodynamics, Hemodynamics, Capillary physiology and anatomy, Tree branching law, Green trees, Arterial trees, Red Blood Cells RBCs speed

Edition: Volume 10 Issue 1, January 2021,

Pages: 1409 - 1418