Flow-Radius Relation of Symmetrical Dichotomous Vascular System from Minimum Work Principle

Hiromi Seno

Department of Mathematics, Faculty of Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima, Hiroshima 724, Japan

(Received April 6, 1994; Accepted February 20, 1995)

Keywords: Mathematical Model, Minimum Work Principle, Fractal, Dichotomous System

Abstract. We set up a mathematical modelling of dichotomous vascular system and derive a relation required for the structural optimality based on the minimum work principle. It is discussed how the exponent n in the relation Q rⁿ between the flow rate Q and the vessel radius r reflects physiologic and structural characteristics of the vascular system. It is shown that the introduction of the fractal nature of the vascular system provides a principle to explain and study the observed variety of the exponent n.