*Forma,* Vol. 10 (No. 1), pp. 29-38, 1995

*Original Paper*

## 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* *r*^{n} 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*.