Optimal Structures of Vascular Branchings

概要

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The system of vascular branchings was considered to be very efficiently constructed for its physiological function and its structure and organization was analysed by the mathematical method of conditional extremum.<BR>A vascular system with many branchings, for example the whole arterial tree, was regarded from its role as a duct system supplying necessary blood flow to the terminals, distributed in the body with constant pressure difference from the origin (from aortic pressure to precapillary pressure). The optimal structure of this system was reasoned as that of the minimum intravascular volume because as this volume decreases, the exchange rate of blood with substances in capillaries increases and the metabolic energy to maintain active blood decreases.<BR>From these conditions, some formulae at the extreme were deduced and numerical solutions of optimal branchings were obtained for some typical examples of distribution at terminal points.<BR>The minimum required volume of the whole arterial tree was estimated from standard values of the aorta (pressure, flow and diameter) and a very close value to the actual arterial blood volume was obtained.<BR>A computed optimal structure to the peritoneal vascular branching showed close similarity to the original branching.
一般社団法人日本生体医工学会の論文