Preferred fiber orientations in healthy arteries and veins understood from netting analysis

Abstract

In this paper we analyze the reinforcement of blood vessels by collagen fibers using the concept of netting analysis from composite theory. To this end, we interpret preferred fiber reinforcement as the solution to a weighted optimization problem having two competing targets, minimal pulse pressure and minimal material usage, under the constraint of mechanical stability against buckling in a physiologically reasonable range of blood pressures. We demonstrate that the solution to this optimization problem for large arteries is a helical reinforcement with fibers oriented diagonally and for small arteries and veins an orthogonal reinforcement consisting of axial and circumferential fibers. Both findings agree well with experimental data reported by others, which suggests the existence of an underlying mechanical principle for the establishment and maintenance of vascular fiber orientations under normal conditions.