Mechanics of Distension of Dog Veins and Other Very Thin-Walled Tubular Structures

Abstract

We present first phenomenological characterizations of the pressure-volume relationships (a) in veins excised from dogs under anesthesia and (b) in thinwalled latex tubes. We measured their cross-sectional areas and perimeters from cinefluorographic enlargements during distension. From flattened to circular cross sections, the perimeter of latex tubes remained constant while the area increased exclusively by bending of the walls. Compliance was large in this regime. After circular cross sections were reached, further increases in area were associated with increments in perimeter and there was stretching of the wall. Compliance declined sharply. Veins did not show a distinct two-regime behavior but a combination of bending and stretching which extended the region of large compliance to values of transmural pressure of physiological interest. Using classical theory of elasticity, we propose mathematical relationships describing the proportionality between the pressure and the curvature of the wall during the regime where bending is the primary controlling mechanism. We mechanized these relationships on an analog computer and correlated the solutions with the physical experiments. We conclude that no modulus of elasticity, alone, can relate the pressure and the volume when bending is predominant. In this regime the significant quantity is the modulus of flexural rigidity.