Mechanical Properties of Arteries in Vivo

Abstract

Methods have been assembled permitting the simultaneous recording of intra-arterial pressure and arterial diameter with sufficient accuracy so that the mechanical properties of arteries in vivo, under physiologic conditions, can be derived. The analysis necessitates finding the relationships between 5 simultaneous variables; hence the data were recorded on magnetic tape and processed by analog and digital computer technics. Analysis of the data established the fact that the mechanical properties of arteries can be described by a linear, first-order differential equation whose coefficients can be defined as the moduli of elasticity and viscosity. Furthermore, the magnitudes of the coefficients were evaluated. The strain which the arteries undergo as a result of arterial pulse pressure variations is normally between 0.01 and 0.04, i.e., between 1 and 4 per cent change in circumference. The total strain associated with marked constriction and dilation does not usually exceed 10 per cent. Therefore, it is established that the circumferential motion of arteries may be characterized as small strain. The fact that the strain is effectively small is confirmed by analytical consideration, i.e., stress-strain relationships can be linearized under physiologic conditions without introducing significant error. The mass of the artery wall does not play a significant role in determining the mechanical behavior of the arteries and can therefore be neglected in any such considerations. The harmonic content, i.e., the frequency spectrum, comprising the pressure and diameter pulsations associated with the cardiac cycle have been evaluated by Fourier analysis. The magnitudes of the coefficients relating pressure and strain are: elastic (E p ) varies from 1,000 to 6,000 Gm./cm. 2 (with the exception of a value of 500 in the thoracic aorta of a 12-week-old puppy), viscous (R p ) from 10 to 150, and mass (M p ) from 0.0002 to 0.005. The magnitudes of the coefficients vary from individual to individual, from one site to another within the vascular tree and temporally in response to vasoactive factors. The effects of epinephrine, norepinephrine, acetylcholine and autonomic nerve stimulation on the mechanical properties and behavior of arteries are discussed. The differences between the pressure-strain relationships and the wall tension-strain relationships are discussed, since the mechanical properties of the wall material itself is not given directly by the pressure-strain relationships, i.e., radius and wall thickness must be considered. An analytical discussion is developed and mathematical equations are derived which relate pressure, wall tension, radius, strain, elasticity, viscosity and inertia in a tube which has been shown to be a reliable model of the living artery. It is concluded that the concept that the arteries function as a "peripheral heart," i.e., rhythmically contract in synchrony with the heart, is not justified. Probable relationships of these properties to the structure and functions of the arterial system are discussed.