Effects of Viscosity and Constraints on the Dispersion and Dissipation of Waves in Large Blood Vessels: I. Theoretical Analysis

Abstract

The propagation of sounds and pulse waves within the cardiovascular system is subject to strong dissipative mechanisms. To investigate the effects of blood viscosity on dissipation as well as dispersion of small waves in arteries and veins, a parametric study has been carried out. A linearized analysis of axisymmetric waves in a cylindrical membrane that contains a viscous fluid indicates that there are two families of waves: a family of slow waves and one of fast waves. The faster waves are shown to be more sensitive to variations in the elastic properties of the medium surrounding the blood vessels and at high values of the frequency parameter alpha defined by alpha = radicalrhoomegaR(2) (0)/mu the blood viscosity attenuates them more strongly over a length than the slow waves. At low values of alpha, the effects of viscosity on attenuation are reversed; that is, the family of slow waves is much more attenuated than the family of fast waves. For the slow waves the radial displacement component generally exceeds the axial component except at very low frequencies. Conversely the axial displacements are much larger than the radial displacement for the faster waves. The presence of external constraints, however, can modify these results. In the case of the slow waves the phase angle between pressure and radial wall displacement is virtually negligible in the presence of mild external constraints, while the phase angles between pressure and fluid mass flow are at most 45 degrees . The corresponding phase angles for the fast waves exhibit much larger variations with changes in the elastic properties of the surrounding medium.