The Effect of Blood Viscoelasticity on Pulsatile Flow in Stationary and Axially Moving Tubes

Abstract

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient $\nabla \mathit{P}$ waves were derived that would reproduce the starting Q waves for viscoelastic flow. The $\nabla \mathit{P}$ waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published $\nabla \mathit{P}$ and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.

Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.

In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.