Nonlinear Analysis of Aortic Flow in Living Dogs

Abstract

A nonlinear theory which considered the convective accelerations of blood and the nonlinear elastic behavior and taper angle of the vascular wall was used to study the nature of blood flow in the descending thoracic aorta of living dogs under a wide range of pressures and flows. Velocity profiles, wall friction, and discharge waves were predicted from locally measured input data about the pressure-gradient wave and arterial distention. Precision pressure-gradient waves free of static errors were obtained through forward and backward pressure-gradient measurements, and the arterial pressure-radius relation was obtained through cinematography using a telephoto lens. The results indicated that a major part of the mean pressure gradient was balanced by convective accelerations; the theory, which took this factor into account, predicted the correct velocity distributions and flow waves. The results also showed that for high flow rates the magnitude of the peak wall-shear stress became comparable to the yield stress of the endothelial surface and that radial flows of significant magnitude existed with respect to the arterial wall. KEY WORDSpressure-gradient measurement technique vascular mechanics blood velocity fields mass transfer in aorta shearing stress in vascular •wall mechanical factors in arteriosclerosis• Studies by Fry and his associates (1-3) have shown that the intimal surface of an artery is sensitive to adjacent hydrodynamic events. Therefore, it is desirable to devise a technique with which the flow of blood near the wall can be determined and correlated with atherosclerotic lesions. Recently Ling and Atabek (4) have developed a nonlinear theory describing the pulsatile flow in arteries. This theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behavior and the large distention of the arterial wall. Using the locally measured values of pressure and pressure-gradient waves and the pressureradius function and taper angle of the arterial wall, the theory predicts velocity distribution, wall shear, and discharge waves. This method was applied in the present investigation to study the nature of pulsatile flow in the descending aorta of dogs under a wide range of systemic pressures and flows.Since a detailed account of the theory has been given previously ( 4 ) , we will only present a short From the Section on Experimental Atherosclerosis,

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