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. 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.

Nonlinear analysis of aortic flow in living dogs.

An in vitro study of flow response by cells.

Significant parameters in arterial pressure and velocity development.

The resolution of the ultrasound pulsed Doppler for blood velocity measurements

By applying the soliton theory, a method is developed in this paper with an aim to study the flow properties of blood in large blood vessels. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the large deformations of the aortic wall. The solutions of the equations of motion are restricted to the propagation of axisymmetric long waves. As for the equations governing the motion of the aorta, the longitudinal motion of the aortic wall is considered negligible. The radial motion is obtained directly from the pressure wave and the material behaviour of the aorta, by considering the motion of an elementary volume of the wall tissues. By using the experimentally measured values of the system parameters, computational work has been carried out to examine the change in radius, rate of change of radius, the dependence of the radius of the aorta on the longitudinal distance and the axial velocity distribution of blood in the aorta within a cardiac cycle. Variation of the stroke volume of the blood pulse is also determined for different taper angles of the aorta.

A study of solitary waves in a tapered aorta by using the theory of solitons

Recent interest in the hydrodynamic events relating to biomedical problems of the arteries as well as the development of artificial heart-assist devices have prompted one to study the nature of pulsatile flows in arteries. In particular, the problem of atherosclerosis is suspected to be related to the shearing stress developed over the vascular wall. The endothelial cells which normally line the intima of blood vessels can be eroded under high wall shear. It was found by Fry [1] that these cells have an acute yield stress of the order of 350 to 400 dynes/ cm2. Shearing stresses exceeding this limit will cause marked endothelial proliferation and subendothelial lipid deposition. On the other hand, there are problems of keeping the shearing stresses within a range to permit the endothelial cells to establish and to stabilize the newly formed fibrin surfaces over prostheses such as heart valves and heart-assist devices. Basic understanding of these problems could be gained through detailed knowledge of the pulsatile flow fields.

S. C. Ling

Papers

Pulsatile flows in arteries