Analysis of coronary flow fields in thoracotomized dogs.

A nonlinear theory of pulsatile flow was used to investigate the detailed flow field in the left circumflex coronary artery of anesthetized open-chest dogs. Studies were carried out under a wide range of blood pressures and flow rates induced by intravenous infusions of dipyridamole. The results indicated that (1) the flow profiles, although less blunt than those in the descending aorta, are still nonparabolic, (2) the wall shear in the coronary arteries maintains a high value through diastole, and (3) during intravenous infusions of dipyridamole both coronary flow and wall shear increase. The peak value of the shear stress during these infusions, which reached 360 dynes/cm2, can approach the yield stress value of 400 dynes/cm2 reported by Fry for endothelial cells.

Wave propagation through a viscous fluid contained in a tethered, initially stresses, orthotropic elastic tube.

To give a realistic representation of the pulse propagation in arteries a theoretical analysis of the wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube is considered. The tube is assumed to be orthotropic and its longitudinal motion is constrained by a uniformly distributed additional mass, a dashpot and a spring. The fluid is assumed to be Newtonian. The analysis is restricted to propagation of small amplitude harmonic waves whose wavelength is large compared to the radius of the vessel. Elimination of arbitrary constants from the general solutions of the equations of motion of the fluid and the wall gives a frequency equation to determine the velocity of propagation. Two roots of this equation give the velocity of propagation of two distinct outgoing waves. One of the waves propagates slower than the other. The propagation properties of s lower waves are very slightly affected by the degree of anisotropy of the wall. The velocity of propagation of faster waves decreases as the ratio of the longitudinal modulus of elasticity to the circumferential modulus decreases; transmission of these waves is very little affected. The influence of the tethering on the propagation velocity of slower waves is negligibly small; transmission of these waves is seriously affected. In tethered tubes faster waves are completely attenuated.

Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube.

To have a better understanding of the flow of blood in arteries a theoretical analysis of the pressure wave propagation through a viscous incompressible fluid contained in an initially stressed tube is considered. The fluid is assumed to be Newtonian. The tube is taken to be elastic and isotropic. The analysis is restricted to tubes with thin walls and to waves whose wavelengths are very large compared with the radius of the tube. It is further assumed that the amplitude of the pressure disturbance is sufficiently small so that nonlinear terms of the inertia of the fluid are negligible compared with linear ones. Both circumferential and longitudinal initial stresses are considered; however, their origins are not specified. Initial stresses enter equations as independent parameters. A frequency equation, which is quadratic in the square of the propagation velocity is obtained. Two out of four roots of this equation give the velocity of propagation of two distinct outgoing waves. The remaining two roots represent incoming waves corresponding to the first two waves. One of the waves propagates more slowly than the other. As the circumferential and/or longitudinal stress of the wall increases, the velocity of propagation and transmission per wavelength of the slower wave decreases. The response of the fast wave to a change in the initial stress is on the opposite direction.