Pulse wave propagation.

Abstract

This report evaluates pulse wave propagation with respect to contributions by vascular wall elastic and geometric properties, vessel wall and blood viscosity, and nonlinearities in system parameters and in the equations of motion. Discrepancies in results obtained with different experimental methods and theory are discussed and resolved. A three-point pressure technique was used to obtain measurements from the abdominal aorta, carotid, iliac, and femoral arteries of dogs. Computations involved linear, as well as nonlinear methods. Results are presented along a continuous path of transmission (abdominal aorta, iliac, femoral), and it is shown that variations in phase velocity can be explained entirely by the geometric variation of these vessels. Phase velocities are shown to be frequency independent at approximately greater than 4 Hz whereas attenuation increases progressively for higher frequencies. Determination of propagation coefficients using maximal, compounded values of reported viscoelastic and geometric properties just manages to span the range of phase velocities, determined in different laboratories, but does not do so for attenuation. Also, differences in experimental techniques cannot explain these discrepancies. Consideration of geometric taper, nonlinear compliance, all the terms in the equation of motion, and the effect of wall and blood viscosity resolves discrepancies between theoretical and experimentally derived phenomena.

Pulse wave reflection: can it explain the differences between systemic and pulmonary pressure and flow waves? A study in dogs.

“…Calculation of input impedance is only permitted for linear systems. Although the linear behavior of the entire arterial tree has been challenged (Milnor and Nichols, 1975;Milnor and Bertram, 1978), several reports show that linearity is a reasonable assumption (Dick et al, 1966;Noble et al, 1967;Li et al, 1981). We have measured the input impedances before and during the interventions (Fig.…”

Laboratory testing the Anaconda

“…Since blood viscosity is clearly a factor, a frequent starting point for modelling the flow in blood vessels (e.g. [8][9][10]) is Womersley's solution [11] for the oscillatory motion of a viscous fluid in a thin-walled elastic tube. In fact, many studies use simplified approximations of Womersley's velocity profiles, such as a Stokes layer near the boundaries with a central uniform core, a power law, the Poiseuille profile or even simply uniform flow [5].…”

Comparison of Linear Methods for the Determination of Propagation Coefficient in Arterials Systems: Numerical Investigation

“…This finding is in harmony with previous experimental studies where authors found attenuation values completely higher than the theoretical ones. Li et al (18) , who used transducer distance of 2-3 cm and Milnor et al (11), (24) , who used 3.5-5.3 cm, obtained attenuation values much higher than those predicted by linear theories when applying the three-point method. However, Ursino et al (22) , who used transducer distance of 10 and 40 cm and Reuderink et al (25) , who used transducer distance of 10 cm and found good agreement between calculated and theoretical values of propagation coefficient.…”

“…These methods, supposing a uniform artery with linear behaviour and the same phase velocity for the forward and backward waves, provide a true propagation coefficient. The merits, disadvantages and errors inherent in the determination of propagation coefficient by three-point and two-point method have been discussed by several authors (12), (13), (14), (18) . Results obtained by such methods are conflicting and led different groups to different conclusions especially concerning the three-point method.…”

“…Inaccuracy of the three-point method has been proposed by Buss et al (13) as an explanation for these discrepancies. Li et al (18) attributed the disparity of results to difference in the degrees of sensitivity of each method to non-linearities. Ursino et al suggested that the three-point method may be introducing significant errors at low frequencies when distance between two consecutive transducers becomes much lower than the wavelength (21) .…”