RESEARCH PAPERS: Other Research Papers

Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics

[+] Author and Article Information
K. H. Parker, C. J. H. Jones

Physiological Flow Studies Unit, Imperial College of Science, Technology and Medicine, London, SW7 2AZ England

J Biomech Eng 112(3), 322-326 (Aug 01, 1990) (5 pages) doi:10.1115/1.2891191 History: Received January 20, 1989; Revised April 03, 1990; Online March 17, 2008


The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.

Copyright © 1990 by The American Society of Mechanical Engineers
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