In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechnaical wave guides which are of interest in the mammalian circulation.
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On the Propagation of a Wave Front in Viscoelastic Arteries
R. Holenstein,
R. Holenstein
Institute of Biomedical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland
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R. M. Nerem,
R. M. Nerem
Department of Mechanical Engineering, University of Houston, Houston, Tex. 77004
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P. F. Niederer
P. F. Niederer
Institute of Biomedical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland
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R. Holenstein
Institute of Biomedical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland
R. M. Nerem
Department of Mechanical Engineering, University of Houston, Houston, Tex. 77004
P. F. Niederer
Institute of Biomedical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland
J Biomech Eng. May 1984, 106(2): 115-122 (8 pages)
Published Online: May 1, 1984
Article history
Received:
April 6, 1983
Revised:
November 8, 1983
Online:
June 15, 2009
Citation
Holenstein, R., Nerem, R. M., and Niederer, P. F. (May 1, 1984). "On the Propagation of a Wave Front in Viscoelastic Arteries." ASME. J Biomech Eng. May 1984; 106(2): 115–122. https://doi.org/10.1115/1.3138467
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