Summary
Theoretical and experimental evidence is available for the occurrence of shock waves in arterial blood flow. A sudden increase of pressure at the entrance of a fluid-filled semi-infinite elastic tube is considered as a model to investigate mathematically the possibility of shock-wave formation. By use of the method of wavefront expansions explicit results are obtained about the circumstances under which shocks may form and about the time and distance at which this may occur.
Zusammenfassung
Es gibt theoretische und experimentelle Hinweise für das Auftreten von Stoßwellen bei Blutströmungen in Arterien. Ein Drucksprung am Eintritt eines halbunendlich langen, elastischen Rohres wird als Modell benutzt, um mathematisch die Möglichkeit der Bildung einer Stoßwelle zu untersuchen.
Durch Entwicklung in der Umgebung der Wellenfront ergeben sich explizite Ergebnisse über Ort und Zeit der Stoßbildung.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Anliker, M., Rockwell, R. L., Ogden, E.: Nonlinear analysis of flow pulses and shock waves in arteries, Pt. I & II. ZAMP22, 217–246, 563–581 (1971).
Rudinger, G.: Shock waves in mathematical models of the aorta. ASME J. Appl. Mech.37, 34–37 (1970).
Whitham, G. B.: Linear and nonlinear waves. Wiley-Interscience. 1974.
Olsen, J. H., Shapiro, A. S.: Large-amplitude unsteady flow in liquid-filled elastic tubes. J. Fluid Mech.29, 513–538 (1967).
Author information
Authors and Affiliations
Additional information
With 1 Figure
Rights and permissions
About this article
Cite this article
Hoogstraten, H.W., Smit, C.H. A mathematical theory of shock-wave formation in arterial blood flow. Acta Mechanica 30, 145–155 (1978). https://doi.org/10.1007/BF01177445
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01177445