The resonance of the arterial system
The arterial system is assumed to consist of two elastic chambers connected by a conducting channel. It is assumed that a current of fluid enters one chamber, whereas the other chamber is drained by a pipe with a certain peripheral resistance. The continuity of the fluid is described by a differential equation for each chamber. The inertia resistance of the conducting channel is taken into consideration.
It is shown that the system may possess a resonance frequency. The latter, if it exists, as well as the damping coefficients are expressed in terms of the elastic moduli of the chambers, the conductivity of the channel, and the peripheral resistance. It is shown that with plausible values of the latter variables the resonance frequency as determined theoretically has the right order of magnitude as found experimentally.
KeywordsStanding Wave Arterial System Peripheral Resistance Conducting Channel Inertia Resistance
Unable to display preview. Download preview PDF.
- Alexander, R. S. 1952. “Factors Determining the Contour of Pressure Pulses Recorded from the Aorta.”Fed. Proc. Physiol. Soc.,11, 738–49.Google Scholar
- — 1953. “The Genesis of the Aortic Standing Wave.”Circulation Research,1, 145–51.Google Scholar
- Apéria, A. 1940. “Hemodynamical Studies.”Skand. Arch. f. Physiol.,83, Suppl. 16, 1–230.Google Scholar
- Bazett, H. C., F. S. Cotton, L. B. Laplace, and J. C. Scott. 1935. “The Calculation of Cardiac Output and Effective Peripheral Resistance from Blood Pressure Measurements with an Appendix on the Size of the Aorta in Man.”Am. Jour. Physiol.,113, 312–34.Google Scholar
- Best, Ch. H. and N. B. Taylor. 1945.The Physiological Basis of Medical Practice. Baltimore: The Williams & Wilkins Co.Google Scholar
- Broemser, Ph. 1932. “Beitrag zur Windkesseltheorie des Kreislaufs.”Zeitschr. f. Biol.,93, 154–63.Google Scholar
- Frank, O. 1899. “Die Grundform des arteriellen Pulses.”Zeitschr. f. Biol.,37, 483–553.Google Scholar
- Gomez, D. 1937.Les lois physiques de l'hémodynamique. Actualités scientifiques, recherches d'hémodynamique et cardiologie. Nr. 511. Paris: Hermann et Cie.Google Scholar
- Green, H. D. 1950. “Circulatory System: Physical Principles.”Medical Physics (Ed. O. Glasser). Chicago: The Year Book Publishers.Google Scholar
- Hamilton, W. F. 1944. “The Patterns of the Arterial Pressure Pulse.”Am. Jour. Physiol.,144, 235–41.Google Scholar
- — and P. Dow. 1939. “An Experimental Study of the Standing Waves in the Pulse Propagated through the Aorta.”Ibid.,,125, 48–59.Google Scholar
- Ince, E. L. 1944.Ordinary Differential Equations. New York: Dover Publications.Google Scholar
- Rayleigh, Lord. 1896.The Theory of Sound II. London: Macmillan and Co.Google Scholar