Dynamics of Fluid Filled Tubes
Models for describing pressure pulse propagation in arteries can, with few exceptions, be separated into two categories depending upon the emphasis placed on the fluid mechanics or the solid mechanics. Models in the first category employ ideas first put forward by Euler (1844) who proposed combining the equation of motion for an inviscid fluid together with the continuity equation and a third equation relating the pressure in the tube to its cross-sectional area. Euler’s equations were first solved in the context of blood flow by Lambert (1958) who used a pressure-area relation based on experimental data rather than the one proposed by Euler. These ideas have been considerably refined and developed to employ general pressure-area relations, include outflow through porous walls (Rudinger, 1966), and study the development of shocks (Rudinger, 1970), (Teipel, 1973), (Forbes, 1979).
KeywordsDispersion Relation Shear Deformation Tube Wall Rotatory Inertia Elastic Tube
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Literature and References
- 1.Brigham, E.O. (1974), The Fast Fourier Transform, Prentice Hall.Google Scholar
- 2.Euler, L. (1844), Principia pro motu sanguins per arterias detetminado, opera posthuma mathematica et physica anno 1844 détecta, eiderant P.H. Fuss et N. Fuss. Petropoli: Apud Eggers et Socios, Vol. 2, 1862.Google Scholar
- 5.Hermann, G. and Mirsky, I. (1956), Three dimensional and shell theory analysis of axially symmetric motions of cylinders, J. Appl. Mech. 23, 563.Google Scholar
- 6.Klip, W. (1962), Velocity and Damping of the Pulse Wave, Martinus Nÿhoff, The Hague.Google Scholar
- 7.Lamb, H. (1898), On the velocity of sound in a tube, as affected by the elasticity of the walls, Manchester Lit. Phil. Soc. Mem. Proc. 42 (9), 1.Google Scholar
- 9.Rubinaw, S.I. and Keller, J.B. (1968), Hydrodynamic aspects of the circulatory system, In Hemorheology, Proc. 1st. Int. Conf. Univ. of Iceland, A.L. Copley, Ed., Pergamon.Google Scholar
- 12.Rudinger, G. (1966), Review of current mathematical methods for the analysis of blood flow, Biomedical Fluids Symposium, ASME, New York.Google Scholar
- 14.Skalak, R. (1966), Wave propagation in blood flow in biomechanics, Proc. Symp. Appl. Mech. Div. ASME, Y.C. Fung, Ed.Google Scholar
- 17.Witzig, K. (1914), Uber erzwungene Wellenbewegungen zäher, inkompressibler Flussigkeiten in elastischen Röhren, Inaugural Dissertation, Universitat Bern, K.J. Wyss, Bern.Google Scholar