Wave modes of an elastic tube conveying blood

The conventional theories for circulation of arteries are emphasized on fluid behavior or some simplified models for experimental utility. In this study, a new mathematical theory is proposed to describe the wave propagation through the elastic tube filled with viscous and incompressible fluid. The radial, longitudinal and flexural vibrations of a tube wall are introduced simultaneously. Meanwhile, the linearlized momentum and continuity equations of tube flow field are expressed in the integral form. Based on these considerations, three wave modes are obtained simultaneously. These wave modes are the flexural, Young and Lamb modes, respectively. The characteristics of these modes are clearly demonstrated. In the literature, according to different assumptions, the Young and Lamb modes were independently derived. It is usually thought that all the energies of the Young mode and the Lamb mode were transmitted through the liquid and the tube, respectively. Because these conventional models are over simplified, the corresponding investigations are incomplete and inaccurate. In this study, it is found that almost all the energies of the flexural and Lamb modes are transmitted through the tube. However, only about sixty percent of the energy of the Young mode is transmitted through the liquid. Finally, the effects of several important parameters on the dispersion curves and the energy transmissions of these modes are investigated.