Large amplitude wave propagation in arteries and veins
A numerical method has been described for the calculation of the unsteady flow of an incompressible viscous fluid in a distensible tapered tube possessing orthotropic viscoelastic properties. The formulation is quite general, including the fluid-wall interaction, the tube wall being characterized as a thin shell with negligible bending moments.
Illustrative solutions have been presented for the biomedical phenomena of a pulsed flow of blood in an excised segment of human aorta, subjected to both radial and longitudinal deformations. The complete solution includes the time variations of wall shape, stresses, strains and fluid velocity, computed in conjunction with a realistic dynamic constitutive model for the aortic wall.
The example presented possesses an impulsive inlet flow sufficient to produce "shock-like" signals along the vessel wall. These sharp wave fronts do not endanger the inherent stability of the numerical two-step Lax-Wendroff scheme, provided that the stability criteria are properly observed.
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