Abstract
In order to better understand the effect of initial stress in blood flow in arteries, a theoretical analysis of wave propagation in an initially inflated and axially stretched cylindrical thick shell is investigated. For simplicity in the mathematical analysis, the blood is assumed to be an incompressible inviscid fluid while the arterial wall is taken to be an isotropic, homogeneous and incompressible elastic material. Employing the theory of small deformations superimposed on a large initial field the governing differential equations of perturbed solid motions are obtained in cylindrical polar coordinates. Considering the difficulty in obtaining a closed form solution for the field equations, an approximate power series method is utilized. The dispersion relations for the most general case of this approximation and for the thin tube case are thoroughly discussed. The speeds of waves propagating in an unstressed tube are obtained as a special case of our general treatment. It is observed that the speeds of both waves increase with increasing inner pressure and axial stretch.
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Erbay, H.A., Erbay, S. & Demiray, H. Pulse waves in prestressed arteries. Bltn Mathcal Biology 49, 289–305 (1987). https://doi.org/10.1007/BF02460121
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DOI: https://doi.org/10.1007/BF02460121