Theoretical mathematical modeling provides a dispersion relation to understand how initial stresses affect blood flow wave speeds and transmission in arteries.
In order to understand the effect of initial stresses on the blood flow in arteries, a theoretical analysis of wave propagation in an initially inflated and axially stretched thick cylindrical shell filled with a viscous fluid is investigated. For simplicity in mathematical analysis, the blood is assumed to be an incompressible Newtonian fluid while the arterial wall material is taken to be incompressible, homogeneous, isotropic and elastic. Utilizing the theory of small deformations superimposed on a large initial deformation, the governing differential equations of the perturbed solid motions are obtained in cylindrical polar coordinates. Because of the difficulties in solving the set of differential equations with variable coefficients, an approximate power series method is utilized and the dispersion relation is obtained for thin tubes. Various results concerning the wave speeds and transmission coefficients are numerically evaluated and the results are depicted on some graphics.
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Demiray et al. (1987) studied this question.
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