Building the solution of the Lame problem for a cylinder with a spiral anisotropy and its applications in hemodynamics of arterial vessels

A cylinder with spiral anisotropy may be presented, in particular, as a result of spiral wrapping of a cylindrical surface by layers of thin threads of rigid material with simultaneous covering by a polymer material. Thus, there will be locally transversely isotropic composite material with a symmetry axis directed tangentially to helical spirals; in order to determine its elastic characteristics, one can use homogenization methods. To construct a mathematical model of propagation of sphygmic “pressure waves” in arterial vessels whose walls possess spiral anisotropy, we give a description of the method to calculate a radial stiffness and phase velocity of a certain wave. In the same way, we present a comparative analysis of radial stiffness values, various theories and calculation results illustrating the dependency of rigidity and phase velocity on geometric parameters.