Geodesic
Building the solution of the Lame problem for a cylinder with a spiral anisotropy and its applications in hemodynamics of arterial vessels
Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 1, pp. 59-66

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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. 
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     author = {E. N. Portnov and U. A. Ustinov},
     title = {Building the solution of the {Lame} problem for a cylinder with a spiral anisotropy and its applications in hemodynamics of arterial vessels},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
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E. N. Portnov; U. A. Ustinov. Building the solution of the Lame problem for a cylinder with a spiral anisotropy and its applications in hemodynamics of arterial vessels. Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 1, pp. 59-66. http://geodesic.mathdoc.fr/item/VMJ_2017_19_1_a7/