Dimensional analysis of the hyperelastic behavior of the arterial blood vessel subject to a multiaxial stress state

Abstract

A study of the behavior of the arterial blood vessel was performed by resorting to the mechanics of hyperelastic solids, for this is a currently well-established means to understanding a number of phenomena of concern among physicians and biomedical engineers. As regards this organ, it was modelled as a thick walled cylindrical vessel where the material energy function comprised the characterization of microstructural features of the tissue, such as anisotropy and fiber orientation dispersion. The static equilibrium problem for implementing this model represented the adventitia and media layers of the arterial wall, while its solution was simple thanks to assuming an axisymmetric deformation pattern. It is found that the fiber orientation factor along with the other dimensionless quantities of the same order of magnitude had the most influence on the arterial blood vessel radial stiffness. These results were processed using dimensional groups, thereby facilitating interpretation in the light of the many parameters that the whole model considers.