Abstract
The mechanical behavior of vascular walls has been analysed by using a homogeneous, incompressible and curvilinearly orthotropic thick cylinder model based on the finite deformation theory.
First, for the deformation of vascular tissues, an existence of a (pseudo) strain energy density function has been assumed. The difference between the circumferential and radial stress components and the difference between the axial and radial stress components were expressed in two sets of series, the coefficients of which were determined from the pressure-volume and the force-volume relationships obtained experimentally. The strain energy density function and the stresses in the vascular wall were obtained accurately from the series just determined. The stress-strain relation of the vascular wall element was also derived in a simple manner.
The method proposed here is different from the works so far reported on the following points: (1) The differences of the stress components are not assumed as the specific form such as an exponential function or a polynomial, so that the results are accurate over the full range of the experimental data. (2) The expressions of the strain energy density function, the stress components in the wall and the stress-strain relation of the wall element are derived analytically, so that they may be determined by a simple calculation without using numerical integrations and/or iterative calculations.
