Simulation of residual stresses (Strains) in arteries

Abstract

Residual stresses and strains contribute substantially to stress-strain states in arteries. They manifest themselves by opening of the artery after having been cut longitudinally and can be quantified by means of the opening angle of a ring cut out of the artery and cut longitudinally afterwards. The magnitude of the opening angle changes with species, age of the individual, artery location, etc. Although the magnitude of these stresses appears slight, they can influence the stress (and strain) distribution in the arterial wall substantially by reducing the extreme values throughout the wall. Their surprisingly high influence on the resulting stresses is given by the non-linear stress-strain characteristics of vascular wall. When applied to the blood pressure, the uniform stress and uniform strain hypotheses have been formulated to explain this phenomenon. The usual way of their modeling is based on using a model with the geometry of the opened arterial ring; the residual stresses are then induced in the model by closing it into the original approximately circular shape. This method, however, is not applicable for more complex non-symmetric arterial geometries, because the induced strains depend on local bending stiffness. Therefore another approach is used in the paper, based on introducing an interference between two layers of aorta represented in the model. The method is demonstrated with a circular ring used typically in experimental assessment of residual strains and results of both methods are compared. In addition, the proposed interference method is numerically more stable, because of the two orders lower displacements, and it is able to induce constant strains throughout all the wall thickness by using more than two layers in the arterial wall model. © 2011 Springer-Verlag Berlin Heidelberg.