Mathematical Analysis of Aortic Deformation in Aneurysm and Wall Dissection

Aortic dissection is an extremely severe pathology. From the mechanics point of view, the aorta is a multilayered anisotropic reinforced shell, which is subjected to periodic loading under the action of pulse blood pressure. The questions of mathematical modeling of aorta and large arteries dissection are considered. A review of modern mathematical models of aortic and arterial wall structure obtained on the basis of experimental data processing on biaxial stretching of samples is carried out. Mathematical models can be conditionally divided into two classes: 1) effective models, when the internal structure of the wall structure is ignored, but the mechanical parameters of the material "averaged" over the wall thickness are introduced; 2) structured models, when the multilayer (up to three layers) structure of the artery is taken into account with the addition of one to four families of reinforcing fibers. One of the most widely used artery models, the Holzapfel – Hasser – Ogden model, is considered in detail. This model describes a two or three-layered artery with two families of reinforcing fibers. For this model tables of design parameters are given, numerical calculations of arterial rupture and dissection are carried out. The blood vessel is subjected to pulse pressure of blood flowing through it. It is shown that rupture of the inner layer of the vessel leads to an increase in the stress on the outer wall of the vessel. Increasing the thickness and length of the rupture increases the stresses on the outer wall of the vessel. The presence of an aneurysm of the vessel increases stresses twice as much as a vessel without an aneurysm. Splitting of the inner wall of the vessel leads to an increase in stresses on the wall – stresses fall with increasing rupture width for a straight vessel and rise for a vessel with an aneurysm. Stress calculations at the “tip” of delamination showed that the maximum stress is reached at the outer wall of the rupture.