Buckling of Human Aorta Related to Dissection due to Flow-Pressure Conditions

Human aortas are subjected to large mechanical stresses and loads due to blood flow pressurization and through contact with the surrounding tissue and muscle. It is essential that the aorta does not lose stability for proper functioning. The present work investigates the buckling of human aorta relating it to dissection by means of an analytical model. A full bifurcation analysis is used employing a nonlinear model to investigate the nonlinear stability of the aorta conveying blood flow. The artery is modeled as a shell by means of Donnell’s nonlinear shell theory retaining in-plane inertia, while the fluid is modelled by a Newtonian inviscid flow theory but taking into account viscous stresses via the time-averaged Navier-Stokes equation. The three shell displacements are expanded using trigonometric series that satisfy the boundary conditions exactly. A parametric study is undertaken to determine the effect of aorta length, thickness, Young’s modulus, and transmural pressure on the nonlinear stability of the aorta. As a first attempt to study dissection, a quasi-steady approach is taken, in which the flow is not pulsatile but steady. The effect of increasing flow velocity is studied, particularly where the system loses stability, exhibiting static collapse. Regions of large mechanical stresses on the artery surface are identified for collapsed arteries indicating possible ways for dissection to be initiated.