Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates.

We study the nonlinear interaction of an aortic heart valve, composed of hyperelastic corrugated leaflets of finite density attached to a stented vessel under physiological flow conditions. In our numerical simulations, we use a 2D idealised representation of this arrangement. Blood flow is caused by a time-varying pressure gradient that mimics that of the aortic valve and corresponds to a peak Reynolds number equal to 4050. Here, we fully account for the shear-thinning behaviour of the blood and large deformations and contact between the leaflets by solving the momentum and mass balances for blood and leaflets. The mixed finite element/Galerkin method along with linear discontinuous Lagrange multipliers for coupling the fluid and elastic domains is adopted. Moreover, a series of challenging numerical issues such as the finite length of the computational domain and the conditions that should be imposed on its inflow/outflow boundaries, the accurate time integration of the parabolic and hyperbolic momentum equations, the contact between the leaflets and the non-conforming mesh refinement in part of the domain are successfully resolved. Calculations for the velocity and the shear stress fields of the blood reveal that boundary layers appear on both sides of a leaflet. The one along the ventricular side transfers blood with high momentum from the core region of the vessel to the annulus or the sinusoidal expansion, causing the continuous development of flow instabilities. At peak systole, vortices are convected in the flow direction along the annulus of the vessel, whereas during the closure stage of the valve, an extremely large vortex develops in each half of the flow domain.

The influence of contrast agent injection on physiological flow in the circle of Willis.

X-ray videodensitometry allows in vivo flow measurements from gradients in contrast agent concentration. However, the injection of contrast agent alters the flow to be measured. Here, the temporal, spatial, and inter-patient variability of the response to injection are examined. To this purpose, an injection is prescribed in the internal carotid in a 1D wave propagation model of the arterial circulation. Although the resulting effect of injection is constant over a cardiac cycle, the response does vary with the location within the cerebral circulation and the geometry of the circle of Willis. At the injection site, the injection partly suppresses the incoming blood flow, such that the distal flow is increased by approximately 10%. This corresponds to approximately 20% of the injection rate added to the blood flow during injection, depending on the vascular geometry. In the communicating arteries, the flow direction is reversed during injection. Since the measured flow is not equal to the physiological blood flow, the effect of injection should be taken into account when deriving the flow from travelling contrast agent.