Fluid–structure interaction simulation of pulse propagation in arteries: Numerical pitfalls and hemodynamic impact of a local stiffening

Abstract

When simulating the propagation of a pressure pulse in arteries, the discretization parameters (i.e. the time step size Δt and the grid size Δx) need to be chosen carefully in order to avoid a decrease in amplitude of the traveling wave due to numerical dissipation. In this paper the effect of numerical dissipation is examined using a numerical fluid–structure interaction (FSI) model of the pulse propagation in an artery. More insight in the influence of the temporal and spatial resolution of the wave on the results of these simulations is gained using an analytical study in which the scalar linear one-dimensional transport equation is considered. Although this model does not take into account the full complexity of the problem under consideration, the results can be used as a guidance for the selection of the numerical parameters. Furthermore, this analysis illustrates the difference in accuracy that can be obtained using a second-order implicit time integration scheme instead of a first-order scheme.The results from the analytical and numerical studies are subsequently used to determine the settings necessary to obtain a grid and time step converged simulation of the wave propagation and reflection in a simplified model of an aorta with repaired aortic coarctation. This FSI model allows to study the hemodynamic impact of a stiff segment and demonstrates that the presence of a stiff segment has an important impact on a short pressure pulse, but has almost no influence on a physiological pressure pulse. This phenomenon is explained by analyzing the reflections induced by the stiff segment.