Numerical Studies of Pulse Wave Propagations along Inhomogeneous and Stented Aortas

Estimating the focal variations in the stiffness of the aortic wall has been found as an effective method for cardiovascular diseases diagnosis. Direct measurement of the wall stiffness noninvasively may not prove readily possible, and therefore the velocity of the pulse wave along the aortic wall has been shown to be an effective surrogate to estimate the wall stiffness. Given that the majority of vascular diseases entail focal alterations in arterial wall stiffness, effective diagnosis methods would be achieved only by obtaining regional pulse wave velocity (PWV) and propagations. In this paper, fluid structure interaction (FSI) simulations are performed to describe the pulse propagations along aortas with focal wall softening as well as endografted aortas, aiming at examining the effects of the wall regional variations on the pulse wave propagations and velocities. The results indicated the remarkable change in pulse wave propagations that were correlated to the properties and nature of the aortic wall alterations. I. MATERIALS AND METHODS 3-dimentional-geometry, fully coupled fluid-solid-interactions, dynamic model of pulse wave propagation was established using Coupled Eulerian-Lagrangian (CEL) explicit solver of Abaqus. For the aortas with local softening, one homogenous aorta (baseline model) and nine inhomogeneous aortas with focal soft inclusions of different inclusion sizes, inclusion stiffness, and numbers of inclusion, were considered. For the endografted aorta, the geometry consisted of a three layer descending portion of the aorta with a stent placed inside the aorta. In all models, the Lagrangian domain was composed of aortic wall, being modeled as a purely elastic material for straight-geometry soft inclusion aortas, Fig.1, and hyperelastic for three layer descending aortas, Fig.2. The Eulerian domains consisted of Newtonian fluid encompassed the Lagrangian domains. An initial velocity was applied on the inlet of the lumen, serving as the driving force at the FSI problem and causing the dynamic wall motions. The radial displacement of the entire wall along the tube was obtained on multiple time-points and the information was used to generate a 2D spatio-temporal map of the wall displacement, allowing for the visualization of the entire wave propagation, and analyzing the regional pulse waves, quantitatively and qualitatively. II. RESULTS AND DISCUSSIONS Figure 3 shows the 2D spatial temporal plot of the wall displacement of the homogeneous model (baseline), with Young’s Modulus of 5.12 MPa. The PWV is determined from this plot as 17 m/s by taking the slope of the line on the wave peaks. Figure 4 represents similar wave propagation in an inhomogeneous model with a single soft inclusion of size 2 mm and modulus E=2.56 MPa (wall modulus of 5.12 MPa), displaying the presence of a stationary wave at the site of the local softening. Reflective wave is seen in 2D plot as well as an increase in wall displacement due to a softer region. The PWV does not seem to be affected post-inclusion. Figure 5 shows how the wave propagations on the endografted aortic wall and the disruption of the wave arriving at the site of the Stent. Similar spatiotemporal maps are obtained showing the presence of reflective wave. Figure 5. 3D abaqus model showing the deformation of the aortic wall as the pulse wave travels along the wall and reaches the stent.