Waves and fluid–solid interaction in stented blood vessels

Abstract

This paper focuses on the modelling of fluid–structure interaction and wave propagation problems in a stented artery. Reflection of waves in blood vessels is well documented in the literature, but it has always been linked to a strong variation in geometry, such as the branching of vessels. The aim of this work is to detect the possibility of wave reflection in a stented artery due to the repetitive pattern of the stents. The investigation of wave propagation and possible blockages under time-harmonic conditions is complemented with numerical simulations in the transient regime.

Dispersion of waves and transmission–reflection in blood vessels with structured stents

“…The dispersion curves are plotted in the first Brillouin zone, specifically in the interval [0, π ]. Figure 2 presents a comparison of the dispersion curves for an artery without stent ( C = 1) corresponding to the one-dimensional model and the three-dimensional model of [20]. The actual frequency v d (in Hz) in the three-dimensional model is related to the non-dimensional frequency ω according to vd=ωc02πL.The reference pulse wave speed c 0 is obtained from the dispersion diagram of the three-dimensional model of [20] for an unstented artery.…”

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Figure 2.Dispersion curves for the unit cell without stent. The dashed line represents the dispersion curves obtained using the three-dimensional FEM model of [20], while the solid line represents the results of the one-dimensional model presented in this paper. (Online version in colour.

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“…This applies both to the first and second stop-bands. The three-dimensional computational model of [20] includes general vibration modes and the actual geometry of the stent. Here we use three-dimensional computation for calibration of the semi-analytical one-dimensional model, which is highly effective in the analysis of transmission–reflection of waves across the stented region.…”

“…The mean value of the normalized wave speed in the stented artery is evaluated using equation (2.14). We also note that the corresponding dimensional considerations for the actual blood vessels with the actual stents were included in the earlier paper [20].…”

“…The approach introduced in the recent paper [20] offers a new model and theoretical concept, which considers blood vessels containing stents (alterations of the arterial properties and geometry). In addition to acoustic waves, the dynamic response of elastic solids was also considered, and thus the model was extended to include elastic waves propagating in the blood vessels reinforced by stents.…”