Wave reflection and transmission in multiply stented blood vessels

Abstract

Closed circulatory systems display an exquisite balance between vascular elasticity and viscous fluid effects, to induce pulse-smoothing and avoid resonance during the cardiac cycle. Stents in the arterial tree alter this balance through stiffening and because a periodic structure is introduced, capable of interacting with the fluid in a complex way. While the former feature has been investigated, the latter received no attention so far. But periodic structures are the building blocks of metamaterials, known for their ‘non-natural’ behaviour. Thus, the investigation of a stent's periodic microstructure dynamical interactions is crucial to assess possible pathological responses. A one-dimensional fluid–structure interaction model, simple enough to allow an analytical solution for situations of interest involving one or two interacting stents, is introduced. It is determined: (i) whether or not frequency bands exist in which reflected blood pulses are highly increased and (ii) if these bands are close to the characteristic frequencies of arteries and finally, (iii) if the internal structure of the stent can sensibly affect arterial blood dynamics. It is shown that, while the periodic structure of an isolated stent can induce anomalous reflection only in pathological conditions, the presence of two interacting stents is more critical, and high reflection can occur at frequencies not far from the physiological values.

Waves and fluid–solid interaction in stented blood vessels

“…This raises the question as to whether it is better to put in multiple small stents or one long stent to treat several areas of disease at once. The case of multiple stents provides a different and very interesting pattern of the reinforcement of the vessel, linked to the periodicity of the structure, as shown by Papathanasiou et al [ 29 ].…”

“…In this section, an in-depth investigation of the case in which more stents are installed in different sections of the arteries is provided for the three-dimensional model, thus generalizing the one-dimensional analysis by Papathanasiou et al [ 29 ]. To this purpose, a unit cell is composed of a finite-length stent (denoted by L sc ) and unstented section of the artery, which is then repeated periodically with a specific spacing L fc .…”

“…Many computational models were performed for haemodynamics, but only a limited number of investigations addressed the propagation of waves in blood vessels [ 28 ] and, in particular, when the systems exhibit a repetitive pattern in their geometry [ 29 ]. A recent work by Jaganathan et al .…”

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

“…As is often the case for the analysis of acoustic waveguides, mathematical modelling is very important in biomech- anics problems that include pulsating flow. Analytical models and numerical simulations for pulsating blood flow for an unstented artery can be found, for example, in [1–9]. In particular, it is known that the junctions between blood vessels act as scatterers, and reflection of acoustic waves from branched blood vessels is observed in routine measurements [10,11].…”

Free vibration analysis of infinitely long thick-walled hollow elliptical cylinder

“…Casciaro et al [14], Jaganathan et al [15] worked on hemodynamic computational modeling by wave propagation in blood vessels. Papathanasiou et al [16], Auricchio et al [17] compared the natural frequencies of different types of metallic structure of heart stent. Mesh-free method has been also used to handle complicated geometries [18][19][20].…”