Fluid rheology effect on wave propagation in an elastic tube with viscoelastic liquid, containing fine bubbles

In our prior paper, a fluid–structure interaction model of pulse wave propagation, called the elastic tube model, has been developed. The focus of this paper is wall shear stress (WSS) in this model and the effects of different parameters, including rigid walls, wall thickness, and internal radius. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic isotropic, and incompressible. A fluid–structure interaction scheme is constructed using a finite element method. The results demonstrate the elastic tube plays an important role in WSS distributions of wave propagation. It is shown that there is a time delay between the WSS waveforms at different locations in the elastic tube model while the time delay cannot be observed clearly in the rigid tube model. Compared with the elastic tube model, the increase of the wall thickness makes disturbed WSS distributions, however WSS values are increased greatly due to the decrease of the internal radius. The results indicate that the effects of different parameters on WSS distributions are significant. The proposed model gives valid results.

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Wave Propagation in a Viscous Fluid Contained in an Orthotropic Elastic Tube

Biophysical Journal ◽

10.1016/s0006-3495(67)86582-2 ◽

1967 ◽

Vol 7 (2) ◽

pp. 165-186 ◽

Cited By ~ 57

Author(s):

I. Mirsky

Keyword(s):

Wave Propagation ◽

Viscous Fluid ◽

Elastic Tube

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Syrinx Fluid Transport: Modeling Pressure-Wave-Induced Flux Across the Spinal Pial Membrane

Journal of Biomechanical Engineering ◽

10.1115/1.4005849 ◽

2012 ◽

Vol 134 (3) ◽

Cited By ~ 16

Author(s):

N. S. J. Elliott

Keyword(s):

Spinal Cord ◽

Wave Propagation ◽

Spinal Canal ◽

Pressure Wave ◽

Elastic Tube ◽

Analytical Models ◽

Perivascular Spaces ◽

Interstitial Flow ◽

Fluid Exchange ◽

Wave Induced

Syrinxes are fluid-filled cavities of the spinal cord that characterize syringomyelia, a disease involving neurological damage. Their formation and expansion is poorly understood, which has hindered successful treatment. Syrinx cavities are hydraulically connected with the spinal subarachnoid space (SSS) enveloping the spinal cord via the cord interstitium and the network of perivascular spaces (PVSs), which surround blood vessels penetrating the pial membrane that is adherent to the cord surface. Since the spinal canal supports pressure wave propagation, it has been hypothesized that wave-induced fluid exchange across the pial membrane may play a role in syrinx filling. To investigate this conjecture a pair of one-dimensional (1-d) analytical models were developed from classical elastic tube theory coupled with Darcy’s law for either perivascular or interstitial flow. The results show that transpial flux serves as a mechanism for damping pressure waves by alleviating hoop stress in the pial membrane. The timescale ratio over which viscous and inertial forces compete was explicitly determined, which predicts that dilated PVS, SSS flow obstructions, and a stiffer and thicker pial membrane—all associated with syringomyelia—will increase transpial flux and retard wave travel. It was also revealed that the propagation of a pressure wave is aided by a less-permeable pial membrane and, in contrast, by a more-permeable spinal cord. This is the first modeling of the spinal canal to include both pressure-wave propagation along the spinal axis and a pathway for fluid to enter and leave the cord, which provides an analytical foundation from which to approach the full poroelastic problem.

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Numerical Investigation of Pulse Wave Propagation in Arteries Using Fluid Structure Interaction Capabilities

Computational and Mathematical Methods in Medicine ◽

10.1155/2017/4198095 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Hisham Elkenani ◽

Essam Al-Bahkali ◽

Mhamed Souli

Keyword(s):

Wave Propagation ◽

Pulse Wave ◽

Regression Line ◽

Computing Time ◽

Fluid Structure Interaction ◽

Elastic Tube ◽

Contour Plot ◽

Fluid Structure ◽

Structure Interaction ◽

Constitutive Material Model

The aim of this study is to present a reliable computational scheme to serve in pulse wave velocity (PWV) assessment in large arteries. Clinicians considered it as an indication of human blood vessels’ stiffness. The simulation of PWV was conducted using a 3D elastic tube representing an artery. The constitutive material model specific for vascular applications was applied to the tube material. The fluid was defined with an equation of state representing the blood material. The onset of a velocity pulse was applied at the tube inlet to produce wave propagation. The Coupled Eulerian-Lagrangian (CEL) modeling technique with fluid structure interaction (FSI) was implemented. The scaling of sound speed and its effect on results and computing time is discussed and concluded that a value of 60 m/s was suitable for simulating vascular biomechanical problems. Two methods were used: foot-to-foot measurement of velocity waveforms and slope of the regression line of the wall radial deflection wave peaks throughout a contour plot. Both methods showed coincident results. Results were approximately 6% less than those calculated from the Moens-Korteweg equation. The proposed method was able to describe the increase in the stiffness of the walls of large human arteries via the PWV estimates.

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