Nonlinear Wave Modulation in a Fluid-Filled Elastic Tube with Stenosis

2008 ◽  
Vol 63 (1-2) ◽  
pp. 24-34 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Variable Coefficient ◽  
Wave Speed ◽  
Harmonic Wave ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Axial Distance ◽  
Nls Equation ◽  
Wave Speeds ◽  
Straight Lines

In the present work, treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation was obtained as the variable coefficient nonlinear Schr¨odinger (NLS) equation. By setting the stenosis function equal to zero, we observed that this variable coefficient NLS equation reduces to the conventional NLS equation. After introducing a new dependent variable and a set of new independent coordinates, we reduced the evolution equation to the conventional NLS equation. By seeking a progressive wave type of solution to this evolution equation we observed, that the wave trajectories are not straight lines anymore; they are rather some curves in the (ξ ,τ ) plane. It was further observed that the wave speeds for both enveloping and harmonic waves are variable, and the speed of the enveloping wave increases with increasing axial distance, whereas the speed of the harmonic wave decreases with increasing axial coordinates. The numerical calculations indicated that the speed of the harmonic wave decreases with increasing time parameter, but the sensitivity of wave speed to this parameter is quite weak.

scholarly journals Modulation of nonlinear waves in a fluid-filled elastic tube with stenosis

2004 ◽  
Vol 2004 (60) ◽  
pp. 3205-3218 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Amplitude Modulation ◽  
Nonlinear Waves ◽  
Variable Coefficient ◽  
Composite System ◽  
Harmonic Wave ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Reductive Perturbation ◽  
Thin Walled

Treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation is obtained as the variable-coefficient nonlinear Schrödinger equation. It is observed that the speed of the harmonic wave increases with distance from the center of stenosis.

The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

2006 ◽  
Vol 61 (12) ◽  
pp. 641-651
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Wave Speed ◽  
Kdv Equation ◽  
Order Term ◽  
Perturbation Expansion ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Inviscid Fluid ◽  
Weakly Nonlinear ◽  
Elastic Tubes

Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid, we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is found to be the linearized KdV equation with a nonhomogeneous term, which contains the contribution of the stenosis. A progressive wave type solution is sought for the evolution equation, and it is observed that the wave speed is variable, which results from the stenosis. We study the variation of the wave speed with the distance parameter τ for various amplitude values of the stenosis. It is observed that near the center of the stenosis the wave speed decreases with increasing stenosis amplitude. However, sufficiently far from the center of the stenosis stenosis amplitude becomes negligibly small.

scholarly journals Modulation of Electron-Acoustic Waves in a Plasma with Vortex Electron Distribution

2015 ◽  
Vol 16 (2) ◽  
pp. 61-66 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Acoustic Waves ◽  
Harmonic Wave ◽  
Fractional Power ◽  
Reductive Perturbation Method ◽  
Field Equations ◽  
Nls Equation ◽  
Electron Acoustic Waves ◽  
Electron Acoustic ◽  
Trapped Vortex

AbstractIn the present work, employing a one-dimensional model of a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we study the amplitude modulation of electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the nonlinear Schrödinger equation as the evolution equation of the same order of nonlinearity. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation it is found that the NLS equation with fractional power assumes envelope type of solitary waves.

THE EFFECT OF RESIDUAL STRESSES ON WAVE SPEED IN ARTERIES

1996 ◽  
Vol 04 (02) ◽  
pp. 171-180
Author(s):  
H.R. CHAUDHRY ◽  
B. BUKIET ◽  
M. LACKER
Keyword(s):  
Blood Flow ◽  
Stress Distribution ◽  
Residual Stresses ◽  
Wave Speed ◽  
Traditional Approach ◽  
Clinical Applications ◽  
Arterial Pulse ◽  
Wave Speeds ◽  
Nonlinear Elasticity Theory ◽  
As Stress

The traditional approach to calculating stress distribution in arteries has been to assume (incorrectly) that the unloaded intact artery is stress-free. We consider the unloaded intact artery to have initial (i.e. residual) stresses and study how this affects the calculated wave speed of the arterial pulse. We use a set of equations that describe, in a simplified way, the blood flow in arteries and apply nonlinear elasticity theory to derive a formula for wave speed. We compare wave speed calculations under two assumptions (considering unloaded intact arteries as stress-free and considering these arteries to have residual stresses). We find that wave speeds calculated assuming residual stresses are more realistic. Clinical applications of this work are suggested.

Sensitivity of the Shear Wave Speed-Stress Relationship to Soft Tissue Material Properties and Fiber Alignment

2021 ◽  
Author(s):  
Jonathon Blank ◽  
Darryl Thelen ◽  
Matthew S. Allen ◽  
Joshua Roth
Keyword(s):  
Wave Propagation ◽  
Shear Modulus ◽  
Shear Wave ◽  
Wave Speed ◽  
Axial Stress ◽  
Beam Model ◽  
Fiber Alignment ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Constitutive Properties

The use of shear wave propagation to noninvasively gauge material properties and loading in tendons and ligaments is a growing area of interest in biomechanics. Prior models and experiments suggest that shear wave speed primarily depends on the apparent shear modulus (i.e., shear modulus accounting for contributions from all constituents) at low loads, and then increases with axial stress when axially loaded. However, differences in the magnitudes of shear wave speeds between ligaments and tendons, which have different substructures, suggest that the tissue’s composition and fiber alignment may also affect shear wave propagation. Accordingly, the objectives of this study were to (1) characterize changes in the apparent shear modulus induced by variations in constitutive properties and fiber alignment, and (2) determine the sensitivity of the shear wave speed-stress relationship to variations in constitutive properties and fiber alignment. To enable systematic variations of both constitutive properties and fiber alignment, we developed a finite element model that represented an isotropic ground matrix with an embedded fiber distribution. Using this model, we performed dynamic simulations of shear wave propagation at axial strains from 0% to 10%. We characterized the shear wave speed-stress relationship using a simple linear regression between shear wave speed squared and axial stress, which is based on an analytical relationship derived from a tensioned beam model. We found that predicted shear wave speeds were both in-range with shear wave speeds in previous in vivo and ex vivo studies, and strongly correlated with the axial stress (R2 = 0.99). The slope of the squared shear wave speed-axial stress relationship was highly sensitive to changes in tissue density. Both the intercept of this relationship and the apparent shear modulus were sensitive to both the shear modulus of the ground matrix and the stiffness of the fibers’ toe-region when the fibers were less well-aligned to the loading direction. We also determined that the tensioned beam model overpredicted the axial tissue stress with increasing load when the model had less well-aligned fibers. This indicates that the shear wave speed increases likely in response to a load-dependent increase in the apparent shear modulus. Our findings suggest that researchers may need to consider both the material and structural properties (i.e., fiber alignment) of tendon and ligament when measuring shear wave speeds in pathological tissues or tissues with less well-aligned fibers.

scholarly journals A Pilot Study of Wet Lung Using Lung Ultrasound Surface Wave Elastography in an Ex Vivo Swine Lung Model

2019 ◽  
Vol 9 (18) ◽  
pp. 3923 ◽  
Author(s):  
Xiaoming Zhang ◽  
Boran Zhou ◽  
Alex X. Zhang
Keyword(s):  
Surface Wave ◽  
Pilot Study ◽  
Wave Speed ◽  
Lung Ultrasound ◽  
Ex Vivo ◽  
Lung Model ◽  
Water Volume ◽  
Lung Water ◽  
Wave Speeds ◽  
Lung Sample

Extravascular lung water (EVLW) is a basic symptom of congestive heart failure and other conditions. Computed tomography (CT) is standard method used to assess EVLW, but it requires ionizing radiation and radiology facilities. Lung ultrasound reverberation artifacts called B-lines have been used to assess EVLW. However, analysis of B-line artifacts depends on expert interpretation and is subjective. Lung ultrasound surface wave elastography (LUSWE) was developed to measure lung surface wave speed. This pilot study aimed at measureing lung surface wave speed due to lung water in an ex vivo swine lung model. The surface wave speeds of a fresh ex vivo swine lung were measured at 100 Hz, 200 Hz, 300 Hz, and 400 Hz. An amount of water was then filled into the lung through its trachea. Ultrasound imaging was used to guide the water filling until significant changes were visible on the imaging. The lung surface wave speeds were measured again. It was found that the lung surface wave speed increases with frequency and decreases with water volume. These findings are confirmed by experimental results on an additional ex vivo swine lung sample.

Solutions of solitary-wave for the variable-coefficient nonlinear Schrödinger equation with two power-law nonlinear terms

2018 ◽  
Vol 32 (28) ◽  
pp. 1850310 ◽  
Author(s):  
Le Xin ◽  
Ying Kong ◽  
Lijia Han
Keyword(s):  
Solitary Wave ◽  
Power Law ◽  
Optical Lattice ◽  
Variable Coefficient ◽  
Transformation Method ◽  
Potential Space ◽  
Nls Equation ◽  
Quadratic Potential ◽  
Nonlinear Schrödinger ◽  
Constant Coefficients

In this paper, we consider the variable-coefficient power-law nonlinear Schrödinger equations (NLSEs) with external potential as well as the gain or loss function. First, we generalize the similarity transformation method, which converts the variable coefficient NLSE with two power-law nonlinear terms to the autonomous dual-power NLS equation with constant coefficients. Then, we obtain the exact solutions of the variable-coefficient NLSE. Moreover, we discuss the solitary-wave solutions for equations with vanishing potential, space-quadratic potential and optical lattice potential, which are applied to many branches of physics.

A variable coefficient nonlinear Schrödinger equation: localized waves on the plane wave background and their dynamics

2019 ◽  
Vol 33 (10) ◽  
pp. 1850121 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Variable Coefficient ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Plane Wave Background ◽  
Localized Waves ◽  
Similarity Reductions

In this work, a variable coefficient nonlinear Schrödinger (vc-NLS) equation is under investigation, which can describe the amplification or absorption of pulses propagating in an optical fiber with distributed dispersion and nonlinearity. By means of similarity reductions, a similar transformation helps us to relate certain class of solutions of the standard NLS equation to the solutions of integrable vc-NLS equation. Furthermore, we analytically consider nonautonomous breather wave, rogue wave solutions and their interactions in the vc-NLS equation, which possess complicated wave propagation in time and differ from the usual breather waves and rogue waves. Finally, the main characteristics of the rational solutions are graphically discussed. The parameters in the solutions can be used to control the shape, amplitude and scale of the rogue waves.

Longitudinal Motion of a Thick Transversely Isotropic Hollow Cylinder

1991 ◽  
Vol 113 (4) ◽  
pp. 585-589 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Harmonic Wave ◽  
Transversely Isotropic ◽  
Longitudinal Motion ◽  
Isotropic Shell ◽  
Wave Speeds ◽  
Typical Sample ◽  
Wide Range ◽  
Second Mode ◽  
Ultrasonic Techniques ◽  
Composite Cylinders

The propagation of a longitudinal harmonic wave in a transversely isotropic shell has been investigated in the development of ultrasonic techniques for thick hollow composite cylinders. The characteristic equation for satisfying the stress-fee inner and outer cylindrical boundaries has been obtained in an exact form in terms of the wavelength, the cylinder radii and the material constants. The phase velocity of the fundamental mode is calculated for a wide range of the wavelength for various cylinder radii for some typical sample materials. The shell wave speeds for the second mode of vibration are also presented. Comparisons are made between shell wave speeds and plate wave speeds. The spread of the wave speeds for the composite shells is shown to be much wider than that for an isotropic shell.

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