Wave Propagation through a Viscous Fluid Contained in a Tethered, Initially Stressed, Orthotropic Elastic Tube

Atabek, H. B.

doi:10.1016/s0006-3495(68)86512-9

Cited by 136 publications

(53 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using these techniques we have demonstrated the importance of the convective accelerations caused by both the arterial distention and the arterial taper Comparison of axial velocity profiles and discharge waves predicted by the linear and the nonlinear theory: a and b, c, d and e, and f represent results obtained by using the input data from dogs A, B, and C given in Figures 4,5,6,and 7,respectively. It is important to note that the plot of linear velocity profiles includes the contribution due to the mean flow in contrast to similar plots given in literature (12,13), which only show the velocity profiles due to the pulsatile part of the flow. These latter profiles look more blunt and tend to resemble the nonlinear velocity profiles.…”

Section: Comparison With Linear Theorymentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Analysis of Aortic Flow in Living Dogs

Ling

et al. 1973

Circulation Research

View full text Add to dashboard Cite

A nonlinear theory which considered the convective accelerations of blood and the nonlinear elastic behavior and taper angle of the vascular wall was used to study the nature of blood flow in the descending thoracic aorta of living dogs under a wide range of pressures and flows. Velocity profiles, wall friction, and discharge waves were predicted from locally measured input data about the pressure-gradient wave and arterial distention. Precision pressure-gradient waves free of static errors were obtained through forward and backward pressure-gradient measurements, and the arterial pressure-radius relation was obtained through cinematography using a telephoto lens. The results indicated that a major part of the mean pressure gradient was balanced by convective accelerations; the theory, which took this factor into account, predicted the correct velocity distributions and flow waves. The results also showed that for high flow rates the magnitude of the peak wall-shear stress became comparable to the yield stress of the endothelial surface and that radial flows of significant magnitude existed with respect to the arterial wall. KEY WORDSpressure-gradient measurement technique vascular mechanics blood velocity fields mass transfer in aorta shearing stress in vascular •wall mechanical factors in arteriosclerosis• Studies by Fry and his associates (1-3) have shown that the intimal surface of an artery is sensitive to adjacent hydrodynamic events. Therefore, it is desirable to devise a technique with which the flow of blood near the wall can be determined and correlated with atherosclerotic lesions. Recently Ling and Atabek (4) have developed a nonlinear theory describing the pulsatile flow in arteries. This theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behavior and the large distention of the arterial wall. Using the locally measured values of pressure and pressure-gradient waves and the pressureradius function and taper angle of the arterial wall, the theory predicts velocity distribution, wall shear, and discharge waves. This method was applied in the present investigation to study the nature of pulsatile flow in the descending aorta of dogs under a wide range of systemic pressures and flows.Since a detailed account of the theory has been given previously ( 4 ) , we will only present a short From the Section on Experimental Atherosclerosis,

show abstract

Section: Comparison With Linear Theorymentioning

confidence: 99%

“…This condition is in part due to strong vascular tethering (6,7) and in part due to the predominantly circumferential orientation of the elastic and collagen fibers (8) which minimizes the coupling of the circumferential strain to the longitudinal strain. Therefore, we can neglect the longitudinal motion of the arterial wall.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Analysis of Aortic Flow in Living Dogs

Ling

et al. 1973

Circulation Research

View full text Add to dashboard Cite

show abstract

“…The arterial vessels are multilayer tubes of viscoelastic orthotropic material and blood is a concentrated suspension of aggregating particles; therefore taking into account the fluid and wall rheology leads to fairly cumbersome mathematical models [6,7] that can be investigated only numerically. However, many aspects associated with wave propagation and reflection in arterial beds can be studied using fairly simple models [8][9][10][11][12].Blood flow in large arteries is characterized by high Reynolds numbers (Re ≥ 500) and can be investigated on the basis of models of ideal incompressible fluid flow in compliant thin-walled tubes (h/R ≤ 0.1, where h is the wall thickness and R is the inner radius of the tube). The viscoelastic properties of blood, associated with the presence of blood cells and high-molecular compounds, are manifested only in turbulent flow regimes [13].…”

mentioning

confidence: 99%

Pressure wave propagation in liquid-filled tubes of viscoelastic material

Kizilova¹

2006

Fluid Dyn

View full text Add to dashboard Cite

-The propagation of small-amplitude waves in a thick-walled long viscoelastic tube of variable cross-section, filled with a viscous incompressible fluid, is considered with account for wave reflection at the tube end in application to arterial pulse wave propagation. A solution is obtained in the form of expansions in a small parameter. The effect of the coefficient of wave reflection at the tube end and the wall material parameters on the fluid volume flow-rate and the tube wall displacement is investigated. It is shown that the volume flow-rate phase spectrum characteristics depend only slightly on the wall properties and can be used in clinical diagnostics for finding the reflection coefficient from pressure and flow-rate records.Keywords: pulse wave, viscoelastic tube, wave reflection.The propagation of pressure waves in liquid-filled compliant tubes has been intensely investigated in connection with the analysis of pulse waves in arteries [1][2][3][4][5]. The arterial vessels are multilayer tubes of viscoelastic orthotropic material and blood is a concentrated suspension of aggregating particles; therefore taking into account the fluid and wall rheology leads to fairly cumbersome mathematical models [6,7] that can be investigated only numerically. However, many aspects associated with wave propagation and reflection in arterial beds can be studied using fairly simple models [8][9][10][11][12].Blood flow in large arteries is characterized by high Reynolds numbers (Re ≥ 500) and can be investigated on the basis of models of ideal incompressible fluid flow in compliant thin-walled tubes (h/R ≤ 0.1, where h is the wall thickness and R is the inner radius of the tube). The viscoelastic properties of blood, associated with the presence of blood cells and high-molecular compounds, are manifested only in turbulent flow regimes [13]. When modeling flows in small arteries, the blood is mostly considered to be a homogeneous pseudoplastic fluid and the arteries to be thick-walled tubes of viscoelastic material [1,6]. Comparison of the results of simulating the pulse waves in arteries with account for the viscosity, compressibility and non-Newtonian characteristics of the blood and the compressibility and anisotropy of the wall material has shown that for the aorta and medium-sized arteries the main experimental laws of wave propagation and reflection can be satisfactorily described on the basis of the model of a thick-walled homogeneous isotropic viscoelastic tube filled with homogeneous incompressible viscous fluid [14].The wave motion of the blood is generated by periodic heart contractions. Reflected waves arise in those segments in which the conductivities of the vessels are uncoordinated [1,6]. These are regions where the mechanical properties of the wall have changed due to pathologies (densifications, atherosclerotic plaques), as well as vessel bifurcations, contractions and expansions, normal or pathological (stenoses, aneurisms).Thus, the intravascular pressure p(t) curves recorded using micromanomete...

show abstract

“…Witzig (1914) was the first to show the effects of fluid viscosity on propagation characteristics, impedance and velocity profiles. Significant developments of the theory took place in the 1950s and 1960s: Womersley (1955Womersley ( , 1957, Atabek & Lew (1961) and Atabek (1968), among † Email address for correspondence: g.papadakis@ic.ac.uk 466 G. Papadakis many others). A survey of the work in the area until the late 1960s is provided by Cox (1969).…”

Section: Introductionmentioning

confidence: 99%

New analytic solutions for wave propagation in flexible, tapered vessels with reference to mammalian arteries

Papadakis

2011

J. Fluid Mech.

View full text Add to dashboard Cite

Novel, closed-form, analytic solutions for the pressure and velocity fields are derived for the linear problem of wave propagation inside a tapered flexible vessel of conical shape. It is shown that pressure and velocity can be written in terms of Bessel functions of orders 1/3 and 4/3 respectively. An expression is also derived that quantifies the effect of the cone angle on the wave propagation velocity. The analytic solutions are general and valid for tube variations at any length scale in relation to the wavelength of the wave. In other words, the requirement that the changes in vessel properties with distance should take place over a length scale large compared to the wavelength of the wave, is not employed or needed. This is the basic condition for the application of WKB theory to tapered vessels. However, this condition is not satisfied in pressure pulses propagating in mammalian arteries. The general expressions derived in this paper are directly applicable to the cardiovascular system of mammals. It is further shown that the presented solution naturally tends to the asymptotic WKB solution when the assumptions of the theory are applied to the general expressions. An explicit formula is provided for the time-averaged energy flux of the wave that shows clearly the effect of the continuous reflection of the wave from the vessel wall. Viscous effects are incorporated by coupling the derived analytic solution with the radial velocity profile of Womersley. The results are compared with full nonlinear fluid-structure interaction simulations and very good agreement is found (maximum differences are ∼1 % and 1.6 % for area-averaged pressure and velocity respectively, and 4-6 % for local velocity values).

show abstract

Wave Propagation through a Viscous Fluid Contained in a Tethered, Initially Stressed, Orthotropic Elastic Tube

Cited by 136 publications

References 5 publications

Nonlinear Analysis of Aortic Flow in Living Dogs

Nonlinear Analysis of Aortic Flow in Living Dogs

Pressure wave propagation in liquid-filled tubes of viscoelastic material

New analytic solutions for wave propagation in flexible, tapered vessels with reference to mammalian arteries

Contact Info

Product

Resources

About