Co-Immobilization and Interaction of Heparin and Plasmin on Collageno-Elastic Tubes

Circular thin-walled elastic tubes under concentric axial loading usually fail by shell buckling, and in practical design procedures the buckling load can be determined by modifying the local buckling stress to account empirically for the imperfection sensitive response that is typical in Donnell shell theory. While the local buckling stress of a hollow thin-walled tube under concentric axial compression has a solution in closed form, that of a thin-walled circular tube with an elastic infill, which restrains the local buckling mode, has received far less attention. This paper addresses the local buckling of a tubular member subjected to axial compression, and formulates an energy-based technique for determining the local buckling stress as a function of the stiffness of the elastic infill by recourse to a transcendental equation. This simple energy formulation, with one degree of buckling freedom, shows that the elastic local buckling stress increases from 1 to [Formula: see text] times that of a hollow tube as the stiffness of the elastic infill increases from zero to infinity; the latter case being typical of that of a concrete-filled steel tube. The energy formulation is then recast into a multi-degree of freedom matrix stiffness format, in which the function for the buckling mode is a Fourier representation satisfying, a priori, the necessary kinematic condition that the buckling deformation vanishes at the point where it enters the elastic medium. The solution is shown to converge rapidly, and demonstrates that the simple transcendental formulation provides a sufficiently accurate representation of the buckling problem.

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Bending instabilities of elastic tubes

International Journal of Solids and Structures ◽

10.1016/s0020-7683(02)00085-9 ◽

2002 ◽

Vol 39 (8) ◽

pp. 2059-2085 ◽

Cited By ~ 73

Author(s):

Spyros A. Karamanos

Keyword(s):

Elastic Tubes

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Anomalous bubble propagation in elastic tubes

Physics of Fluids ◽

10.1063/1.2963495 ◽

2008 ◽

Vol 20 (8) ◽

pp. 081702 ◽

Cited By ~ 14

Author(s):

Alexandra Heap ◽

Anne Juel

Keyword(s):

Elastic Tubes

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Modeling expiratory flow from excised tracheal tube laws

Journal of Applied Physiology ◽

10.1152/jappl.1999.87.5.1973 ◽

1999 ◽

Vol 87 (5) ◽

pp. 1973-1980 ◽

Cited By ~ 11

Author(s):

Nikolai Aljuri ◽

Lutz Freitag ◽

José G. Venegas

Keyword(s):

Static Pressure ◽

Pressure Recovery ◽

High Frequency Ventilation ◽

Flow Limitation ◽

Flow Conditions ◽

Expiratory Flow Limitation ◽

Elastic Tubes ◽

Viscous Losses ◽

Forced Expiratory Flow ◽

Expiratory Flow

Flow limitation during forced exhalation and gas trapping during high-frequency ventilation are affected by upstream viscous losses and by the relationship between transmural pressure (Ptm) and cross-sectional area ( A tr) of the airways, i.e., tube law (TL). Our objective was to test the validity of a simple lumped-parameter model of expiratory flow limitation, including the measured TL, static pressure recovery, and upstream viscous losses. To accomplish this objective, we assessed the TLs of various excised animal tracheae in controlled conditions of quasi-static (no flow) and steady forced expiratory flow. A tr was measured from digitized images of inner tracheal walls delineated by transillumination at an axial location defining the minimal area during forced expiratory flow. Tracheal TLs followed closely the exponential form proposed by Shapiro (A. H. Shapiro. J. Biomech. Eng. 99: 126–147, 1977) for elastic tubes: Ptm = K p[( A tr/ A tr0)− n − 1], where A tr0 is A tr at Ptm = 0 and K p is a parametric factor related to the stiffness of the tube wall. Using these TLs, we found that the simple model of expiratory flow limitation described well the experimental data. Independent of upstream resistance, all tracheae with an exponent n < 2 experienced flow limitation, whereas a trachea with n > 2 did not. Upstream viscous losses, as expected, reduced maximal expiratory flow. The TL measured under steady-flow conditions was stiffer than that measured under expiratory no-flow conditions, only if a significant static pressure recovery from the choke point to atmosphere was assumed in the measurement.

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Viscoelasticity of the trachea and its effects on flow limitation

Journal of Applied Physiology ◽

10.1152/japplphysiol.00689.2005 ◽

2006 ◽

Vol 100 (2) ◽

pp. 384-389 ◽

Cited By ~ 6

Author(s):

Nikolai Aljuri ◽

Jose G. Venegas ◽

Lutz Freitag

Keyword(s):

Wave Speed ◽

Mathematical Representation ◽

Forced Expiration ◽

Flow Limitation ◽

Time Dependency ◽

Cross Sectional ◽

Elastic Tubes ◽

Forced Expiratory Flow ◽

Expiratory Flow ◽

The Relationship

To test the hypothesis that peak expiratory flow is determined by the wave-speed-limiting mechanism, we studied the time dependency of the trachea and its effects on flow limitation. For this purpose, we assessed the relationship between transmural pressure and cross-sectional area [the tube law (TL)] of six excised human tracheae under controlled conditions of static (no flow) and forced expiratory flow. We found that TLs of isolated human tracheae followed quite well the mathematical representation proposed by Shapiro (Shapiro AH. J Biomech Eng 99: 126–147, 1977) for elastic tubes. Furthermore, we found that the TL measured at the onset of forced expiratory flow was significantly stiffer than the static TL. As a result, the stiffer TL measured at the onset of forced expiratory flow predicted theoretical maximal expiratory flows far greater than those predicted by the more compliant static TL, which in all cases studied failed to explain peak expiratory flows measured at the onset of forced expiration. We conclude that the observed viscoelasticity of the tracheal walls can account for the measured differences between maximal and “supramaximal” expiratory flows seen at the onset of forced expiration.

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The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques

Journal of Applied Mechanics ◽

10.1115/1.2789053 ◽

1998 ◽

Vol 65 (1) ◽

pp. 99-106

Author(s):

T. J. McDevitt ◽

J. G. Simmonds

Keyword(s):

Anisotropic Material ◽

Large Strain ◽

Axisymmetric Deformation ◽

Large Strains ◽

Shells Of Revolution ◽

Large Rotation ◽

Elastic Tubes ◽

Axisymmetric Bending ◽

Combined Parameters ◽

Nonlinearly Elastic

We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.

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Interactions of Nonlinear Waves in Fluid-Filled Elastic Tubes

Zeitschrift für Naturforschung A ◽

10.1515/zna-2007-1-204 ◽

2007 ◽

Vol 62 (1-2) ◽

pp. 21-28

Author(s):

Hilmi Demiray

Keyword(s):

Solitary Waves ◽

Nonlinear Waves ◽

Elastic Tube ◽

Wave Number ◽

Inviscid Fluid ◽

Leading Order ◽

Elastic Tubes ◽

Longwave Approximation ◽

Thin Walled ◽

Analytical Phase

In this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincaré-Lighthill-Kuo) perturbation method. The results show that up to O(k3), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.

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Pumping Patterns and Work Done During Peristalsis in Finite-Length Elastic Tubes

Journal of Biomechanical Engineering ◽

10.1115/1.4050284 ◽

2021 ◽

Author(s):

Shashank Acharya ◽

Wenjun Kou ◽

Sourav Halder ◽

Dustin A. Carlson ◽

Peter J. Kahrilas ◽

...

Keyword(s):

Physiological State ◽

Balloon Dilation ◽

Elastic Tube ◽

Peristaltic Wave ◽

Immersed Boundary ◽

Healthy Human ◽

Elastic Tubes ◽

Peristaltic Pumping ◽

1D Model ◽

Work Done

Abstract Balloon dilation catheters are often used to quantify the physiological state of peristaltic activity in tubular organs and comment on their ability to propel fluid which is important for healthy human function. To fully understand this system's behavior, we analyzed the effect of a solitary peristaltic wave on a fluid-filled elastic tube with closed ends. A reduced order model that predicts the resulting tube wall deformations, flow velocities and pressure variations is presented. This simplified model is compared with detailed fluid-structure 3D immersed boundary simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our 1D model under laminar flow conditions. Using the 1D model, several pumping regimes were investigated and presented in the form of a regime map that summarizes the system's response for a range of physiological conditions. Finally, the amount of workdone during a peristaltic event in this configuration was defined and quantified. The variation of elastic energy and work done during pumping was found to have a unique signature for each regime. An extension of the 1D model is applied to enhance patient data collected by the device and find the work done for a typical esophageal peristaltic wave. This detailed characterization of the system's behavior aids in better interpreting the clinical data obtained from dilation catheters. Additionally, the pumping capacity of the esophagus can be quantified for comparative studies between disease groups.

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