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T J Pedley - One of the best experts on this subject based on the ideXlab platform.
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flow and oscillations in collapsible tubes Physiological Applications and low dimensional models
Sadhana-academy Proceedings in Engineering Sciences, 2015Co-Authors: T J Pedley, Draga PihlerpuzovicAbstract:The motivation for this subject comes from physiology: Air-flow in the lungs, where flow limitation during forced expiration is a consequence of large-airway collapse, and wheezing, which is a manifestation of self-excited mechanical oscillations; Blood flow in veins, such as those of giraffes, in which the return of blood to the heart from the head must be accompanied by partial venous collapse, and in arteries, which exhibit self-excited oscillations (Korotkov sounds) when compressed by a blood-pressure cuff. Laboratory experiments are frequently conducted in a Starling resistor, a finite length of flexible tube, mounted between two rigid tubes and contained in a pressurised chamber. Steady conditions upstream and downstream give rise not only to steady flows, but also to a rich variety of self-excited oscillations, which theoreticians have been seeking to understand for at least five decades. Some of the observations have been reproduced in full Navier–Stokes computations for a two-dimensional model, but these do not provide physical understanding. We seek a self-consistent mathematical model for the oscillations. We concentrate first on 1D models, in which the key dependent variables are the cross-sectional area A and the cross-sectionally averaged velocity u and pressure p, all taken to be functions of longitudinal coordinate x and time t. The governing equations are those of conservation of mass and momentum and a tube law representing the elastic properties of the vessel. In the momentum equation, the viscous resistance term is conventionally modelled either as a linear function of fluid velocity, accurate at low Reynolds number, or with an ad hoc representation of the energy loss at flow separation. Even with such crude approximations, the predictions of 1D models agree quite well both with observations in the giraffe and with some of the 2D computations and 3D experiments. For a more rational model, we examine a 2D model problem, in which part of one wall of a parallel sided channel is replaced by a membrane under tension. One approach, for large Reynolds-number flow, and a long membrane, is to consider small deflections of the membrane and use interactive boundary-layer theory. This leads to interesting predictions, such as the impossibility of simultaneously prescribing the flow rate and the upstream pressure, but not to oscillations, except in cases where wall inertia is important (flutter). Another approach is to assume a parabolic velocity profile everywhere, leading to a rational choice for the inertia and viscous terms in the 1D momentum equation. If, further, the undisturbed membrane is taken to be flat, by a suitable choice of external pressure distribution, the system leads to an oscillatory instability even without wall inertia. Whether these oscillations have the same physics as those computed numerically at lower Reynolds number remains to be seen.
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numerical solutions for unsteady gravity driven flows in collapsible tubes evolution and roll wave instability of a steady state
Journal of Fluid Mechanics, 1999Co-Authors: Bindi S Brook, S A E G Falle, T J PedleyAbstract:Unsteady flow in collapsible tubes has been widely studied for a number of different Physiological Applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes. The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method. Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.
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Theoretical and Computational © Springer-Verlag 1998 Fluid Dynamics Modelling Flow and Oscillations in Collapsible Tubes1
1997Co-Authors: T J Pedley, X. Y. LuoAbstract:Abstract. Laboratory experiments designed to shed light on fluid flow through collapsible tubes, a problem with several Physiological Applications, invariably give rise to a wide variety of self-excited oscillations. The object of modelling is to provide scientific understanding of the complex dynamical system in question. This paper outlines some of the models that have been developed to describe the standard experiment, of flow along a finite length of elastic tube mounted at its ends on rigid tubes and contained in a chamber whose pressure can be independently varied. Lumped and one-dimensional models have been developed for the study of steady flow and its instability, and a variety of oscillation types are indeed predicted. However, such models cannot be rationally derived from the full governing equations, relying as they do on several crude, ad hoc assumptions such as that concerning the energy loss associated with flow separation at the time-dependent constriction during large-amplitude oscillations. A complete scientific description can be given, however, for a related two-dimensional configuration, of flow in a parallel-sided channel with a segment of one wall replaced by a membrane under longitudinal tension T. The flow and membrane displacement have been calculated successively by lubrication theory, Stokes-flow computation, steady Navier–Stokes computation and unsteady Navier–Stokes computation. For a given Reynolds number, Re, steady flow becomes unstable when T falls below a critical value (equivalently, when Re exceeds a critical value for fixed T), and th
Vakhtang Putkaradze - One of the best experts on this subject based on the ideXlab platform.
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swirling fluid flow in flexible expandable elastic tubes variational approach reductions and integrability
Physica D: Nonlinear Phenomena, 2020Co-Authors: Rossen I Ivanov, Vakhtang PutkaradzeAbstract:Abstract Many engineering and Physiological Applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life Applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and unshearable tube with a straight centerline. In the absence of vorticity, our model reduces to previous models considered in the literature, yielding the equations of conservation of fluid momentum, wall momentum and the fluid volume. We pay special attention to the case when the vorticity is present but kept at a constant value. We show the conservation of energy-like quality and find an additional momentum-like conserved quantity. Next, we develop an alternative formulation, reducing the system of three conservation equations to a single compact equation for the back-to-labels map. That single equation shows interesting instability in solutions when the velocity exceeds a critical value. Furthermore, the equation in stable regime can be reduced to Boussinesq-type, KdV and Monge–Ampere equations in several appropriate limits, namely, the first two in the limit of a long time and length scales and the third one in the additional limit of the small cross-sectional area. For the unstable regime, the numerical solutions demonstrate the spontaneous appearance of large oscillations in the cross-sectional area.
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swirling fluid flow in flexible expandable elastic tubes variational approach reductions and integrability
arXiv: Fluid Dynamics, 2019Co-Authors: Rossen I Ivanov, Vakhtang PutkaradzeAbstract:Many engineering and Physiological Applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life Applications like blood flow, there is often an additional complexity of vorticity being present in the fluid. We present a theory for the dynamics of interaction of fluids and structures. The equations are derived using the variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and unshearable tube with a straight centerline. In the absence of vorticity, our model reduces to previous models considered in the literature, yielding the equations of conservation of fluid momentum, wall momentum and the fluid volume. We show that even when the vorticity is present, but is kept at a constant value, the case of an inextensible, unshearable and straight tube with elastics walls carrying a fluid allows an alternative formulation, reducing to a single compact equation for the back-to-labels map instead of three conservation equations. That single equation shows interesting instability in solutions when the vorticity exceeds a certain threshold. Furthermore, the equation in stable regime can be reduced to Boussinesq-type, KdV and Monge-Ampere equations equations in several appropriate limits, namely, the first two in the limit of long time and length scales and the third one in the additional limit of the small cross-sectional area. For the unstable regime, we numerical solutions demonstrate the spontaneous appearance of large oscillations in the cross-sectional area.
Robert K Dyer - One of the best experts on this subject based on the ideXlab platform.
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Ann Orol Rhinol Laryngo/llO:2001 MASS LOADING ON THE OSSICLES AND MIDDLE EAR FUNCTION
2016Co-Authors: Rong Z Gan, Mark W Wood, Robert K DyerAbstract:The middle ear as a levered vibrating system for sound transmission from the external to the inner ear is affected by changes in ossicular chain mass. Mass loading of the ossicles may impair ossicular dynamics and sound transmission to the inner ear. It is incumbent on otologic surgeons and researchers of middle ear mechanics to consider the mass loading effect on middle ear function in clinical and Physiological Applications. The residual hearing and frequency response can change after surgery or implantation of middle ear prostheses. We conducted experiments on mass loading effects on the middle ear transfer functions by using laser Doppler interferometry and a human temporal bone model. Two implant mass loading conditions were tested on 17 fresh or fresh-frozen temporal bones and compared with the unloaded condition for the frequencies 250 to 8,000 Hz. The results show that the linearity of the middle ear function did not change, although displacement of the stapes footplate decreased after the increased masses were placed on the incudostapedial joint. The greater the mass of the implant, the less displacement was measured at the stapes footplate. We conclude that there is a quantitative limit to increased mass on the ossicular chain above which the mass will remarkably impair hearing thresholds. KEY WORDS- implantable hearing device, laser Doppler interferometry, mass loading, middle ear, ossicle, temporal bone
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mass loading on the ossicles and middle ear function
Annals of Otology Rhinology and Laryngology, 2001Co-Authors: Rong Z Gan, Mark W Wood, Robert K Dyer, Kenneth J DormerAbstract:The middle ear as a levered vibrating system for sound transmission from the external to the inner ear is affected by changes in ossicular chain mass. Mass loading of the ossicles may impair ossicular dynamics and sound transmission to the inner ear. It is incumbent on otologic surgeons and researchers of middle ear mechanics to consider the mass loading effect on middle ear function in clinical and Physiological Applications. The residual hearing and frequency response can change after surgery or implantation of middle ear prostheses. We conducted experiments on mass loading effects on the middle ear transfer functions by using laser Doppler interferometry and a human temporal bone model. Two implant mass loading conditions were tested on 17 fresh or fresh-frozen temporal bones and compared with the unloaded condition for the frequencies 250 to 8000 Hz. The results show that the linearity of the middle ear function did not change, although displacement of the stapes footplate decreased after the increased masses were placed on the incudostapedial joint. The greater the mass of the implant, the less displacement was measured at the stapes footplate. We conclude that there is a quantitative limit to increased mass on the ossicular chain above which the mass will remarkably impair hearing thresholds.
Rong Z Gan - One of the best experts on this subject based on the ideXlab platform.
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Ann Orol Rhinol Laryngo/llO:2001 MASS LOADING ON THE OSSICLES AND MIDDLE EAR FUNCTION
2016Co-Authors: Rong Z Gan, Mark W Wood, Robert K DyerAbstract:The middle ear as a levered vibrating system for sound transmission from the external to the inner ear is affected by changes in ossicular chain mass. Mass loading of the ossicles may impair ossicular dynamics and sound transmission to the inner ear. It is incumbent on otologic surgeons and researchers of middle ear mechanics to consider the mass loading effect on middle ear function in clinical and Physiological Applications. The residual hearing and frequency response can change after surgery or implantation of middle ear prostheses. We conducted experiments on mass loading effects on the middle ear transfer functions by using laser Doppler interferometry and a human temporal bone model. Two implant mass loading conditions were tested on 17 fresh or fresh-frozen temporal bones and compared with the unloaded condition for the frequencies 250 to 8,000 Hz. The results show that the linearity of the middle ear function did not change, although displacement of the stapes footplate decreased after the increased masses were placed on the incudostapedial joint. The greater the mass of the implant, the less displacement was measured at the stapes footplate. We conclude that there is a quantitative limit to increased mass on the ossicular chain above which the mass will remarkably impair hearing thresholds. KEY WORDS- implantable hearing device, laser Doppler interferometry, mass loading, middle ear, ossicle, temporal bone
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mass loading on the ossicles and middle ear function
Annals of Otology Rhinology and Laryngology, 2001Co-Authors: Rong Z Gan, Mark W Wood, Robert K Dyer, Kenneth J DormerAbstract:The middle ear as a levered vibrating system for sound transmission from the external to the inner ear is affected by changes in ossicular chain mass. Mass loading of the ossicles may impair ossicular dynamics and sound transmission to the inner ear. It is incumbent on otologic surgeons and researchers of middle ear mechanics to consider the mass loading effect on middle ear function in clinical and Physiological Applications. The residual hearing and frequency response can change after surgery or implantation of middle ear prostheses. We conducted experiments on mass loading effects on the middle ear transfer functions by using laser Doppler interferometry and a human temporal bone model. Two implant mass loading conditions were tested on 17 fresh or fresh-frozen temporal bones and compared with the unloaded condition for the frequencies 250 to 8000 Hz. The results show that the linearity of the middle ear function did not change, although displacement of the stapes footplate decreased after the increased masses were placed on the incudostapedial joint. The greater the mass of the implant, the less displacement was measured at the stapes footplate. We conclude that there is a quantitative limit to increased mass on the ossicular chain above which the mass will remarkably impair hearing thresholds.
David Elad - One of the best experts on this subject based on the ideXlab platform.
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General tube law for collapsible thin and thick-wall tubes
Journal of Biomechanics, 2014Co-Authors: Pavel Kozlovsky, Uri Zaretsky, Ariel Jaffa, David EladAbstract:Modeling the complex deformations of cylindrical tubes under external pressure is of interest in engineering and Physiological Applications. The highly non linear post buckling behavior of cross section of the tube during collapse attracted researchers for years. Major efforts were concentrated on studying the behavior of thin wall tubes. Unfortunately, the knowledge on post buckling of thick wall tubes is still incomplete, although many experimental and several theoretical studies have been performed. In this study we systematically studied the effect of the wall thickness on post buckling behavior of the tube. For this purpose, we utilized a computational model for evaluation of the real geometry of the deformed cross sectional area due to negative transmural (internal minus external) pressure. We also developed an experimental method to validate the computational results. Based on the computed cross sections of tubes with different wall thicknesses, we developed a general tube law that accounts for thin or thick wall tubes and fits the numerical data of computed cross sectional areas versus transmural pressures.