Collapsible Tube Research Articles

Experimental optimization of composite collapsible tubular energy absorber device

A four-phase program to improve the specific energy absorbed by axially crushed composite collapsible tubular energy absorber devices was undertaken. In the first phase, examining of the crushing behaviour of non-triggered tubes was carried out. The second phase is aimed at obtaining the best position for the triggered wall. The third phase focuses on the effects of material sizing in order to understand the influence of triggered wall length on the responses of composite circular tubes to the axial crushing load. The results of these three phases of the study contribute to the fourth whose objective is to optimize the shape geometry of the cross-section area to further improving in tube energy absorption capability. The experimental results demonstrated the strong potential benefits of optimizing the material distribution. The sizing and shape optimization of composite collapsible tubes exhibited a pronounced effect on their capability to absorb high specific energy under axial compressive load.

The onset of flow-rate limitation and flow-induced oscillations in collapsible tubes

Experiments were mounted to investigate the onset in a ‘Starling resistor’ of collapsible-tube oscillation, at the lowest possible Reynolds number so as to facilitate matched numerical simulations. The protocol adopted was to set pressure outside the tube and inside the tube at the upstream end, constant and equal to each other, then to progressively lower the downstream pressure past the point of tube collapse and, when this occurred, of oscillation onset. The working fluid was a glycerine/water mixture, and the silicone-rubber tube was suspended horizontally in air. Measurements were made of pressures and flow-rates and of the cross-sectional area at the approximate location of maximum oscillation; separately, the cross-sectional area of the tube in relation to transmural pressure was measured. Parameters varied in the flow experiments were the length of rigid pipe downstream of the collapsing tube, and the fluid viscosity. The pressure/flow-rate coordinates of both the point of peak flow-rate achieved before flow-rate limitation, and the point of oscillation onset, were satisfactorily independent of the pipe length downstream. Both points occurred at flow-rates that decreased with increasing fluid viscosity, so that the corresponding Reynolds numbers decreased more so. Oscillation did not break out below a Reynolds number of about 290 unless there was external mechanical agitation of the apparatus. The amplitude of oscillation decreased progressively towards zero at this point as viscosity was raised. After the flow-rate peak, flow limitation causes a local flow-rate minimum. When oscillation occurred, it started just before this minimum, and died away at the minimum.

Wave propagation in physiological collapsible tubes and a proposal for a Shapiro number

Abstract In this Brief Communication, a few introductory comments are made first, regarding wave propagation in collapsible tubes and flow limitation, as well as what is commonly referred to as the “speed index”, namely the ratio of the flow velocity in the collapsible tube divided by the wave-propagation velocity. It is then proposed that it is fitting for this speed index to be henceforth named as the Shapiro number.

Numerical Simulation of Noninvasive Blood Pressure Measurement

In this paper, a simulation model based on the partially pressurized collapsible tube model for reproducing noninvasive blood pressure measurement is presented. The model consists of a collapsible tube, which models the pressurized part of the artery, rigid pipes connected to the collapsible tube, which model proximal and distal region far from the pressurized part, and the Windkessel model, which represents the capacitance and the resistance of the distal part of the circulation. The blood flow is simplified to a one-dimensional system. Collapse and expansion of the tube is represented by the change in the cross-sectional area of the tube considering the force balance acting on the tube membrane in the direction normal to the tube axis. They are solved using the Runge-Kutta method. This simple model can easily reproduce the oscillation of inner fluid and corresponding tube collapse typical for the Korotkoff sounds generated by the cuff pressure. The numerical result is compared with the experiment and shows good agreement.

Transverse flows in rapidly oscillating elastic cylindrical shells

We analyse the flows in fluid-conveying tubes whose elastic walls perform small-amplitude high-frequency oscillations. We show that the velocity perturbations induced by the wall motion are dominated by their transverse components and use numerical simulations to analyse the two-dimensional flows that develop in the tube's cross-sections. Asymptotic methods are then employed to derive explicit predictions for the flow fields and for the total viscous dissipation, whose magnitude plays an important role in the development of self-excited oscillations. We show that in cases with fluid–structure interaction, the coupled oscillations are controlled by the ratio of the fluid and wall densities, and by a material parameter that is equivalent to the Womersley number, and indicates the importance of fluid inertia and wall elasticity relative to the fluid's viscosity. We present numerical simulations of the coupled oscillations and use asymptotic techniques to derive explicit predictions for their period and decay rate. Finally, we discuss the implications of our results for the development of self-excited oscillations in three-dimensional collapsible tubes.

639 喘息の模擬実験 : 二重壁を持つ気道モデルの座屈に関する生体外実験(G02-7 シミュレーション(2),G02 バイオエンジニアリング)

Bronchial asthma is a kind of chronic bronchitis. It causes an airway narrowing and so makes breathing difficult. It is important to clarify its mechanism. The characteristic of asthmatic airway is that its bucked cross-section consists of many folds in the airway lumen. It is considered to be caused by a rapid constriction of smooth muscle. We paid attention to a rapid change in the transmural pressure as a model of the constriction of smooth muscle. In this study, to clarify the mechanism of the buckling, we used two-layered collapsible tubes as a model of the airway and used a shock tube which gave a sudden decrease in the pressure inside the collapsible tube. The cross-sectional shape of the tube was visualized by a laser sheet method and its behavior during the buckling was photographed by using a high speed video camera. We examined the influence of wall structure and Young's modules of the tube on buckling behavior.

Semi-analytical solution of a constrained fourth-order integro-differential equation of steady flow–structure interaction in a model collapsible tube

We provide accurate, non-perturbative, semi-analytical solutions to a constrained fourth-order integro-differential equation derived by Djorjevic and Vukobratovic [On a steady, viscous flow in two-dimensional channels, Acta Mech. 163 (2003) 189–205] in the study of a steady incompressible flow through a flexible 2D tube. Our numerical experiments motivate the introduction of a global parameter that monitors the deformation of the tube as a function of material properties and flow characteristics. Physically, this parameter is proportional to the work done by the longitudinal tension on the wall. An example is provided on how this global parameter can be used to monitor coronary lesion progression. In particular, this parameter is used to define an index of criticality of such lesions.

A One Dimensional Model to Predict Steady Flow Through a Collapsible Tube

Flow through tubes that can collapse during normal operation characterizes virtually every bodily fluid-carrying vessel. A MATLAB program was developed to solve a one-dimensional numerical model for steady state collapsible tube flow. The numerical results were then compared with experimental findings of Bertram [10]. The model included a novel polynomial-defined relationship between the Reynolds number and skin friction coefficient. The results are in strong agreement with experiment (r > 0.95). Further correlation analysis showed significance at the 0.025 level [r 14 = 0.986; r 17 = 0.975; r 15 = 0.990; r 15 = 0.956; r 19 = 0.943; p ≪ 0.001]. An average error of less than ten percent existed between computations and experiment.

Stability analysis of blood flow in multilayered viscoelastic tubes

Blood flow in arteries and veins as collapsible tubes is determined by fluid–structure interaction. Multilayered structure of the vessel wall and mechanical properties of its layers may influence t...

The siphon controversy counterpoint: the brain need not be “baffling”

The application of siphon principles to the cerebral circulation has engendered a surprising amount of controversy (1–3, 11, 19, 22, 23). The reluctance to apply siphon principles to the cerebral circulation probably stems more from its inescapable, but counterintuitive, corollary: if the

Pressure reflectometry: in vitro recordings with a new technique for simultaneous measurement of cross-sectional area and pressure in a collapsible tube

Pressure reflectometry is a new and easily applicable technique for simultaneous measurement of cross-sectional area and pressure in a collapsible biological tube. Related values of pressure and cross-sectional area are relevant for assessment of the mechanical properties of a biological tube. A very thin and highly flexible 6 cm long polyurethane bag with a diameter of 5 mm when expanded was introduced into test models. The cross-sectional area of the first 6 cm of the cavities up to 16 mm2 (depending of the size of the bag) can be measured at the same time. The cross-sectional area was measured by acoustic reflectometry while pressures of 10–200 cmH2O were applied by a pump. The echoes from the cavity were analyzed and displayed by a computer technique. The aim of the study was to evaluate the technical capabilities and limitations of this new method. The accuracy and reproducibility were examined in eight different models with known cross-sectional areas in the interval of 4–16 mm2. Two of the models had two successive constrictions reducing the cavity to 50% and 25% respectively. Measurements were reliable from about 1 to 5 cm within the cavity and at pressures from 10 to 200 cmH2O. The absolute error in models without constrictions did not exceed 0.9 mm2 and at the first constriction the error did not exceed 1.2 mm2. In cavities without constrictions, the coefficients of variation (CVs) were 0.2–11%. In models with constrictions the CVs were 6–25% at the first constriction when different pressures were applied to the plastic bag. The reproducibility was not influenced significantly by change in background noise, temperature, catheters, geometries of the cavities or new calibration. In conclusion, the accuracy of this new technique depends on the size of the measured cavity, on the pressure in the models and whether the model has constrictions or not. The measurements seem reliable for clinical use in the range of 4–16 mm2 and at pressures from 10 to 200 cmH2O.

Preface: Biofluid mechanics

Why biofluid mechanics? It is a fair question since Physics of Fluids embarked on this special section of papers dedicated to the subject. After some thought, my answer is the relatively simple view that life is a wet and sticky business, to be sure. And to our knowledge it is mostly immersed in our earthly atmosphere. So as long as people and other organisms strive to live, reproduce, and interact with who and what is around them, biofluid mechanics will have a steady stream of challenges. The vast scope of fluid physics, from nano/micro to galactic scales, is certainly understood by the audience of this journal. Biofluid mechanics, while not stretched to such a range of characteristic lengths, is equally vast in its richness of complex fluid properties and unique boundary conditions. For example, phonation derives from the interplay of airflow through the vocal cords, the results varying from love songs to crying to lectures in introductory fluid mechanics. The coupling of air vibrations to the cochlear apparatus of the ear gives the speaker/singer an audience. And it is the homeostatic balance of fluid flow in the eye that lets the reader read. Without healthy biofluid mechanics, we are all potentially deaf, dumb, and blind. By the way, biofluid mechanics researchers are busy in developing diagnostic and assistive modalities for those who do face such obstacles in their daily life. The field of biofluid mechanics is a growing area of research and Physics of Fluids welcomes original contributions. One clear indicator of the increasing interest and activity in this field is the rapid expansion of presentations witnessed at the 57th Annual Meeting of the Division of Fluid Dynamics during 21–23 November 2004 in Seattle, Washington. There were 10 sessions entitled Bio-Fluid Dynamics I–X over the three-day conference period. In addition to the 94 talks in those sessions, there were many others involving biological flows scattered elsewhere in the program. The list of treated topics is quite broad, including flows related to: aneurysms, stenotic blood vessels, stents, flapping flight, experimental methods, dispersion, biomimetics, bioreactors, microfluidics, microcirculation, lab-on-chip devices, animal-on-chip devices, large blood vessels, heart valves, fluid-elastic interactions, non-Newtonian flows, respiration, vocalization, artificial lungs, swimming by animals and actuated models, walking on water with feet or tails, collapsible tubes as conduits or as pumps, interactions with cells, and the mosquito proboscis. The range of applications was perhaps best seen in one of the sessions where “Measuring vortex breakdown flows within open cylindrical bioreactors using stereoscopic particle image velocimetry” was immediately followed by “Sniffers.” The collection of papers in this special section of Physics of Fluids is dedicated to biofluid mechanics and is representative of those seeking new fluid physics in the biological realm. From this interface, one hopes that there is both new fluid mechanics and new biology. These goals often go handin-hand. The papers cover interesting aspects of two-phase flow and stability in the lung where moving and elastic wall boundaries interact with surface tension and flow dynamics, cell–cell and cell–wall interactions in blood flow with complex cell and wall models to account for micro and molecular structure and function, and swimming of spirochetes. I wish to express my thanks to these authors for sharing this work with us. PHYSICS OF FLUIDS 17, 031401 s2005d

The Flow Field Downstream of an Oscillating Collapsed Tube

A two-component laser Doppler anemometer was used to determine the velocity of aqueous flow in the region from 0.25 to 2.5 diameters downstream of a collapsible tube while the tube was executing vigorous repetitive flow-induced oscillations. The Reynolds number for the time-averaged flow was 10,750. A simultaneous measurement of the pressure at the downstream end of the tube was used to align all the results in time at sixty locations in each of the two principal planes defined by the axes of collapse of the flexible tube upstream. The raw data of seed-particle velocity were used to create a periodic waveform for each measured velocity component at each location by least-squares fitting of a Fourier series. The results are presented as both velocity vectors and interpolated contours, for each of ten salient instants during the cycle of oscillation. In the plane of the collapse major axis, the dominant feature is the jet which emerges from each of the two tube lobes when it collapses, but transient retrograde flow is observed on both the central and lateral edges of this jet. In the orthogonal, minor-axis plane, the dominant feature is the retrograde flow, which during part of the cycle extends over the whole plane. All these features are essentially confined to the first 1.5 diameters of the rigid pipe downstream of the flexible tube. These data map the temporal and spatial extent of the highly three-dimensional reversing flow just downstream of an oscillating collapsed tube.

The length and collapsibility of the ureter play roles in the augmented reflection of intraabdominal pressure into the renal pelvis

Background/purpose Flow of a fluid through a collapsible tube is under the influence of various factors including the external compressing pressure. The intraabdominal pressure (IAP) should influence the flow through the ureter. Therefore, an experimental study was planned to investigate the effects of ureteral length and external compressing pressure onto the intrapelvic pressure (IPP) in rabbits. Methods Nineteen adult rabbits were used for the experiment. Under general anesthesia, an intraperitoneal and an intrapelvic catheter were placed to measure IAP and IPP. A urethral catheter was placed for bladder decompression. After this standard preparation, a ureteric stent was placed in the ureter in group 1 (n = 7). Distal or proximal ureter transection was performed in group 2 (n = 6) and group 3 (n = 6), respectively. Basal pressure measurements have been recorded. Then the pressures were recorded every 5 minutes, and IAP was increased gradually for 4 cm of water pressure in each subsequent 30-minute period. All analyses were performed for a standard IAP interval (5 to 25 cm H 2O). Results IAP did not differ between groups ( P = .08). IPP values were significantly higher than the corresponding IAP values in each group ( P = .0001). IPP showed significant difference between IAP values of groups ( P = .0001). IPP was significantly increased in group 2 when compared with group 1 and group 3 ( P = .0001; P = .0001), but no difference was encountered between groups 1 and 3 ( P = .1). There has been a strong relationship between IPP and IAP values in all groups. The Rsq values were 0.912, 0.783, and 0.943 for group 1, group 2, and group 3, respectively ( P < .0001). Mathematic relations between IPP and IAP also were analyzed. The relations were IPP = 3.9 + 1.10 × IAP, IPP = 10.3 + 1.10 × IAP, and IPP = 3.3 + 1.12 × IAP for groups 1, 2, and 3, respectively. Conclusions Renal pelvis pressure responds with augmented increases to increments in IAP in urinary tracts with different ureteric lengths. Increase in IPP is more pronounced in longer ureters possibly owing to increased resistance to flow. Prevention of ureteric wall collapse reverses the augmented increase in IPP responses. Therefore, both the length and collapsibility of the ureter play a detrimental role in the generation of augmented IPP responses to increments in IAP. The magnitude of IPP as a response to increments in IAP can be estimated by using mathematical relations between IPP and IAP. Increases in IAP may simulate proximal ureteric obstruction and may take part in the pathogenesis of hydronephrosis.

Venous Flow Restriction: The Role of Vein Wall Motion in Venous Admixture

Objectives. There are wide differences in flow between vascular beds at rest, even more during stress. The hydrodynamic energy (Energy grade line or EGL) of venous outflows must also vary considerably between vascular beds. We explored the mechanism of venous admixture of differing energy flows using a mechanical model.Materials and methods. The model simulated two venous flows coalescing at a venous junction and then flowing through collapsible venous pumps. Flow rates and pressures were monitored when the venous pumps were full (steady state) and when they were compressed and allowed to refill inducing wall motion (pump flow).Results. With increasing EGL differences between two coalescing venous flows, reduction or cessation (venous flow restriction) of the weaker flow occurred during steady state; higher base EGL of both flows ameliorated venous flow restriction and lower base EGL the opposite. Outflow obstruction favoured venous flow restriction. Pump action in the vicinity of the venous junction abolished venous flow restriction and maximized both venous flows.Conclusion. The model suggests a pivotal role for vein wall motion in venous admixture and regional perfusion. Observations in the model are explained on the basis of network flow principles and collapsible tube mechanics.

A physiologically representative in vitro model of the coronary circulation

With the development of clinical diagnostic techniques to investigate the coronary circulation in conscious humans, the in vitro validation of such newly developed techniques is of major importance. The aim of this study was to develop an in vitro model that is able to mimic the coronary circulation in such a way that coronary pressure and flow signals under baseline as well as hyperaemic conditions are approximated as realistically as possible and are in accordance with recently gained insights into such signals in conscious man. In the present in vitro model the heart, the systemic and coronary circulation are modelled on the basis of the elements of a lumped parameter mathematical model only consisting of elements that can be represented by segments in an experimental set-up. A collapsible tube, collapsed by the ventricular pressure, represents the variable resistance and volume behaviour of the endocardial part of the myocardium. The pressure and flow signals obtained are similar to physiological human coronary pressure and flow, both for baseline and hyperaemic conditions. The model allows for in vitro evaluation of clinical diagnostic techniques.

Venous Flow Restriction: The Role of Vein Wall Motion in Venous Admixture

Objectives. There are wide differences in flow between vascular beds at rest, even more during stress. The hydrodynamic energy ( Energy grade line or EGL) of venous outflows must also vary considerably between vascular beds. We explored the mechanism of venous admixture of differing energy flows using a mechanical model. Materials and methods. The model simulated two venous flows coalescing at a venous junction and then flowing through collapsible venous pumps. Flow rates and pressures were monitored when the venous pumps were full (steady state) and when they were compressed and allowed to refill inducing wall motion (pump flow). Results. With increasing EGL differences between two coalescing venous flows, reduction or cessation ( venous flow restriction) of the weaker flow occurred during steady state; higher base EGL of both flows ameliorated venous flow restriction and lower base EGL the opposite. Outflow obstruction favoured venous flow restriction. Pump action in the vicinity of the venous junction abolished venous flow restriction and maximized both venous flows. Conclusion. The model suggests a pivotal role for vein wall motion in venous admixture and regional perfusion. Observations in the model are explained on the basis of network flow principles and collapsible tube mechanics.

Numerical Model of the Human Cardiovascular System–Korotkoff Sound Simulation

The numerical simulation of the Korotkoff sounds is realized by a 14 segment hemodynamic model of the cardiovascular system developed in the Institute of Thermomechanics, Czech Academy of Sciences. The cardiovascular system is modeled by four segments of the pulsating heart and by 10 vascular segments of pulmonary and systemic circuits connected with the heart in series. To better understand the generation of Korotkoff sounds the systemic arterial flow is studied in detail by a distributed parameter model. The analysis of self-excited oscillations in a collapsible tube (i.e., the systemic artery) is based on a one-dimensional model where the effect of expected flow separation is replaced by the change of viscous friction along the tube.

Variability of inspiratory conductance quantifies flow limitation.

In the present study, our aim was to investigate whether the variability of conductance over the course of inspiration reflects flow limitation. Pressure/flow conditions in the upper airway were modelled by a collapsible tube within a rigid chamber and a pump simulating respiration. Instantaneous conductance was estimated every 20 ms as flow/resistive pressure, and its variability during inspiration expressed as the 90th/50th percentile ratio. Accuracy of this ratio to quantify flow limitation was evaluated by observing whether it changed predictably with adjustments of model parameters. To illustrate the potential of this ratio to quantify flow limitation in a clinical setting, we recorded pneumotachographic airflow and oesophageal pressure in 11 patients with obstructive sleep apnoea during nasal continuous positive airway pressure (CPAP) ventilation, and observed changes in the 90th/50th percentile ratio of inspiratory lung conductance induced by mask pressure titration. Rising pressure surrounding the collapsible tube from subatmospheric to positive values induced progressive inspiratory collapse and increased 90th/50th percentile ratios of inspiratory conductance as predicted. Changes in flow limitation induced by other model modifications were also correctly tracked by the 90th/50th conductance percentile ratio. Increasing mask pressure during CPAP ventilation in sleep apnoea patients from subtherapeutic to therapeutic pressure levels was associated with the expected decrease in the 90th/50th percentile ratio of inspiratory lung conductance from a mean of 6.5+/-3.1 to 1.6+/-0.3 ( P <0.001). We conclude that variability of inspiratory conductance quantified by the 90th/50th percentile ratio may serve as a measure of flow limitation that is independent of the absolute value of conductance.

Contribution of Inertia on Venous Flow in the Lower Limb during Stationary Gait

Blood flows toward the heart through collapsible vessels, the veins. The equations of flow in collapsible tubes in motion show a strong dependence on body forces resulting from gravity and acceleration. This paper analyzes the contribution of body forces to venous blood flow during walking on level ground. It combines the biomechanics of gait and theory of collapsible tubes to point out that body forces due to gravity and limb acceleration cannot be overlooked when considering the determinants of venous blood flow during locomotion. The study involved the development of a kinematic model of the limb as a multi-pendulum arrangement in which the limb segments undergo angular displacements. Angular velocities and accelerations were determined and the body forces were calculated during various phases of the gait cycle. A vascular model of the leg's major venous system was also constructed, and the accelerations due to body and gravity forces were calculated in specific venous segments, using the data from the kinematic model. The results showed there were large, fast variations in the axial component (Gx–Mx) of the body forces in veins between the hip and the ankle. Acceleration peaks down to –2G were obtained at normal locomotion. At fast locomotion, a distal vein in the shank displayed values of (Gx–Mx)/G equal to –3.2. Given the down-to-up orientation of the x-axis, the axial component Mx was usually positive in the axial veins, and Mx could shift from positive to negative during the gait cycle in the popliteal vein and the dorsal venous arch.