RESUMEN
A previously developed model of a lymphatic vessel as a chain of lymphangions was investigated to determine whether lymphangions of unequal length reduce pumping relative to a similar chain of equal-length ones. The model incorporates passive elastic and active contractile properties taken from ex vivo measurements, and intravascular lymphatic valves as transvalvular pressure-dependent resistances to flow with hysteresis and transmural pressure-dependent bias to the open state as observed experimentally. Coordination of lymphangion contractions is managed by marrying an autonomous transmural pressure-dependent pacemaker for each lymphangion with bidirectional transmission of activation signals between lymphangions, qualitatively matching empirical observations. With eight lymphangions as used here and many nonlinear constraints, the model is capable of complex outcomes. The expected flow-rate advantage conferred by longer lymphangions everywhere was confirmed. However, the anticipated advantage of uniform lymphangions over those of unequal length, compared in chains of equal overall length, was not found. A wide variety of dynamical outcomes was observed, with the most powerful determinant being the adverse pressure difference, rather than the arrangement of long and short lymphangions. This work suggests that the wide variation in lymphangion length which is commonly observed in collecting lymphatic vessels does not confer disadvantage in pumping lymph.
Asunto(s)
Vasos Linfáticos , Modelos Biológicos , Sistema Linfático/fisiología , Vasos Linfáticos/fisiología , Linfa/fisiología , Presión , Contracción MuscularRESUMEN
The phasic contractions of collecting lymphatic vessels are reduced in strength and occur at diminished frequency when a favorable pressure difference and the resulting antegrade flow create large fluid shear stresses at the luminal surface. This paper describes a minimal phenomenological model of this mechanism that is applied to a previously validated numerical model of a phasically contracting lymphangion. The parameters of the inhibition model are quantitatively matched to observations in isolated segments of rat lymphatic vessel, first for mesenteric lymphatics then for thoracic duct, and outcomes from the numerical model are then qualitatively compared with recent observations in isolated segments of rat thoracic duct.
RESUMEN
An existing axisymmetric fluid/structure-interaction (FSI) model of the spinal cord, pia mater, subarachnoid space, and dura mater in the presence of syringomyelia and subarachnoid-space stenosis was modified to include porous solids. This allowed investigation of a hypothesis for syrinx fluid ingress from cerebrospinal fluid (CSF). Gross model deformation was unchanged by the addition of porosity, but pressure oscillated more in the syrinx and the subarachnoid space below the stenosis. The poroelastic model still exhibited elevated mean pressure in the subarachnoid space below the stenosis and in the syrinx. With realistic cord permeability, there was slight oscillatory shunt flow bypassing the stenosis via the porous tissue over the syrinx. Weak steady streaming flow occurred in a circuit involving craniocaudal flow through the stenosis and back via the syrinx. Mean syrinx volume was scarcely altered when the adjacent stenosis bisected the syrinx, but increased slightly when the syrinx was predominantly located caudal to the stenosis. The fluid content of the tissues over the syrinx oscillated, absorbing most of the radial flow seeping from the subarachnoid space so that it did not reach the syrinx. To a lesser extent, this cyclic swelling in a boundary layer of cord tissue just below the pia occurred all along the cord, representing a mechanism for exchange of interstitial fluid (ISF) and cerebrospinal fluid which could explain recent tracer findings without invoking perivascular conduits. The model demonstrates that syrinx volume increase is possible when there is subarachnoid-space stenosis and the cord and pia are permeable.
Asunto(s)
Líquido Cefalorraquídeo , Modelos Biológicos , Médula Espinal/fisiopatología , Espacio Subaracnoideo/patología , Espacio Subaracnoideo/fisiopatología , Siringomielia/líquido cefalorraquídeo , Siringomielia/fisiopatología , Simulación por Computador , Constricción Patológica/patología , Constricción Patológica/fisiopatología , Módulo de Elasticidad , Humanos , Hidrodinámica , Porosidad , Reología/métodosRESUMEN
Chronic dysfunction of the lymphatic vascular system results in fluid accumulation between cells: lymphoedema. The condition is commonly acquired secondary to diseases such as cancer or the associated therapies. The primary driving force for fluid return through the lymphatic vasculature is provided by contractions of the muscularized lymphatic collecting vessels, driven by electrochemical oscillations. However, there is an incomplete understanding of the molecular and bioelectric mechanisms involved in lymphatic muscle cell excitation, hampering the development and use of pharmacological therapies. Modelling in silico has contributed greatly to understanding the contributions of specific ion channels to the cardiac action potential, but modelling of these processes in lymphatic muscle remains limited. Here, we propose a model of oscillations in the membrane voltage (M-clock) and intracellular calcium concentrations (C-clock) of lymphatic muscle cells. We modify a model by Imtiaz and colleagues to enable the M-clock to drive the C-clock oscillations. This approach differs from typical models of calcium oscillators in lymphatic and related cell types, but is required to fit recent experimental data. We include an additional voltage dependence in the gating variable control for the L-type calcium channel, enabling the M-clock to oscillate independently of the C-clock. We use phase-plane analysis to show that these M-clock oscillations are qualitatively similar to those of a generalised FitzHugh-Nagumo model. We also provide phase plane analysis to understand the interaction of the M-clock and C-clock oscillations. The model and methods have the potential to help determine mechanisms and find targets for pharmacological treatment of lymphoedema.
Asunto(s)
Vasos Linfáticos , Potenciales de Acción , Calcio/metabolismo , Canales de Calcio Tipo L/química , Canales de Calcio Tipo L/metabolismo , Vasos Linfáticos/metabolismo , Células MuscularesRESUMEN
The aim of this investigation was to achieve the first step toward a comprehensive model of the lymphatic system. A numerical model has been constructed of a lymphatic vessel, consisting of a short series chain of contractile segments (lymphangions) and of intersegmental valves. The changing diameter of a segment governs the difference between the flows through inlet and outlet valves and is itself governed by a balance between transmural pressure and passive and active wall properties. The compliance of segments is maximal at intermediate diameters and decreases when the segments are subject to greatly positive or negative transmural pressure. Fluid flow is the result of time-varying active contraction causing diameter to reduce and is limited by segmental viscous and valvular resistance. The valves effect a smooth transition from low forward-flow resistance to high backflow resistance. Contraction occurs sequentially in successive lymphangions in the forward-flow direction. The behavior of chains of one to five lymphangions was investigated by means of pump function curves, with variation of valve opening parameters, maximum contractility, lymphangion size gradation, number of lymphangions, and phase delay between adjacent lymphangion contractions. The model was reasonably robust numerically, with mean flow-rate generally reducing as adverse pressure was increased. Sequential contraction was found to be much more efficient than synchronized contraction. At the highest adverse pressures, pumping failed by one of two mechanisms, depending on parameter settings: either mean leakback flow exceeded forward pumping or contraction failed to open the lymphangion outlet valve. Maximum pressure and maximum flow-rate were both sensitive to the contractile state; maximum pressure was also determined by the number of lymphangions in series. Maximum flow-rate was highly sensitive to the transmural pressure experienced by the most upstream lymphangions, suggesting that many feeding lymphatics would be needed to supply one downstream lymphangion chain pumping at optimal transmural pressure.
Asunto(s)
Vasos Linfáticos/fisiología , Modelos Biológicos , Ingeniería Biomédica , Impedancia Eléctrica , Humanos , Vasos Linfáticos/anatomía & histología , Presión , ReologíaRESUMEN
A finite-element numerical model was constructed of the spinal cord, pia mater, filum terminale, cerebrospinal fluid in the spinal subarachnoid space (SSS), and dura mater. The cord was hollowed out by a thoracic syrinx of length 140 mm, and the SSS included a stenosis of length 30 mm opposite this syrinx. The stenosis severity was varied from 0% to 90% by area. Pressure pulse excitation was applied to the model either at the cranial end of the SSS, simulating the effect of cranial arterial pulsation, or externally to the abdominal dura mater, simulating the effect of cough. A very short pulse was used to examine wave propagation; a pulse emulating cardiac systole was used to examine the effects of fluid displacement. Additionally, repetitive sinusoidal excitation was applied cranially. Bulk fluid flow past the stenosis gave rise to prominent longitudinal pressure dissociation ("suck") in the SSS adjacent to the syrinx. However, this did not proportionally increase the longitudinal motion of fluid in the syrinx. The inertia of the fluid in the SSS, together with the compliance of this space, gave a resonance capable of being excited constructively or destructively by cardiac or coughing impulses. The main effect of mild stenosis was to lower the frequency of this resonance; severe stenosis damped out to-and-fro motions after the end of the applied excitation. Syrinx fluid motion indicated the fluid momentum and thus the pressure developed when the fluid was stopped by the end of the syrinx; however, the tearing stress in the local cord material depended also on the instantaneous local SSS pressure and was therefore not well predicted by syrinx fluid motion. Stenosis was also shown to give rise to a one-way valve effect causing raised SSS pressure caudally and slight average cord displacement cranially. The investigation showed that previous qualitative predictions of the effects of suck neglected factors that reduced the extent of the resulting syrinx fluid motion and of the cord tearing stress, which ultimately determines whether the syrinx lengthens.
Asunto(s)
Modelos Neurológicos , Médula Espinal/fisiopatología , Estenosis Espinal/líquido cefalorraquídeo , Estenosis Espinal/fisiopatología , Espacio Subaracnoideo/fisiopatología , Fenómenos Biomecánicos , Ingeniería Biomédica , Simulación por Computador , Duramadre/fisiopatología , Análisis de Elementos Finitos , Humanos , Hidrodinámica , Piamadre/fisiopatología , Espacio Subaracnoideo/patología , Siringomielia/líquido cefalorraquídeo , Siringomielia/fisiopatologíaRESUMEN
A three-dimensional finite-element fluid/structure interaction model of an intravascular lymphatic valve was constructed, and its properties were investigated under both favourable and adverse pressure differences, simulating valve opening and valve closure, respectively. The shear modulus of the neo-Hookean material of both vascular wall and valve leaflet was varied, as was the degree of valve opening at rest. Also investigated was how the valve characteristics were affected by prior application of pressure inflating the whole valve. The characteristics were parameterised by the volume flow rate through the valve, the hydraulic resistance to flow, and the maximum sinus radius and inter-leaflet-tip gap on the plane of symmetry bisecting the leaflet, all as functions of the applied pressure difference. Maximum sinus radius on the leaflet-bisection plane increased with increasing pressure applied to either end of the valve segment, but also reflected the non-circular deformation of the sinus cross section caused by the leaflet, such that it passed through a minimum at small favourable pressure differences. When the wall was stiff, the inter-leaflet gap increased sigmoidally during valve opening; when it was as flexible as the leaflet, the gap increased more linearly. Less pressure difference was required both to open and to close the valve when either the wall or the leaflet material was more flexible. The degree of bias of the valve characteristics to the open position increased with the inter-leaflet gap in the resting position and with valve inflation pressure. The characteristics of the simulated valve were compared with those specified in an existing lumped-parameter model of one or more collecting lymphangions and used to estimate a revised value for the constant in that model which controls the rate of valve opening/closure with variation in applied pressure difference. The effects of the revised value on the lymph pumping efficacy predicted by the lumped-parameter model were evaluated.
Asunto(s)
Vasos Linfáticos/anatomía & histología , Vasos Linfáticos/fisiología , Diseño de Prótesis , Animales , Simulación por Computador , Prótesis Valvulares Cardíacas , Humanos , Ensayo de Materiales , Ratones , Modelos Biológicos , Modelos Cardiovasculares , Modelos Teóricos , Distribución de Poisson , Presión , Resistencia al Corte , Estrés MecánicoRESUMEN
In the published paper, we argued that, although there appear to be no data available on the subject, it is inherently unlikely that lymph having traversed a network of initial lymphatics and pre-collectors then encounters an abrupt transition to vessels with all of the typical properties of collecting lymphatics.
RESUMEN
Initial lymphatic vessels are made up of overlapped endothelial cells that act as unidirectional valves enabling one-way drainage of tissue fluid into the lumen of the initial lymphatics when there is a favourable pressure gradient. Initial lymphatics subsequently drain this fluid into the collecting lymphatics. This paper describes a computational model for a network of passive rat mesenteric lymphatic vessels with sparse secondary valves. The network was simulated with the secondary valves both operational and non-operational. The effects on the cycle-mean outflow-rate from the network of both inflammation and the resistance of the surrounding interstitium were considered. The cycle-mean outflow-rate is sensitive to vessel stiffness. If the influence of primary-valve resistance is reduced relative to that of interstitial resistance and intravascular resistance, there is no absolute advantage of extrinsic pumping, since maximum outflow-rate occurs when vessels are rigid. However, there is relative advantage, in that the outflow-rate at intermediate stiffness is higher with the secondary valves functioning than when they are deactivated. If primary-valve resistance dominates, then extrinsic pumping of non-rigid vessels provides absolute advantage. The nonlinear relation between pressure drop and flow-rate of the endothelial primary valves, combined with downstream compliance and pulsatile external pressure, constitutes a separate mechanism of pumping. By enabling the consideration of interactions between multiple phenomena (primary valves, secondary valves, a real network geometry with multiple branches, deformable vessel walls, interstitial resistance and external pressures), the model offers a perspective for delineating physiological phenomena that have not yet been fully linked to the biomechanics of fluid flow through initial lymphatic networks.
Asunto(s)
Sistema Linfático/fisiología , Modelos Biológicos , Animales , Fenómenos Biomecánicos , Inflamación/patología , Vasos Linfáticos/fisiología , Arterias Mesentéricas/fisiología , Presión , Ratas , Reología , Factores de TiempoRESUMEN
1. Flow in single vascular conduits is reviewed, divided into distended and deflated vessels. 2. In distended vessels with pulsatile flow, wave propagation and reflection dominate the spatial and temporal distribution of pressure, determining the shape, size and relative timing of measured pressure waveforms, as well as the instantaneous pressure gradient everywhere. Considerable research has been devoted to accessing the information on pathological vascular malformations contained in reflected waves. Slow waves of contraction of vessel wall muscle, responsible for transport of oesophageal, ureteral and gut contents, have also been modelled. 3. The pressure gradient in a vessel drives the flow. Flow rate can be predicted both analytically and numerically, but analytical theory is limited to idealized geometry. The complex geometry of biological system conduits necessitates computation instead. Initially limited to rigid boundaries, numerical methods now include fluid-structure interaction and can simultaneously model solute transport, thus predicting accurately the environment of the mechanosensors and chemosensors at vessel surfaces. 4. Deflated vessels display all phenomena found in distended vessels, but have additional unique behaviours, especially flow rate limitation and flow-induced oscillation. Flow rate limitation is widespread in the human body and has particular diagnostic importance in respiratory investigation. Because of their liquid lining, the pulmonary airways are also characterized by important two-phase flows, where surface tension phenomena create flows and determine the patency and state of collapse of conduits. 5. Apart from the vital example of phonation, sustained self-excited oscillation is largely avoided in the human body. Where it occurs in snoring, it is implicated in the pathological condition of sleep apnoea.
Asunto(s)
Circulación Sanguínea/fisiología , Vasos Sanguíneos/fisiología , Modelos Biológicos , Flujo Pulsátil/fisiología , Líquidos Corporales/fisiología , Humanos , Peristaltismo/fisiologíaRESUMEN
A pneumatically driven ventricular assist device (VAD) of unconventional geometry, designed to mitigate adverse haemostatic phenomena by optimization of flow patterns, was investigated using two-component laser Doppler anemometry (LDA). Data were taken on a rectilinear grid over two orthogonal traverses, allowing synthesis of three-dimensional velocity vectors over most of the grid. The resulting data were examined by two-dimensional and three-dimensional static and animated computer graphic visualizations of the time-varying vector fields. This analysis revealed illuminating and previously unobserved features of the complex flow fields within pulsatile VADs and identified design considerations that bear upon minimization of turbulence and of flow recirculation and stasis. The findings of this study suggest that, while total abolition of undesirable flow phenomena in a diaphragm-type blood pump is probably impossible, comprehensive investigation in vitro can engender considerable improvements in the efficacy of a device.
Asunto(s)
Velocidad del Flujo Sanguíneo/fisiología , Corazón Auxiliar , Flujometría por Láser-Doppler/métodos , Modelos Cardiovasculares , Flujo Pulsátil/fisiología , Función Ventricular , Simulación por Computador , HumanosRESUMEN
The paper describes the extension of a previously developed model of pressure-dependent contraction rate to the case of multiple lymphangions. Mechanical factors are key modulators of active lymphatic pumping. As part of the evolution of our lumped-parameter model to match experimental findings, we have designed an algorithm whereby the time until the next contraction depends on lymphangion transmural pressure in the contraction just completed. The functional dependence of frequency on pressure is quantitatively matched to isobaric contraction experiments on isolated lymphatic segments. When each of several lymphangions is given this ability, a scheme for their coordination must be instituted to match the observed synchronization. Accordingly, and in line with an experiment on an isolated lymphatic vessel segment in which we measured contraction sequence and conduction delay, we took the fundamental principle to be that local timing can be overridden by signals to initiate contraction that start in adjacent lymphangions, conducted with a short delay. The scheme leads to retrograde conduction when the lymphangion chain is pumping against an adverse pressure difference, but antegrade conduction when contractions occur with no or a favourable pressure difference. Abolition of these conducted signals leads to chaotic variation of cycle-mean flow-rate from the chain, diastolic duration in each lymphangion, and inter-lymphangion delays. Chaotic rhythm is also seen under other circumstances. Because the model responds to increasing adverse pressure difference by increasing the repetition rate of contractions, it maintains time-average output flow-rate better than one with fixed repetition rate.
Asunto(s)
Sistema Linfático/fisiología , Contracción Muscular/fisiología , Presión , Animales , Diástole/fisiología , Procesamiento de Imagen Asistido por Computador , Masculino , Modelos Biológicos , Ratas Sprague-DawleyRESUMEN
Lymph is transported along collecting lymphatic vessels by intrinsic and extrinsic pumping. The walls have muscle of a type intermediate between blood-vascular smooth muscle and myocardium; a contracting segment between two valves (a lymphangion) constitutes a pump. This intrinsic mechanism is investigated ex vivo in isolated, spontaneously contracting, perfused segments subjected to controlled external pressures. The reaction to varying afterload is probed by slowly ramping up the outlet pressure until pumping fails. Often the failure occurs when the contraction raises intra-lymphangion pressure insufficiently to overcome the outlet pressure, open the outlet valve and cause ejection, but many segments fail by other means, the mechanisms of which are not clear. We here elucidate those mechanisms by resort to a numerical model. Experimental observations are paired with comparable findings from computer simulations, using a lumped-parameter model that incorporates previously measured valve properties, plus new measurements of active contractile and passive elastic properties, and the dependence of contraction frequency on transmural pressure, all taken from isobaric twitch contraction experiments in the same vessel. Surprisingly, the model predicts seven different possible modes of pump failure, each defined by a different sequence of valve events, with their occurrence depending on the parameter values and boundary conditions. Some, but not all, modes were found experimentally. Further model investigation reveals routes by which a vessel exhibiting one mode of failure might under altered circumstances exhibit another.
Asunto(s)
Válvulas Cardíacas/fisiología , Corazón Auxiliar , Sistema Linfático/fisiología , Análisis Numérico Asistido por Computador , Animales , Simulación por Computador , Modelos Biológicos , Contracción Muscular , Fibras Musculares Esqueléticas/fisiología , Perfusión , Presión , RatasRESUMEN
The transport capacity of a contractile segment of lymphatic vessel is defined by its pump function curve relating mean flow-rate and adverse pressure difference. Numerous system characteristics affect curve shape and the magnitude of the generated flow-rates and pressures. Some cannot be varied experimentally, but their separate and interacting effects can be systematically revealed numerically. This paper explores variations in the rate of change of active tension and the form of the relation between active tension and muscle length, factors not known from experiment to functional precision. Whether the pump function curve bends toward or away from the origin depends partly on the curvature of the passive pressure-diameter relation near zero transmural pressure, but rather more on the form of the relation between active tension and muscle length. A pump function curve bending away from the origin defines a well-performing pump by maximum steady output power. This behaviour is favoured by a length/active-tension relationship which sustains tension at smaller lengths. Such a relationship also favours high peak mechanical efficiency, defined as output power divided by the input power obtained from the lymphangion diameter changes and active-tension time-course. The results highlight the need to pin down experimentally the form of the length/active-tension relationship.
Asunto(s)
Vasos Linfáticos/fisiología , Fenómenos Mecánicos , Modelos Biológicos , Fenómenos BiomecánicosRESUMEN
Rotary blood pumps offer a cost-effective way to assist the failing heart. Relative to their pulsatile cousins, they can consist of remarkably few moving parts, with attendant advantages in reliability. These advantages are realized in full only if the entire assist system is kept maximally simple. Control of the pump must therefore be based on a minimum number of measurement devices. This paper reviews the measurements that are made in the wide range of implantable rotary blood pump designs that are in development for ventricular assist. In a number of these, fluid-mechanical variables are estimated indirectly from measurements of motor speed and current or power. The introduction explains the goals of rotary blood pump control by comparison to the innate properties of the natural heart. Then motor and fluid-mechanical variables that may be transduced are discussed. Methods of indirect estimation of pressure drop and flow-rate are dealt with, followed by ways of detecting unusual states such as inflow obstruction. It is found that detection of these alone can be the basis of an adequate control strategy. Some groups have estimated variables pertaining to the heart that is being assisted, and there has also been work on monitoring the ongoing health of the assist system itself. The review concludes with a brief look at the wider measurement context for the intensive-care facility that proposes to use such devices to provide circulatory support.
Asunto(s)
Análisis de Falla de Equipo/métodos , Corazón Auxiliar , Hemorreología/instrumentación , Hemorreología/métodos , Prótesis e Implantes , Evaluación de la Tecnología Biomédica/métodos , Diseño Asistido por Computadora , Diseño de Equipo , RotaciónRESUMEN
Vein flow in the large extraparenchymal pulmonary veins is pulsatile and its wave form has an inverse relationship to left atrial pressure. Extraparenchymal pulmonary veins are thin walled and collapsible. This enables them to behave as highly compliant structures. Dimensional measurements of their cross sectional area in living open chested dogs showed them to be non circular at low left atrial pressures. They rapidly assumed a circular cross section as left atrial pressure rose. Only at pressures above 1.5 kPa (11 mmHg) were the pulmonary veins circular in cross section. The aggregate volume of the large extraparenchymal pulmonary veins, when fully distended, was found to be equal to or greater than one stroke volume of the heart. The extraparenchymal pulmonary veins act as a reservoir to the left atrium so that left ventricular stroke volume can be maintained relatively unaffected by beat by beat changes in right ventricular stroke output. Their behaviour at normal mean left atrial pressures also enables them to isolate the lung capillaries from retrograde transmission of positive pressure transients from the left atrium, which could otherwise impede venous outflow of blood from the lung capillary bed.
Asunto(s)
Circulación Pulmonar , Venas Pulmonares/fisiología , Animales , Función Atrial , Biometría , Presión Sanguínea , Adaptabilidad , Perros , Venas Pulmonares/anatomía & histología , Volumen Sistólico , UltrasonografíaRESUMEN
Blood-contacting surface modifications aimed at reduction of thromboembolic complications have included the texturing of surfaces so as to promote the formation of a stable pseudo-neointima. A technique has been developed whereby a textured surface consisting of regularly spaced micro-fibres was produced on a smooth base plane. Polyurethane vascular patches with and without the textured luminal surface were fabricated and implanted bilaterally in ovine carotid arteries for 1- and 3-week implantation periods (n = 6 per period). One of 6 arteries with textured patches in the 1-week group was occluded. All other arteries were patent. At 1 week, all patent textured patches had adherent thrombus covering the entire patch surface. By 3 weeks, the thrombus had organised to form a stable pseudo-neointima. Non-textured patches at 1 week had only partial surface coverage of thrombus. At 3 weeks, 4 of 6 non-textured patches had significant red thrombus in the lumen. At 3 weeks, there was also evidence of cellular migration from artery onto both textured and non-textured patches. These findings suggest that the major role of the textured surface was as a promoter of a stabilised thrombus base onto which subsequent cellular migration and tissue healing occurred more rapidly than onto a smooth polyurethane surface.
Asunto(s)
Materiales Biocompatibles , Prótesis Vascular , Sangre , Animales , Arterias Carótidas/cirugía , Masculino , Ensayo de Materiales , Microscopía Electrónica de Rastreo , Poliuretanos , Ovinos , Propiedades de Superficie , Tromboembolia/prevención & control , Factores de TiempoRESUMEN
Segments of silicone rubber tube were suspended between rigid pipes and subjected to slowly varying transmural pressure covering a range from slight distension to collapse with osculation. The local inside cross-sectional area at a chosen axial site was simultaneously measured via catheter by an electrical impedance method. Pressure-area relations were recorded thus at various axial sites, under varying conditions of axial tube wall tension, in tubes of two different wall thickness (0.3 and 0.4 of mean radius). Unsupported tube segment length was also varied by means of an insert device. The relations were used to calculate the variation of wave velocity with area according to Young's equation. First opposite wall contact during collapse was shown to occur at a smaller fraction of undistended circular cross-sectional area than in the thin-walled tubes investigated previously by others.
Asunto(s)
Presión Hidrostática , Músculo Liso/fisiología , Presión , Presión Sanguínea , Humanos , Modelos Cardiovasculares , Músculo Liso Vascular/fisiología , ReologíaRESUMEN
Thick-walled silicone rubber tube connected to rigid pipes upstream and downstream was externally pressurised (pe) to cause collapse while aqueous fluid flowed through propelled by a constant upstream head. Three types of equilibrium were found: stable equilibria (steady flow) at high downstream flow resistance R2, self-excited oscillations at low R2, and 'unattainable' (by varying external pressure) or exponentially unstable equilibria at intermediate R2. The self-excited oscillations were highly non-linear and appeared in four, apparently discrete, frequency bands: 2.7 Hz, 3.8-5.0 Hz, 12-16 Hz and 60-63 Hz, suggesting that the possible oscillation modes may be harmonically related. Stable, intermediate 'two-in-every-three-beats' oscillation was also observed, with a repetition frequency in the 3.8-5.0 Hz band. As pe was increased, self-excited oscillations were eventually suppressed, leaving internal fluid pressure varying with no single dominant frequency as a result of turbulent jet dissipation at the downstream rigid pipe connection. Comparison of pressure-wave velocity calculated from the local pressure-area relation for the tube with fluid velocity indicated that supercritical velocities were attained in the course of the self-excited oscillations.
Asunto(s)
Líquidos Corporales/fisiología , Modelos Anatómicos , Fenómenos Biomecánicos , Humanos , ReologíaRESUMEN
A simple, third-order lumped parameter model is presented to describe unsteady flow in a short segment of collapsible tube held between two rigid segments and contained in a pressurised chamber. Equilibrium states and their stability are analysed in detail, as is fully non-linear time dependent behaviour, including in particular the excitation and sustenance of limit--cycle oscillations. The model explicitly neglects both wave propagation (and hence the possibility of choking) and the influence on the elastic properties of the tube of longitudinal tension, but it is otherwise firmly based on fluid mechanical principles. The results emphasise the profound importance of (a) the unsteady head loss (but with some pressure recovery) in the separated flow at the oscillating throat, and (b) the mechanical properties of the parts of the system both downstream and upstream of the collapsible segment. The nature of the upstream segment in particular determines whether it is an upstream pressure head or the inflow to the collapsible segment that is held constant during oscillations. The results are discussed in the context both of other models and of experiment.