Hemodynamic aspects of obliterative processes in peripheral blood vessel--rigid and soft narrowing.

Hemodynamic aspects of obliterative processes in peripheral blood vessels were studied on a mechanical model built of distensible tubing, with a fixed peripheral resistance, through which citrated blood was circulated by pulsatile flow. Hemodynamics of progressive focal stenosis, elongated soft stenosis, and elongated rigid stenosis were assessed. By the use of a hydrodynamic model and a series of in vitro experiments, we have measured the pressure and flow characteristics, and calculated the pressure and energy losses for the various stenotic sites. The critical stricture was found to be larger for a rigid stenosis than a soft stenosis. The length of the stenosis was also an important factor. Increasing the length of a rigid stenosis, for example, by 50 percent resulted in an increase of 25 percent in the flow through the stenosis. The energy dissipation was determined as a preferred indication for several parameters such as: pressure drop, pulsed flow, pulse rate, and the geometry and mechanical properties of the stenosis.     

Attenuation of flow disturbances in tapered arterial grafts

Flow disturbances in tapered arterial grafts of angles of taper between 0.5 and 1.0 deg were measured in vitro using a pulsed ultrasound Doppler velocimeter. The increase in transition Reynolds numbers with angle of taper and axial distance was determined for steady flow. The instantaneous centerline velocities were measured distal to a 50 percent area stenosis (as a model of a proximal anastomosis), in steady and pulsatile flow, from which the disturbance intensities were calculated. A significant reduction in post-stenotic disturbance intensity was recorded in the tapered grafts, relative to a conventional cylindrical graft. In pulsatile flow with a large backflow component, however, there was an increase in disturbance intensity due to diverging flow during flow reversal. This was observed only in the 1.0 deg tapered graft. These findings indicate that taper is an important consideration in the design of vascular prostheses.     

Disorder distal to modeled stenoses in steady and pulsatile flow

Measurements of the velocity and energy spectra were made in the distal region of modeled stenoses in a rigid tube with both steady and pulsatile water flows. Reynolds numbers of 318–2540 and a pulsatile flow frequency parameter of 15 were employed. The effects of the degree of stenosis, the stenosis geometry and the presence or absence of the downstream confining wall on the development of flow disturbances were investigated. Visualization of the distal flow patterns in stenotic and free jets illustrated the existence of complex fields which included vortex shedding, highly turbulent regions, and recirculation zones. Significant flow disorder was created by a mild stenosis in pulsatile, but not in steady, flow. Nondimensionalization employing the stenosis diameter and flow velocity in the throat of the constriction correlates the vortex shedding frequency and energy spectra within a limited postestenotic region.     

Finite element simulation of pulsatile flow through arterial stenosis.

The problem of blood flow through a stenosis is solved using the incompressible Navier-Stokes equations in a rigid circular tube presenting a partial occlusion. Calculations are based on a Galerkin finite element method. The time marching scheme employs a predictor-corrector technique using a variable time step. Results are obtained for steady and physiological pulsatile flows. Computational experiments analyse the effect of varying the degree of stenosis, the stricture length, the Reynolds number and Womersley number. The method gives results which agree well with previous computations for steady flows and experimental findings for steady and pulsatile flows.     

Experimental analysis of the influence of stenotic geometry on steady flow.

We studied the flow behavior under steady flow conditions in four models of cylindrical stenoses at Reynolds numbers from 150 to 920. The flow upstream of the constrictions was always fully developed. The constriction ratios of the rigid tubes (D) to the stenoses (d) were d/D = 0.273; 0.505; 0.548; 0.786. The pressure drop at various locations in the stenotic models was measured with water manometers. The flow was visualized with a photoelasticity apparatus using an aqueous birefringent solution. We also studied the flow behavior at pulsatile flow in a dog aorta with a constriction of 71%. The flow through stenotic geometries depends on the Reynolds number of the flow generated in the tube and the constriction ratio d/D. At low d/D ratios, (with the increased constriction), the flow separation zones (recirculation zones, so-called reattachment length) and flow disturbances increased with larger Reynolds numbers. At lower values, eddies were generated. At high Re, eddies were observed in the pre-stenotic regions. The pressure drop is a function of the length and internal diameter of the stenosis, respective ratio of stenosis to the main vessel and the Reynolds numbers. At low Re-numbers and low d/D, distinct recirculation zones were found close to the stenosis. The flow is laminar in the distal areas. Further experiments under steady and unsteady flow conditions in a dog aorta model with a constriction of 71% showed similar effects. High velocity fluctuations downstream of the stenosis were found in the dog aorta. A videotape demonstrates these results.     

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.     

In vitro system to study realistic pulsatile flow and stretch signaling in cultured vascular cells

We developed a novel real-timeservo-controlled perfusion system that exposes endothelial cells grownin nondistensible or distensible tubes to realistic pulse pressures andphasic shears at physiological mean pressures. A rate-controlled flowpump and linear servo-motor are controlled by digitalproportional-integral-derivative feedback that employspreviously digitized aortic pressure waves as a command signal. Theresulting pressure mirrors the recorded waveform and can be digitallymodified to yield any desired mean and pulse pressure amplitude,typically 0-150 mmHg at shears of 0.5-15 dyn/cm².The system accurately reproduces the desired arterial pressure waveformand cogenerates physiological flow and shears by the interaction ofpressure with the tubing impedance. Rectangular glass capillary tubes[1-mm inside diameter (ID)] are used for real-time fluorescentimaging studies (i.e., pH_i, NO, Ca²⁺), whereassilicon distensible tubes (4-mm ID) are used for more chronic (i.e.,2-24 h) studies regarding signal transduction and geneexpression. The latter have an elastic modulus of12.4 · 10⁶ dyn/cm² similar to in vivovessels of this size and are studied with the use of a benchtop system.The new approach provides the first in vitro application of realisticmechanical pulsatile forces on vascular cells and should facilitatestudies of phasic shear and distension interaction and pulsatile signal transduction.

     

Fluid-Dynamic Optimal Design of Helical Vascular Graft for Stenotic Disturbed Flow

Although a helical configuration of a prosthetic vascular graft appears to be clinically beneficial in suppressing thrombosis and intimal hyperplasia, an optimization of a helical design has yet to be achieved because of the lack of a detailed understanding on hemodynamic features in helical grafts and their fluid dynamic influences. In the present study, the swirling flow in a helical graft was hypothesized to have beneficial influences on a disturbed flow structure such as stenotic flow. The characteristics of swirling flows generated by helical tubes with various helical pitches and curvatures were investigated to prove the hypothesis. The fluid dynamic influences of these helical tubes on stenotic flow were quantitatively analysed by using a particle image velocimetry technique. Results showed that the swirling intensity and helicity of the swirling flow have a linear relation with a modified Germano number (Gn*) of the helical pipe. In addition, the swirling flow generated a beneficial flow structure at the stenosis by reducing the size of the recirculation flow under steady and pulsatile flow conditions. Therefore, the beneficial effects of a helical graft on the flow field can be estimated by using the magnitude of Gn*. Finally, an optimized helical design with a maximum Gn* was suggested for the future design of a vascular graft.     

Differential effects of pulsatile versus steady flow on coronary endothelial membrane potential

Steady shear stress stimulates transient hyperpolarization coupled to calcium-sensitive potassium (KCa) channels and sustained depolarization linked to chloride-selective channels. Physiological flow is pulsatile not static, and whereas in vivo data suggest phasic shear stress may preferentially activate KCa channels, its differential effects on both currents remain largely unknown. To determine this interaction, coronary endothelial cells were cultured in glass capillary flow tubes, loaded with the voltage-sensitive dye bis-(1,3-dibutylbarbituric acid)trimethine oxonol, and exposed to constant or pulsatile shear stress. The latter was generated by a custom servoperfusion system employing physiological pressure and flow waveforms. Steady shear induced a sustained depolarization inhibited by the Cl- channel blocker DIDS. Even after exposure to steady flow, subsequent transition to pulsatile shear stress further stimulated DIDS-sensitive depolarization. DIDS pretreatment "unmasked" a pulsatile flow-induced hyperpolarization of which magnitude was further enhanced by nifedipine, which augments epoxygenase synthesis. Pulse-shear hyperpolarization was fully blocked by KCa channel inhibition (charybdotoxin + apamin), although these agents had no influence on membrane potential altered by steady flow. Thus KCa-dependent hyperpolarization is preferentially stimulated by pulsatile over steady flow, whereas both can stimulate Cl--dependent depolarization. This supports studies showing greater potency of pulsatile flow for triggering KCa-dependent vasorelaxation.     

Comparison of physiological and simple pulsatile flows through stenosed arteries.

Most experimental and numerical studies of pulsatile flow through stenosed arteries have been performed for a first harmonic oscillatory flow. In this paper, numerical solutions are presented for a physiological pulsatile flow as well as for an equivalent simple pulsatile flow, having the same stroke volume as the physiological flow, and the differences in their flow behavior are discussed. The analysis is restricted to laminar flow, Newtonian fluid and axisymmetric rigid stenosis. Comparison of results shows that the behaviors of the two flows are similar at some instances of time, however, important observed differences indicate that for thorough understanding of pulsatile flow behavior in stenosed arteries, the actual physiological flow should be simulated.     

The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: an in vitro model study.

A steady flow, in vitro model of distal arterial bypass graft junctions was used to examine the effects of junction angle and flow rate on the local velocity field. Three test sections were fabricated from Plexiglas tubing having anastomotic junction angles of either 30, 45, or 60 deg. Flow visualization revealed velocity profiles skewed toward the outer wall with a flow split around a clear stagnation point along the outer wall. Laser Doppler anemometry [LDA] measurements confirmed a distinct stagnation point at the outer wall and both reverse and forward shear were detected immediately upstream and downstream, respectively, of this site. Axial velocities and shear rates along the outer wall were higher than along the inner wall and occurred in the junction angle order: 45, 60, and 30 deg. This study clearly identified changes in wall shear which varied with the anastomotic angle and flow rate.     

An experimental study of pressure losses in pulsatile flows through rigid and pulsating stenosis

The time-dependent pressure curves of a pulsatile flow across rigid and pulsating stenoses were investigated experimentally in a laboratory simulator of the outflow tract of the heart right ventricle. The experiments were performed within the range of physiological conditions of frequency and flow rate. The experimental setup consisted of a closed flow system which was operated by a pulsatile pump, and a test chamber which enabled checking different modes of stenosis. Rigid constrictions were simulated by means of axisymmetric blunt-ended annular plugs with moderate-to-severe area reductions. The pulsating stenosis consisted of a short starling resistor device operated by a pulsating external pressure which was synchronized by the pulsatile flow. It was found that the shape of the time-dependent pressure curve upstream of the stenosis was different in the case of rigid stenosis than in the pulsating one. Potential clinical applications of the work may relate to diagnosis of the type of stenosis in the congenital heart disease known as Tetralogy of Fallot.     

Turbulent flow evaluation of the venous needle during hemodialysis

Arteriovenous (AV) grafts and fistulas used for hemodialysis frequently develop intimal hyperplasia (IH) at the venous anastomosis of the graft, leading to flow-limiting stenosis, and ultimately to graft failure due to thrombosis. Although the high AV access blood flow has been implicated in the pathogenesis of graft stenosis, the potential role of needle turbulence during hemodialysis is relatively unexplored. High turbulent stresses from the needle jet that reach the venous anastomosis may contribute to endothelial denudation and vessel wall injury. This may trigger the molecular and cellular cascade involving platelet activation and IH, leading to eventual graft failure. In an in-vitro graft/needle model dye injection flow visualization was used for qualitative study of flow patterns, whereas laser Doppler velocimetry was used to compare the levels of turbulence at the venous anastomosis in the presence and absence of a venous needle jet. Considerably higher turbulence was observed downstream of the venous needle, in comparison to graft flow alone without the needle. While turbulent RMS remained around 0.1 m/s for the graft flow alone, turbulent RMS fluctuations downstream of the needle soared to 0.4-0.7 m/s at 2 cm from the tip of the needle and maintained values higher than 0.1 m/s up to 7-8 cm downstream. Turbulent intensities were 5-6 times greater in the presence of the needle, in comparison with graft flow alone. Since hemodialysis patients are exposed to needle turbulence for four hours three times a week, the role of post-venous needle turbulence may be important in the pathogenesis of AV graft complications. A better understanding of the role of needle turbulence in the mechanisms of AV graft failure may lead to improved design of AV grafts and venous needles associated with reduced turbulence, and to pharmacological interventions that attenuate IH and graft failure resulting from turbulence.     

Visualization of vortex shedding at the proximal side-to-end artery-graft anastomosis

The motion of guanine particles was recorded by video to visualize transitional flow phenomena in models of a proximal side-to-end anastomosis. Close examination of successive video fields revealed that above a critical Reynolds number, particles were periodically shed into the graft from a vortex situated near the anastomosis heel, and this disturbed the flow patterns in the graft causing vortex shedding to occur near to the toe of the anastomosis. The images clearly demonstrated that periodic flow structures propagated distally along the graft for over 15 tube diameters from the proximal anastomosis. The frequency of the vortex shedding was found to increase with Reynolds number. Under pulsatile conditions, the primary vortex at the heel of the anastomosis became unstable during the deceleration phase of the flow cycle and particles were shed downstream into the graft. Although it was possible briefly to observe the characteristic banded structure in the bypass graft, the flow patterns were highly three-dimensional and were quickly broken up by the accelerating flow. Dynamic flow visualization using guanine particles was found to be a complementary technique to particle tracer flow visualization and was highly effective in identifying transitional flow phenomena and the mass transport mechanisms associated with them.     

Flow in tubes and arteries--a comparison

The cardiovascular circulatory system of the human body can be compared with a network of tubes. It consists of a pump and a system of branched vessels. The arteries transport the blood to the periphery in a manner similar to that of a water supply network. It is important to know what kind of forces act upon "fittings", bends and bifurcations. It is also essential to assess whether the flow is laminar or turbulent, attached or separated. The flow should be optimized in such a manner as to minimize the drop in pressure. This means that no additional pressure loss due to separation or turbulence should occur, since such losses increase the pump power requirements. The loss appears in heating and acoustic energy. The necessary understanding of blood flow in human vessels is also of great interest to physicians since it is believed that the local flow behavior of blood determines the formation of atherosclerotic plaques. As in tubing systems, deposits in blood vessels are found close to bends and bifurcations. These deposits lead to impaired cerebral circulation and to myocardial infarction. A partial review of recent research into the details of flow behavior (like separation, stagnation and reattachment points) in bends and bifurcations of arterial models is presented. Studies involving steady and pulsatile flow conditions in rigid and elastic models with Newtonian and non-Newtonian fluids are shown here. The most important differences between blood vessels and tubes are discussed. This modern biofluidmechanical approach of detailed flow examination is compared with the more classical hemodynamic approach considering only gross features such as pressure loss coefficients.     

Comparison of the hemodynamics in 6mm and 4-7 mm hemodialysis grafts by means of CFD

The aim of our study is to investigate with computational fluid dynamics (CFD) whether different arterial anastomotic geometries result in a different hemodynamics at the arterial (AA) and venous anastomosis (VA) of hemodialysis vascular access grafts. We have studied a 6mm graft (CD) and a 4-7 mm graft (TG). A validated three-dimensional CFD model is developed to simulate flow in the two graft types. Only the arterial anastomosis (AA) geometry differs. The boundary conditions applied are a periodic velocity signal at the arterial inlet and a periodic pressure wave at the venous outlet. Flow rate is set to 1,000 ml/min. The time dependent Navier-Stokes equations are solved. Wall shear stress (WSS), wall shear stress gradient (WSSG) and pressure gradient (PG) are calculated. Anastomotic flow is asymmetric although the anastomosis geometry is symmetric. The hemodynamic parameters, WSS, WSSG and PG, values at the suture line of the arterial anastomosis of the TG are at least twice as much as in the CD. Comparing the parameters at the two AA indicate that little flow rate increase introduces the risk of hemolysis in the TG whereas the CD is completely free of hemolysis. The hemodynamic parameter values at the venous anastomosis of the CD are 24 till 35% higher compared to the values of the TG. WSS values (> 3 Pa) in the VA are in the critical range for stenosis development in both graft geometries. The zones where the parameters reach extreme values correspond to the locations where intimal hyperplasia formation is reported in literature. In all anastomoses, the hemodynamic parameter levels are in the range where leucocytes and platelets get activated. Our simulations confirm clinical results where TG did not show a better outcome when compared to the CD.     

Fluid particle motion and Lagrangian velocities for pulsatile flow through a femoral artery branch model

A flow visualization study using selective dye injection and frame by frame analysis of a movie provided qualitative and quantitative data on the motion of marked fluid particles in a 60 degree artery branch model for simulation of physiological femoral artery flow. Physical flow features observed included jetting of the branch flow into the main lumen during the brief reverse flow period, flow separation along the main lumen wall during the near zero flow phase of diastole when the core flow was in the downstream direction, and inference of flow separation conditions along the wall opposite the branch later in systole at higher branch flow ratios. There were many similarities between dye particle motions in pulsatile flow and the comparative steady flow observations.     

Computational Study of Anastomosis Angle of Arteriovenous Fistula for Hemodialysis

Arteriovenous fistula (AVF) is the endorsed method of vascular access for hemodialysis in end-stage renal disease (ESRD). However, more than 60% of AVF fail to mature for hemodialysis. Intimal hyperplasia leads to stenosis is the primary cause of fistula failure. Wall shear stress (WSS) is one of the important parameters that enact a crucial role in building of intimal hyperplasia. The prime purpose of this research work is to investigate the effect of anastomosis angle on WSS, pressure drop, venous outflow rate and identify the optimal angle of anastomosis of AVF, so that it helps to standardize the surgical technique. In this research work, three-dimensional idealized geometries of end-to-side type AVF for the four different angles of anastomosis are created. Numerical simulation performed using incompressible, Newtonian blood to calculate the WSS, blood flow rate at the distal end of the vein and pressure drop across the anastomosis for the three arterial inflow 350, 500 and 900 ml/min. For all three arterial inflow, the WSS is high at 75° compared to other angles and it is less at 60°. The WSS at 45° and 90° are moderate. The venous outflow is increasing with the increase in arterial inflow condition for all anastomosis angles except for 45°. The outflow rate at distal venous end is highest, 344.85 ml/min at 45° for 500 ml/min arterial inflow. Pressure drop high at 45° and lowest at 90°. The intensity of disturbed flow and recirculation zone was observed at the area of anastomosis and it is high at 75°. From the results and observations, it can be concluded that 45° angle is the best choice for the anastomosis of AVF. This finding will standardize the surgical technique and subsequently, it will help to mature the AVF early and for a long time.     

Vortex generation in pulsatile flow through arterial bifurcation models including the human carotid artery

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.     

Fluid flow structure in arterial bypass anastomosis

The fluid flow through a stenosed artery and its bypass graft in an anastomosis can substantially influence the outcome of bypass surgery. To help improve our understanding of this and related issues, the steady Navier-Stokes flows are computed in an idealized arterial bypass system with partially occluded host artery. Both the residual flow issued from the stenosis--which is potentially important at an earlier stage after grafting--and the complex flow structure induced by the bypass graft are investigated. Seven geometric models, including symmetric and asymmetric stenoses in the host artery, and two major aspects of the bypass system, namely, the effects of area reduction and stenosis asymmetry, are considered. By analyzing the flow characteristics in these configurations, it is found that (1) substantial area reduction leads to flow recirculation in both upstream and downstream of the stenosis and in the host artery near the toe, while diminishes the recirculation zone in the bypass graft near the bifurcation junction, (2) the asymmetry and position of the stenosis can affect the location and size of these recirculation zones, and (3) the curvature of the bypass graft can modify the fluid flow structure in the entire bypass system.