Platelet adhesion to fibrinogen-coated glass at an abrupt tubular expansion viewed with fluorescent video-microscopy

The adhesion and detachment of human washed platelets was studied on the surface of the larger tube of a tubular expansion. Measurements were made within the vortex, at the reattachment point and downstream of the vortex. Fluorescent video-microscopy of mepacrine labelled platelets was used to record data continuously. Flow was from the smaller to the larger tube at Reynolds numbers (based on upstream conditions) of 75.4 and 212.2. Measurements of the adhesion efficiency for initially contacting cells and an overall adhesion efficiency were made. These efficiencies decreased with increasing Reynolds number. There was a pattern of variability for both efficiencies with respect to position and Reynolds number which is consistent with the generation of the unstable flow at the reattachment point.     

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.     

Characteristics of secondary flow in steady and pulsatile flows through a symmetrical bifurcation

Steady and pulsatile flow in a glass model simulating an arterial bifurcation was investigated by flow visualization techniques. Secondary flow generated at the bifurcation has a similar pattern to a vortex, called the horseshoe vortex, produced around a wall-based protuberance in a circular tube. The same flow disturbance was clearly observed during the decelerating phase of pulsatile flow. The vortex produces a stagnation point on the top and bottom wall just upstream from the bifurcation apex. When aluminium dust was suspended in the test fluid perfusing the blood vessel model, particles deposited over an area spreading from the stagnation point to the lateral corners of the bifurcation. Comparison between the present results and topographical patterns of atherosclerosis reported in the literature suggests that it is in such low shear regions that lipid deposition tends to occur most.     

Particle flow behavior in models of branching vessels. II. Effects of branching angle and diameter ratio on flow patterns

To further elucidate the role of fluid mechanical factors in the localization of atherogenesis and thrombogenesis, we have studied the 3-dimensional flow patterns in square T-junctions with branching angles theta from 30 degrees to 150 degrees and diameter ratios d/D (side: main tube) from 1.05/3.0 to 1.0. Cine films of the motions of tracer microspheres in dilute suspensions were taken at inflow Reynolds numbers from 15 to 400 and flow ratios (main: side tube) from 0.1 to 4.0. Flow patterns with suspension entering through the main tube were similar to those previously described in uniform 3 mm diameter T-junctions: paired vortices (spiral secondary flows) symmetrical about the common median plane formed at the entrances of the main and side daughter tubes. Particles circulated through the main vortex, some crossing above and below the mainstream into and through the side vortex. At the geometrical flow ratio, the main vortex became smaller and smaller as the branching angle (theta less than 90 degrees) and diameter ratio decreased, and was confined to a thin side tube was a minimum. In obtuse angle T-junctions the stagnation point shifted from the flow divider into the side tube, enhancing the flow disturbance there. The velocity distributions in main and side tubes were skewed towards the inner walls close to the flow divider. When flow entered through the side tube, a pair of recirculation zones formed in the main tube at the inner wall of the bend with a sharper angle.     

Local hemodynamics affect monocytic cell adhesion to a three-dimensional flow model coated with E-selectin.

Monocyte adhesion to the endothelium depends on concentrations of receptors/ligands, local concentrations of chemoattractants, monocyte transport to the endothelial surface and hemodynamic forces. Monocyte adhesion to the inert surface of a three-dimensional perfusion model was shown to correlate inversely with wall shear stress, but was also affected by flow patterns which influenced the near-wall cell availability. We hypothesized that (a) under the same flow conditions, insolubilized E-selectin on the model's surface may mediate adhesive interactions at higher wall shear stresses, compared to an uncoated model, and (b) pulsatile flow may modify the adhesion profile obtained under steady flow. An axisymmetric flow model with a stenosis and a sudden expansion produced a range of wall shear stresses and a separated flow with recirculation and reattachment. Pre-activated U937 cells were perfused through the model under either steady (Re = 100, 140) or pulsatile (Remean = 107) flow. The velocity field was characterized through computational fluid dynamics and validated by inert particle tracking. Surface E-selectin greatly increased cell adhesion in all regions at Re = 100 and 140, compared to an uncoated model under the same flow conditions. In regions where the cells near the wall were abundant (taper and stenosis), adhesion to E-selectin correlated with the reciprocal of local wall shear stress when flow was steady. Pulsatile flow distributed the adherent cells more evenly throughout the coated model. Hence, characterizing both the local hemodynamics and the biological activity on the vessel wall is important in leukocyte adhesion.     

Visualization and finite element analysis of pulsatile flow in models of the abdominal aortic aneurysm

Pulsatile flows in glass models simulating fusiform and lateral saccular aneurysms were investigated by a flow visualization method. When resting fluid starts to flow, the initial fluid motion is practically irrotational. After a short period of time, the flow began to separate from the proximal wall of the aneurysm. Then the separation bubble or vortex grew rapidly in size and filled the whole area of the aneurysm circumferentially. During this period of time, the center of the vortex moved from the proximal end to the distal point of the aneurysm. The transient reversal flow, for instance, which may occur at the end of the ejection period, passed between the wall of the aneurysm and the centrally located vortex. When the rate and pulsatile frequency of flow were high, the vortex broke down into highly disturbed flow (or turbulence) at the distal portion of the aneurysm. The same effect was observed when the length of the aneurysm was increased. A reduction in pulsatile amplitude made the flow pattern close to that in steady flow. A finite element analysis was made to obtain velocity and pressure fields in pulsatile flow through a tube with an axisymmetric expansion. Calculations were performed with the pulsatile flows used in the visualization experiment in order to study the effects of change in the pulsatile wave form by keeping the time-mean Reynolds number and Womersley's parameter unchanged. Calculated instantaneous patterns of velocity field and stream lines agreed well with the experimental results. The appearance and disappearance of the vortex in the dilated portion and its development resulted in complex distributions of pressure and shear fields. Locally minimum and maximum values of wall shear stress occurred at points just upstream and downstream of the distal end of the expansion when the flow rate reached its peak.     

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.     

Model experiments on platelet adhesion in stagnation point flow

Experiments with glass models of arterial branchings and bends, perfused with bovine platelet rich plasma (PRP), revealed platelet deposition being strongly dependent on fluid dynamic factors. Predilection sites of platelet deposits are characterized by flow vectors directed against the wall, so-called stagnation point flow. Thus collision of suspended particles with the wall, an absolute prerequisite for adhesion of platelets to surfaces even as thrombogenic as glass, appears mediated by convective forces. The extent of platelet deposition is correlated to the magnitude of flow components normal to the surface as well as to the state of biological activation of the platelets. The latter could be effective by an increase in hydrodynamically effective volume, invariably associated with the platelet shape change reaction to biochemical stimulants like ADP. The effect of altered rheological properties of platelets upon their deposition and of mechanical properties of surfaces was examined in a stagnation point flow chamber. Roughnesses in the order of 5 microns, probably by creating local flow disturbances, significantly enhance platelet adhesion, as compared to a smooth surface of identical chemical composition.     

Comparison of blood particle deposition models for non-parallel flow domains

Adhesions of monocytes and platelets to a vascular surface, particularly in regions of flow stagnation, recirculation, and reattachment, are a significant initial event in a broad spectrum of particle-wall interactions that significantly influence the formation of stenotic lesions and mural thrombi. A number of approximations are available for the simulation of both monocyte and platelet interactions with the vascular surface. For the simulation of blood particle adhesion, this study hypothesizes that: (a) the discrete element approach, which accounts for finite particle size and inertia, is advantageous in the context of non-parallel flow domains including stagnation, recirculation, and reattachment; and (b) the likelihood for particle deposition may be effectively approximated as being non-linearly proportional to local particle concentration, residence time, and wall proximity. Models such as wall shear stress correlations, the multicomponent mixture approach, and Lagrangian particle tracking with and without hydrodynamic particle-wall interactions were evaluated. Quantitative performance of the selected models was established by comparisons to available experimental data sets for non-parallel axisymmetric suspension flows of monocytes and platelets. Factors including the convective-diffusive transport of particles, finite particle size and inertia, as well as near-wall hydrodynamic interactions were found to significantly influence blood particle deposition. Of the models studied, the near-wall residence time approach was found to be a particularly effective indicator for the deposition of monocytes (r2=0.74) and platelets (r2=0.57), given that nano-scale physical and biochemical effects must be greatly approximated in computational simulations involving relatively large-scale geometries and complex flow fields.     

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.     

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.     

Adhesion of leukocytes under oscillating stagnation point conditions: a numerical study

Leukocyte recruitment from blood to the endothelium plays an important role in atherosclerotic plaque formation. Cells show a primary and secondary adhesive process with primary bonds responsible for capture and rolling and secondary bonds for arrest. Our objective was to investigate the role played by this process on the adhesion of leukocytes in complex flow. Cells were modelled as rigid spheres with spring like adhesion molecules which formed bonds with endothelial receptors. Models of bond kinetics and Newton's laws of motion were solved numerically to determine cell motion. Fluid force was obtained from the local shear rate obtained from a CFD simulation of the flow over a backward facing step.In stagnation point flow the shear rate near the stagnation point has a large gradient such that adherent cells in this region roll to a high shear region preventing permanent adhesion. This is enhanced if a small time dependent perturbation is imposed upon the stagnation point. For lower shear rates the cell rolling velocity may be such that secondary bonds have time to form. These bonds resist the lower fluid forces and consequently there is a relatively large permanent adhesion region.     

Flow patterns at the major T-junctions of the dog descending aorta

Using a novel technique developed in our own laboratory, an isolated transparent arterial segment containing the whole descending aorta and its four major branches was prepared from a dog. The flow patterns at each aortic T-junction were studied in detail under the conditions of steady flow by means of flow visualization and cinemicrographic techniques. It was found that a standing recirculation zone consisting of a pair of thin-layered spiral secondary flows located symmetrically about the common median plane of the aorta and side branches was formed at each T-junction over a wide range of flow conditions including the time-averaged estimated mean values of physiological flow rates and flow rate ratios. The results support the recent in vivo findings by other investigators that flow reversal occurs at some junctions of the dog abdominal aorta during each cardiac cycle. The flow patterns at the aortic T-junctions were very much similar to those previously observed in various glass model T-junctions. However, due to the particular anatomical structure of the vessel wall at each branching site (the curvature of the wall was very sharp at the flow divider, but gently rounded at the bend opposite to it) no recirculation zone was formed in the side branches. At a given flow rate ratio, the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher in aortic T-junctions than those in glass model T-junctions having equivalent branching angles and diameter ratios. These results indicate that, in the circulation, conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows.     

Mechanical buckling of artery under pulsatile pressure

Tortuosity that often occurs in carotid and other arteries has been shown to be associated with high blood pressure, atherosclerosis, and other diseases. However the mechanisms of tortuosity development are not clear. Our previous studies have suggested that arteries buckling could be a possible mechanism for the initiation of tortuous shape but artery buckling under pulsatile flow condition has not been fully studied. The objectives of this study were to determine the artery critical buckling pressure under pulsatile pressure both experimentally and theoretically, and to elucidate the relationship of critical pressures under pulsatile flow, steady flow, and static pressure. We first tested the buckling pressures of porcine carotid arteries under these loading conditions, and then proposed a nonlinear elastic artery model to examine the buckling pressures under pulsatile pressure conditions. Experimental results showed that under pulsatile pressure arteries buckled when the peak pressures were approximately equal to the critical buckling pressures under static pressure. This was also confirmed by model simulations at low pulse frequencies. Our results provide an effective tool to predict artery buckling pressure under pulsatile pressure.     

Patterns of flow in the left coronary artery

The purpose of this investigation is to describe our preliminary observations of the overall pattern of flow in a mold of the left coronary artery of a pig. Flow in the coronary mold was visualized by the injection of dye into the sinus of Valsalva. Studies were performed during steady flow at rates of 100, 200, 300, 400, and 500 mL/min. Studies were also performed during pulsatile flow, using a pulse duplicator that simulated the magnitude and phasic pattern of coronary flow at rest and during reactive hyperemia. At conditions that simulated rest, mean coronary flow was adjusted to 121 mL/min of which 24 mL/min (20 percent) was systolic. During simulated reactive hyperemia, mean flow was 440 mL/min. Visualization of flow revealed the absence of disturbances of turbulence during both steady and pulsatile flow in the left anterior descending (LAD) and left circumflex (CIRC) coronary arteries throughout the entire range of flow studied. Prominent spiraling of flow occurred during steady and pulsatile flow. Spiraling of flow was not observed in the LAD at rest during pulsatile flow, but developed during simulated reactive hyperemia. Helical flows were observed in the CIRC both during simulated rest and reactive hyperemia. These observations suggest that helical flows may be characteristic features of flow in the left coronary artery; whereas turbulence may not be a feature of this flow field. Whether the spiraling of flow that we observed related to the spiral distribution of early atheroma reported by others, is undetermined.     

Comparison of steady and pulsatile flow in a double branching arterial model

Data are presented to compare fluid flow parameters for steady flow with those for time-varying flow in a simplified two branch model which simulates the region of the abdominal aorta near the celiac and superior mesenteric branches of the dog. Measurements in the model included laser doppler anemometry velocity profiles during steady flow, sinusoidal flow with a superimposed mean flow (referred to as simple oscillatory flow) and arterial pulsatile flow. Shear rate measurements were made by an electrochemical technique during steady flow. Flow visualization studies were done during steady and pulsatile flow. Fluid flow effects in the simplified model during steady flow showed many similarities to the results from previous steady flow studies in a canine aortic cast. Shear rates in the region of the proximal (first, or celiac) branch were independent of flow rates in the distal (second, or mesenteric) branch, but the shear pattern within the proximal branch changed significantly as flow in the proximal branch increased. Shear rates on the proximal flow divider (leading edge into the distal branch) depended primarily on the flow rate to the proximal branch, but not on flow to the distal branch. At certain daughter branch flow ratios (approximately 2:1, proximal to distal), flow separation was promoted at the outer wall of the second branch, but flow separation did not occur in the first branch. In contrast to the canine aortic case results, flow separation was never detected on the distal (mesenteric) flow divider of the simplified model. This observation reflects the subtle effects of geometry on flow since the mesenteric flow divider in the canine cast protrudes into the main flow whereas the distal flow divider in the simplified model does not. There were distinct differences in the flow phenomena between steady, simple oscillatory and arterial pulsatile flow. Peak shear rates during pulsatile flow were as much as 10--100 times greater than steady flow shear rates at comparable mean flow rates. Particularly noteworthy for the pulsatile flow with a Womersley parameter of sixteen were very blunt velocity profiles throughout systole, and the absence of flow separation or reversal in those regions of the model that exhibited flow separation during steady flow. The shape of the waveform influences the nature of the flow during time-varying flows. Future studies of fluid dynamics in model systems must consider the pulsatile nature of the flow if a true interpretation of arterial flow phenomena is to be made.     

Laser anemometry measurements of pulsatile flow past aortic valve prostheses

Experimental results are presented on physiological pulsatile flow past caged ball and tilting disc aortic valve prostheses mounted in an axisymmetric chamber incorporated in a mock circulatory system. The measurements of velocity profiles and turbulent normal stresses during several times in a cardiac cycle were obtained using laser-Doppler anemometry. Our results show that with increased angle of opening for the tilting disc valves, a large but locally confined vortex is observed along the wall in the minor flow region throughout most of the cardiac cycle. The turbulent normal stresses measured downstream to the tilting disc in the minor flow region parallel to the tilt axis were found to be larger than those measured downstream to the caged ball valves. Comparison of measurements with steady flow at flow rates comparable to peak pulsatile flow rate show that the turbulent normal stresses are larger by a factor of two in pulsatile flow with a frequency of 1.2 Hz.     

Flow investigations in a model of a three-dimensional human artery with Newtonian and non-Newtonian fluids. Part I

Together with biochemical factors, fluid mechanical factors play a role in atherogenesis and the deposition of blood platelets at bends and bifurcations in human arteries. Hence, flow patterns were investigated in a simplified 3-dimensional model of a human renal artery bifurcation using Newtonian (aqueous glycerol) and non-Newtonian (aqueous solution of polyacrylamide) fluids. Studies were carried out in steady as well as pulsatile flow at inflow Reynolds numbers of 498 and 951 with flow rate ratios main tube V1: right branch V4: left branch V3 of 1: 0.25: 0.25 and 1: 0.18: 0.18 respectively. The velocity distribution proximal and distal to the bifurcations was measured using a laser-Doppler anemometer. In steady flow, zones of flow separation and reverse flow were observed distal to the bifurcations. In pulsatile flow using non-Newtonian fluids, there was a significant enlargement of these zones. Differences between the Newtonian and non-Newtonian fluids occurred especially distal to the bifurcations. Shear stresses along all measuring positions were computed from the velocity gradients.     

In vitro pulsatile flow velocity and shear stress measurements in the vicinity of mechanical mitral heart valve prostheses

A three beam laser Doppler anemometer system was used to study the flow fields created by various types of mitral heart valve prostheses under physiological pulsatile flow conditions. The prosthetic valves studied were: Beall caged disc valve, Bjork-Shiley tilting disc valve, Medtronic-Hall tilting disc valve and St. Jude bileaflet valve. The results indicate that all four prosthetic valve designs studied create very disturbed flow fields with elevated turbulent shear stresses and regions of flow separation and/or stagnation. The observed elevated turbulent shear stresses could cause sublethal and/or lethal damage to red cells and platelets. The regions of flow separation and/or stagnation, could lead to thrombus formation and/or tissue overgrowth on the valve structure, as observed on clinically recovered prosthetic valves.