Role of blood cell-wall interactions in thrombogenesis and atherogenesis: a microrheological study

The relationship between blood flow and the localization of thrombosis and atherosclerosis in vivo was investigated using the approach and techniques of microrheology. The flow patterns and wall-adhesion of platelets were studied in the captive annular vortex formed at a sudden tubular expansion at various hematocrits in steady and pulsatile flow. The adhesion density exhibited a peak within the vortex and just downstream of the reattachment point, which is also a stagnation point. The peaks flattened out with increasing Reynolds number in steady flow and also in pulsatile flow. Platelet adhesion increased markedly with increasing hematocrit. The localization of adhesion peaks was explained by curvature of the streamlines carrying platelets to the wall on either side of the reattachment point. The relevance of these results to the circulation is that stagnation points are found in regions of disturbed flow at various sites in the arterial and venous circulations. This was shown in experiments using a technique whereby flow was visualized in isolated transparent natural blood vessels prepared from dogs and humans postmortem. In dog saphenous vein bileaflet valves, there was a large primary spiral vortex as well as a smaller secondary vortex, the latter acting as a trap and generator of thrombi. Recirculation zones also existed in the dog aorta at T-junctions of the celiac, cranial mesenteric and renal arteries. Finally, in the human carotid bifurcation, a large standing recirculation zone consisting of spiral secondary flows formed in the carotid sinus at physiological flow conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Recirculation zone length in renal artery is affected by flow spirality and renal-to-aorta flow ratio

Haemodynamic perturbations such as flow recirculation zones play a key role in progression and development of renal artery stenosis, which typically originate at the aorta-renal bifurcation. The spiral nature of aortic blood flow, division of aortic blood flow in renal artery as well as the exercise conditions have been shown to alter the haemodynamics in both positive and negative ways. This study focuses on the combinative effects of spiral component of blood flow, renal-to-aorta flow ratio and the exercise conditions on the size and distribution of recirculation zones in renal branches using computational fluid dynamics technique. Our findings show that the recirculation length was longest when the renal-to-aorta flow ratio was smallest. Spiral flow and exercise conditions were found to be effective in reducing the recirculation length in particular in small renal-to-aorta flow ratios. These results support the hypothesis that in renal arteries with small flow ratios where a stenosis is already developed an artificially induced spiral flow within the aorta may decelerate the progression of stenosis and thereby help preserve kidney function.     

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.     

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.     

Spiral blood flow in aorta–renal bifurcation models

The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta–renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta–renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta–renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.     

Aortic velocity contours at abdominal branches in anesthetized dogs

Pulsed Doppler velocimetry was used to record a grid of velocity waveforms 0.5 cm downstream of the cephalic mesenteric and left renal branches of the aorta in anesthetized dogs. Aortic velocity contours at different phases of the pulse cycle were developed from the grid of waveforms. Transient flow recirculation occurred in the post-systolic phase of the pulse cycle at the aortic wall opposite the branch artery. There was no recirculation at the systolic peak but there was asymmetry of the velocity profile. In contrast, in the in vivo post-stenotic velocity field recirculation persists throughout most of the cycle. These results compare well with similar results from pulsatile model studies. Spectral width of the Doppler signal was not increased in any of the velocity waveforms immediately downstream of the branches, this suggests that flow is relatively undisturbed in these locations.     

Unsteady and three-dimensional simulation of blood flow in the human aortic arch

A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

Some flow visualization and laser-Doppler-velocity measurements in a true-to-scale elastic model of a human aortic arch--a new model technique.

Flow studies were done in an elastic true-to-scale silicone rubber model of an aortic arch to study further hemodynamic influences on atherosclerosis. The model was prepared from a cast of a young woman. A revised model technique was used. The model had a compliance similar to that of the human aortic arch. Velocity measurements were done in the model with a two component laser-Doppler-anemometer in steady and pulsatile flow using a calcium chloride solution with a viscosity of eta = 3.18 mPas and density of rho = 1.28 kg/m3 at 20 degrees C. The time average Reynolds numbers over a whole cycle in the ascending aorta was Re = 1350. The Womersley parameter for pulsatile flow was a = 20. The pulse wave velocity in the ascending aorta was about c = 5.4 m/sec. The secondary flow behavior was discussed for steady and pulsatile flow. Reverse flows were found, especially along the inner radius of the aortic arch in the descending aorta in steady and pulsatile flow and also in small areas of the ascending aorta and at the branches of the aortic arch. The formation of atherosclerotic plaques at preferred local flow regions is discussed.     

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.     

Steady Flow Visualization in a Rigid Model of the Aortic Bifurcation: Application to Atherosclerosis

Hemodynamics have long been implicated in atherogenesis. The studiesreported here seek to explain the mechanisms for the formation ofatherosclerotic plaque in an aortic bifurcation. Flow studies were made ina model constructed from plexiglass to represent an aortic bifurcation. Under steady flow conditions at inflow Reynolds numbers of 80–1250,the streamline flow patterns and the boundary layer separation zones wereinvestigated in relation to the location of atherosclerotic plaques clinicallyfound at regions in the human aortic bifurcation. The streamline flowswere visualized by a slow injection of dye over the cross section of the tubeentrance and along the tube walls. The studies revealed a complex flowfield where secondary flows, induced by the centrifugal and viscous forces,cause the fluid to move towards the inner walls of the aortic bifurcation. The effect was more clearly seen with increasing Reynolds number. Boundary layer separation zones were observed to occur at the outercorners of the branching. The nature of the separation zone formed wasfound to be dependent on Reynolds number. The residence time of fluidparticles within such a separation zone was estimated by measuring thewashout time of a bolus of dye injected at strategic locations along the tubewalls. The residence time was found to decrease exponentially withincreasing Reynolds number. These observations provide strong support forthe role of flow separation in the accumulation of LDL and plateletaggregation within the aortic bifurcation.     

Velocity distribution along an elastic model of human arterial tree

An experimental investigation of an elastic model of the human arterial tree, has been performed for physiological type flow by pulsed Doppler ultrasonic velocimetry. The arterial tree model, fabricated in clear polyurethane, includes the aortic arch, with a Starr-Edwards ball valve mounted in the root of the aorta, the descending aorta and the iliac bifurcation. Our study showed that the velocity profile, a few centimeters beyond the valve, is skewed, with higher velocities towards the top and the inner wall (anatomically the posterior and left lateral wall). An inward shift of the maximum velocity and reverse flow are denoted along the inner wall of the aortic arch. The velocity profiles in the descending aorta are blunted. Downstream from the vertex of the iliac bifurcation, there is vorticity creation, but the branching effect is quickly damped by the pulsatility of the flow and the elasticity of the wall.     

Why are there so many threat displays?

The morphology of branching trees in general, and of the bronchial tree in particular, can be described in terms of three parameters, the diameter, length and branching ratios. These are the factors by which mean diameter and mean length increase in successive orders towards the trachea, and by which the number of branches increases in successive orders away from the trachea. Orders of branching are counted from the periphery towards the trachea, according to the method of Strahler. A model of from two to nine orders, and of constant total length and volume, was used to investigate the effect of varying the above parameters on the calculated pressure difference across the model during flow. In particular, the branching ratio was set at known values for dog and human lungs, and diameter and length ratios were independently varied. Known data from dog and human lungs were found to be close to the points predicted by the model where the lines of minimal resistance and minimal entropy production crossed. Other factors which may affect the values of these parameters are discussed.     

Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches

Flow in the aortic arch is characterized primarily by the presence of a strong secondary flow superimposed over the axial flow, skewed axial velocity profiles and diastolic flow reversals. A significant amount of helical flow has also been observed in the descending aorta of humans and in models. In this study a computational model of the abdominal aorta complete with two sets of outflow arteries was adapted for three-dimensional steady flow simulations. The flow through the model was predicted using the Navier-Stokes equations to study the effect that a rotational component of flow has on the general flow dynamics in this vascular segment. The helical velocity profile introduced at the inlet was developed from magnetic resonance velocity mappings taken from a plane transaxial to the aortic arch. Results showed that flow division ratios increased in the first set of branches and decreased in the second set with the addition of rotational flow. Shear stress varied in magnitude with the addition of rotational flow, but the shear stress distribution did not change. No regions of flow separation were observed in the iliac arteries for either case. Helical flow may have a stabilizing effect on the flow patterns in branches in general, as evidenced by the decreased difference in shear stress between the inner and outer walls in the iliac arteries.     

Optimal branching structure of the vascular tree

Optimality in branching structure of the vascular tree was studied. Analysis on its physiological roles as the duct system for blood supply to the capillaries predicted that the vascular tree should be constructed with minimum volume under restriction of determinant pressure, flow and location at the origin and the terminals. Mathematical derivations of this conditional extremum problem yielded some equations expressing the relations between the radii of the branches and their branching angles, which provided numerical solutions for branching points of bi- and poli-terminal minimum volume trees. Comparison of the peritoneal vascular tree in a dog with the minimum volume one computed under the same restrictive conditions showed good agreement in their branching structure.     

Flow patterns in three-dimensional porcine epicardial coronary arterial tree

The branching pattern of epicardial coronary arteries is clearly three-dimensional, with correspondingly complex flow patterns. The objective of the present study was to perform a detailed hemodynamic analysis using a three-dimensional finite element method in a left anterior descending (LAD) epicardial arterial tree, including main trunk and primary branches, based on computed tomography scans. The inlet LAD flow velocity was measured in an anesthetized pig, and the outlet pressure boundary condition was estimated based on scaling laws. The spatial and temporal wall shear stress (WSS), gradient of WSS (WSSG), and oscillatory shear index (OSI) were calculated and used to identify regions of flow disturbances in the vicinity of primary bifurcations. We found that low WSS and high OSI coincide with disturbed flows (stagnated, secondary, and reversed flows) opposite to the flow divider and lateral to the junction orifice of the main trunk and primary branches. High time-averaged WSSG occurs in regions of bifurcations, with the flow divider having maximum values. Low WSS and high OSI were found to be related through a power law relationship. Furthermore, zones of low time-averaged WSS and high OSI amplified for larger diameter ratio and high inlet flow rate. Hence, different focal atherosclerotic-prone regions may be explained by different physical mechanism associated with certain critical levels of low WSS, high OSI, and high WSSG, which are strongly affected by the diameter ratio. The implications of the flow patterns for atherogenesis are enumerated.     

An LDA and flow visualization study of pulsatile flow in an aortic bifurcation model

The structure of pulsatile flow in a rigid aortic bifurcation model was studied by means of a flow visualization technique and three-dimensional laser-Doppler anemometry. The model was made of glass, having the same shape as that of the average human aortic bifurcation. It was installed into a mock circulatory loop that generated physiological pulsatile flow. Flow separation was observed during accelerated and decelerated flow periods. Double helical flow existed inside the flow separation in the early accelerated flow period. In the decelerated flow period, disturbed flow appeared behind the separation zone. Flow was strongly disturbed during the back flow period, and then was gradually stabilized in the forward flow period. The flow separation and the disturbances released from the flow separation zone greatly influenced near-wall velocities along the lateral wall. The wave form of the near-wall velocity in the flow separation zone was much different from that observed in the aortic portion and behind the separation zone; for example, the magnitude of the negative peak velocity in the direction of the tube axis was larger than that of the positive one, and mean velocity in a cycle was very low. This abnormal phasic change of the near-wall velocity may be associated with atherogenesis. The three-dimensional velocity measurement is very useful for the detailed analysis of near-wall velocity patterns.     

Flow visualization studies in a mold of the normal human aorta and renal arteries

To study the flow behavior in regions where hemodynamic effects have been suggested to participate in atherogenesis, we evaluated flow in a mold of the aorta and renal arteries of a previously healthy 27-year-old woman who died of trauma. A birefringent solution (vanadium-pentoxide) was used. When diluted, this material behaves like a Newtonian fluid. This method gives a complete picture of the entire flow field. Zones of flow separation and disturbed flow can be seen and the location and size of disturbed areas observed. Unseparated flow regions downstream from disturbed zones can be properly visualized and the method can be used for pulsatile flow as well as steady flow. During steady flow (only at branch to-trunk flow ratios greater than 0.20), zones of flow separation were observed in the aorta distal to the renal arteries. During pulsatile flow, disturbances were found at nearly all branch-to-trunk flow ratios.     

Flow visualisation study of spiral flow in the aorta–renal bifurcation

The aim of this study was to analyse the flow dynamics in an idealised model of the aorta–renal bifurcation using flow visualisation, with a particular focus on the effect of aorta-to-renal flow ratio and flow spirality. The recirculation length was longest when there was low flow in the renal artery and smaller in the presence of spiral flow. The results also indicate that patients without spiral flow or who have low flow in the renal artery due to the presence of stenosis may be susceptible to heightened development of atherosclerotic lesions.