Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions

Extensive flow studies are conducted in two carotid bifurcation flow phantoms. These phantoms exactly replicate the lumen of the plaque excised intact from two patients with severe carotid atherosclerosis. The input flow into the phantom's common carotid artery is steady. Novel scanning techniques for flow visualization and particle image velocimetry are used. In addition, a novel boundary treatment technique is employed in velocimetry to extract first order accurate velocity gradients at walls. The data show that the flow fields are highly three-dimensional. Numerous separation and recirculation zones dominate the flow domain, except at the lowest Reynolds numbers. The separation regions are often so severe that highly directed internal jets form. At high Reynolds numbers, the flows become unsteady and chaotic, even though the input flow is steady. Flow fields have large regions of energetic flow and almost stagnant recirculation zones. These recirculation zones range in size from the full size of the arteries to zones within crevasses smaller than 1 mm. Velocity field and streamline patterns conform well to the lumen geometry. The streamlines are highly tortuous. Stagnation points correlate well with the topological features of the stenosis. Vorticity maps confirm the highly complex and three dimensional nature of the flow. Wall shear stresses at the stenoses are estimated to be on the order of 10 Pa. These studies conclusively show that the nature of the flow in the diseased bifurcation is primarily dictated by the lumen geometry.     

Numerical simulation of steady flow in a model of the aortic bifurcation.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200 < or = Re < or = 1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.     

Steady flow visualization in a rigid canine aortic cast

Steady flow studies were conducted in a transparent canine aortic cast. The cast segment stretched from the aortic valve to beyond the renal arteries and included all major branches. Flow was visualized by analysis of dye streaklines. Flow rates for basal and exercising cardiovascular states were simulated. The Reynolds numbers in the ascending aorta for basal and exercising conditions were 900 and 1587 respectively. Aortic core flow was laminar in basal simulations. Disturbed flow commenced in the upper descending aorta with exercising flow rates. Separation zones existed along the inner curvature of the aortic arch and the proximal walls of the brachiocephalic, left subclavian, and coeliac arteries. Such zones may exist over a portion of the cardiac cycle. If either renal artery was occluded, then a vortex formed. This vortex is associated with high shear regions which correlate well with sites where sudanophilic lesions have been reported in cholesterol-fed nephrectomized rabbits.     

LDA measurements and numerical prediction of pulsatile laminar flow in a plane 90-degree bifurcation

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.     

Entry flow in a circular tube of aortic arch dimensions

Steady flow within a uniform circular curved tube formed by two 90-deg elbows was studied as a function of psi, the angle between the planes of curvature of the two elbows. Boundary layer separation was found at two locations. The sites of these separation zones were observed to be essentially independent of psi while the Reynolds number at which separation was first detected was found to decrease as psi increased. The relation between separation and the pathogenesis of atherosclerosis is discussed. Secondary flow pattern was found to depend on psi and in some instances on Reynolds number as well.     

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 in axisymmetrical glass model aneurysms

Experiments have been performed on the flow of water with a dye tracer in rigid glass models of axisymmetrical spherical aneurysms. Streamlines have been visualized, pressure drops over the surface of the bulbs have been measured, and a critical Reynolds number for the onset of turbulence in the aneurysms has been determined. Boundary layer separation and recirculating flow with closed streamlines was observed in all models for flow rates below those necessary for turbulence. Pressures on the aneurysm walls for both laminar and turbulent flow were found to be of the same order of magnitude as those immediately upstream and downstream with no large pressure differences over the bulb surfaces. An inviscid mathematical model of the flow field was developed and shown to give good agreement with experiment for high Reynolds number laminar flow. The use of a suitably defined critical Reynolds number as an aid in the decision to operate on fusiform aneurysms is noted, as well as the limitations imposed on the experimental and theoretical results by the neglect of flow periodicity and nonhomogeneity.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Computational investigations on the hemodynamic performance of a new swirl generator in bifurcated arteries

Hemodynamic behaviour of blood in the bifurcated arteries are closely related to the development of cardiovascular disease. The secondary flows generated at the bifurcation zone promotes the deposition of atherogenic particles on the outer walls. The present study aims at suppressing the development of atherosclerosis plaque by inducing helical flow structure in the arterial passage. To realize this objective a novel swirl generator (stent like structure with an internal groove) has been developed to induce helicity in the bifurcated passage. The functional requirement of the swirl generator is to minimize the relative residence time (RRT) of the fluid layer near the endothelial wall without generating any additional pressure drop. Different configurations of the swirl generator have been tested computationally using large eddy simulation (LES) model. It is observed that the induced helical flow redistributes the kinetic energy from the centre to the periphery. A single rib swirl flow generator proximal to the stent treated passage can generate sufficient helicity to bring down the RRT by 36% without generating any additional pressure drop. The swirl flow adds azimuthal instability which increase vortex formations in the passage. The induced helical flow in the domain provokes more linked vortices, which may act as self-cleaning mechanism to the arterial wall.     

Computational study of the effect of geometric and flow parameters on the steady flow field at the rabbit aorto-celiac bifurcation

Arterial hemodynamic forces may play a role in the localization of early atherosclerotic lesions. We have been developing numerical techniques based on overset or "Chimera" type formulations to solve the Navier-Stokes equations in complex geometries simulating arterial bifurcations. This paper presents three-dimensional steady flow computations in a model of the rabbit aorto-celiac bifurcation. The computational methods were validated by comparing the numerical results to previously-obtained flow visualization data. Once validated, the numerical algorithms were used to investigate the sensitivity of the computed flow field and resulting wall shear stress distribution to various geometric and hemodynamic parameters. The results demonstrated that a decrease in the extent of aortic taper downstream of the celiac artery induced looping fluid motion along the lateral walls of the aorta and shifted the peak wall shear stress from downstream of the celiac artery to upstream. Increasing the flow Reynolds number led to a sharp increase in spatial gradients of wall shear stress. The flow field was highly sensitive to the flow division ratio, i.e., the fraction of total flow rate that enters the celiac artery, with larger values of this ratio leading to the occurrence of flow separation along the dorsal wall of the aorta. Finally, skewness of the inlet velocity profile had a profound impact on the wall shear stress distribution near the celiac artery. While not physiological due to the assumption of steady flow, these results provide valuable insight into the fluid physics at geometries simulating arterial bifurcations.     

Finite element analysis of two dimensional steady flow in model arterial bifurcation

The purpose of the investigation reported in this paper is to determine theoretically the fluid dynamic field in models of common iliac arterial bifurcation and to identify the flow features which might influence the predominant occurrence of atherosclerotic lesions at such sites. This has been accomplished by numerically simulating fluid flow through 90 degrees symmetric bifurcations with branch-to-trunk area ratios of 0.8-1.414 and for Reynolds numbers ranging from 100 to 400. The analysis predicts flow reversal along the outer wall in models with area ratios over unity for high Reynolds number range, while no flow reversal occurred in models with area ratio below unity; a low shear zone along the outer wall and high shear stresses at the divider lip. Adverse pressure gradients are observed along the outer wall downstream of the corner point, the magnitudes increased with Reynolds number for a given branch to area ratio. Biological implication of the results is discussed with specific reference to the sites of atherosclerotic lesions found in man for these geometries.     

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.     

Pulsatile flow visualization in the abdominal aorta under differing physiologic conditions: implications for increased susceptibility to atherosclerosis.

The infrarenal abdominal aorta is a common site for clinically significant atherosclerosis. As has been shown in other susceptible locations, vessel geometry, flow division rates, and pulsatility may result in hemodynamic conditions which influence the preferential localization of disease in the abdominal aorta segment. Pulsatile flow visualization was performed in a glass model of the aorta constructed from measurements of angiograms and cadaver aortas. Flow rates and pulsatile waveforms were varied to reflect typical physiological conditions. Under normal resting conditions, the flow patterns in the infrarenal aorta were more complex than those in the suprarenal location. Time varying vortex patterns appeared at the level of the renal arteries and propagated through the infrarenal aorta into the common iliac arteries. A region of oscillating velocity direction extended from the renal arteries to the aortic bifurcation along the posterior wall. Dye became trapped along the posterior wall, requiring several cardiac cycles for clearance. In contrast, there was rapid clearance of the dye in the anterior aorta. Under postprandial conditions, the flow patterns in the aorta were basically unchanged. Simulated exercise conditions created laminar hemodynamic features very different from the resting conditions, including a decrease in dye residence time. This study reveals significant time-dependent variations in the hemodynamics of the abdominal aorta under differing physiologic conditions. Hemodynamic factors such as low wall shear stress, oscillating shear direction, and high particle residence time may be related to the clinically seen preferential plaque localization in the infrarenal aorta.     

Wall shear stress distribution in a model human aortic arch: assessment by an electrochemical technique

Wall shear stress (WSS) distribution in a human aortic arch model is studied using 130 cathode electrodes flush-mounted on the model walls. Flow visualizations are made in a transparent geometry model to identify the regions of fluid mechanical interests, e.g. regions of flow separation, eddy formation and flow stagnancy. The 130 electrodes are strategically positioned in the arch based on information obtained from the flow visualizations. The measured data indicate that the aortic arch may be categorized into eight regions: three along the inner wall of the arch (A,B,C); and five near the outer wall (D,E,F,G,H). (1) The regions of low WSS are distributed along the inner wall of the ascending aorta A; the inner wall of the descending aorta C; and the upstream inner wall of the innominate and the common carotid branchings F. (2) The high WSS regions are distributed along the outer wall of the arch E; and the inner wall in the arch opposite to the left subclavian branching B. (3) In certain regions, high and low WSS may be found next to each other (e.g. G and H) without a definable boundary in between; and (4) as the Reynolds number increases, the areas of low WSS decrease, while the high WSS areas increase with no obvious change in magnitude of the stress along the inner wall of the arch. At the branchings, the WSS distribution is not affected by the Reynolds number within the range of observations. The measured WSS distribution is compared with Rodkiewicz's map of early atherosclerotic lesions in the aortic arch of cholesterol fed rabbits.     

Comparison of axisymmetric and three-dimensional models for gas uptake in a single bifurcation during steady expiration

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.     

An experimental analysis of the flow field in a three-dimensional model of the human carotid artery bifurcation

Steady flow measurements were carried out in a rigid three-dimensional model of the human carotid artery bifurcation at a Reynolds number of 640 and a flow division ratio of 50/50. Both axial and secondary velocities were measured with a laser-Doppler anemometer. In the bulb opposite to the flow divider a zone with negative axial velocities was found with a maximal diameter of about 60% of the local diameter of the branch and a cross-sectional extent of about 25% of the local cross-sectional area. In the bulb the maximum axial velocity shifted towards the divider wall and at the end of the bulb an axial velocity plateau arose near the non-divider wall. Halfway through the bulb, secondary flow showed a vortex through which fluid flowed towards the divider wall near the bifurcation plane and back towards the non-divider wall near the upper walls.     

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.     

Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.