Flow measurements in an atherosclerotic curved, tapered femoral artery model of man

Flow visualization and pressure measurements were made for physiological conditions in a model derived from a femoral angiogram of a patient with lesion localization on the inner curvature wall and with vessel taper. Effects of curvature and taper were evaluated separately in other curved, tapered, smooth and straight, tapered, smooth models. Double helical secondary flow patterns were modified by plaque on the inner wall, and flow separations were observed between plaques at higher flow rates and Reynolds numbers. Pressure drop data for the plaque simulation model were similar in trend with Reynolds number as for the smooth model, but flow resistances were 25 to 40 percent higher. Significant pressure drops were measured due to the mild taper which could be estimated from momentum considerations, and smaller increased pressure drops were found due to curvature effects at the higher Dean numbers. Flow resistances for in vivo pulsatile flow simulation were about 10 percent higher than for steady flow for the plaque model, whereas no differences were observed for the smooth model.     

Flow measurements in a human femoral artery model with reverse lumen curvature

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle "s" shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600-700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.     

Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows

Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.     

Numerical simulation on the effects of drug eluting stents at different Reynolds numbers on hemodynamic and drug concentration distribution

Background

The changes of hemodynamics and drug concentration distribution caused by the implantation of drug eluting stents (DESs) in curved vessels have significant effects on In-Stent Restenosis.

Methods

A 3D virtual stent with 90°curvature was modelled and the distribution of wall shear stress (WSS) and drug concentration in this model were numerically studied at Reynolds numbers of 200, 400, 600, 800.

Results

The results showed that (1) the intensity of secondary flow at the 45° cross-section was stronger than that at the 90° cross-section; (2) As the Reynolds number increases, the WSS decreases. When the Reynolds number reaches 600, the low-WSS region only accounts for 3% of the total area. (3) The effects of Reynolds number on drug concentration in the vascular wall decreases in proportionally and then the blood velocity increased 4 times, the drug concentration in the vascular wall decreased by about 30%. (4) The size of the high drug concentration region is inversely proportional to the Reynolds number. As the blood velocity increases, the drug concentration in the DES decreases, especially at the outer bend.

Conclusions

It is beneficial for the patient to decrease vigorous activities and keep calm at the beginning of the stent implantation, because a substantial amount of the drug is released in the first two months of stent implantation, thus a calm status is conducive to drug release and absorption; Subsequently, appropriate exercise which increases the blood velocity is helpful in decreasing regions of low-WSS.

     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part I--steady flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Homogeneous, Newtonian blood flow is simulated under steady conditions for the range of Reynolds numbers 10 < or =Re < or =2265. Flow hemodynamics are quantified by calculating the distributions of wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG). A correlation between maximum values of hemodynamic stresses and Reynolds number is established, and the spatial distribution of WSSG is considered as a hemodynamic force that may cause damage to the arterial wall at an intermediate stage of AAA growth. The temporal distribution of hemodynamic stresses in pulsatile flow and their physical implications in AAA rupture are discussed in Part II of this paper.     

Phasic flow patterns at a hemodialysis venous anastomosis

A phase-by-phase analysis of local flow patterns at the venous anastomosis of an arteriovenous hemodialysis angioaccess loop graft (AVLG) was made. The study was carried out in an elastic, transparent Silastic in vitro flow model, which duplicates the detail geometry of the AVLG obtained from an animal model (30+ kg dogs with 12 weeks bilateral femoral AVLG implantation). The flow model was installed in a mock pulsatile flow loop system designed to simulate physiological conditions. Flow visualization was made in laser-illuminated flow fields using a high-speed cine camera. Analysis of the high-speed cine indicates there is a distinct separation region downstream of the anastomotic toe in the median plane and a stagnation region that oscillates along the opposite wall. During inward motion of the vessel wall, accumulation of particles in the separation region and the nearby stagnation region is observed. A large swirl appears in the distal vein during end-systolic period. A double-helical flow pattern occurs further down in the distal vein. Retrograde flow in the distal vein occurs in an "oscillating" manner following each cardiac cycle.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

Biofilm formation in laminar flow usingPseudomonas fluorescens EX101

The relationship between biofilm formation and Reynolds number in laminar flow has been investigated usingPseudomonas fluorescens EX101. It was shown using a Modified Robbins Device that in laminar flow, numbers of viable cells in a developed biofilm increased with Reynolds number (Re 2, 17 and 51.5), as would be expected in a system where molecular transport to the wall is limited by diffusion. By monitoring fluorescent beads in a flowcell with a scanning confocal laser microscope at similar low Reynolds numbers, the velocity profile close to the solid surface was determined. It was shown that the presence of a thin bacterial film (up to 12 m) displaced the flow profile away from the wall by a distance equivalent to the film thickness. Total cell counts from the Modified Robbins Device samples were not significantly different at the different flow rates but were higher than viable counts. Interruption of the flow had no significant effect on colonisation by the bacteria through the Modified Robbins Device in the first few hours. However, viable numbers were reduced when the flow was stopped at 7 h after initial colonisation.     

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.     

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.     

The impedance of curved artery models

The impedance (pressure drop/flow rate) of four curved artery models has been determined experimentally for steady and periodic flows simulating conditions in the aortic arch. Steady flow results indicate that very short entry lengths are required for flow development in curved artery models, and impedance is elevated above straight tube values by a factor of 3-4 for mean flow conditions in the aortic arch. Results for periodic flow with a nonzero mean show a significant elevation of mean flow impedance relative to values for steady flow at the mean flow rate--a factor of 2-3 for aortic arch flow conditions. The impedance of the first harmonic of periodic flows follows straight tube theory at high values of the unsteadiness parameter in agreement with available theory for curved tubes. The implications of the impedance measurements for wall shear stress in the aortic arch are discussed.     

Wall shear rate measurements in an elastic curved artery model

Since atherosclerotic lesions tend to be localized at bends and branching points, knowledge of wall shear rate patterns in models of these geometries may help elucidate the mechanism of atherogenesis. This study uses the photochromic method of flow visualization to determine both the mean and amplitude of the wall shear rate waveform in straight and curved elastic arterial models to demonstrate the effects of curvature, elasticity, and the phase angle between the flow and pressure waveforms (impedance phase angle). Under sinusoidal flow conditions characteristic of large arteries, the mean shear rate at the inner wall of the curved tube is reduced 40–56% from its steady flow value, depending on the phase angle. Wall shear rate amplitudes in the curved tube are significantly reduced by wall motion (36–55% of the Womersley amplitude for a straight rigid tube). The shear rate amplitude at the outer wall decreases 30% as the phase angle is reduced from −20° to −66°, while the shear rate amplitude at the inner wall increases 45%. As a result, the oscillatory nature of flow at the outer wall decreases with decreasing negative phase angle, but flow at the inner wall becomes much more oscillatory. At large negative phase angles, characteristic of hypertension or vasoactive agents, the shear rate at the inner wall has a small mean and cycles through positive and negative values; the shear rate at the outer wall remains positive throughout the flow cycle. Thus, the impedance phase angle could affect atherogenesis along the inner wall if temporal and directional changes in wall shear rate play a role.     

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.     

Experimental investigation of branch flow ratio, angle, and Reynolds number effects on the pressure and flow fields in arterial branch models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.     

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.     

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.     

Turbulent flow of red cells in dilute suspensions. Effect on kinetics of O2 uptake.

The turbulent flow properties of dilute (0.06% by volume) suspensions of human red blood cells in 4-mm-bore glass tubing were estimated by laser anemometry. The flow properties of the dilute red cell suspension were similar to those of a dilute suspension of polystyrene spheres (0.5 micron diameter) in isotonic NaCl solution. Flow was found to be laminar when the Reynolds number was below 2,000, transitional in the range of Reynolds numbers from 2,000 to 3,000, and fully turbulent above Reynolds number 3,000. These results differ from previous studies of more concentrated red cell suspensions. The length scales of the turbulence were also estimated: at a Reynolds number near 4,000 the macroscale is about 1.25 mm, the Taylor microscale is about 0.85 mm, and the Kolmogoroff scale is near 0.075 mm. The results are discussed in relation to previous measurements of the rate of oxygen uptake by dilute red cell suspensions in the flow-type rapid reaction apparatus. Our results suggest that under the conditions of most of these oxygen uptake measurements, the turbulent flow is characterized by eddies about 1 mm across, mixing with each other on a time scale of about 45 ms. Since most of the reported oxygen uptake measurements involve a similar time scale, it is possible that an effective "unstirred layer" influenced the reported rate of oxygen uptake.     

Effects of curved inlet tubes on air flow and particle deposition in bifurcating lung models

In vivo bifurcating airways are complex and the airway segments leading to the bifurcations are not always straight, but curved to various degrees. How do such curved inlet tubes influence the motion as well as local deposition and hence the biological responses of inhaled particulate matter in lung airways? In this paper steady laminar dilute suspension flows of micron-particles are simulated in realistic double bifurcations with curved inlet tubes, i.e., 0 degrees < or =theta< or =90 degrees, using a commercial finite-volume code with user-enhanced programs. The resulting air-flow patterns as well as particle transport and wall depositions were analyzed for different flow inlet conditions, i.e., uniform and parabolic velocity profiles, and geometric configurations. The curved inlet segments have quite pronounced effects on air-flow, particle motion and wall deposition in the downstream bifurcating airways. In contrast to straight double bifurcations, those with bent parent tubes also exhibit irregular variations in particle deposition efficiencies as a function of Stokes number and Reynolds number. There are fewer particles deposited at mildly curved inlet segments, but the particle deposition efficiencies at the downstream sequential bifurcations vary much when compared to those with straight inlets. Under certain flow conditions in sharply curved lung airways, relatively high, localized particle depositions may take place. The findings provide necessary information for toxicologic or therapeutic impact assessments and for global lung dosimetry models of inhaled particulate matter.     

Helical flow around arterial bends for varying body mass

The three dimensionally curved aortic arch is modeled as a portion of a helical pipe. Pulsatile blood flow therein is calculated assuming helical symmetry and an experimentally measured pressure pulse. Appropriate values for the Womersley and Reynolds numbers are taken from allometric scaling relations for a variety of body masses. The flow structure is discussed with particular reference to the wall shear, which is believed to be important in the inhibition of atheroma. It is found that nonplanar curvature limits the severity of flow separation at the inner bend, and reduces spatial variation of wall shear.     

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.