Pulsatile flow of non-Newtonian fluid in distensible models of human arteries

In addition to biochemical factors, hydromechanical influences are responsible for atherogenesis and deposits of blood platelets at bends and bifurcations of human arteries. Hence the flow patterns were simulated in a true-to-scale three-dimensional bifurcation of a human renal artery model and of an arterial femoralis with Newtonian and non-Newtonian blood like fluid. Investigations were made with steady and pulsatile flow. The velocity profiles (at physiological Re-numbers) were measured after the bifurcations with a laser-Doppler-anemometer. In previous works Newtonian fluids were used to investigate the flow in bends and bifurcations of rigid and elastic simplified models. In this paper, emphasis is placed on the difference between rigid and elastic models and also Newtonian and non Newtonian flow behavior. Differences between Newtonian and non Newtonian fluids may especially be expected to occur after branches where the flow has local strong convective elements such as in reverse zones and flow separation points.     

Studies of fluids simulating blood-like rheological properties and applications in models of arterial branches

We studied several non-Newtonian fluids to determine how closely they simulate the flow behavior of human blood. The viscous and viscoelastic properties of these fluids were compared with human blood samples in steady flow and transient flow Couette viscometers and in an oscillatory tube flow viscoelasticity analyzer. We examined: 1) A polyacrylamide suspension (Separan AP30 and AP45) to which we added 4% isopropanol and 0.01% magnesium chloride. 2) A suspension of 2% Dextran with 16% by weight biconcave disc-shaped particles simulating red blood cells. 3) 40% ghost cells prepared according to Dodge in Tri (hydroxymethyl) aminomethane. These ghost cells were used to simulate the two-phase flow behavior of blood. 4) A suspension of 5% Dextran (70,000) with 12% polystyrene particles (diameter of 1 micron) and 10 mMol calcium chloride. All these fluids closely approximate the flow behavior of blood and can be used in a variety of different experimental situations. To measure velocity distribution using a laser-Doppler-anemometer, we used fluids #1 and #3 in a rigid T-junction simulating the first septal branch of the left descending coronary artery. The measurements were done in steady and pulsatile flow experiments at different flow rate ratios. The fluids showed large differences in velocity profiles compared to Newtonian fluids.     

Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

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.     

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.     

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

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow 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.     

Flow in tubes and arteries--a comparison

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

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.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

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.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Blood modeling using polystyrene microspheres

The steady flow viscosity at shear rates 0 to 120 sec-1 and dynamic viscoelasticity at frequencies 0.02 to 0.8 Hz were determined for aqueous suspensions of uniform polystyrene microspheres of 1.0 micron diameter. Rheological properties of the microsphere suspensions were Newtonian for particle concentrations up to 32%. By introducing dextran and calcium chloride into the particle suspensions, non-Newtonian behavior was produced similar to that observed for human blood. The cooperative effects of dextran and calcium ions promoted aggregation of particles at a concentration as low as 12%. Thus, a suspension of uniform sized spherical polystyrene particles in aqueous solution of dextran may be made to mimic blood by controlling the surface charge on the polystyrene spheres using addition of calcium ions to the medium.     

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.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Influence of pulsatility on the development of intracardiac jets: an in vitro laser Doppler study.

So far, it has been hypothesized that numerical data obtained in steady flow conditions apply to pulsatile flows. In order to study the modifications of the velocity fields due to pulsatility, jets were produced by 8 orifices (with a diameter "D" of 4.4 to 11.3 mm) included in a chamber of 50 mm. The velocity was measured using laser Doppler anemometry with a pulsatile flow ("pf") and compared to the values obtained in steady ("sf"): at maximum velocity, the longitudinal velocity profile is qualitatively similar to this observed in steady flow: it is made of a plateau followed by an hyperbolic velocity decay in the turbulent area. The length of the core ("Lpf") is strongly related to "D" (Lpf = 3.72 D + 5.49, r = .99) and the velocity decay depends on the ratio between the distance "x" from the orifice and "D" (V/Vo = 2.83D/x + 3.46, r = .85, where V is the velocity at "x" and Vo the initial velocity). During the acceleration and the deceleration, the laminar core is disturbed by turbulences. The comparison of "pf" data with "sf" data demonstrated similar diameters at the origin of the jets (Dpf = 0.96 Dsf + .12, r = .99), but significant (p less than .0001) differences both for "L" and "V/Vo": Lpf = .91Lsf + 6.58, r = .97, V/Vopf = .63 V/Vosf + .34, r = .76. Thus, pulsatility modifies velocity fields and the results obtained in steady flow conditions do not apply to pulsatile jets.