Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis

The laminar steady flow of non-Newtonian fluid (biviscosity fluid) through an axisymmetric stenosis is calculated using the finite element methods. The flow pattern, the separation and reattachment points, and the distributions of pressure and shear stress at the wall are obtained. Then, the axial force acting on the stenosis is evaluated. It is suggested by the authors that this force can become one of the causes of post-stenotic dilatation. Calculated results show that the non-Newtonian property of blood weakens the distortion of flow pattern, pressure and shear stress at the wall associated with the stenosis and that the non-Newtonian property of blood decreases the axial force acting on the stenosis.     

Influence of non-Newtonian properties of blood on the wall shear stress in human atherosclerotic right coronary arteries

The objective of this work is to investigate the effect of non-Newtonian properties of blood on the wall shear stress (WSS) in atherosclerotic coronary arteries using both Newtonian and non-Newtonian models. Numerical simulations were performed to examine how the spatial and temporal WSS distributions are influenced by the stenosis size, blood viscosity, and flow rate. The computational results demonstrated that blood viscosity properties had considerable effect on the magnitude of the WSS, especially where disturbed flow was observed. The WSS distribution is highly non-uniform both temporally and spatially, especially in the stenotic region. The maximum WSS occurred at the proximal side of the stenosis, near the outer wall in the curved artery with no stenosis. The lumen area near the inner wall distal to the stenosis region experienced a lower WSS during the entire cardiac cycle. Among the factors of stenosis size, blood viscosity, and flow rate, the size of the stenosis has the most significant effect on the spatial and temporal WSS distributions qualitatively and quantitatively.     

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.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.     

Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models

Symmetrical 30-60% stenosis in a common carotid artery under unsteady flow condition for Newtonian and six non-Newtonian viscosity models are investigated numerically. Results show power-law model produces higher deviations, in terms of velocity and wall shear stress in comparison with other models while generalized power-law and modified-Casson models are more prone to Newtonian state. Comparing separation length of recirculation region at different critical points of cardiac cycle confirms the necessity of considering blood flow in unsteady mode. Increasing stenosis intensity causes flow patterns more disturbed downstream of the stenosis and WSS appear to develop remarkably at the stenosis throat.     

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.     

Dynamic response of wall shear stress on the stenosed artery

The present study deals with an appropriate mathematical model of an artery in the presence of constriction in which the generated wall shear stress due to blood flow is analysed. The geometry of the stenosed arterial segment in the diseased state, causing malfunction of the cardiovascular system, is formed mathematically. The flowing blood contained in the stenosed artery is treated as non-Newtonian and the flow is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow-field can be obtained primarily following the radial coordinate transformation, using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of flow unsteadiness, the arterial wall distensibility and the presence of stenosis on the flow-field and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.     

Effects of stenosis on non-newtonian flow of the blood in an artery

It has been shown that the resistance of flow and the wall shear increase with the size of the stenosis but these increases are comparatively small due to non-Newtonian behaviour of the blood indicating the usefulness of its rheological character in the functioning of the diseased arterial circulation.     

Coupled oxygen transport analysis in the avascular wall of a post-angioplasty coronary artery stenosis

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied by numerically solving the convection-diffusion equations. Geometry, replicating residual stenosis after percutaneous transluminal coronary angioplasty (PTCA), is used for the analysis. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. Mean blood flow rate in the lumen is varied from basal to hyperemic conditions. The results show that the P(O2) in the medial region of the arterial wall is approximately 10 mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation there is a small rise and a sharp fall in the oxygen flux. The minimum P(O2) in the avascular wall, P(O2, min ), at the point of flow reattachment reduces to approximately 6 mmHg for a 300 micron wall thickness. For a thinner wall of 200 micron, the P(O2, min ) at the location of flow reattachment increases to 6 times that of a 300 micron wall. The P(O2, min ) in the wall decreases by 60% when volumetric oxygen consumption is increased by 30% for the same avascular wall thickness.     

狭窄血管远心端低密度脂蛋白浓度极化促进动脉粥样硬化形成

低密度脂蛋白（low density lipoprotein,LDL）浓度极化可能是动脉粥样硬化局灶性的重要原因,本文以狭窄血管远心端为研究对象,探讨LDL浓度极化对动脉粥样硬化发生、发展的影响。用数值计算模拟狭窄血管远心端LDL的壁面浓度分布,用激光扫描共聚焦显微镜测定狭窄血管远心端LDL沿z轴的浓度分布;用外科手术方法建立颈总动脉局部狭窄的实验模型,从整体动物水平观察LDL浓度极化对动脉粥样硬化形成的影响。数值计算和激光扫描共聚焦显微镜测定的结果表明,狭窄血管远心端存在显著的LDL浓度极化现象,且LDL壁面浓度与入口液流速度和狭窄程度有关：在相同的速率下,LDL壁面浓度在狭窄度为40％的圆管内最大;在狭窄程度相同的情况下,雷诺数（Re）为250时测得的LDL壁面浓度高于Re为500时测得的壁面浓度。整体动物实验表明,在狭窄血管远心端LDL浓度极化显著的区域形成明显的动脉粥样硬化病变,并且有大量的脂质沉积。以上结果提示,LDL浓度极化可能是导致动脉粥样硬化局灶性的重要因素。     

Influence of arterial wall compliance on the pressure drop across coronary artery stenoses under hyperemic flow condition

Hemodynamic endpoints such as flow and pressure drop are often measured during angioplasty procedures to determine the functional severity of a coronary artery stenosis. There is a lack of knowledge regarding the influence of compliance of the arterial wall-stenosis on the pressure drop under hyperemic flows across coronary lesions. This study evaluates the influence in flow and pressure drop caused by variation in arterial-stenosis compliance for a wide range of stenosis severities. The flow and pressure drop were evaluated for three different severities of stenosis and tested for limiting scenarios of compliant models. The Mooney-Rivlin model defined the non-linear material properties of the arterial wall and the plaque regions. The non-Newtonian Carreau model was used to model the blood flow viscosity. The fluid (blood)-structure (arterial wall) interaction equations were solved numerically using the finite element method. Irrespective of the stenosis severity, the compliant models produced a lower pressure drop than the rigid artery due to compliance of the plaque region. A wide variation in the pressure drop was observed between different compliant models for significant (90% area occlusion) stenosis with 41.0, 32.1, and 29.8 mmHg for the rigid artery, compliant artery with calcified plaque, and compliant artery with smooth muscle cell proliferation, respectively. When compared with the rigid artery for significant stenosis the pressure drop decreased by 27.7% and 37.6% for the calcified plaque and for the smooth muscle cell proliferation case, respectively. These significant variations in pressure drop for the higher stenosis may lead to misinterpretation and misdiagnosis of the stenosis severity.     

Coupled oxygen transport analysis in the avascular wall of a coronary artery stenosis during angioplasty

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied numerically by solving the convection-diffusion equations. Two geometries replicating stenosis before and after percutaneous transluminal coronary angioplasty (PTCA) are used for the analysis. The results are compared to evaluate the effect of the degree of stenosis on oxygen transport. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. The results show that the PO2 in the medial region of the arterial wall is approximately 10mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation, there is a small rise followed by a sharp fall in the oxygen flux. The drop in the oxygen flux to the wall at the point of flow reattachment for pre-PTCA stenosis is four times that for post-PTCA stenosis. The minimum PO2 in the avascular wall, PO2,min, at this location decreases to approximately 6.0 and 4.2mmHg for post- and pre-PTCA stenosis, respectively. The drop in PO2,w and PO2,min at the point of flow reattachment for pre-PTCA is approximately 2 times that for post-PTCA stenosis. Thus, the present study quantifies the oxygen transport to the arterial wall before and after cardiovascular intervention.     

Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model.

Numerical analysis of flow phenomena and wall shear stresses in the human carotid artery bifurcation has been carried out using a three-dimensional geometrical model. The primary aim of this study is the detailed discussion of non-Newtonian flow velocity and wall shear stress during the pulse cycle. A comparison of non-Newtonian and Newtonian results is also presented. The applied non-Newtonian behavior of blood is based on measured dynamic viscosity. In the foreground of discussion are the flow characteristics in the carotid sinus. The investigation shows complex flow patterns especially in the carotid sinus where flow separation occurs at the outer wall throughout the systolic deceleration phase. The changing sign of the velocity near the outer sinus wall results in oscillating shear stress during the pulse cycle. At the outer wall of the sinus at maximum diameter level the shear stress ranges from -1.92 N/m2 to 1.22 N/m2 with a time-averaged value of 0.04 N/m2. At the inner wall of the sinus at maximum diameter level the shear stress range is from 1.16 N/m2 to 4.18 N/m2 with a mean of 1.97 N/m2. The comparison of non-Newtonian and Newtonian results indicates unchanged flow phenomena and rather minor differences in the basic flow characteristics.     

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 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.     

Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

Non-Newtonian blood flow in human right coronary arteries: transient simulations

This study looks at pulsatile blood flow through four different right coronary arteries, which have been reconstructed from biplane angiograms. A non-Newtonian blood model (the Generalised Power Law), as well as the usual Newtonian model of blood viscosity, is used to study the wall shear stress in each of these arteries over the entire cardiac cycle. The difference between Newtonian and non-Newtonian blood models is also studied over the whole cardiac cycle using the recently generalised global non-Newtonian importance factor. In addition, the flow is studied by considering paths of massless particles introduced into the flow field. The study shows that, when studying the wall shear stress distribution for transient blood flow in arteries, the use of a Newtonian blood model is a reasonably good approximation. However, to study the flow within the artery in greater detail, a non-Newtonian model is more appropriate.     

Effects of non-Newtonian blood and metabolic states of the blood and vessel wall on the optimum design of single vessels and the vascular bifurcation

Employing the optimality principle, we attempted to predict the effects of non-Newtonian blood and the metabolic states of individual vessel segments on the optimum vascular design. Our results implied that irrespective of the vessel caliber, the optimum flow rate of non-Newtonian blood through a cylindrical vessel is less than that of Newtonian blood by not more than some 12-13%, even though the non-Newtonian nature is within the pathologically-realistic highest range. Non-Newtonian blood does not exert the slightest degree of influence on the optimum geometry of the vascular bifurcation. In contrast, as the metabolic state of the vessel wall overwhelms that of the blood, the optimum flow through the cylindrical vessel becomes markedly increased: the optimum relative caliber of the branch of the bifurcation decreases and the optimum branching angle increases.     

In vitro oxidative footprinting provides insight into apolipoprotein B‐100 structure in low‐density lipoprotein

Low‐density lipoprotein (LDL) is a major cholesterol carrier in human blood. Oxidations of apolipoprotein B‐100 (apo B‐100, LDL protein) could be proatherogenic and play critical roles in early stages of plaque formation in the arterial wall. The structure of apo B‐100 is still poorly understood, partially due to its size (550 KDa, 4563 amino acids). To gain an insight into LDL structure, we mapped the regions of apo B‐100 in human LDL that were prone to oxidation using peroxynitrite and hypochlorite as probes. In this study, LDL was incubated with various concentrations of peroxynitrite and sodium hypochlorite in bicarbonate buffer. The LDL protein apo B‐100 was delipidated, denatured, alkylated, and subjected to tryptic digestion. Tryptic peptides were analyzed employing LC‐MS/MS. Database search was performed against the apo B‐100 database (SwissProt accession #P04114) using “SEQUEST” algorithm to identify peroxynitrite and hypochlorite‐mediated oxidations markers nitrotyrosine, nitrotryptophan, hydroxy‐tryptophan, and 3‐chlorotyrosine. Several site‐specific oxidations were identified in apo B‐100 after treatment of intact LDL particles with the oxidants. We hypothesize that these regions could be accessible to oxidant and critical for early events in atherosclerotic plaque deposition.