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.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

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.     

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

A multiphase transient non-Newtonian three-dimensional (3-D) computational fluid dynamics (CFD) simulation has been performed for pulsatile hemodynamics in an idealized curved section of a human coronary artery. We present the first prediction, to the authors' knowledge, of particulate buildup on the inside curvature using the multiphase theory of dense suspension hemodynamics. In this study, the particulates are red blood cells (RBCs). The location of RBC buildup on the inside curvature correlates with lower wall shear stress (WSS) relative to the outside curvature. These predictions provide insight into how blood-borne particulates interact with artery walls and hence, have relevance for understanding atherogenesis since clinical observations show that atherosclerotic plaques generally form on the inside curvatures of arteries. The buildup of RBCs on the inside curvature is driven by the secondary flow and higher residence times. The higher viscosity in the central portion of the curved vessel tends to block their flow, causing them to migrate preferentially through the boundary layer. The reason for this is the nearly neutrally buoyant nature of the dense two-phase hemodynamic flow. The two-phase non-Newtonian viscosity model predicts greater shear thinning than the single-phase non-Newtonian model. Consequently, the secondary flow induced in the curvature is weaker. The waveforms for computed hemodynamic parameters, such as hematocrit, WSS, and viscosity, follow the prescribed inlet velocity waveforms. The lower oscillatory WSS produced on the inside curvature has implications for understanding thickening of the intimal layer.     

Comparative study of Newtonian and non-Newtonian simulations of drug transport in a model drug-eluting stent

To elucidate the difference between Newtonian and shear thinning non-Newtonian assumptions of blood in the analysis of DES drug delivery, we numerically simulated the local flow pattern and the concentration distribution of the drug at the lumen-tissue interface for a structurally simplified DES deployed in a curved segment of an artery under pulsatile blood flow conditions. The numerical results showed that when compared with the Newtonian model, the Carreau (shear thinning) model could lead to some differences in the luminal surface drug concentration in certain areas along the outer wall of the curved vessel. In most areas of the vessel, however, there were no significant differences between the 2 models. Particularly, no significant difference between the two models was found in terms of the area-averaged luminal surface drug concentration. Therefore, we believe that the shear thinning property of blood may play little roles in DES drug delivery. Nevertheless, before we draw the conclusion that Newtonian assumption of blood can be used to replace its non-Newtonian one for the numerical simulation of drug transport in the DES implanted coronary artery, other more complex mechanical properties of blood such as its thixotropic behavior should be tested.     

Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments

The spatial and temporal distributions of wall shear stress (WSS) in prototype vessel geometries of coronary segments are investigated via numerical simulation, and the potential association with vascular disease and specifically atherosclerosis and plaque rupture is discussed. In particular, simulation results of WSS spatio-temporal distributions are presented for pulsatile, non-Newtonian blood flow conditions for: (a) curved pipes with different curvatures, and (b) bifurcating pipes with different branching angles and flow division. The effects of non-Newtonian flow on WSS (compared to Newtonian flow) are found to be small at Reynolds numbers representative of blood flow in coronary arteries. Specific preferential sites of average low WSS (and likely atherogenesis) were found at the outer regions of the bifurcating branches just after the bifurcation, and at the outer-entry and inner-exit flow regions of the curved vessel segment. The drop in WSS was more dramatic at the bifurcating vessel sites (less than 5% of the pre-bifurcation value). These sites were also near rapid gradients of WSS changes in space and time – a fact that increases the risk of rupture of plaque likely to develop at these sites. The time variation of the WSS spatial distributions was very rapid around the start and end of the systolic phase of the cardiac cycle, when strong fluctuations of intravascular pressure were also observed. These rapid and strong changes of WSS and pressure coincide temporally with the greatest flexion and mechanical stresses induced in the vessel wall by myocardial motion (ventricular contraction). The combination of these factors may increase the risk of plaque rupture and thrombus formation at these sites.     

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.     

Development of a general method for designing microvascular networks using distribution of wall shear stress

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.     

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.     

On the relative importance of rheology for image-based CFD models of the carotid bifurcation

BACKGROUND: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. METHOD OF APPROACH: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. RESULTS: Sensitivity of WSS to the various rheological assumptions was roughly 1.0 dyn/cm(2) or 8%, nearly seven times less than that due to geometric uncertainty (6.7 dyn/cm(2) or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. CONCLUSIONS: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.     

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.     

Flow patterns and wall shear stress distribution in human internal carotid arteries: the geometric effect on the risk for stenoses

It has been widely observed that atherosclerotic stenosis occurs at sites with complex hemodynamics, such as arteries with high curvature or bifurcations. These regions usually have very low or highly oscillatory wall shear stress (WSS). In the present study, 3D sinusoidally pulsatile blood flow through the models of internal carotid artery (ICA) with different geometries was investigated with computational simulation. Three preferred sites of stenoses were found along the carotid siphon with low and highly oscillatory WSS. The risk for stenoses at these sites was scaled with the values of time-averaged WSS and oscillating shear index (OSI). The local risk for stenoses at every preferred site of stenoses was found different between 3 types of ICA, indicating that the geometry of the blood vessel plays significant roles in the atherogenesis. Specifically, the large curvature and planarity of the vessel were found to increase the risk for stenoses, because they tend to lower WSS and elevate OSI. Therefore, the geometric study makes it possible to estimate the stenosis location in the ICA siphon as long as the shape of ICA was measured.     

Mis-sizing of stent promotes intimal hyperplasia: impact of endothelial shear and intramural stress

Stent can cause flow disturbances on the endothelium and compliance mismatch and increased stress on the vessel wall. These effects can cause low wall shear stress (WSS), high wall shear stress gradient (WSSG), oscillatory shear index (OSI), and circumferential wall stress (CWS), which may promote neointimal hyperplasia (IH). The hypothesis is that stent-induced abnormal fluid and solid mechanics contribute to IH. To vary the range of WSS, WSSG, OSI, and CWS, we intentionally mismatched the size of stents to that of the vessel lumen. Stents were implanted in coronary arteries of 10 swine. Intravascular ultrasound (IVUS) was used to size the coronary arteries and stents. After 4 wk of stent implantation, IVUS was performed again to determine the extent of IH. In conjunction, computational models of actual stents, the artery, and non-Newtonian blood were created in a computer simulation to yield the distribution of WSS, WSSG, OSI, and CWS in the stented vessel wall. An inverse relation (R(2) = 0.59, P < 0.005) between WSS and IH was found based on a linear regression analysis. Linear relations between WSSG, OSI, and IH were observed (R(2) = 0.48 and 0.50, respectively, P < 0.005). A linear relation (R(2) = 0.58, P < 0.005) between CWS and IH was also found. More statistically significant linear relations between the ratio of CWS to WSS (CWS/WSS), the products CWS × WSSG and CWS × OSI, and IH were observed (R(2) = 0.67, 0.54, and 0.56, respectively, P < 0.005), suggesting that both fluid and solid mechanics influence the extent of IH. Stents create endothelial flow disturbances and intramural wall stress concentrations, which correlate with the extent of IH formation, and these effects were exaggerated with mismatch of stent/vessel size. These findings reveal the importance of reliable vessel and stent sizing to improve the mechanics on the vessel wall and minimize IH.     

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.     

The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.     

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.     

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.     

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.