Large Negative Stress Phase Angle (SPA) attenuates nitric oxide production in bovine aortic endothelial cells

Hemodynamics plays an important role in cardiovascular physiology and pathology. Pulsatile flow (Q), pressure (P), and diameter (D) waveforms exert wall shear stress (WSS), normal stress, and circumferential strain (CS) on blood vessels. Most in vitro studies to date have focused on either WSS or CS but not their interaction. Recently, we have shown that concomitant WSS and CS affect EC biochemical response modulated by the temporal phase angle between WSS and CS (stress phase angle, SPA). Large negative SPA has been shown to occur in regions of the circulation where atherosclerosis and intimal hyperplasia are prevalent. Here, we report that nitric oxide (NO) biochemical secretion was significantly decreased in response to a large negative SPA of -180 deg with respect to an SPA of 0 degrees in bovine aortic endothelial cells (BAEC) at 5 h. A new hemodynamic simulator for the study of the physiologic SPA was used to provide the hemodynamic conditions of pro-atherogenic (SPA = -180 deg) and normopathic (SPA = 0 deg) states. The role of complex hemodynamics in vascular remodeling, homeostasis, and pathogenesis can be advanced by further assessment of the hypothesis that a large negative SPA is pro-atherogenic.     

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.     

A numerical study of flow in curved tubes simulating coronary arteries

Numerical simulations of pulsatile flow in coronary arteries which take into account the curvature associated with the bending of arteries over the surface of the heart are presented for resting, excited and drug induced states. The study was motivated by reported observations of atherosclerotic plaque localization on the inner curvature of coronary arteries. The simulated flow field appears quasi-steady under resting conditions with wall shear stress always highest on the outside wall and only a single secondary flow vortex in the half tube. However, reversal of wall shear stress direction at the inside wall does occur under resting flow conditions and this is not a quasi-steady characteristic. The flow field is markedly unsteady under excited conditions with wall shear stress sometimes peaking on the inside wall and an increase in the magnitude of wall shear stress reversal on the inside wall. However, only a single secondary flow vortex in the half tube is observed. Implications of the simulations for the role of fluid mechanics in coronary artery atherosclerosis are also discussed.     

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.     

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.     

Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree

The compliance of the vessel wall affects hemodynamic parameters which may alter the permeability of the vessel wall. Based on experimental measurements, the present study established a finite element (FE) model in the proximal elastic vessel segments of epicardial right coronary arterial (RCA) tree obtained from computed tomography. The motion of elastic vessel wall was measured by an impedance catheter and the inlet boundary condition was measured by an ultrasound flow probe. The Galerkin FE method was used to solve the Navier–Stokes and Continuity equations, where the convective term in the Navier–Stokes equation was changed in the arbitrary Lagrangian–Eulerian (ALE) framework to incorporate the motion due to vessel compliance. Various hemodynamic parameters (e.g., wall shear stress—WSS, WSS spatial gradient—WSSG, oscillatory shear index—OSI) were analyzed in the model. The motion due to vessel compliance affects the time-averaged WSSG more strongly than WSS at bifurcations. The decrease of WSSG at flow divider in elastic bifurcations, as compared to rigid bifurcations, implies that the vessel compliance decreases the permeability of vessel wall and may be atheroprotective. The model can be used to predict coronary flow pattern in subject-specific anatomy as determined by noninvasive imaging.     

Effects of different stent designs on local hemodynamics in stented arteries

Following the deployment of a coronary stent and disruption of an atheromatous plaque, the deformation of the arterial wall and the presence of the stent struts create a new fluid dynamic field, which can cause an abnormal biological response. In this study 3D computational models were used to analyze the fluid dynamic disturbances induced by the placement of a stent inside a coronary artery. Stents models were first expanded against a simplified arterial plaque, with a solid mechanics analysis, and then subjected to a fluid flow simulation under pulsatile physiological conditions. Spatial and temporal distribution of arterial wall shear stress (WSS) was investigated after the expansion of stents of different designs and different strut thicknesses. Common oscillatory WSS behavior was detected in all stent models. Comparing stent and vessel wall surfaces, maximum WSS values (in the order of 1Pa) were located on the stent surface area. WSS spatial distribution on the vascular wall surface showed decreasing values from the center of the vessel wall portion delimited by the stent struts to the wall regions close to the struts. The hemodynamic effects induced by two different thickness values for the same stent design were investigated, too, and a reduced extension of low WSS region (<0.5Pa) was observed for the model with a thicker strut.     

Myocardial bridging and endothelial dysfunction – Computational fluid dynamics study

Myocardial bridging (MB) is associated with endothelial dysfunction in patients with angina and non-obstructive coronary artery disease. This study aims to determine if there is a link between abnormal blood flow patterns and endothelial dysfunction in patients with MB. Ten patients with MB in their left anterior descending (LAD) artery were selected, 5 of whom had endothelial dysfunction and 5 had no endothelial dysfunction based on their response to acetylcholine. Similarly, 10 patients without MB in their LAD, 5 of whom had endothelial dysfunction and 5 of whom had no endothelial dysfunction, were studied as a control group. Transient computational fluid dynamics simulations were performed to derive wall shear stress (WSS) over the entire vessel including proximal, middle and distal segments. Patients with MB and endothelial dysfunction had lower WSS in the proximal LAD and greater WSS in the mid-LAD than patients with MB but without endothelial dysfunction. When comparing patients with endothelial dysfunction, those with MB had significantly lower shear stress in the proximal LAD (0.32 ± 0.14 Pa (with MB) vs 0.71 ± 0.38 Pa (without MB), p = 0.01) and greater shear stress in the mid-LAD (2.81 ± 1.20 Pa (with MB) vs 1.66 ± 0.31 Pa (without MB), p = 0.014) than patients without MB. Our findings demonstrated that the presence of MB significantly contributes to low WSS and endothelial dysfunction relationship.     

Curvature effect on hemodynamic conditions at the inner bend of the carotid siphon and its relation to aneurysm formation

Although high-impact hemodynamic forces are thought to lead to cerebral aneurysmal change, little is known about the aneurysm formation on the inner aspect of vascular bends such as the internal carotid artery (ICA) siphon where wall shear stress (WSS) is expected to be low. This study evaluates the effect of vessel curvature and hemodynamics on aneurysm formation along the inner carotid siphon. Catheter 3D-rotational angiographic volumes of 35 ICA (10 aneurysms, 25 controls) were evaluated in 3D for radius of curvature and peak curvature of the siphon bend, followed by univariate statistical analysis. Computational fluid dynamic (CFD) simulations were performed on patient-derived models after aneurysm removal and on synthetic variants of increasing curvature. Peak focal siphon curvature was significantly higher in aneurysm bearing ICAs (0.36±0.045 vs. 0.30±0.048 mm⁻¹, p=0.003), with no difference in global radius of curvature (p=0.36). In CFD simulations, increasing parametric curvature tightness (from 5 to 3 mm radius) resulted in dramatic increase of WSS and WSS gradient magnitude (WSSG) on the inner wall of the bend. In patient-derived data, the location of aneurysms coincided with regions of low WSS (<4 Pa) flanked by high WSS and WSSG peaks. WSS peaks correlated with the aneurysm neck. In contrast, control siphon bends displayed low, almost constant, WSS and WSSG profiles with little spatial variation. High bend curvature induces dynamically fluctuating high proximal WSS and WSSG followed by regions of flow stasis and recirculation, leading to local conditions known to induce destructive vessel wall remodeling and aneurysmal initiation.     

Hemodynamic impacts of various types of stenosis in the left coronary artery bifurcation: A patient-specific analysis

This study investigates the hemodynamic changes to various types of coronary stenosis in the left coronary artery bifurcation, based on a patient-specific analysis. Twenty two patients with left coronary artery disease were included in this study. All stenoses involving the left coronary artery bifurcation were classified into four types, according to their locations: A) left circumflex (LCx) and left anterior descending (LAD), B) LCx only, C) left main stem only, and D) LAD only. Computational fluid dynamics (CFD) was performed to analyze the flow and wall shear stress (WSS) changes in all reconstructed left coronary geometries. Our results showed that the flow velocity and WSS were significantly increased at stenotic locations. High WSS was found at >70% lumen stenosis, which ranged from 2.5 Pa to 3.5 Pa. This study demonstrates that in patients with more than 50% stenosis in the left coronary artery bifurcation, WSS plays an important role in providing information about the extent of coronary atherosclerosis in the left coronary artery branch.     

Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation

Finite element simulations of fluid-solid interactions were used to investigate inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans (normal volunteers: NV1, NV2, NV4). Subject-specific calculations were based on MR images of structural anatomy and ultrasound measurements of flow at domain boundaries. For all subjects, the largest contiguous region of low wall shear stress (WSS) occurred at the carotid bulb, WSS was high (6-10 Pa) at the apex, and a small localized region of WSS > 10 Pa occurred close to the inner wall of the external carotid artery (ECA). NV2 and NV4 had a "spot" of low WSS distal to the bifurcation at the inner wall of the ECA. Low WSS patches in the common carotid artery (CCA) were contiguous with the carotid bulb low WSS region in NV1 and NV2, but not in NV4. In all three subjects, areas of high oscillatory shear index (OSI) were confined to regions of low WSS. Only NV4 exhibited high levels of OSI on the external adjoining wall of the ECA and CCA. For all subjects, the maximum wall shear stress temporal gradient (WSSTG) was highest at the flow divider (reaching 1,000 Pa/s), exceeding 300 Pa/s at the walls connecting the ECA and CCA, but remaining below 250 Pa/s outside of the ECA. In all subjects, (maximum principle) cyclic strain (CS) was greatest at the apex (NV1: 14%; NV2: 11%; NV4: 6%), and a second high CS region occurred at the ECA-CCA adjoining wall (NV1: 11%, NV2: 9%, NV4: 5%). Wall deformability was included in one simulation (NV2) to verify that it had little influence on the parameters studied. Location and magnitude of low WSS were similar, except for the apex (differences of up to 25%). Wall distensibility also influenced OSI, doubling it in most of the CCA, separating the single high OSI region of the carotid bulb into two smaller regions, and shrinking the ECA internal and external walls' high OSI regions. These observations provide further evidence that significant intra-subject variability exists in those factors thought to impact atherosclerosis.     

Numerical investigations of the haemodynamic changes associated with stent malapposition in an idealised coronary artery

The deployment of a coronary stent near complex lesions can sometimes lead to incomplete stent apposition (ISA), an undesirable side effect of coronary stent implantation. Three-dimensional computational fluid dynamics (CFD) calculations are performed on simplified stent models (with either square or circular cross-section struts) inside an idealised coronary artery to analyse the effect of different levels of ISA to the change in haemodynamics inside the artery. The clinical significance of ISA is reported using haemodynamic metrics like wall shear stress (WSS) and wall shear stress gradient (WSSG). A coronary stent with square cross-sectional strut shows different levels of reverse flow for malapposition distance (MD) between 0 mm and 0.12 mm. Chaotic blood flow is usually observed at late diastole and early systole for MD=0 mm and 0.12 mm but are suppressed for MD=0.06 mm. The struts with circular cross section delay the flow chaotic process as compared to square cross-sectional struts at the same MD and also reduce the level of fluctuations found in the flow field. However, further increase in MD can lead to chaotic flow not only at late diastole and early systole, but it also leads to chaotic flow at the end of systole. In all cases, WSS increases above the threshold value (0.5 Pa) as MD increases due to the diminishing reverse flow near the artery wall. Increasing MD also results in an elevated WSSG as flow becomes more chaotic, except for square struts at MD=0.06 mm.     

A study on the compliance of a right coronary artery and its impact on wall shear stress

A computational model incorporating physiological motion and uniform transient wall deformation of a branchless right coronary artery (RCA) was developed to assess the influence of artery compliance on wall shear stress (WSS). Arterial geometry and deformation were derived from modern medical imaging techniques, whereas the blood flow was solved numerically employing a moving-grid approach using a well-validated in-house finite element code. The simulation results indicate that artery compliance affects the WSS in the RCA heterogeneously, with the distal region mostly experiencing these effects. Under physiological inflow conditions, coronary compliance contributed to phase changes in the WSS time history, without affecting the temporal gradient of the local WSS nor the bounds of the WSS magnitude. Compliance does not cause considerable changes to the topology of WSS vector patterns nor to the localization of WSS minima along the RCA. We conclude that compliance is not an important factor affecting local hemodynamics in the proximal region of the RCA while the influence of compliance in the distal region needs to be evaluated in conjunction with the outflow to the myocardium through the major branches of the RCA.     

Wall shear stress in normal left coronary artery tree

Despite the fact that the role of wall shear stress (WSS) as a local mechanical factor in atherogenesis is well established, its distribution over the entire normal human left coronary artery (LCA) tree has not yet been studied. A three-dimensional computer generated model of the epicardial LCA tree, based on averaged human data set extracted from angiographies, was adopted for finite-element analysis of the Navier-Stokes flow equations treating blood as non-Newtonian fluid. The LCA tree includes the left main coronary artery (LMCA), the left anterior descending (LAD), the left circumflex artery (LCxA) and their major branches. In proximal LCA tree regions where atherosclerosis frequently occurs, low WSS appears. Low WSS regions occur at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development. On the LMCA bifurcation, at regions opposite to the flow divider, dominant low WSS values occur ranging from 0.75 to 2.25 N/m2. High WSS values are encountered at all flow dividers. This work determines, probably for the first time, the topography of the WSS in the entire normal human LCA epicardial tree. It is also the first work determining the spatial WSS differentiation between proximal and distal normal human LCA parts. The haemodynamic analysis of the entire epicardial LCA tree further verifies the implications of the WSS in atherosclerosis mechanisms.     

Pulsatile flow in a coronary artery using multiphase kinetic theory

Pulsatile flow in a model of a right coronary artery (RCA) was previously modeled as a single-phase fluid and as a two-phase fluid using experimental rheological data for blood as a function of hematocrit and shear rate. Here we present a multiphase kinetic theory model which has been shown to compute correctly the viscosity of red blood cells (RBCs) and their migration away from vessel walls: the Fahraeus–Lindqvist effect. The computed RBC viscosity decreases with shear rate and vessel size, consistent with measurements. The pulsatile computations were performed using a typical cardiac waveform until a limit cycle was well established. The RBC volume fractions, shear stresses, shear stress gradients, granular temperatures, viscosities, and phase velocities varied with time and position during each cardiac cycle. Steady-state computations were also performed and were found to compare well with time-averaged transient results. The wall shear stress and wall shear stress gradients (both spatial and temporal) were found to be highest on the inside area of maximum curvature. Potential atherosclerosis sites are identified using these computational results.     

Curvature and tortuosity of the superficial femoral artery: a possible risk factor for peripheral arterial disease.

Atherosclerosis in the superficial femoral artery (SFA) resulting in peripheral arterial disease is more common in men than women and shows a predilection for the region of the adductor canal. Blood flow patterns are related to development of atherosclerosis, and we investigated if curvature and tortuosity of the femoral artery differed between young men and women and if differences resulted in adverse flow patterns. Magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) were combined in 18 young adult volunteers (9 men) to assess the relationship of flow features to likely sites of future atherosclerosis formation. Subjects underwent MRI of the right SFA, three-dimensional vascular geometry was reconstructed, and measures of tortuosity and curvature were calculated. Tortuosity and curvature were significantly greater for men than women, and this was related to increased body surface area, body mass index, or weight in men. In both sexes, "tortuosity" increased from the midthigh to the popliteal fossa. The greatest curvature was found within the distal quarter of the SFA. CFD modeling was undertaken on MRI-based reconstructions of the SFA. Wall shear stresses (WSS) were extracted from the computations. WSS showed greater spatial variation in the men than in the women, and the men exhibited lower mean WSS. These data indicate that sex differences related to body size and anatomical course of the femoral artery may contribute to the enhanced risk of focal atherosclerosis in the adductor canal.     

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.     

Analysis of blood flow in an out-of-plane CABG model

Coronary artery bypass graft (CABG) is a routine surgical treatment for ischemic and infarcted myocardium. A large number of CABG fail postoperatively because of intimal hyperplasia within months or years. The cause of this failure is thought to be partly related to the flow patterns and shear stresses acting on the endothelial cells. An accurate representation of the flow field and associated wall shear stress (WSS) requires a detailed three-dimensional (3D) model of the CABG. The purpose of this study is to present a detailed analysis of blood flow in a 3D aorto/left CABG, bypassing the occluded left anterior descending coronary (LAD) artery. The analysis takes into account the influence of the out-of-plane geometry of the graft. The finite volume technique was employed to model the 3D blood flow pattern to determine the velocity and WSS distributions. This study presents the flow field distributions of the velocity and WSS at four instances of the cardiac cycle, two in systole and two in diastole. Our results reveal that the CABG geometry has a significant effect on the velocity distribution. The axial velocity profiles at different instances of the cardiac cycle exhibit strong skewing; significant secondary flow and vortex structures are seen in the in-plane velocity patterns. The maximum WSS on the bed of the occluded LAD artery opposite to the graft junction is 14 Pa in middiastole, whereas there is a significantly lower and more uniform distribution of WSS on the bed of the anastomosis. The present results indicate that nonplanarity of the blood vessel along with the inflow conditions has a substantial effect on the fluid mechanics of CABG that contribute to the patency of graft.     

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.