Volume flow and wall shear stress quantification in the human conjunctival capillaries and post-capillary venules in vivo

Understanding the mathematical relationships of volume blood flow and wall shear stress with respect to microvessel diameter is necessary for the study of vascular design. Here, for the first time, volume flow and wall shear stress were quantified from axial red blood cell velocity measurements in 104 conjunctival microvessels of 17 normal human volunteers. Measurements were taken with a slit lamp based imaging system from the post capillary side of the bulbar conjunctiva in microvessel diameters ranging from 4 to 24 micrometers. The variation of the velocity profile with diameter was taken into account by using a profile factor function. Volume flow ranged from 5 to 462 pl/s with a mean value of 102 pl/s and gave a second power law best fitting line (r=0.97) deviating significantly from the third power law relation with diameter. The estimated wall shear stress declined hyperbolically (r=0.93) from a maximum of 9.55 N/m(2) at the smallest capillaries, down to a minimum of 0.28 N/m(2) at the higher diameter post capillary venules. The mean wall shear stress value for all microvessels was 1.54 N/m(2).     

Shear stress paradigm for perinatal fractal arterial network remodeling in lambs with pulmonary hypertension and increased pulmonary blood flow

Congenital heart disease with increased blood flow commonly leads to the development of increased pulmonary vascular reactivity and pulmonary arterial hypertension by mechanisms that remain unclear. We hypothesized a shear stress paradigm of hemodynamic reactivity and network remodeling via the persistence and/or exacerbation of a fetal diameter bifurcation phenotype [parent diameter d(0) and daughters d(1) >or= d(2) with alpha < 2 in (d(1)/d(0))(alpha) + (d(2)/d(0))(alpha) and area ratio beta < 1 in beta = (d(1)(2)+ d(2)(2))/ d(0)(2)] that mechanically acts as a high resistance magnifier/shear stress amplifier to blood flow. Evidence of a hemodynamic influence on network remodeling was assessed with a lamb model of high-flow-induced secondary pulmonary hypertension in which an aortopulmonary graft was surgically placed in one twin in utero (Shunt twin) but not in the other (Control twin). Eight weeks after birth arterial casts were made of the left pulmonary arterial circulation. Bifurcation diameter measurements down to 0.010 mm in the Shunt and Control twins were then compared with those of an unoperated fetal cast. Network organization, cumulative resistance, and pressure/shear stress distributions were evaluated via a fractal model whose dimension D(0) approximately alpha delineates hemodynamic reactivity. Fetus and Control twin D(0) differed: fetus D(0)=1.72, a high-resistance/shear stress amplifying condition; control twin D(0) = 2.02, an area-preserving transport configuration. The Shunt twin (D(0)=1.72) maintained a fetal design but paradoxically remodeled diameter geometry to decrease cumulative resistance relative to the Control twin. Our results indicate that fetal/neonatal pulmonary hemodynamic reactivity remodels in response to shear stress, but the response to elevated blood flow and pulmonary hypertension involves the persistence and exacerbation of a fetal diameter bifurcation phenotype that facilitates endothelial dysfunction/injury.     

Heterogeneous perfusion is a consequence of uniform shear stress in optimized arterial tree models

Using optimized computer models of arterial trees we demonstrate that flow heterogeneity is a necessary consequence of a uniform shear stress distribution. Model trees are generated and optimized under different modes of boundary conditions. In one mode flow is delivered to the tissue as homogeneously as possible. Although this primary goal can be achieved, resulting shear stresses between blood and the vessel walls show very large spread. In a second mode, models are optimized under the condition of uniform shear stress in all segments which in turn renders flow distribution heterogeneous. Both homogeneous perfusion and uniform shear stress are desirable goals in real arterial trees but each of these goals can only be approached at the expense of the other. While the present paper refers only to optimized models, we assume that this dual relation between the heterogeneities in flow and shear stress may represent a more general principle of vascular systems.     

Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions

Shear stress plays a pivotal role in pathogenesis of coronary heart disease. The spatial and temporal variation in hemodynamics of blood flow, especially shear stress, is dominated by the vessel geometry. The goal of the present study was to investigate the effect of 2D and 3D geometries on the numerical modeling of coronary blood flow and shear stress distribution. We developed physiologically realistic 2D and 3D models (with similar geometries) of the human left coronary artery under normal and stenosis conditions (30%, 60%, and 80%) using PROE (WF 3). Transient blood flows in these models were solved using laminar and turbulent (k-ω) models using a computational fluid dynamics solver, FLUENT (v6.3.26). As the stenosis severity increased, both models predicted a similar pattern of increased shear stress at the stenosis throat, and in recirculation zones formed downstream of the stenosis. The 2D model estimated a peak shear stress value of 0.91, 2.58, 5.21, and 10.09 Pa at the throat location under normal, 30%, 60%, and 80% stenosis severity. The peak shear stress values at the same location estimated by the 3D model were 1.41, 2.56, 3.15, and 13.31 Pa, respectively. The 2D model underestimated the shear stress distribution inside the recirculation zone compared with that of 3D model. The shear stress estimation between the models diverged as the stenosis severity increased. Hence, the 2D model could be sufficient for analyzing coronary blood flow under normal conditions, but under disease conditions (especially 80% stenosis) the 3D model was more suitable.     

Scaling of myocardial mass to flow and morphometry of coronary arteries.

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5 +/- 32.7) were used in this study. Various coronary subtrees of the left anterior descending, right coronary, and left circumflex arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter, and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters, and volumetric flow show an approximately 3/4, 3/8, and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease.     

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

Temporal and spatial variations of cell-free layer width in arterioles

Separation of red blood cells and plasma in microcirculatory vessels produces a cell-free layer at the wall. This layer may be an important determinant of blood viscosity and wall shear stress in arterioles, where most of the hydraulic pressure loss in the circulatory system occurs and flow regulatory mechanisms are prominent. With the use of a newly developed method, the width of the cell-free layer was rapidly and repeatedly determined in arterioles (10- to 50-microm inner diameter) in the rat cremaster muscle at normal arterial pressure. The temporal variation of the cell-free layer width was non-Gaussian, but calculated mean and median values differed by <0.2 microm. The correlation length of the temporal variations downstream (an indication of mixing) was approximately 30 microm and was independent of pseudoshear rate (ratio of mean velocity to vessel diameter) and of vessel diameter. The cell-free layer width was significantly different on opposite sides of the vessel and inversely related. Increasing red blood cell aggregability reduced this inverse relation but had no effect on correlation length. In the diameter range studied, the mean width of the cell-free layer increased from 0.8 to 3.1 microm and temporal variations increased from 30% to 70% of the mean width. Increased aggregability did not alter either relationship. In summary, the cell-free layer width in arterioles is diameter dependent and shows substantial non-Gaussian temporal variations. The temporal variations increase as diameter increases and are inversely related on opposite sides of the vessel.     

Distribution of stress and strain along the porcine aorta and coronary arterial tree

The existence of a homeostatic state of stresses and strains has been axiomatic in the cardiovascular system. The objective of this study was to determine the distribution of circumferential stress and strain along the aorta and throughout the coronary arterial tree to test this hypothesis. Silicone elastomer was perfused through the porcine aorta and coronary arterial tree to cast the arteries at physiological pressure. The loaded and zero-stress dimensions of the vessels were measured. The aorta (1.8 cm) and its secondary branches were considered down to 1.5 mm diameter. The left anterior descending artery (4.5 mm) and its branches down to 10 microm were also measured. The Cauchy mean circumferential stress and midwall stretch ratio were calculated. Our results show that the stretch ratio and Cauchy stress were lower in the thoracic than in the abdominal aorta and its secondary branches. The opening angle (theta) and midwall stretch ratio (lambda) showed a linear variation with order number (n) as follows: theta = 10.2n + 63.4 (R(2) = 0.989) and lambda = 4.47 x 10(-2)n + 1.1 (R(2) = 0.995). Finally, the stretch ratio and stress varied between 1.2 and 1.6 and between 10 and 150 kPa, respectively, along the aorta and left anterior descending arterial tree. The relative uniformity of strain (50% variation) from the proximal aorta to a 10-microm arteriole implies that the vascular system closely regulates the degree of deformation. This suggests a homeostasis of strain in the cardiovascular system, which has important implications for mechanotransduction and for vascular growth and remodeling.     

A fractal continuum model of the pulmonary arterial tree.

The extant morphometric data from the intrapulmonary arteries of dog, human, and cat lungs produce graphs of the log of the vessel number, (N) or length (l) in each level vs. the log of the mean diameter (D) in each level that are sufficiently linear to suggest that a scale-independent self-similar or fractal structure may underlie the observed relationships. These data can be correlated by the following formulas: Nj = a1Dj-beta 1, and lj = a2Dj beta 2, where j denotes the level (order or generation) number measured from the largest vessel at the entrance to the arterial tree to the smallest vessel at the entrance to the capillary bed. With the hemodynamic resistance (R) represented by Rj = 128 microliterj/(Nj pi Dj4) and the vascular volume (Q) by Qj = Nj pi Dj2lj/4, the continuous cumulative distribution of vascular resistance (Rcum) vs. cumulative vascular volume (Qcum) (where Rcum and Qcum represent the total resistance or volume, respectively, upstream from the jth level) can be calculated from [formula: see text] where r = Dj/Dj+1 is a constant independent of j. Analogous equations are developed for the inertance and compliance distributions, providing simple formulas to represent the hemodynamic consequences of the pulmonary arterial tree structure.     

Periodic acceleration: effects on vasoactive, fibrinolytic, and coagulation factors.

Cellular and isolated vessel experiments have shown that pulsatile and laminar shear stress to the endothelium produces significant release of mediators into the circulation. Periodic acceleration (pG(z)) applied to the whole body in the direction of the spinal axis adds pulses to the circulation, thereby increasing pulsatile and shear stress to the endothelium that should also cause release of mediators into the circulation. The purpose of this study was to determine whether addition of pulses to the circulation through pG(z) would be sufficient to increase shear stress in whole animals and to acutely release mediators and how such a physical maneuver might affect coagulation factors. Randomized control experiments were performed on anesthetized, supine piglets. The treatment group (pG(z)) (n = 12) received pG(z) with a motion platform that moved them repetitively head to foot at +/-0.4 g at 180 cpm for 60 min. The control group (n = 6) was secured to the platform but remained on conventional ventilation throughout the 4-h protocol. Compared with control animals and baseline, pulsatile stress produced significant increases of serum nitrite, prostacyclin, PGE(2), and tissue plasminogen activator antigen and activity, as well as D-dimer. There were no significant changes in epinephrine, norepinephrine, cortisol, and coagulation factors between groups or from baseline values. Pulsatile and laminar shear stress to the endothelium induced by pG(z) safely produces increases of vasoactive and fibrinolytic activity. pG(z) has potential to achieve mediator-related benefits from the actions of nitric oxide and prostaglandins.     

Adaptive regulation of wall shear stress optimizing vascular tree function

The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm²), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.     

Cell-free plasma layer in cerebral microvessels.

Two diameters of vessel and red cell column in cerebral microvessels (> 29.8 microns in diameter) of cat were measured together with red cell velocity, using a two fluorescent tracer method. A fluorescein isothiocyanate (FITC)-labeled red cell was adopted as a flow tracer to measure the cell velocity with a dual window technique. Based on the fluorescence image, the red cell column diameter was measured. Plasma was stained with rhodamine-B isothiocyanate (RITC)-labeled dextran to measure the vessel diameter. The thickness of the cell-free plasma layer could be determined from the difference of the two diameters. The obtained thickness of the cell-free layer was not described by a simple function of vessel diameter or red cell velocity; it was dependent on the pseudo shear rate defined by the ratio of cell velocity to vessel radius. The layer thickness increased with a decrease in the pseudo shear rate.     

Local heat produces a shear-mediated biphasic response in the thermoregulatory microcirculation of the Pallid bat wing

Investigators report that local heat causes an increase in skin blood flow consisting of two phases. The first is solely sensory neural, and the second is nitric oxide mediated. We hypothesize that mechanisms behind these two phases are causally linked by shear stress. Because microvascular blood flow, endothelial shear stress, and vessel diameters cannot be measured in humans, bat wing arterioles (26.6 +/- 0.3, 42.0 +/- 0.4, and 58.7 +/- 2.2 microm) were visualized noninvasively on a transparent heat plate via intravital microscopy. Increasing plate temperature from 25 to 37 degrees C increased flow in all three arterial sizes (137.1 +/- 0.3, 251.9 +/- 0.5, and 184.3 +/- 0.6%) in a biphasic manner. With heat, diameter increased in large arterioles (n = 6) by 8.7 +/- 0.03% within 6 min, medium arterioles (n = 8) by 19.7 +/- 0.5% within 4 min, and small arterioles (n = 8) by 31.6 +/- 2.2% in the first minute. Lidocaine (0.2 ml, 2% wt/vol) and NG-nitro-L-arginine methyl ester (0.2 ml, 1% wt/vol) were applied topically to arterioles (approximately 40 microm) to block sensory nerves, modulate shear stress, and block nitric oxide generation. Local heat caused only a 10.4 +/- 5.5% increase in diameter with neural blockade (n = 8) and only a 7.5 +/- 4.1% increase in diameter when flow was reduced (n = 8), both significantly lower than control (P < 0.001). Diameter and flow increases were significantly reduced with NG-nitro-L-arginine methyl ester application (P < 0.05). Our novel thermoregulatory animal model illustrates 1) regulation of shear stress, 2) a nonneural component of the first phase, and 3) a shear-mediated second phase. The time course of dilation suggests that early dilation of small arterioles increases flow and enhances second-phase dilation of the large arterioles.     

Arterial Shear Stress Reduces Eph-B4 Expression in Adult Human Veins

Vein graft adaptation to the arterial environment is characterized by loss of venous identity, with reduced Ephrin type-B receptor 4 (Eph-B4) expression but without increased Ephrin-B2 expression. We examined changes of vessel identity of human saphenous veins in a flow circuit in which shear stress could be precisely controlled. Medium circulated at arterial or venous magnitudes of laminar shear stress for 24 hours; histologic, protein, and RNA analyses of vein segments were performed. Vein endothelium remained viable and functional, with platelet endothelial cell adhesion molecule (PECAM)-expressing cells on the luminal surface. Venous Eph-B4 expression diminished (p = .002), Ephrin-B2 expression was not induced (p = .268), and expression of osteopontin (p = .002) was increased with exposure to arterial magnitudes of shear stress. Similar changes were not found in veins placed under venous flow or static conditions. These data show that human saphenous veins remain viable during ex vivo application of shear stress in a bioreactor, without loss of the venous endothelium. Arterial magnitudes of shear stress cause loss of venous identity without gain of arterial identity in human veins perfused ex vivo. Shear stress alone, without immunologic or hormonal influence, is capable of inducing changes in vessel identity and, specifically, loss of venous identity.     

黄河三角洲滨海盐碱地11个造林树种细根解剖性状对土壤条件的响应

细根作为植物与土壤连接的重要部位,能够反映植物对生存环境的适应性。以黄河三角洲滨海盐碱地不同立地条件下11个造林树种为对象,基于细根分支等级划分1-4级根序并进行解剖特征测定,分析细根解剖性状对滨海盐碱地不同土壤条件的响应规律。结果表明：（1）不同根序的细根直径存在显著差异,细根直径随根序升高呈增大趋势,而同根序的细根直径在不同树种间表现出显著的种间差异（P < 0.05）。1-2级细根皮层厚度、3-4级细根导管密度在树种间的差异均达显著水平（P < 0.05）。（2）在较为严重盐渍化土壤条件下（立地1）,细根皮层厚度较其他立地显著增大,但细根导管密度较小;在轻度盐碱立地条件下（立地3）,细根导管密度较大;较为严重的盐碱立地具有更为发达的细根直径及维管柱直径。（3）树种1-2级细根解剖结构与土壤环境关系最为密切,其中1级根直径与土壤pH值显著正相关（P < 0.05）,与土壤硝态氮含量呈显著负相关（P < 0.05）。对土壤理化性质与细根解剖性状的冗余分析表明,前两个轴的特征值达0.640和0.196,土壤速效养分含量与轴一（RDA1）呈正相关,低级根解剖性状则与轴二（RDA2）呈显著负相关。低级根解剖结构以及土壤的pH值能解释较多树种的差异性,其中低级根直径与皮层厚度对盐碱环境表现出较强的响应。     

Coronary stent implantation changes 3-D vessel geometry and 3-D shear stress distribution

Mechanisms of in-stent restenosis are not fully understood. Shear stress is known to play a role in plaque and thrombus formation and is sensitive to changes in regional vessel geometry. Hence, we evaluated the regional changes in 3-D geometry and shear stress induced by stent placement in coronary arteries of pigs.Methods. 3-D reconstruction was performed, applying a combined angiographic and IVUS technique (ANGUS), from seven Wallstents (diameter 3.5 (n=3) and 5mm (n=4)), which were implanted in seven coronary arteries of five pigs. This 3-D geometry was used to calculate locally the curvature, while the shear stress distribution was obtained by computational fluid dynamics. Local changes in shear stress were obtained at the entrance and exit of the stent for baseline (0. 65+/-0.22 ml/s) and hyperemic flow (2.60+/-0.86 ml/s) conditions. Results. After stent implantation, the curvature increased by 121% at the entrance and by 100% at the exit of the stent, resulting in local changes in shear stress. In general, at the entrance of the stent local maxima in shear stress were generated, while at the exit both local maxima and minima in shear stress were observed (p<0.05). Additionally, the shear stress at the entrance and exit of the stent were correlated with the local curvature (r: 0.30-0.84).Conclusion. Stent implantation changes 3-D vessel geometry in such a way that regions with decreased and increased shear stress occur close to the stent edges. These changes might be related to the asymmetric patterns of in-stent restenosis.     

Mechanistic analysis of xanthan gum production in a stirred tank

The overall effect of agitation on xanthan gum production by Xanthomonas campestris ATCC13951 in a stirred vessel was mechanistically analyzed considering local variation of the specific production rate due to variation of shear stress in the vessel. The whole liquid volume in a fermentor was roughly divided into three regions; the micromixing region around the impeller with high shear stress, the macromixing region dominated by a circulating flow and the stagnant region. The value of the shear rate was first ascertained by experiments in order to obtain a picture of shear rate variation in a radial direction from the impeller, and the equivalence between the volumes of the high shear stress region and micromixing region was confirmed. The shear stress obtained using a correlation between the shear rate at the impeller tip and Reynolds number of Wichterle et al. was used as a representative of the shear stress in the micromixing region, and the shear stress estimated by use of an empirical correlation between the average shear rate in a fermentor and agitation speed derived by Metzner et al. was adopted as a representative of the shear stress in the macromixing region. The information about the circulation time distribution was also used to take into account oxygen deficiency during circulation of liquid elements in the macromixing region, considering that oxygen from the gas phase was supplied mainly in the high shear region. The calculated values of xanthan gum concentrations which were obtained by the proposed simulation method agreed well with the experimental data in the time course of xanthan gum production at various agitation speeds. Experimental results of the relationship between the overall specific production rate and ND (N, agitation speed, and D, impeller diameter) was also verified by the proposed method.     

Investigating Murray's law in the chick embryo.

According to the optimization principle known as Murray's law, the blood vessel geometry at a bifurcation satisfies the relation alpha = (D3(1) + D3(2))/D3(0) = 1, where D0, D1, and D2 are the diameters of the parent and two daughter vessels, respectively. Previous investigations have shown that mature blood vessels adhere to this law fairly closely. The purpose of this study was to test Murray's law in the developing extraembryonic blood vessels of 2-4 day-old chick embryos. Vessel diameters were measured manually using image analysis software. The measurements for the group of all vessels at all studied stages (n = 449) gave alpha = 1.01+/-0.34 (mean +/- SD), and the value of alpha is similar at all stages. These results indicate that Murray's law holds in the chick embryo, even before medial smooth muscle becomes functional, suggesting that blood vessels follow the same basic morphogenetic rules throughout life.     

Procedure for Human Saphenous Veins Ex Vivo Perfusion and External Reinforcement

The mainstay of contemporary therapies for extensive occlusive arterial disease is venous bypass graft. However, its durability is threatened by intimal hyperplasia (IH) that eventually leads to vessel occlusion and graft failure. Mechanical forces, particularly low shear stress and high wall tension, are thought to initiate and to sustain these cellular and molecular changes, but their exact contribution remains to be unraveled. To selectively evaluate the role of pressure and shear stress on the biology of IH, an ex vivo perfusion system (EVPS) was created to perfuse segments of human saphenous veins under arterial regimen (high shear stress and high pressure). Further technical innovations allowed the simultaneous perfusion of two segments from the same vein, one reinforced with an external mesh. Veins were harvested using a no-touch technique and immediately transferred to the laboratory for assembly in the EVPS. One segment of the freshly isolated vein was not perfused (control, day 0). The two others segments were perfused for up to 7 days, one being completely sheltered with a 4 mm (diameter) external mesh. The pressure, flow velocity, and pulse rate were continuously monitored and adjusted to mimic the hemodynamic conditions prevailing in the femoral artery. Upon completion of the perfusion, veins were dismounted and used for histological and molecular analysis. Under ex vivo conditions, high pressure perfusion (arterial, mean = 100 mm Hg) is sufficient to generate IH and remodeling of human veins. These alterations are reduced in the presence of an external polyester mesh.     

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.