Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis

Numerical simulations of pulsatile blood flow in straight tube stenosis models were performed to investigate the poststenotic flow phenomena. In this study, three axisymmetrical and three asymmetrical stenosis models with area reduction of 25%, 50% and 75% were constructed. A measured human common carotid artery blood flow waveform was used as the upstream flow condition which has a mean Reynold's number of 300. All calculations were performed with high spatial and temporal resolutions. Flow features such as velocity profiles, flow separation zone (FSZ), and wall shear stress (WSS) distributions in the poststenotic region for all models are presented. The results have demonstrated that the formation and development of FSZs in the poststenotic region are very complex, especially in the flow deceleration phase. In axisymmetric stenoses the poststenotic flow is more sensitive to changes in the degree of stenosis than in asymmetric models. For severe stenoses, the stenosis influence length is shorter in asymmetrical models than in axisymmetrical cases. WSS oscillations (between positive and negative values) have been observed at various downstream locations in some models. The amplitude of the oscillation depends strongly on the axial location and the degree of stenosis.     

Laminar-to-turbulent transition in pulsatile flow through a stenosis

Laminar-to-turbulent transition in pulsatile flow through a stenosis is studied by means of three-dimensional numerical simulations. The flow transition is associated with the occurrence of a flow instability initiating in the stenosis region. The instability is manifested by a three-dimensional symmetry-breaking and leads to asymmetric separation and intense swirling motion downstream of the stenosis. The above have profound effects on the wall shear stress (WSS). The simulations reveal that the asymmetric separation is extended several radii downstream of the stenosis with substantial WSS fluctuations, in both space and time, occurring in the poststenotic region.     

Blood flow in stented arteries: a parametric comparison of strut design patterns in three dimensions

BACKGROUND: Restenosis after stent implantation varies with stent design. Alterations in secondary flow patterns and wall shear stress (WSS) can modulate intimal hyperplasia via their effects on platelet and inflammatory cell transport toward the wall, as well as direct effects on the endothelium. METHOD OF APPROACH: Detailed flow characteristics were compared by estimating the WSS in the near-strut region of realistic stent designs using three-dimensional computational fluid dynamics (CFD), under pulsatile high and low flow conditions. The stent geometry employed was characterized by three geometric parameters (axial strut pitch, strut amplitude, and radius of curvature), and by the presence or lack of the longitudinal connector. RESULTS: Stagnation regions were localized around stent struts. The regions of low WSS are larger distal to the strut. Under low flow conditions, the percentage restoration of mean axial WSS between struts was lower than that for the high flow by 10-12%. The largest mean transverse shear stresses were 30-50% of the largest mean axial shear stresses. The percentage restoration in WSS in the models without the longitudinal connector was as much as 11% larger than with the connector The mean axial WSS restoration between the struts was larger for the stent model with larger interstrut spacing. CONCLUSION: The results indicate that stent design is crucial in determining the fluid mechanical environment in an artery. The sensitivity of flow characteristics to strut configuration could be partially responsible for the dependence of restenosis on stent design. From a fluid dynamics point of view, interstrut spacing should be larger in order to restore the disturbed flow; struts should be oriented to the flow direction in order to reduce the area of flow recirculation. Longitudinal connectors should be used only as necessary, and should be parallel to the axis. These results could guide future stent designs toward reducing restenosis.     

Circumferential vascular deformation after stent implantation alters wall shear stress evaluated with time-dependent 3D computational fluid dynamics models.

The success of vascular stents in the restoration of blood flow is limited by restenosis. Recent data generated from computational fluid dynamics (CFD) models suggest that stent geometry may cause local alterations in wall shear stress (WSS) that have been associated with neointimal hyperplasia and subsequent restenosis. However, previous CFD studies have ignored histological evidence of vascular straightening between circumferential stent struts. We tested the hypothesis that consideration of stent-induced vascular deformation may more accurately predict alterations in indexes of WSS that may subsequently account for histological findings after stenting. We further tested the hypothesis that the severity of these alterations in WSS varies with the degree of vascular deformation after implantation. Steady-state and time-dependent simulations of three-dimensional CFD arteries based on canine coronary artery measurements of diameter and blood flow were conducted, and WSS and WSS gradients were calculated. Circumferential straightening introduced areas of high WSS between stent struts that were absent in stented vessels of circular cross section. The area of vessel exposed to low WSS was dependent on the degree of circumferential vascular deformation and axial location within the stent. Stents with four vs. eight struts increased the intrastrut area of low WSS in vessels, regardless of cross-sectional geometry. Elevated WSS gradients were also observed between struts in vessels with polygonal cross sections. The results obtained using three-dimensional CFD models suggest that changes in vascular geometry after stent implantation are important determinants of WSS distributions that may be associated with subsequent neointimal hyperplasia.     

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.     

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.     

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.     

Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling

Localization of atherosclerotic lesions in the abdominal aorta has been previously correlated to areas of adverse hemodynamic conditions, such as flow recirculation, low mean wall shear stress, and high temporal oscillations in shear. Along with its many systemic benefits, exercise is also proposed to have local benefits in the vasculature via the alteration of these regional flow patterns. In this work, subject-specific models of the human abdominal aorta were constructed from magnetic resonance angiograms of five young, healthy subjects, and computer simulations were performed under resting and exercise (50% increase in resting heart rate) pulsatile flow conditions. Velocity fields and spatial variations in mean wall shear stress (WSS) and oscillatory shear index (OSI) are presented. When averaged over all subjects, WSS increased from 4.8 +/- 0.6 to 31.6 +/- 5.7 dyn/cm2 and OSI decreased from 0.22 +/- 0.03 to 0.03 +/- 0.02 in the infrarenal aorta between rest and exercise. WSS significantly increased, whereas OSI decreased between rest and exercise at the supraceliac, infrarenal, and suprabifurcation levels, and significant differences in WSS were found between anterior and posterior sections. These results support the hypothesis that exercise provides localized benefits to the cardiovascular system through acute mechanical stimuli that trigger longer-term biological processes leading to protection against the development or progression of atherosclerosis.     

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.     

Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements

The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry. Studies on postmortem human arteries and on the experimental animal show positive correlation between the presence of plaque thickness and low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Numerical simulations of arterial blood flow and direct blood flow velocity measurements by magnetic resonance imaging (MRI) are two approaches for the assessment of arterial blood flow patterns. In order to verify that both approaches give equivalent results magnetic resonance velocity data measured in a compliant anatomical carotid bifurcation model were compared to the results of numerical simulations performed for a corresponding computational vessel model. Cross sectional axial velocity profiles were calculated and measured for the midsinus and endsinus internal carotid artery. At both locations a skewed velocity profile with slow velocities at the outer vessel wall, medium velocities at the side walls and high velocities at the flow divider (inner) wall were observed. Qualitative comparison of the axial velocity patterns revealed no significant differences between simulations and in vitro measurements. Even quantitative differences such as for axial peak flow velocities were less than 10%. Secondary flow patterns revealed some minor differences concerning the form of the vortices but maximum circumferential velocities were in the same range for both methods.     

Wall shear stress and near-wall flows in the stenosed femoral artery

Stenotic artery hemodynamics are often characertised by metrics including oscillatory shear index (OSI) and residence time (RT). This analysis was conducted to clarify the link between the near-wall flow behaviour and these resultant flow metrics. A computational simulation was conducted of a stenosed femoral artery, with an idealised representative geometry and a physiologically realistic inlet profile. The overall flow behaviour was characterised through consideration of the axial flow, which was non-dimensionalised against mean flow velocity. The OSI and RT metrics, which are a useful indicator of likely atherosclerotic sites, were explained through a discussion of the WSS values at different time points, the velocity behaviour and velocity profiles, with a particular focus on the near-wall behaviour which influences wall shear stress and the transient evolution of the wall shear stress. While, the stenosis throat experiences high values of wall shear stress, the smooth flow through this contracted region results in low variation in wall shear stress vectors and limited opportunity for any particle stasis. However, regions were noted distal and proximal (though to a lesser extent), where the change in recirculation zones over the cycle created highly elevated regions of both OSI and RT.     

Wall shear stress fixed points in cardiovascular fluid mechanics

Complex blood flow in large arteries creates rich wall shear stress (WSS) vectorial features. WSS acts as a link between blood flow dynamics and the biology of various cardiovascular diseases. WSS has been of great interest in a wide range of studies and has been the most popular measure to correlate blood flow to cardiovascular disease. Recent studies have emphasized different vectorial features of WSS. However, fixed points in the WSS vector field have not received much attention. A WSS fixed point is a point on the vessel wall where the WSS vector vanishes. In this article, WSS fixed points are classified and the aspects by which they could influence cardiovascular disease are reviewed. First, the connection between WSS fixed points and the flow topology away from the vessel wall is discussed. Second, the potential role of time-averaged WSS fixed points in biochemical mass transport is demonstrated using the recent concept of Lagrangian WSS structures. Finally, simple measures are proposed to quantify the exposure of the endothelial cells to WSS fixed points. Examples from various arterial flow applications are demonstrated.     

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.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

A longitudinal study of remodeling in a revised peripheral artery bypass graft using 3D ultrasound imaging and computational hemodynamics

We report a study of the role of hemodynamic shear stress in the remodeling and failure of a peripheral artery bypass graft. Three separate scans of a femoral to popliteal above-knee bypass graft were taken over the course of a 16 month period following a revision of the graft. The morphology of the lumen is reconstructed from data obtained by a custom 3D ultrasound system. Numerical simulations are performed with the patient-specific geometries and physiologically realistic flow rates. The ultrasound reconstructions reveal two significant areas of remodeling: a stenosis with over 85% reduction in area, which ultimately caused graft failure, and a poststenotic dilatation or widening of the lumen. Likewise, the simulations reveal a complicated hemodynamic environment within the graft. Preliminary comparisons with in vivo velocimetry also showed qualitative agreement with the flow dynamics observed in the simulations. Two distinct flow features are discerned and are hypothesized to directly initiate the observed in vivo remodeling. First, a flow separation occurs at the stenosis. A low shear recirculation region subsequently develops distal to the stenosis. The low shear region is thought to be conducive to smooth muscle cell proliferation and intimal growth. A poststenotic jet issues from the stenosis and subsequently impinges onto the lumen wall. The lumen dilation is thought to be a direct result of the high shear stress and high frequency pressure fluctuations associated with the jet impingement.     

Developed pulsatile flow in a deployed coronary stent

The patho-physiologic process of restenosis and tissue growth may not be completely eliminated and is the primary concern of clinicians performing angioplasty and stent implantation procedures. Recent evidence suggests that the restenosis process is influenced by several factors: (1) geometry and size of vessel; (2) stent design; and (3) it's location that alter hemodynamic parameters, including local wall shear stress (WSS) distributions. The present three-dimensional (3D) analysis of pulsatile flow in a deployed coronary stent: (1) shows complex 3D variation of hemodynamic parameters; and (2) quantifies the changes in local WSS distributions for developed flow and compares with recently published WSS data for developing flow. Higher order of magnitude of WSS of 290 dyn/cm(2) is observed on the surface of cross-link intersections at the entrance of the stent for developed flow, which is about half of that for developing flow. Low WSS of 0.8 dyn/cm(2) and negative WSS of -8 dyn/cm(2) are seen at the immediate upstream and downstream regions of strut intersections. Persistent recirculation is observed at the downstream region of each strut cross-link and the regions of low and negative WSS may lead to patho-physiologic conditions near the stented region. The key finding of this study is that the location of stent in the coronary artery determines the developing or developed nature of the flow, which in turn, results in varied level of WSS.     

Dependence of adhesive behavior of neutrophils on local fluid dynamics in a region with recirculating flow

We have recently described patterns of adhesion of different types of leukocytes downstream of a backward facing step. Here the predicted fluid dynamics in channels incorporating backward facing steps are described, and related to the measured velocities of flowing cells, patterns of attachment and characteristics of rolling adhesion for neutrophils perfused over P-selectin. Deeper (upstream depth 300 microm, downstream depth 600 microm, maximum wall shear stress approximately 0.1 Pa) and shallower (upstream depth 260 microm, downstream depth 450 microm, maximum wall shear stress approximately 0.3 Pa) channels were compared. Computational fluid dynamics (CFD) predicted the presence of vortices downstream of the steps, distances to reattachment of flow, local wall shear stresses and components of velocity parallel and perpendicular to the wall. Measurements of velocities of perfused neutrophils agreed well with predictions, and suggested that adhesion to P-selectin should be possible in the regions of recirculating flow, but not downstream in re-established flow in the high shear channel. When channels were coated with a P-selectin-Fc chimaera, neutrophils were captured from flow and immobilised. Capture showed local maxima around the reattachment points, but was absent elsewhere in the high shear chamber. In the low shear chamber there was depression of adhesion just beyond the reattachment point because of expansion of flow and depletion of neutrophils near the wall. Inside the recirculation zones, adhesion decreased approaching the step because of an increasing, vertically upward velocity component. When channels were coated with P-selectin, neutrophils rolled in all regions, but lifted off the surface as they rolled backwards into low shear regions near the step. Rolling velocity in the recirculation zone was independent of shear stress, possibly because of the effects of vertical lift. We conclude that while local wall shear stress influences adhesive behavior, delivery of cells to the wall and their behavior after capture also depend on components of flow perpendicular to the wall.     

In Vitro Shear Stress Measurements Using Particle Image Velocimetry in a Family of Carotid Artery Models: Effect of Stenosis Severity,Plaque Eccentricity,and Ulceration

Atherosclerotic disease, and the subsequent complications of thrombosis and plaque rupture, has been associated with local shear stress. In the diseased carotid artery, local variations in shear stress are induced by various geometrical features of the stenotic plaque. Greater stenosis severity, plaque eccentricity (symmetry) and plaque ulceration have been associated with increased risk of cerebrovascular events based on clinical trial studies. Using particle image velocimetry, the levels and patterns of shear stress (derived from both laminar and turbulent phases) were studied for a family of eight matched-geometry models incorporating independently varied plaque features – i.e. stenosis severity up to 70%, one of two forms of plaque eccentricity, and the presence of plaque ulceration). The level of laminar (ensemble-averaged) shear stress increased with increasing stenosis severity resulting in 2–16 Pa for free shear stress (FSS) and approximately double (4–36 Pa) for wall shear stress (WSS). Independent of stenosis severity, marked differences were found in the distribution and extent of shear stress between the concentric and eccentric plaque formations. The maximum WSS, found at the apex of the stenosis, decayed significantly steeper along the outer wall of an eccentric model compared to the concentric counterpart, with a 70% eccentric stenosis having 249% steeper decay coinciding with the large outer-wall recirculation zone. The presence of ulceration (in a 50% eccentric plaque) resulted in both elevated FSS and WSS levels that were sustained longer (∼20 ms) through the systolic phase compared to the non-ulcerated counterpart model, among other notable differences. Reynolds (turbulent) shear stress, elevated around the point of distal jet detachment, became prominent during the systolic deceleration phase and was widely distributed over the large recirculation zone in the eccentric stenoses.     

Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation

Patient-specific computational fluid dynamics (CFD) is a powerful tool for researching the role of blood flow in disease processes. Modern clinical imaging technology such as MRI and CT can provide high resolution information about vessel geometry, but in many situations, patient-specific inlet velocity information is not available. In these situations, a simplified velocity profile must be selected. We studied how idealized inlet velocity profiles (blunt, parabolic, and Womersley flow) affect patient-specific CFD results when compared to simulations employing a "reference standard" of the patient's own measured velocity profile in the carotid bifurcation. To place the magnitude of these effects in context, we also investigated the effect of geometry and the use of subject-specific flow waveform on the CFD results. We quantified these differences by examining the pointwise percent error of the mean wall shear stress (WSS) and the oscillatory shear index (OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles of the mean WSS and OSI in the internal carotid artery bulb. The parabolic inlet velocity profile produced the most similar mean WSS and OSI to simulations employing the real patient-specific inlet velocity profile. However, anatomic variation in vessel geometry and the use of a nonpatient-specific flow waveform both affected the WSS and OSI results more than did the choice of inlet velocity profile. Although careful selection of boundary conditions is essential for all CFD analysis, accurate patient-specific geometry reconstruction and measurement of vessel flow rate waveform are more important than the choice of velocity profile. A parabolic velocity profile provided results most similar to the patient-specific velocity profile.     

Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf

The purpose of this study was to estimate wall shear stress (WSS) in individual vessels of the venous circulation of the calf and quantify the effects of elastic compression based on change of vessel geometry and velocity waveform. The great saphenous vein and either a peroneal or posterior tibial vein have been imaged in four healthy subjects using magnetic resonance imaging, with and without the presence of a grade 1 medical stocking. Flow through image-based reconstructed geometries was numerically simulated for both a range of steady flow rates and ultrasound-derived transient velocity waveforms, scaled to give a standardized time averaged flow rate. For steady flow, the stocking produced an average percentage increase in mean WSS of approximately 100% in the great saphenous vein across a range of 0.125-1.25 ml/s. The percentage increase in the peroneal/posterior tibial veins varied from 490 to 650% across a range of 0.5-5 ml/s. In addition, application of the stocking eliminated periods of very low or zero flow from the transient waveforms. The average minimum value of WSS in all vessels without the stocking was <0.1 Pa. With the stocking, this was increased to 0.7 Pa in the great saphenous and 0.9 Pa in the peroneal/posterior tibial veins. The pathophysiological effects of these changes are discussed. In conclusion, the flight stocking was effective in raising venous WSS levels in prone subjects, and this effect was much more pronounced in the deep vessels. The stocking also tended to prevent cessation of flow during periods of increased downstream pressure produced by respiration.