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.     

Flow patterns in three-dimensional porcine epicardial coronary arterial tree

The branching pattern of epicardial coronary arteries is clearly three-dimensional, with correspondingly complex flow patterns. The objective of the present study was to perform a detailed hemodynamic analysis using a three-dimensional finite element method in a left anterior descending (LAD) epicardial arterial tree, including main trunk and primary branches, based on computed tomography scans. The inlet LAD flow velocity was measured in an anesthetized pig, and the outlet pressure boundary condition was estimated based on scaling laws. The spatial and temporal wall shear stress (WSS), gradient of WSS (WSSG), and oscillatory shear index (OSI) were calculated and used to identify regions of flow disturbances in the vicinity of primary bifurcations. We found that low WSS and high OSI coincide with disturbed flows (stagnated, secondary, and reversed flows) opposite to the flow divider and lateral to the junction orifice of the main trunk and primary branches. High time-averaged WSSG occurs in regions of bifurcations, with the flow divider having maximum values. Low WSS and high OSI were found to be related through a power law relationship. Furthermore, zones of low time-averaged WSS and high OSI amplified for larger diameter ratio and high inlet flow rate. Hence, different focal atherosclerotic-prone regions may be explained by different physical mechanism associated with certain critical levels of low WSS, high OSI, and high WSSG, which are strongly affected by the diameter ratio. The implications of the flow patterns for atherogenesis are enumerated.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Flow-induced Wall Shear Stress in Abdominal Aortic Aneurysms: Part II - Pulsatile Flow Hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 h Re m h 300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure ( p w ), wall shear stress ( w ), Wall Shear Stress Gradient (WSSG), time-average wall shear stress ( w *), and time-average Wall Shear Stress Gradient WSSG *. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Hemodynamic factors at the distal end-to-side anastomosis of a bypass graft with different POS:DOS flow ratios

A pulsatile flow in vitro model of the distal end-to-side anastomosis of an arterial bypass graft was used to examine the effects that different flow ratios between the proximal outlet segment (POS) and the distal outlet segment (DOS) have on the flow patterns and the distributions of hemodynamic factors in the anastomosis. Amberlite particles were tracked by flow visualization to determine overall flow patterns and velocity measurements were made with Laser Doppler anemometry (LDA) to obtain detailed hemodynamic factors along the artery floor and the graft hood regions. These factors included wall shear stress (WSS), spatial wall shear stress gradient (WSSG), and oscillatory index (OSI). Statistical analysis was used to compare these hemodynamic factors between cases having different POS:DOS flow ratios (Case 1-0:100, Case 2-25:75, Case 3-50:50). The results showed that changes in POS:DOS flow ratios had a great influence on the flow patterns in the anastomosis. With an increase in proximal outlet flow, the range of location of the stagnation point along the artery floor decreased, while the extent of flow separation along the graft hood increased. The statistical results showed that there were significant differences (p<0.05) for the mean WSS between cases along the graft hood, but no significant differences were detected along the artery floor. There were no significant differences for the spatial WSSG along both the artery floor and the graft hood. However, there were significant differences (p<0.05) in the mean OSI between Cases 1 and 2 and between Cases 1 and 3 both along the artery floor and along the graft hood. Comparing these mechanical factors with histological findings of intimal hyperplasia formation obtained by previous canine studies, the results of the statistical analysis suggest that regions exposed to a combination of low mean WSS and high OSI may be most prone to the formation of intimal hyperplasia.     

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.     

Blood flow in abdominal aortic aneurysms: pulsatile flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-averaged Reynolds numbers 50< or =Re(m)< or =300, corresponding to a range of peak Reynolds numbers 262.5< or =Re(peak) < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is characterized by a sequence of five different flow phases in one period of the flow cycle. Hemodynamic disturbance is evaluated for a modified set of indicator functions, which include wall pressure (p(w)), wall shear stress (tau(w)), and Wall Shear Stress Gradient (WSSG). At peak flow, the highest shear stress and WSSG levels are obtained downstream of both aneurysms, in a pattern similar to that of steady flow. Maximum values of wall shear stresses and wall shear stress gradients obtained at peak flow are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Local hemodynamics affect monocytic cell adhesion to a three-dimensional flow model coated with E-selectin.

Monocyte adhesion to the endothelium depends on concentrations of receptors/ligands, local concentrations of chemoattractants, monocyte transport to the endothelial surface and hemodynamic forces. Monocyte adhesion to the inert surface of a three-dimensional perfusion model was shown to correlate inversely with wall shear stress, but was also affected by flow patterns which influenced the near-wall cell availability. We hypothesized that (a) under the same flow conditions, insolubilized E-selectin on the model's surface may mediate adhesive interactions at higher wall shear stresses, compared to an uncoated model, and (b) pulsatile flow may modify the adhesion profile obtained under steady flow. An axisymmetric flow model with a stenosis and a sudden expansion produced a range of wall shear stresses and a separated flow with recirculation and reattachment. Pre-activated U937 cells were perfused through the model under either steady (Re = 100, 140) or pulsatile (Remean = 107) flow. The velocity field was characterized through computational fluid dynamics and validated by inert particle tracking. Surface E-selectin greatly increased cell adhesion in all regions at Re = 100 and 140, compared to an uncoated model under the same flow conditions. In regions where the cells near the wall were abundant (taper and stenosis), adhesion to E-selectin correlated with the reciprocal of local wall shear stress when flow was steady. Pulsatile flow distributed the adherent cells more evenly throughout the coated model. Hence, characterizing both the local hemodynamics and the biological activity on the vessel wall is important in leukocyte adhesion.     

Mathematical analysis of mural thrombogenesis. Concentration profiles of platelet-activating agents and effects of viscous shear flow.

The concentration profiles of adenosine diphosphate (ADP), thromboxane A2 (TxA2), thrombin, and von Willebrand factor (vWF) released extracellularly from the platelet granules or produced metabolically on the platelet membrane during thrombus growth, were estimated using finite element simulation of blood flow over model thrombi of various shapes and dimensions. The wall fluxes of these platelet-activating agents were estimated for each model thrombus at three different wall shear rates (100 s-1, 800 s-1, and 1,500 s-1), employing experimental data on thrombus growth rates and sizes. For that purpose, whole human blood was perfused in a parallel-plate flow chamber coated with type l fibrillar human collagen, and the kinetic data collected and analyzed by an EPl-fluorescence video microscopy system and a digital image processor. It was found that thrombin concentrations were large enough to cause irreversible platelet aggregation. Although heparin significantly accelerated thrombin inhibition by antithrombin lll, the remaining thrombin levels were still significantly above the minimum threshold required for irreversible platelet aggregation. While ADP concentrations were large enough to cause irreversible platelet aggregation at low shear rates and for small aggregate sizes, TxA2 concentrations were only sufficient to induce platelet shape change over the entire range of wall shear rates and thrombi dimensions studied. Our results also indicated that the local concentration of vWF multimers released from the platelet alpha-granules could be sufficient to modulate platelet aggregation at low and intermediate wall shear rates (less than 1,000 s-1). The sizes of standing vortices formed adjacent to a growing aggregate and the embolizing stresses and the torque, acting at the aggregate surface, were also estimated in this simulation. It was found that standing vortices developed on both sides of the thrombus even at low wall shear rates. Their sizes increased with thrombus size and wall shear rate, and were largely dependent upon thrombus geometry. The experimental observation that platelet aggregation occurred predominantly in the spaces between adjacent thrombi, confirmed the numerical prediction that those standing vortices are regions of reduced fluid velocities and high concentrations of platelet-activating substances, capable of trapping and stimulating platelets for aggregation. The average shear stress and normal stress, as well as the torque, acting to detach the thrombus, increased with increasing wall shear rate. Both stresses were found to be nearly independent of thrombus size and only weekly dependent upon thrombus geometry. Although both stresses had similar values at low wall shear rates, the average shear stress became the predominant embolizing stress at high wall shear rates.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part I--steady flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Homogeneous, Newtonian blood flow is simulated under steady conditions for the range of Reynolds numbers 10 < or =Re < or =2265. Flow hemodynamics are quantified by calculating the distributions of wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG). A correlation between maximum values of hemodynamic stresses and Reynolds number is established, and the spatial distribution of WSSG is considered as a hemodynamic force that may cause damage to the arterial wall at an intermediate stage of AAA growth. The temporal distribution of hemodynamic stresses in pulsatile flow and their physical implications in AAA rupture are discussed in Part II of this paper.     

Comparison of blood rheological models for physiological flow simulation

The present study investigates the flow effects that different blood constitutive equations induce when employed in numerical simulations in the framework of computational hemodynamics. In accord with experimental studies on the rheological behavior of blood, three blood constitutive equations namely the Casson, Power-Law and Quemada models were used for simulating the shear flow behavior of blood. The case studied is the flow in a channel with a moving part of the boundary and was selected because it reproduces the flow phenomena occurring in realistic arterial conditions. Flow simulation for every model is carried out assuming the same flow rate at the inlet of the channel and different Strouhal numbers reflecting different intensities of the boundary movement. Results show that the modeling of blood as non-Newtonian fluid has marked qualitative and quantitative effects on both the flow field and the wall shear stress whereas comparison of the different models shows good agreement between the flow effects by the Casson and Quemada models.     

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

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

Comparison of the hemodynamics in 6mm and 4-7 mm hemodialysis grafts by means of CFD

The aim of our study is to investigate with computational fluid dynamics (CFD) whether different arterial anastomotic geometries result in a different hemodynamics at the arterial (AA) and venous anastomosis (VA) of hemodialysis vascular access grafts. We have studied a 6mm graft (CD) and a 4-7 mm graft (TG). A validated three-dimensional CFD model is developed to simulate flow in the two graft types. Only the arterial anastomosis (AA) geometry differs. The boundary conditions applied are a periodic velocity signal at the arterial inlet and a periodic pressure wave at the venous outlet. Flow rate is set to 1,000 ml/min. The time dependent Navier-Stokes equations are solved. Wall shear stress (WSS), wall shear stress gradient (WSSG) and pressure gradient (PG) are calculated. Anastomotic flow is asymmetric although the anastomosis geometry is symmetric. The hemodynamic parameters, WSS, WSSG and PG, values at the suture line of the arterial anastomosis of the TG are at least twice as much as in the CD. Comparing the parameters at the two AA indicate that little flow rate increase introduces the risk of hemolysis in the TG whereas the CD is completely free of hemolysis. The hemodynamic parameter values at the venous anastomosis of the CD are 24 till 35% higher compared to the values of the TG. WSS values (> 3 Pa) in the VA are in the critical range for stenosis development in both graft geometries. The zones where the parameters reach extreme values correspond to the locations where intimal hyperplasia formation is reported in literature. In all anastomoses, the hemodynamic parameter levels are in the range where leucocytes and platelets get activated. Our simulations confirm clinical results where TG did not show a better outcome when compared to the CD.     

Structural and hydrodynamic simulation of an acute stenosis-dependent thrombosis model in mice

Platelet activation under blood flow is thought to be critically dependent on the autologous secretion of soluble platelet agonists (chemical activators) such as ADP and thromboxane. However, recent evidence challenging this model suggests that platelet activation can occur independent of soluble agonist signalling, in response to the mechanical effects of micro-scale shear gradients. A key experimental tool utilized to define the effect of shear gradients on platelet aggregation is the murine intravital microscopy model of platelet thrombosis under conditions of acute controlled arteriolar stenosis. This paper presents a computational structural and hydrodynamic simulation of acute stenotic blood flow in the small bowel mesenteric vessels of mice. Using a homogeneous fluid at low Reynolds number (0.45) we investigated the relationship between the local hydrodynamic strain-rates and the severity of arteriolar stensosis. We conclude that the critical rates of blood flow acceleration and deceleration at sites of artificially induced stenosis (vessel side-wall compression or ligation) are a function of tissue elasticity. By implementing a structural simulation of arteriolar side wall compression, we present a mechanistic model that provides accurate simulations of stenosis in vivo and allows for predictions of the effects on local haemodynamics in the murine small bowel mesenteric thrombosis model.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Measured wall shear stress distribution pattern upstream and downstream of a unilateral stenosis by an electrochemical method

An electrochemical surface shear stress measurement was applied to a model of unilateral arterial stenosis. The unilateral stenosis model was made up of a removable stenosis plug, in an electrochemical shear stress measurement test section with 100 cathodes. Three dimensional wall shear stress distribution was measured under steady flow field. At a relatively low Reynolds number, Re = 270, there was a characteristic high and low wall shear distribution pattern downstream of the unilateral stenosis. There were also remarkable high shear stress areas on the opposite wall up- and downstream, and both side walls of the stenosis upstream. It was clearly shown that detailed three dimensional structure of the flow field must be studied in order to correlate it to pathological findings.     

To what extent does a minimal atherosclerotic plaque alter the arterial wall shear stress distribution? A model study by an electrochemical method

An electrochemical surface shear stress measurement was applied to a model of very thin unilateral arterial stenosis (height of 1/8 of the model pipe diameter with very smooth surface). Three dimensional wall shear stress distribution was measured under steady flow field from a relatively low Reynolds number, Re = 270, to a high Reynolds number, Re = 1200. There was a characteristic high and low wall shear distribution pattern around the stenosis. There were also remarkable high shear stress areas on the opposite wall and both side walls of the stenosis. It was clearly shown that three dimensional structure of the flow field, hence, the wall shear stress distribution, is affected by a minimal change on the arterial wall.     

Flow of couple stress fluid through stenotic blood vessels

The effects of an axially symmetric mild stenosis on the flow of blood, when blood is represented by a couple stress fluid model, have been studied. It is found that, for a fixed stenosis size, the resistance to flow and wall shear stress increase as the couple stress parameter eta decreases from unity. A comparison of the results with those of the Newtonian case shows that the magnitude of resistance to flow and wall shear under a given set of conditions, is greater in the case of the couple stress fluid model. It is seen that even in the case of a mild stenosis (19% area reduction), resistance to flow and wall shear values are increased over those for no stenosis by 60% and 62%, respectively, when compared with the case of a Newtonian fluid.