The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

Blood flow dynamics in saccular aneurysm models of the basilar artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by beta = 0 deg and beta = 23.2 deg, where beta is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for beta = 0 deg and single recirculation regions for beta = 23.2 deg during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model (beta = 0 deg) exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model (beta = 23.2 deg). The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.     

Flow investigations in a model of a three-dimensional human artery with Newtonian and non-Newtonian fluids. Part I

Together with biochemical factors, fluid mechanical factors play a role in atherogenesis and the deposition of blood platelets at bends and bifurcations in human arteries. Hence, flow patterns were investigated in a simplified 3-dimensional model of a human renal artery bifurcation using Newtonian (aqueous glycerol) and non-Newtonian (aqueous solution of polyacrylamide) fluids. Studies were carried out in steady as well as pulsatile flow at inflow Reynolds numbers of 498 and 951 with flow rate ratios main tube V1: right branch V4: left branch V3 of 1: 0.25: 0.25 and 1: 0.18: 0.18 respectively. The velocity distribution proximal and distal to the bifurcations was measured using a laser-Doppler anemometer. In steady flow, zones of flow separation and reverse flow were observed distal to the bifurcations. In pulsatile flow using non-Newtonian fluids, there was a significant enlargement of these zones. Differences between the Newtonian and non-Newtonian fluids occurred especially distal to the bifurcations. Shear stresses along all measuring positions were computed from the velocity gradients.     

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.     

Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows

Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.     

Wall shear stress in backward-facing step flow of a red blood cell suspension.

An experimental investigation of the wall shear stress distribution downstream of a backward-facing step is carried out. The wall shear stress distribution was determined by measuring the deformation of a gel layer, attached to the wall downstream of the step. Speckle pattern interferometry was applied to measure the deformation of the gel layer. The measured deformation, combined with the properties of the gel layer, served as an input for a finite element solid mechanics computation to determine the stress distribution in the gel layer. The wall shear stress, required to generate the measured deformation of the gel layer, was determined from these computations. A Newtonian buffer solution and a non-Newtonian red blood cell suspension were used as measuring fluids. The deformation of the gel layer was determined for a Newtonian buffer solution to evaluate the method and to obtain the properties of the gel layer. Subsequently, the wall shear stress distribution for the non-Newtonian red blood cell suspension was determined for three different flow rates. The inelastic non-Newtonian Carreau-Yasuda model served as constitutive model for the red blood cell suspension. Using this model, the velocity and wall shear stress distribution were computed by means of a finite element fluid mechanics computation. From the comparison between the numerical and the experimental results, it can be concluded that wall shear stresses, induced by the red blood cell suspension, can be modeled accurately by employing a Carreau-Yasuda model.     

Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles

Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method, which has been developed recently. The non-Newtonian behaviour of blood is modelled using Casson's relation, based on measured dynamic viscosity. The study concentrates on flow and stress characteristics in the carotid sinus. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation.     

Non-Newtonian blood flow in human right coronary arteries: transient simulations

This study looks at pulsatile blood flow through four different right coronary arteries, which have been reconstructed from biplane angiograms. A non-Newtonian blood model (the Generalised Power Law), as well as the usual Newtonian model of blood viscosity, is used to study the wall shear stress in each of these arteries over the entire cardiac cycle. The difference between Newtonian and non-Newtonian blood models is also studied over the whole cardiac cycle using the recently generalised global non-Newtonian importance factor. In addition, the flow is studied by considering paths of massless particles introduced into the flow field. The study shows that, when studying the wall shear stress distribution for transient blood flow in arteries, the use of a Newtonian blood model is a reasonably good approximation. However, to study the flow within the artery in greater detail, a non-Newtonian model is more appropriate.     

Pulsatile flow of non-Newtonian fluid in distensible models of human arteries

In addition to biochemical factors, hydromechanical influences are responsible for atherogenesis and deposits of blood platelets at bends and bifurcations of human arteries. Hence the flow patterns were simulated in a true-to-scale three-dimensional bifurcation of a human renal artery model and of an arterial femoralis with Newtonian and non-Newtonian blood like fluid. Investigations were made with steady and pulsatile flow. The velocity profiles (at physiological Re-numbers) were measured after the bifurcations with a laser-Doppler-anemometer. In previous works Newtonian fluids were used to investigate the flow in bends and bifurcations of rigid and elastic simplified models. In this paper, emphasis is placed on the difference between rigid and elastic models and also Newtonian and non Newtonian flow behavior. Differences between Newtonian and non Newtonian fluids may especially be expected to occur after branches where the flow has local strong convective elements such as in reverse zones and flow separation points.     

Realistic non-Newtonian viscosity modelling highlights hemodynamic differences between intracranial aneurysms with and without surface blebs

Most computational fluid dynamic (CFD) simulations of aneurysm hemodynamics assume constant (Newtonian) viscosity, even though blood demonstrates shear-thinning (non-Newtonian) behavior. We sought to evaluate the effect of this simplifying assumption on hemodynamic forces within cerebral aneurysms, especially in regions of low wall shear stress, which are associated with rupture. CFD analysis was performed for both viscosity models using 3D rotational angiography volumes obtained for 26 sidewall aneurysms (12 with blebs, 12 ruptured), and parametric models incorporating blebs at different locations (inflow/outflow zone). Mean and lowest 5% values of time averaged wall shear stress (TAWSS) computed over the dome were compared using Wilcoxon rank-sum test. Newtonian modeling not only resulted in higher aneurysmal TAWSS, specifically in areas of low flow and blebs, but also showed no difference between aneurysms with or without blebs. In contrast, for non-Newtonian analysis, bleb-bearing aneurysms showed significantly lower 5% TAWSS compared to those without (p=0.005), despite no significant difference in mean dome TAWSS (p=0.32). Non-Newtonian modeling also accentuated the differences in dome TAWSS between ruptured and unruptured aneurysms (p<0.001). Parametric models further confirmed that realistic non-Newtonian viscosity resulted in lower bleb TAWSS and higher focal viscosity, especially when located in the outflow zone. The results show that adopting shear-thinning non-Newtonian blood viscosity in CFD simulations of intracranial aneurysms uncovered hemodynamic differences induced by bleb presence on aneurysmal surfaces, and significantly improved discriminant statistics used in risk stratification. These findings underline the possible implications of using a realistic model of blood viscosity in predictive computational hemodynamics.     

Numerical analysis of the hemodynamics and embolus capture of a greenfield vena cava filter

BACKGROUND: Vena Cava filters are used to prevent pulmonary embolism in patients with deep vein thrombosis who are unresponsive to anticoagulation therapy. Various filter designs exist in the market with different characteristics distinguishing them. An understanding of the characteristics of these filters is desirable in order to develop better designs. METHODS: A computational fluid dynamical study of the flow over an unoccluded stainless steel Greenfield Vena Cava filter (Boston Scientific, Watertown, MA) to determine its properties has been performed. Simulation of flow over a filter placed axisymmetrically in a rounded inferior vena cava has been performed at a Reynolds numbers of 1000 and the consequences of the flow (by studying parameters like shear stress and stagnation zones) have been discussed. Furthermore, a new finite element based numerical method has been developed that allows the study of capturing properties of Inferior Vena Cava filters. The key idea is the introduction of a thin-wire-model (TWM) that enables a drastic reduction in the computational cost while still maintaining control on the physics of the problem. This numerical technique has been applied to evaluate the embolus capture characteristic of a Greenfield filter. RESULTS: The flow around the unoccluded filter is found to be steady and laminar at the conditions studied. A recirculation/stagnation zone develops immediately downstream of the filter head. This zone is significantly larger when the central hole is occluded. The shear stress and stagnation zone properties for such a flow over a Greenfield filter are compared with existing literature (in vitro studies). A graph showing the regions wherein clots escape or get captured has been determined by a means of numerical simulations. The data has further been analyzed to determine the probability of clot capture as function of the clot size. CONCLUSIONS: The stagnation zone formed behind the head of the Greenfield filter is found to be smaller in size when compared to that of the same filter with the central hole occluded. A map of the shear stress distribution shows a small region having the potential for thrombogenesis. The non-Newtonian properties of blood are not seen to cause much variation in the flow field when compared to the Newtonian model. However variation in the cava size leads to a significant change in the shear stresses. This study also establishes a novel method wherein computational means are used to determine the efficacy of clot capturing of filters. These techniques can further be used to compare the different characteristics among filters.     

Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.     

Shape optimization in unsteady blood flow: A numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier–Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.     

Non-Newtonian flow patterns associated with an arterial stenosis.

A non-Newtonian constitutive equation for blood has been introduced in this paper. Using this equation, blood flow attributes such as velocity profiles, flowrate, pressure gradient, and wall shear stress in both straight and stenotic (constricted) tubes have been examined. Results showed that compared with Newtonian flow at the same flowrate, the non-Newtonian normally features larger pressure gradient, higher wall shear stress, and different velocity profile, especially in stenotic tube. In addition, the non-Newtonian stenotic flow appears to be more stable than Newtonian flow.     

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

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

Simulation of particle-hemodynamics in a partially occluded artery segment with implications to the initiation of microemboli and secondary stenoses.

Computational results of laminar incompressible blood-particle flow analyses in an axisymmetric artery segment with a smooth local area constriction of 75 percent have been presented. The flow input waveform was sinusoidal with a nonzero average. The non-Newtonian behavior of blood was simulated with a modified Quemada model, platelet concentrations were calculated with a drift-flux model, and monocyte trajectories were described and compared for both Newtonian and Quemada rheologies. Indicators of "disturbed flow" included the time-averaged wall shear stress (WSS), the oscillatory shear index (OSI), and the wall shear stress gradient (WSSG). Implications of the vortical flow patterns behind the primary stenosis to the formation of microemboli and downstream stenoses are as follows. Elevated platelet concentrations due to accumulation in recirculation zones mixed with thrombin and ADP complexes assumed to be released upstream in high wall shear stress regions, could form microemboli, which are convected downstream. Distinct near-wall vortices causing a local increase in the WSSG and OSI as well as blood-particle entrainment with possible wall deposition, indicate sites susceptible to the onset of an additional stenosis proximal to the initial geometric disturbance.