Experimental investigation of the flow of a blood analogue fluid in a replica of a bifurcated small artery

The scope of this work is to study the pulsatile flow of a blood mimicking fluid in a micro channel that simulates a bifurcated small artery, in which the Fahraeus-Lindqvist effect is insignificant. An aqueous glycerol solution with small amounts of xanthan gum was used for simulating viscoelastic properties of blood and in vivo flow conditions were reproduced. Local flow velocities were measured using micro Particle Image Velocimetry (μ-PIV). From the measured velocity distributions, the wall shear stress (WSS) and its variation during a pulse were estimated. The Reynolds numbers employed are relatively low, i.e. similar to those prevailing during blood flow in small arteries. Experiments both with a Newtonian and a non-Newtonian fluid (having asymptotic viscosity equal to the viscosity of the Newtonian one) proved that the common assumption that blood behaves as a Newtonian fluid is not valid for blood flow in small arteries. It was also shown that the outer wall of the bifurcation, which is exposed to a lower WSS, is more predisposed to atherosclerotic plaque formation. Moreover, this region in small vessels is shorter than the one in large arteries, as the developed secondary flow decays faster. Finally, the WSS values in small arteries were found to be lower than those in large ones.     

Experimental flow studies in an elastic Y-model.

To determine the causes and history of atherosclerosis it is necessary to understand the hemodynamic parameters of blood circulation. Hemodynamic parameters play an important role in the formation of atherosclerotic plaques, especially near bends and bifurcations where the flow separates from the wall. Here the flow is laminar and non-axial with eddies, secondary flow, flow separation and stagnation points. Stenoses are found predominantly in flow separation areas. Therefore, it is important to separately study the following flow parameters: steady and pulsatile flow, wall elasticity and non-Newtonian flow behavior of blood. A simplified silicon elastic y-model simulating the human carotid artery was used for the analysis of these parameters. This model can be used for numerical studies as well. Flow was visualized at steady flow using dyes and at pulsatile flow with a photoelastic apparatus and a birefringent solution. The local axial velocity at steady and pulsatile flow was determined with a one-component Laser-Doppler-Anemometer (LDA). Pulsatile flow was generated by a piston membrane pump. A glycerin-water solution was used to simulate the Newtonian flow behavior of blood. A DMSO-Separan water solution was used to simulate the non-Newtonian flow behavior. Pulsatile flow creates higher and lower shear rates so called oscillating shear rate compare to steady flow depending on the velocity amplitude. The non-Newtonian fluid showed a markedly different flow behavior than the Newtonian fluid especially in areas of flow separation. Shear gradients were calculated from these velocity measurements using a bicubic spline interpolation. Shear stresses were calculated from these velocity shear gradients and the viscosity of the non-Newtonian fluid at these shear gradients. At special areas, high shear stresses > 10 Pa were found. The elasticity of the model wall also influences the flow behavior. The measurements showed that the characteristics of pulsatile flow and the elasticity of the model wall should be observed concomitantly. This paper presents the steady and pulsatile flow with a Newtonian and non-Newtonian fluid in an elastic model.     

Fontan术血流动力学非牛顿特性研究

目的 分析计算模拟中血液非牛顿特性对Fontan术后血流动力学的影响。方法 基于Fontan术后患者个体化三维血管模型,临床超声实测数据作为边界条件,分别选取常用的牛顿流体模型、非牛顿流体模型中的Casson模型与Carreau模型进行血流动力学模拟,计算血流分配比、能量损失、壁面切应力、非牛顿重要性系数等血流动力学参数,比较不同流体模型之间血流动力学参数差异。结果 流体模型对血流分配比影响小,非牛顿流体模型的能量损失较牛顿流体模型高,其中Casson模型最高。在下腔静脉中有明显回流、血流扰乱区域,并伴有低壁面切应力分布。在低流速时,牛顿流体模型下腔静脉血流扰乱更明显。非牛顿重要性系数显示在下腔静脉的非牛顿特性显著。结论 非牛顿特性在下腔静脉的低速回流区域影响显著,模拟患者个体化的Fontan血流动力学时应考虑血液的非牛顿特性。     

LES of non-Newtonian physiological blood flow in a model of arterial stenosis

Large Eddy Simulation (LES) is performed to study the physiological pulsatile transition-to-turbulent non-Newtonian blood flow through a 3D model of arterial stenosis by using five different blood viscosity models: (i) Power-law, (ii) Carreau, (iii) Quemada, (iv) Cross and (v) modified-Casson. The computational domain has been chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet of the model using the first four harmonic series of the physiological pressure pulse (Loudon and Tordesillas [1]). The effects of the various viscosity models are investigated in terms of the global maximum shear rate, post-stenotic re-circulation zone, mean shear stress, mean pressure, and turbulent kinetic energy. We find that the non-Newtonian viscosity models enlarge the length of the post-stenotic re-circulation region by moving the reattachment point of the shear layer separating from the upper wall further downstream. But the turbulent kinetic energy at the immediate post-lip of the stenosis drops due to the effects of the non-Newtonian viscosity. The importance of using LES in modelling the non-Newtonian physiological pulsatile blood flow is also assessed for the different viscosity models in terms of the results of the dynamic subgrid-scale (SGS) stress Smagorinsky model constant, C(s), and the corresponding SGS normalised viscosity.     

An Experimental Investigation on Rheological Properties of Aqueous Xanthan Gum as a Blood Analog Fluid

Developing a shear thinning non-Newtonian fluid to substitute blood is desirable in studies of biomedicine engineering since blood is a shear thinning nonNewtonian fluid that exhibits both viscous and elastic properties, and generally not available in large volume. The rheological properties of aqueous Xanthan gum with different concentrations and temperatures were studied in present paper. The resuits show that aqueous Xanthan gum is a non-Newtonian fluid which displays remarkable shear thinning behaviour and is a suitable blood analog fluid. There is a power law distribution relationship between shear stress and shear rate, and the higher the solution concentration is, the more strongly it displays shear thinning behaviours. Viscosity values of aqueous Xanthan gum increase with the solution temperature decrease or with the solution concentration increase in linearity. Moreover at the temperature of 37℃, aqueous Xanthan gum with concentration of 0.4%e and 0.6%0 matches human blood best in rheological properties. According to the resuits, the viscosity expression varied with temperature and concentrition is obtained, and the stability of Xanthan gum solution is discussed.     

Comparison of Newtonian and non-Newtonian flows in a two-dimensional carotid artery model using the lattice Boltzmann method

Numerical modelling is a powerful tool for the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall shear is important in the pathogenesis and progression of atherosclerosis. When modelling arterial blood flow it is generally assumed that blood is Newtonian. In this paper, blood flow is modelled in a realistic two-dimensional carotid artery geometry in order to investigate this assumption and its effect on the measurement of near wall shear. The assumption is tested in stenosed and unstenosed geometries and the non-Newtonian blood is modelled using the Carreau-Yasuda model. It is found that the velocity and shear fields, particularly near the walls of the geometries, exhibit small differences in general (<5%) between Newtonian and non-Newtonian models, even in the stenosed geometry with peak differences of 13.6%. Thus, when using numerical modelling to study the haemodynamic influences on atherosclerotic progression, we can safely neglect the non-Newtonian nature of blood.     

Compliant model of a coupled sequential coronary arterial bypass graft: effects of vessel wall elasticity and non-Newtonian rheology on blood flow regime and hemodynamic parameters distribution

We have recently developed a novel design for coronary arterial bypass surgical grafting, consisting of coupled sequential side-to-side and end-to-side anastomoses. This design has been shown to have beneficial blood flow patterns and wall shear stress distributions which may improve the patency of the CABG, as compared to the conventional end-to-side anastomosis. In our preliminary computational simulation of blood flow of this coupled sequential anastomoses design, the graft and the artery were adopted to be rigid vessels and the blood was assumed to be a Newtonian fluid. Therefore, the present study has been carried out in order to (i) investigate the effects of wall compliance and non-Newtonian rheology on the local flow field and hemodynamic parameters distribution, and (ii) verify the advantages of the CABG coupled sequential anastomoses design over the conventional end-to-side configuration in a more realistic bio-mechanical condition. For this purpose, a two-way fluid-structure interaction analysis has been carried out. A finite volume method is applied to solve the three-dimensional, time-dependent, laminar flow of the incompressible, non-Newtonian fluid; the vessel wall is modeled as a linearly elastic, geometrically non-linear shell structure. In an iteratively coupled approach the transient shell equations and the governing fluid equations are solved numerically. The simulation results indicate a diameter variation ratio of up to 4% and 5% in the graft and the coronary artery, respectively. The velocity patterns and qualitative distribution of wall shear stress parameters in the distensible model do not change significantly compared to the rigid-wall model, despite quite large side-wall deformations in the anastomotic regions. However, less flow separation and reversed flow is observed in the distensible models. The wall compliance reduces the time-averaged wall shear stress up to 32% (on the heel of the conventional end-to-side model) and somewhat increases the oscillatory nature of the flow. It is found that the effects of wall compliance and non-Newtonian rheology are not independent, and they interact with each other. In spite of the modest influence of wall compliance and non-Newtonian rheology on the hemodynamic parameters distribution, the inclusion of these properties has unveiled further advantages of the coupled sequential anastomoses model over the conventional end-to-side anastomosis which had not been revealed in the previous study with the rigid-wall and Newtonian fluid models. Hence, the inclusion of wall compliance and non-Newtonian rheology in flow simulation of blood vessels can be essential in quantitative and comparative investigations.     

A numerical and experimental study of periodic flow in a model of a corrugated vessel with application to stented arteries

The investigation presented in this paper has attempted to study, from a fluid dynamics point of view, the consequences of the presence of a stent on the flow of blood. The method adopted is mainly by numerical simulation using a finite element technique, but visualization experiments and an analytical study have also been carried out. The flow of blood is treated as being transient, laminar and Newtonian within a rigid section of the stented vessel. The flow is driven by an imposed pressure gradient in the form of a physiological waveform. A periodic boundary condition has been applied. Particle trajectories, fluid shear rate contours and wall shear stress maps, together with the use of a simplified form of particle image velocimetry in the experimental work, have been used to interpret the results. It was found that the vessel wall experienced oscillating levels of wall shear stress, in particular extensive exposure to low shear stress. Regions of flow recirculation, points of flow separation and reattachment constantly move in regions of low shear stress. Vortices form and then are destroyed rapidly by reversing flow. Their potential physiological significance to stented arteries is discussed.     

Noninvasive Measurement of Steady and Pulsating Velocity Profiles and Shear Rates in Arteries Using Echo PIV: In Vitro Validation Studies

Although accurate measurement of velocity profiles, multiple velocity vectors, and shear stress in arteries is important, there is still no easy method to obtain such information in vivo. We report on the utility of combining ultrasound contrast imaging with particle image velocimetry (PIV) for noninvasive measurement of velocity vectors. This method (echo PIV) takes advantage of the strong backscatter characteristics of small gas-filled microbubbles (contrast) seeded into the flow. The method was tested in vitro. The steady flow analytical solution and optical PIV measurements (for pulsatile flow) were used for comparison. When compared to the analytical solution, both echo PIV and optical PIV resolved the steady velocity profile well. Error in shear rate as measured by echo PIV (8%) was comparable to the error of optical PIV (6.5%). In pulsatile flow, echo PIV velocity profiles agreed well with optical PIV profiles. Echo PIV followed the general profile of pulsatile shear stress across the artery but underestimated wall shear at certain time points. However, error in shear from echo PIV was an order of magnitude less than error from current shear measurement methods. These studies indicate that echo PIV is a promising technique for noninvasive measurement of velocity profiles and shear stress.     

平行平板流动腔中Casson流体脉动流的摄动解

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一，考虑到通常采用的矩形平行平板流动腔内的流动属于小雷诺数流动，本文用雷诺数作为摄动参数求出了矩形平行流动腔内Casson流体脉动流的摄动解，给出了腔内切应力随压力梯度和流量的变化规律。数值结果表明，相同压力梯度下Casson流体和牛顿流体对应的腔内切应力分布无明显不同，而在相同流量条件下，Casson流体和牛顿流体对应的腔内切应力分布有明显差异，本文为Casson流体脉动流条件下平行平板流动腔切应力的确定方法提供了理论依据。     

Unsteady stenosis flow prediction: a comparative study of non-Newtonian models with operator splitting scheme

This paper presents a comparative study of non-Newtonian and Newtonian models of blood. A non-Newtonian incompressible 2-D Navier-Stokes (N-S) solver has been developed using Fasttalk language within the Fastflo environment. It is based on the method of operator splitting with artificial compressibility technique. The Power law and Casson models have been used as the constitutive equations for blood with a hematocrit of approximately 45%. These two non-Newtonian models and the Newtonian model are used to simulate unsteady flow through a hypothetical stenotic geometry over an aperiodic time interval of 1 s. Through comparison of the results of the three models, it was found that the wall shear stress (WSS) distribution over the time interval was comparable for both non-Newtonian models. The peak WSS for the Newtonian model had the lowest value. The peak wall shear stress gradient (WSSG) for the Power law was the highest, followed by the Casson and Newtonian models. Flow characteristics such as higher pressure drop across the stenosis, location and movement of vortex were similar in all three models. Non-Newtonian effects were most significant in the vicinity of the stenosis.     

Virtual Treatment of Basilar Aneurysms Using Shape Memory Polymer Foam

Numerical simulations are performed on patient-specific basilar aneurysms that are treated with shape memory polymer (SMP) foam. In order to assess the post-treatment hemodynamics, two modeling approaches are employed. In the first, the foam geometry is obtained from a micro-CT scan and the pulsatile blood flow within the foam is simulated for both Newtonian and non-Newtonian viscosity models. In the second, the foam is represented as a porous media continuum, which has permeability properties that are determined by computing the pressure gradient through the foam geometry over a range of flow speeds comparable to those of in vivo conditions. Virtual angiography and additional post-processing demonstrate that the SMP foam significantly reduces the blood flow speed within the treated aneurysms, while eliminating the high-frequency velocity fluctuations that are present within the pre-treatment aneurysms. An estimation of the initial locations of thrombus formation throughout the SMP foam is obtained by means of a low fidelity thrombosis model that is based upon the residence time and shear rate of blood. The Newtonian viscosity model and the porous media model capture similar qualitative trends, though both yield a smaller volume of thrombus within the SMP foam.     

Non-Newtonian models for molecular viscosity and wall shear stress in a 3D reconstructed human left coronary artery

The capabilities and limitations of various molecular viscosity models, in the left coronary arterial tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, wall shear stress (WSS) and wall shear stress gradient (WSSG). The vessel geometry was acquired using geometrically correct 3D intravascular ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The WSS distribution yielded a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS and low WSSG values occurred at the outer walls of the major bifurcation in proximal LCA regions. The Newtonian blood flow was found to be a good approximation at mid- and high-strain rates. The non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models gave comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn-Schneck models over-estimated the non-Newtonian global importance factor I(G) and under-estimated the area averaged WSS and WSSG values. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and WSS calculations in a more satisfactory way.     

Fluid mechanics of arterial stenosis: Relationship to the development of mural thrombus

In this study, we analyzed blood flow through a model stenosis with Reynolds numbers ranging from 300 to 3,600 using both experimental and numerical methods. The jet produced at the throat was turbulent, leading to an axisymmetric region of slowly recirculating flow. For higher Reynolds numbers, this region became more disturbed and its length was reduced. The numerical predictions were confirmed by digital particle image velocimetry and used to describe the fluid dynamics mechanisms relevant to prior measurements of platelet deposition in canine blood flow (R.T. Schoephoersteret al., Atherosclerosis and Thrombosis 12:1806–1813, 1993). Actual deposition onto the wall was dependent on the wall shear stress distribution along the stenosis, increasing in areas of flow recirculation and reattachment. Platelet activation potential was analyzed under laminar and turbulent flow conditions in terms of the cumulative effect of the varying shear and elongational stresses, and the duration platelets are exposed to them along individual platelet paths. The cumulative product of shear rate and exposure time along a platelet path reached a value of 500, half the value needed for platelet activation under constant shear (J. M. Ramstacket al., Journal of Biomechanics 12: 113–125, 1979).     

Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models

Computer simulation of pulsatile non-Newtonian blood flow has been carried out in different human carotid artery bifurcation models. In the first part of the investigation, two rigid walled models are analysed, differing in the bifurcation angle (wide angle and acute angle bifurcation) and in the shape of both the sinus (narrow and larger sinus width) and the bifurcation region (small and larger rounding of the flow divider), in order to contribute to the study of the geometric factor in atherosclerosis. The results show a significant difference in the wall shear stress and in the flow separation. Flow recirculation in the sinus is much more pronounced in the acute angle carotid. An important factor in flow separation is the sinus width. In the second part of the study, flow velocity and wall shear stress distribution have been analysed in a compliant carotid artery bifurcation model. In the mathematical model, the non-Newtonian flow field and the idealised elastic wall displacement are coupled and calculated iteratively at each time step. Maximum displacement of approximately 6% of the diastolic vessel diameter occurs at the side wall of the bifurcation region. The investigation demonstrates that the wall distensibility alters the flow feld and the wall shear stress during the systolic phase. Comparison with corresponding rigid wall results shows that flow separation and wall shear stress are reduced in the distensible wall model.     

Pulsatile blood flow in a stenosed artery—a theoretical model

To understand the special flow conditions which may be produced by the presence of stenosis in arteries, an analytical solution is obtained for pulsatile laminar flow in an elliptic tube. Blood is approximated by a Newtonian model and the geometry of the stenosis is introduced by specifying the change in area of cross-section of the stenosed artery with axial distance. The results for velocity, pressure, shear stress and impedance are presented. These are compared with the steady flow results as well as with those of the flow in a stenosed tube of circular cross-section. The study indicates that the fluid dynamic characteristics of the flow are affected by the percentage of stenosis as well as the geometry of the stenosis. The frequency of oscillation is also found to influence shearing stress and the impedance.     

Role of subcellular shear-stress distributions in endothelial cell mechanotransduction

The endothelium of blood vessels presents a wavy surface to the flowing blood. The subcellular distribution of shear stress depends on the shape and orientation of the cells and on their spatial arrangement within the monolayer. By studying details of the distribution of stress at this scale and the morphological responses that serve to modify the distribution, we can gain insight into the physical mechanisms by which the cell senses its fluid mechanical environment. The rapidly growing body of evidence indicates that endothelial cells discriminate between subtle variations in the exact loading conditions including differences in temporal and spatial gradients of shear stress, steady and pulsatile laminar flow, and laminar and turbulent flows. While in a few studies the effects of these individual flow characteristics have been carefully isolated, it is difficult to assess the relative importance of any one parameter. To interpret the relationships between isolated flow characteristics or the integrated effects of combined loading conditions and the biochemical signaling events that mediate the cell response, a full stress analysis of the cell is needed. The microscopic distribution of shear stress acting upon the cell surface provides the boundary condition for such an analysis. Experimental and analytical tools are being developed to assess the stress distribution throughout the cellular structures that might be involved in mechanotransduction. © 2002 Biomedical Engineering Society. PAC2002: 8716Xa, 8719Uv, 8719Xx     

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.     

Effect of Carrier Gas Properties on Aerosol Distribution in a CT-based Human Airway Numerical Model

The effect of carrier gas properties on particle transport in the human lung is investigated numerically in an imaging based airway model. The airway model consists of multi-detector row computed tomography (MDCT)-based upper and intra-thoracic central airways. The large-eddy simulation technique is adopted for simulation of transitional and turbulent flows. The image-registration-derived boundary condition is employed to match regional ventilation of the whole lung. Four different carrier gases of helium (He), a helium-oxygen mixture (He-O(2)), air, and a xenon-oxygen mixture (Xe-O(2)) are considered. A steady inspiratory flow rate of 342 mL/s is imposed at the mouthpiece inlet to mimic aerosol delivery on inspiration, resulting in the Reynolds number at the trachea of Re( t ) ≈ 190, 460, 1300, and 2800 for the respective gases of He, He-O(2), air, and Xe-O(2). Thus, the flow for the He case is laminar, transitional for He-O(2), and turbulent for air and Xe-O(2). The instantaneous and time-averaged flow fields and the laminar/transitional/turbulent characteristics resulting from the four gases are discussed. With increasing Re( t ), the high-speed jet formed at the glottal constriction is more dispersed around the peripheral region of the jet and its length becomes shorter. In the laminar flow the distribution of 2.5-μm particles in the central airways depends on the particle release location at the mouthpiece inlet, whereas in the turbulent flow the particles are well mixed before reaching the first bifurcation and their distribution is strongly correlated with regional ventilation.     

Large-Eddy simulation of pulsatile blood flow

Large-Eddy simulation (LES) is performed to study pulsatile blood flow through a 3D model of arterial stenosis. The model is chosen as a simple channel with a biological type stenosis formed on the top wall. A sinusoidal non-additive type pulsation is assumed at the inlet of the model to generate time dependent oscillating flow in the channel and the Reynolds number of 1200, based on the channel height and the bulk velocity, is chosen in the simulations. We investigate in detail the transition-to-turbulent phenomena of the non-additive pulsatile blood flow downstream of the stenosis. Results show that the high level of flow recirculation associated with complex patterns of transient blood flow have a significant contribution to the generation of the turbulent fluctuations found in the post-stenosis region. The importance of using LES in modelling pulsatile blood flow is also assessed in the paper through the prediction of its sub-grid scale contributions. In addition, some important results of the flow physics are achieved from the simulations, these are presented in the paper in terms of blood flow velocity, pressure distribution, vortices, shear stress, turbulent fluctuations and energy spectra, along with their importance to the relevant medical pathophysiology.