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.     

Newtonian and non-Newtonian blood flow in coiled cerebral aneurysms

Endovascular coiling aims to isolate the aneurysm from blood circulation by altering hemodynamics inside the aneurysm and triggering blood coagulation. Computational fluid dynamics (CFD) techniques have the potential to predict the post-operative hemodynamics and to investigate the complex interaction between blood flow and coils. The purpose of this work is to study the influence of blood viscosity on hemodynamics in coiled aneurysms. Three image-based aneurysm models were used. Each case was virtually coiled with a packing density of around 30%. CFD simulations were performed in coiled and untreated aneurysm geometries using a Newtonian and a Non-Newtonian fluid models. Newtonian fluid slightly overestimates the intra-aneurysmal velocity inside the aneurysm before and after coiling. There were numerical differences between fluid models on velocity magnitudes in coiled simulations. Moreover, the non-Newtonian fluid model produces high viscosity (>0.007$>0.007$ [Pa s]) at aneurysm fundus after coiling. Nonetheless, these local differences and high-viscous regions were not sufficient to alter the main flow patterns and velocity magnitudes before and after coiling. To evaluate the influence of coiling on intra-aneurysmal hemodynamics, the assumption of a Newtonian fluid can be used.     

Numerical investigation of haemodynamics in a helical-type artery bypass graft using non-Newtonian multiphase model

The classic single-phase Newtonian blood flow model ignores the motion of red blood cells (RBCs) and their interaction with plasma. To address these issues, we adopted a multiphase non-Newtonian model to carry out a comparative study between a helical artery bypass graft (ABG) and a conventional ABG in which the blood flow is composed of plasma and RBCs. The investigation focused on the mechanism of RBC buildup in an ABG but the haemodynamic parameters obtained by single-phase and multiphase models were also compared. The aggregation of RBCs along the inside wall of a conventional ABG and at the heel of its distal anastomosis was predicted while a poor aggregation was observed along the helical ABG. In addition, RBCs were observed to gradually sediment along the gravity direction. However, the computed haemodynamic parameters by multiphase model qualitatively agreed well with those by single-phase model. It was concluded that (1) the single-phase computational fluid dynamics (CFD) is reasonable to do the computation of haemodynamic parameters in ABGs; (2) secondary flow does not definitely produce buildup of RBCs in the inside curvature, its configuration played an important role in the movement of RBCs and the dominating one-way rotating flow in a helical ABG guaranteed no buildup of RBCs on its inside wall and (3) gravity direction is important for the movement of RBCs which may help to explain why doing exercise is good for human health. This study helps to shed light on the migration of RBCs in ABGs, which cannot be explored by single-phase CFD models, and provides more understanding of the underlying flow mechanism for ABG failure.     

Analysis of non-Newtonian effects within an aorta-iliac bifurcation region

The geometry of the arteries at or near arterial bifurcation influences the blood flow field, which is an important factor affecting arteriogenesis. The blood can act sometimes as a non-Newtonian fluid. However, many studies have argued that for large and medium arteries, the blood flow can be considered to be Newtonian. In this work a comprehensive investigation of non-Newtonian effects on the blood fluid dynamic behavior in an aorta-iliac bifurcation is presented. The aorta-iliac geometry is reconstructed with references to the values reported in Shah et al. (1978); the 3D geometrical model consists of three filleted cylinders of different diameters. Governing equations with the appropriate boundary conditions are solved with a finite-element code. Different rheological models are used for the blood flow through the lumen and detailed comparisons are presented for the aorta-iliac bifurcation. Results are presented in terms of the velocity profiles in the bifurcation zone and Wall Shear Stress (WSS) for different sides of the bifurcation both for male and female geometries, showing that the Newtonian fluid assumption can be made without any particular loss in terms of accuracy with respect to the other more complex rheological models.     

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.     

Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection

The behavior of blood cells and vessel compliance significantly influence hemodynamic parameters, which are closely related to the development of aortic dissection. Here the two-phase non-Newtonian model and the fluid-structure interaction (FSI) method are coupled to simulate blood flow in a patient-specific dissected aorta. Moreover, three-element Windkessel model is applied to reproduce physiological pressure waves. Important hemodynamic indicators, such as the spatial distribution of red blood cells (RBCs) and vessel wall displacement, which greatly influence the hemodynamic characteristics are analyzed. Results show that the proximal false lumen near the entry tear appears to be a vortex zone with a relatively lower volume fraction of RBCs, a low time-averaged wall shear stress (TAWSS) and a high oscillatory shear index (OSI), providing a suitable physical environment for the formation of atherosclerosis. The highest TAWSS is located in the narrow area of the distal true lumen which might cause further dilation. TAWSS distributions in the FSI model and the rigid wall model show similar trend, while there is a significant difference for the OSI distributions. We suggest that an integrated model is essential to simulate blood flow in a more realistic physiological environment with the ultimate aim of guiding clinical treatment.     

Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

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.     

Numerical investigation of non-Newtonian microcirculatory blood flow in hepatic lobule

The circulation in the liver is unique at macroscopic and microscopic levels. At the macroscopic level, there is an unusual presence of portal and arterial inputs rather than a single arterial input. At the microscopic level, a series of microenvironments in the acinar system is essential in controlling the functional characteristics of hepatic parenchymal cells. Since the hemodynamics is much less studied in the multifunctional liver, an attempt is made to study the hepatic hemodynamics in a segment of a hepatic lobular structure, that is made up of high-pressure oxygenated arteriole, low-pressure nutrient-rich portal venule, fenestrated sinusoidal space and hepatic venule. Our goal is to dispel some of the myths of this complex vascular bed by means of finite volume blood flow simulation. Flow features like high-velocity gradients near the fenestrations, flow reversal and Dean vortices in the sinusoidal space are analyzed within the non-Newtonian framework. Since no distinct exact or numerical solutions are available for this complex vascular bed, the present simulated results are compared with the available clinical observations. Results revealed that the pressure plays a key role in hepatic blood flow.     

Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm

Blood flow is analysed by means of computer simulation in an idealized arterial bifurcation model which is pathologically altered by a saccular aneurysm. The theoretical study of the flow pattern and the paths of fluid particles is carried out under pulsatile Newtonian and non-Newtonian flow conditions. The governing equations are solved numerically with the use of the finite element method. The results show the disturbed blood flow in the bifurcation and the relatively low intra-aneurysmal flow circulation. In addition to the study of basic flow patterns in the segment, a comparison of non-Newtonian and Newtonian results is carried out. This comparison proves that for the considered large artery model under physiological flow conditions where the yield number is relatively low there is no essential difference in the results.     

Stress-modulated collagen fiber remodeling in a human carotid bifurcation

This work concerns with the implementation of a new stress-driven remodeling model for simulating the overall structure and mechanical behavior of a human carotid bifurcation. By means of an iterative finite element based procedure collagen fiber direction and maximal principal stresses are computed. We find that the predicted fibers' architecture at the cylindrical branches and at the apex of the bifurcation correlates well with histological observations. Some insights about the mechanical response of the sinus bulb and the bifurcation apex are revealed and discussed. The results are compared with other, isotropic and orthotropic, models available in the literature.     

Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.     

椎动脉狭窄内血液两相流动数值模拟分析

目的:对应用三维重构得到的人体真实椎动脉进行血液两相流数值模拟,与经典单相流牛顿血液模型对比,分析动脉粥样硬化等病因与椎动脉狭窄处的血流动力学关系。方法:把考虑血细胞和血浆的两相流血液模型应用到逆向工程方法构建的基于人体生理解剖特征的椎动脉三维几何模型中去进行数值模拟,分析血细胞分布情况等血流动力学参数,并与单相流模型的模拟结果进行对比。结果:通过瞬态模拟计算,得到了椎动脉在心动周期内不同时刻的两相流和单相流模型的血流动力学参数。结论:通过对比单相流数值模拟结果,得出血管狭窄处血细胞出现聚集,血流更加复杂和低壁面切应力分布等与动脉粥样硬化及血栓的形成相关的结论。并且与两相流模型相比,单相流模型存在如无法获得如血细胞分布等不足,为进一步深入研究椎动脉等疾病的发病机理提供方法和理论支持。     

Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model.

Numerical analysis of flow phenomena and wall shear stresses in the human carotid artery bifurcation has been carried out using a three-dimensional geometrical model. The primary aim of this study is the detailed discussion of non-Newtonian flow velocity and wall shear stress during the pulse cycle. A comparison of non-Newtonian and Newtonian results is also presented. The applied non-Newtonian behavior of blood is based on measured dynamic viscosity. In the foreground of discussion are the flow characteristics in the carotid sinus. The investigation shows complex flow patterns especially in the carotid sinus where flow separation occurs at the outer wall throughout the systolic deceleration phase. The changing sign of the velocity near the outer sinus wall results in oscillating shear stress during the pulse cycle. At the outer wall of the sinus at maximum diameter level the shear stress ranges from -1.92 N/m2 to 1.22 N/m2 with a time-averaged value of 0.04 N/m2. At the inner wall of the sinus at maximum diameter level the shear stress range is from 1.16 N/m2 to 4.18 N/m2 with a mean of 1.97 N/m2. The comparison of non-Newtonian and Newtonian results indicates unchanged flow phenomena and rather minor differences in the basic flow characteristics.     

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.     

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.     

Numerical Analysis of Blood Flow through COVID-19 Infected Arteries

Computational Fluid Dynamics has become relevant in the study of hemodynamics, where clinical results are challenging to obtain. This paper discusses a 2-Dimensional transient blood flow analysis through an arterial bifurcation for patients infected with the Coronavirus. The geometry considered is an arterial bifurcation with main stem diameter 3 mm and two outlets. The left outlet (smaller) has a diameter of 1.5 mm and the right outlet (larger), 2 mm. The length of the main stem, left branch and right branch are fixed at 35 mm, 20 mm and 25 mm respectively. Viscosity change that occurs in the blood leads to different parametrical changes in blood flow. The blood flow towards the smaller branch is significantly affected by the changed blood viscosity. Extended regions of high pressure and increased velocity towards the larger outlet are obtained. The Time Averaged Wall Shear Stress (TAWSS) for the corona affected artery is found to be 10.4114 Pa at a 90° angle of bifurcation as compared to 2.45002 Pa of the normal artery. For varying angles of bifurcation, an angle of 75° was found to have a maximum Time Averaged Wall Shear Stress of 2.46076 Pa and 10.42542 Pa for normal and corona affected artery, respectively.     

DPD simulation of non-Newtonian electroosmotic fluid flow in nanochannel

We use the dissipative particle dynamics (DPD) method to simulate the non-Newtonian electroosmotic flow (EOF) through nanochannels. Contrary to a large amount of past computational efforts dedicated to the study of EOF profile, this work pays attention to the EOF of non-Newtonian fluids, which has been rarely touched in past publications. Practically, there are many MEMS/NEMS devices, in which the EOF behaviour should be treated assuming both non-continuum and non-Newtonian conditions. Therefore, our concern in this work is to simulate the EOF through nanochannels considering both non-Newtonian fluid properties and non-continuum flow conditions. We have chosen DPD as our working tool because it provides several important advantages comparing with the classical time consuming molecular dynamics method. Using the DPD method, we explore the effect of a few important fluid properties and nanochannel parameters on the EOF behaviour and the resulting flow rate magnitudes. Our investigation will result in a number of findings, which have not been reported in past research works.     

Distribution of carotid body type I cells and other periadventitial type I cells in the carotid bifurcation regions of the rabbit

Summary The distribution of carotid body type I and periadventitial type I cells in the carotid bifurcation regions was investigated unilaterally in seven and bilaterally in two New Zealand White rabbits. Carotid body type I cells occurred in close proximity to the wall of the internal carotid artery immediately rostral to the carotid bifurcation, within a division of connective tissue with defineable but irregular borders. Caudally, and separate from the main mass of carotid body type I cells, isolated groups of periadventitial type I cells lay freely in the connective tissue around the internal carotid artery and alongside the carotid bifurcation and common carotid artery. A overall picture of the carotid body in the rabbit was reconstructed and the occurrence and significance of periadventitial type I cells discussed.The authors are indebted to Mr. Stephen Jones of the Department of Histopathology, St Bartholomew's Hospital, for expert assistance in the preparation of the material, and to Mr. A.J. Aldrich of the Department of Anatomy for photography. This work was supported by a grant from the Wellcome Trust to one of us (M. de B.D.)     

Extension of Murray's law using a non-Newtonian model of blood flow

Background  

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.