Wall shear stress in intracranial aneurysms and adjacent arteries

Hemodynamic parameters play an important role in aneurysm formation and growth. However, it is difficult to directly observe a rapidly growing de novo aneurysm in a patient. To investigate possible associations between hemodynamic parameters and the formation and growth of intracranial aneurysms, the present study constructed a computational model of a case with an internal carotid artery aneurysm and an anterior communicating artery aneurysm, based on the CT angiography findings of a patient. To simulate the formation of the anterior communicating artery aneurysm and the growth of the internal carotid artery aneurysm, we then constructed a model that virtually removed the anterior communicating artery aneurysm, and a further two models that also progressively decreased the size of the internal carotid artery aneurysm. Computational simulations of the fluid dynamics of the four models were performed under pulsatile flow conditions, and wall shear stress was compared among the different models. In the three aneurysm growth models, increasing size of the aneurysm was associated with an increased area of low wall shear stress, a significant decrease in wall shear stress at the dome of the aneurysm, and a significant change in the wall shear stress of the parent artery. The wall shear stress of the anterior communicating artery remained low, and was significantly lower than the wall shear stress at the bifurcation of the internal carotid artery or the bifurcation of the middle cerebral artery. After formation of the anterior communicating artery aneurysm, the wall shear stress at the dome of the internal carotid artery aneurysm increased significantly, and the wall shear stress in the upstream arteries also changed significantly. These findings indicate that low wall shear stress may be associated with the initiation and growth of aneurysms, and that aneurysm formation and growth may influence hemodynamic parameters in the local and adjacent arteries.

Wall shear stress in portal vein of cirrhotic patients with portal hypertension

AIM To investigate wall shear stress(WSS) magnitude and distribution in cirrhotic patients with portal hypertension using computational fluid dynamics. METHODS Idealized portal vein(PV) system models were reconstructed with different angles of the PV-splenic vein(SV) and superior mesenteric vein(SMV)-SV. Patient-specific models were created according to enhanced computed tomography images. WSS was simulated by using a finite-element analyzer, regarding the blood as a Newtonian fluid and the vessel as a rigid wall. Analysis was carried out to compare the WSSin the portal hypertension group with that in healthy controls.RESULTS For the idealized models, WSS in the portal hypertension group(0-10 dyn/cm2) was significantly lower than that in the healthy controls(10-20 dyn/cm2), and low WSS area(0-1 dyn/cm2) only occurred in the left wall of the PV in the portal hypertension group. Different angles of PV-SV and SMV-SV had different effects on the magnitude and distribution of WSS, and low WSS area often occurred in smaller PV-SV angle and larger SMV-SV angle. In the patient-specific models, WSS in the cirrhotic patients with portal hypertension(10.13 ± 1.34 dyn/cm2) was also significantly lower than that in the healthy controls(P < 0.05). Low WSS area often occurred in the junction area of SV and SMV into the PV, in the area of the division of PV into left and right PV, and in the outer wall of the curving SV in the control group. In the cirrhotic patients with portal hypertension, the low WSS area extended to wider levels and the magnitude of WSS reached lower levels, thereby being more prone to disturbed flow occurrence.CONCLUSION Cirrhotic patients with portal hypertension show dramatic hemodynamic changes with lower WSS and greater potential for disturbed flow, representing a possible causative factor of PV thrombosis.

Inner-outer decomposition of wall shear stress fluctuations in turbulent channels

Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components.The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions,and the small-scale one is obtained by subtracting the large-scale one from the total,which fully remove the outer influences.We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000,while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000.Therefore,a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000.The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number,and empirical fitting expressions are given in this work.

Stationary Flow of Blood in a Rigid Vessel in the Presence of an External Magnetic Field: Considerations about the Forces and Wall Shear Stresses

The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several biomedical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.

An improved wall shear stress measurement technique using sandwiched hot-film sensors

In this letter we present a novel wall shear stress measurement technique for a turbulent boundary layer using sandwiched hot-film sensors. Under certain conditions, satisfactory results can be obtained using only the heat generated by one of the hot-film and a calibration of the sensors is not required. Two thin Nickel films with the same size were used in this study, separated by an electrical insulating layer. The upper film served as a sensor and the bottom one served as a guard heater. The two Nickel films were operated at a same temperature, so that the Joule heat flux generated by the sensor film transferred to the air with a minimum loss or gain depending on the uncertainties in the film temperature measurements. Analytical solution of the shear stress based on the aforementioned heat flux was obtained. The preliminary results were promising and the estimated wall shear stresses agreed reasonablywell with the directly measured values （with errors less than 20%） in a fully developed turbulent pipe flow. The proposed technique can be improved to further increase precisions.

Effect of Patient-Specific Aorta Wall Properties on Hemodynamic Parameters

This study deals with the interaction of blood flow with the wall aorta,i.e.,the boundary of the main artery that transports blood in the human body.The problem is addressed in the framework of computational fluid dynamics complemented with(FSI),i.e.,a fluid-structure interaction model.Two fundamental types of wall are considered,namely a flexible and a rigid boundary.The resulting hemodynamic flows are carefully compared in order to determine which boundary condition is more effective in reproducing reality.Special attention is paid to wall shear stress(WSS),a factor known for its ability to produce atherosclerosis and bulges.Laminar flow conditions are assumed.The result show that the flexible wall can produce higher WSS and pressure drop compared to the rigid aorta case.

Couple stress nanofluid flow through a bifurcated artery—Application of catheterization process

In this article,we are exploring the hemodynamics of nanofluid,flowing through a bifurcated artery with atherosclerosis in the presence of a catheter.For treating obstruction in the artery,one can use the catheter whose outer surface is carrying the drug coated with nano-particles.The resultant solvent is considered as blood nano-fluid.Blood being a complex fluid,is modeled by couple stress fluid.In the presence of nano-particles,the temperature and the concentration distribution are understood in a bifurcated stenotic artery.The concluded mathematical model is governed by coupled non-linear equations,and are solved by using the homotopy perturbation method.Consequently,we have explored is the effects of fluid and the embedded geometric parameters on the hemodynamics characteristics.It is also realized that high wall shear stress exists for couple stress nano-fluid when compared to Newtonian nano-fluid.which is computed at a location corresponding to maximum constriction(z=12.5)of the artery.

The Effects of Post-Stenotic Dilatations on the Flow of Couple Stress Fluid through Stenosed Arteries

The flow of incompressible couple stress fluid in a circular tube with stenosis and dilatations has been investigated. The stenosis was assumed to be axially symmetric and mild. The flow equations have been linearized and the expressions for the resistance to the flow, velocity, pressure drop, wall shear stress have been derived. The effects of various parameters on these flow variables have been investigated. It is found that the resistance to the flow and pressure drop increase with height of the stenosis and decrease with post stenotic dilatation. Pressure drop decreases with couple stress fluid parameter for both stenosis and post stenotic dilatation. Further, the wall shear stress increases with height of the stenosis and couple stress parameter but decreases with post stenotic dilatation and couple stress fluid parameter.

Effect of coronary artery dynamics on the wall shear stress vector field topological skeleton in fluid–structure interaction analyses

In this paper,we investigate the impact of coronary artery dynamics on the wall shear stress(WSS)vector field topology by comparing fluid–structure interaction(FSI)and computational fluid dynamics(CFD)techniques.As one of the most common causes of death globally,coronary artery disease(CAD)is a significant economic burden;however,novel approaches are still needed to improve our ability to predict its progression.FSI can include the unique dynamical factors present in the coronary vasculature.To investigate the impact of these dynamical factors,we study an idealized artery model with sequential stenosis.The transient simulations made use of the hyperelastic artery and lipid constitutive equations,non‐Newtonian blood viscosity,and the characteristic out‐of‐phase pressure and velocity distribution of the left anterior descending coronary artery.We compare changes to established metrics of time‐averaged WSS(TAWSS)and the oscillatory shear index(OSI)to changes in the emerging WSS divergence,calculated here in a modified version to handle the deforming mesh of FSI simulations.Results suggest that the motion of the artery can impact downstream patterns in both divergence and OSI.WSS magnitude is also decreased by up to 57%due to motion in some regions.WSS divergence patterns varied most significantly between simulations over the systolic period,the time of the largest displacements.This investigation highlights that coronary dynamics could impact markers of potential CAD progression and warrants further detailed investigations in more diverse geometries and patient cases.

Efficient calculation of fluid-induced wall shear stress within tissue engineering scaffolds by an empirical model

Mechanical stimulation,such as fluid-induced wall shear stress(WSS),is known that can influence the cellular behaviours.Therefore,in some tissue engineering experiments in vitro,mechanical stimulation is applied via bioreactors to the cells in cell culturing to study cell physiology and pathology.In 3D cell culturing,porous scaffolds are used for housing the cells.It is known that the scaffold porous geometries can influence the scaffold permeability and internal WSS in a bioreactor(such as perfusion bioreactor).To calculate the WSS generated on cells within scaffolds,usually computational fluid dynamics(CFD)simulation is needed.However,the limitations of the computational method for WSS calculation are:(i)the high time cost of the CFD simulation(in particular for the highly irregular geometries);(ii)accessibility to the CFD model for some cell culturing experimentalists due to the knowledge gap.To address these limitations,this study aims to develop an empirical model for calculating the WSS based on scaffold permeability.This model can allow the tissue engineers to efficiently calculate the WSS generated within the scaffold and/or determine the bioreactor loading without performing the computational simulations.

Research progress on the influence of local hemodynamics on carotid atherosclerosis

The reasons for the formation of atherosclerosis are diverse and complex,and atherosclerosis as a kind of systemic disease has the characteristics of focal selectivity,which occurs in the carotid bifurcation.The feature enables a large number of studies have found that the severe local hemodynamic characteristics has a great influence to the occurrence of this disease.This paper briefly reviews the related research on the local hemodynamics of carotid bifurcation.The relevant parameters of local hemodynamics were sorted out and summarized,and the effects of wall shear force and its derived parameters on the generation,progression and rupture of carotid atherosclerosis and their clinical applications were reviewed,in order to provide mechanical information for the early warning of carotid plaque rupture.At the same time,this paper describes the transformation of local hemodynamics research in the clinical application of carotid atherosclerosis disease,in order to provide personalized selection and basis for the clinical treatment of this disease.

A Computational Analysis of the Influence of Anastomosis Angle on Stenosis-Prone Locations during Radio-Cephalic Arteriovenous Fistula Maturation

In dialysis treatment, the radio-cephalic arteriovenous fistula (RCAVF) is a commonly used fistula, yet its low maturation rate remains a challenge. To enhance surgical outcomes, the relationship between stenosis-prone locations and RCAVF anastomosis angle is studied during maturation by developing two sets of RCAVF models for early (non-mature) and mature RCAVFs at five anastomosis angles. The impact of hemodynamics and wall shear stress (WSS) is examined to determine optimal anastomotic angles. Results indicate that acute angles produce more physiological WSS distributions and fewer disturbed regions, with early stenosis-prone regions located near the anastomosis that shift to the bending venous segment during remodeling. A pilot study comparing clinical and numerical results is conducted for validation.

Distribution of wall shear stress in carotid plaques using magnetic resonance imaging and computational fluid dynamics analysis： a preliminary study

Background Wall shear stress is an important factor in the destabilization of atherosclerotic plaques. The purpose of this study was to assess the distribution of wall shear stress in advanced carotid plaques using high resolution magnetic resonance imaging and computational fluid dynamics.Methods Eight diseased internal carotid arteries in seven patients were evaluated. High resolution magnetic resonance imaging was used to visualize the plaque structures, and the mechanic stress in the plaque was obtained by combining vascular imaging post-processing with computational fluid dynamics.Results Wall shear stresses in the plaques in all cases were higher than those in control group. Maximal shear stresses in the plaques were observed at the top of plaque hills, as well as the shoulders of the plaques. Among them,the maximal shear stress in the ruptured plaque was observed in the rupture location in three cases and at the shoulder of fibrous cap in two cases. The maximal shear stress was also seen at the region of calcification, in thrombus region and in the thickest region of plaque in the other three cases, respectively.Conclusion Determination of maximal shear stress at the plaque may be useful for predicting the rupture location of the plaque and may play an important role in assessing plaque vulnerability.

SYNERGY OF WALL SHEAR STRESS AND CIRCUMFERENTIAL STRESS IN STRAIGHT ARTERIES

The Wall Shear Stress （WSS） generated by blood flow and Circumferential Stress （CS） driven by blood pressure have been thought to play an important role in blood flow-dependent phenomena such as angiogenesis, vascular remodeling, and atherosgenesis. The WSS and CS in straight arteries were calculated by measuring the blood pressure, center-line velocity, wall thickness, and radius of vessels. The WSS and CS in the time domain were then decomposed into the amplitude and phase in the frequency domain. The CS amplitude to the WSS amplitude ratio （referred as stress ampli tude ratio, Zs ） and the phase difference between the CS and the WSS （referred as stress phase difference, SPA） in the fre quency domain were calculated to characterize the synergy of the CS and WSS. Numerical results demonstrated that the CS is not in phase with the WSS, a time delay in the time domain or a stress phase difference in the frequency domain between the WSS and the CS exists. Theoretical analysis demonstrated that the Zs and SPA are primarily determined by the local fac tors （blood viscosity, local inertial effects, local geometry, loeal elasticity） and the input impedance of whole downstream arterial beds. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and stress phase difference SPA would be thought to be the appropriate indices to reflect the effects of states of whole downstream arterial beds on the local blood flow dependent phenomena such as angiogenesis, vascular remodeling, and atherosgenesis.

Experimental and computational studies on the flow fields in aortic aneurysms associated with deployment of AAA stent-grafts

Pulsatile flow fields in rigid abdominal aortic aneurysm （AAA） models were investigated numerically, and the simulation results are found in good agreement with particle image velocimetry （PIV） measurements. There are one or more vortexes in the AAA bulge, and a fairly high wall shear stress exists at the distal end, and thus the AAA is in danger of rupture. Medical treatment consists of inserting a vascular stent-graft in the AAA, which would decrease the blood impact to the inner walls and reduce wall shear stress so that the rupture could be prevented. A new computational model, based on porous medium model, was developed and results are documented. Therapeutic effect of the stent-graft was verified numerically with the new model.

Influence of coronary bifurcation angle on atherosclerosis

Hemodynamics plays a crucial role in the development and progression of coronary atherosclerosis,which is prone to occur in branch bifurcation.A n individual aortic-coronary artery model and three changed bifurcation angle models are constructed by Mimics and Freeform based on computed tomography angiography.The influence of different coronary bifurcation angles between left main(LM),left anterior descending(LAD),and left circumflex(LCX)on the blood flow field and related hemodynamic parameters are studied.It is shown that a wider bifurcation angle between LAD and LCX can cause a wider low-wall shear stress area,leading to atherosclerosis.Similarly,a decreased angle between LM and LAD is predisposed to prevent atherosclerosis.The results help to better understand the hemodynamic causes of atherosclerosis with various bifurcation angles in coronary arteries and to provide guidance for clinical assessment and prevention.

Turbulent boundary layers and hydrodynamic flow analysis of nanofluids over a plate

A numerical analysis of the log-law behavior for the turbulent boundary layer of a wall-bounded flow is performed over a flat plate immersed in three nanofluids(Zn O-water,SiO_(2)-water,TiO_(2)-water).Numerical simulations using CFD code are employed to investigate the boundary layer and the hydrodynamic flow.To validate the current numerical model,measurement points from published works were used,and the compared results were in good compliance.Simulations were carried out for the velocity series of 0.04,0.4 and 4 m/s and nanoparticle concentrations0.1% and 5%.The influence of nanoparticles’ concentration on velocity,temperature profiles,wall shear stress,and turbulent intensity was investigated.The obtained results showed that the viscous sub-layer,the buffer layer,and the loglaw layer along the potential-flow layer could be analyzed based on their curving quality in the regions which have just a single wall distance.It was seen that the viscous sub-layer is the biggest area in comparison with other areas.Alternatively,the section where the temperature changes considerably correspond to the thermal boundary layer’s thickness goes a downward trend when the velocity decreases.The thermal boundary layer gets deep away from the leading edge.However,a rise in the volume fraction of nanoparticles indicated a minor impact on the shear stress developed in the wall.In all cases,the thickness of the boundary layer undergoes a downward trend as the velocity increases,whereas increasing the nanoparticle concentrations would enhance the thickness.More precisely,the log layer is closed with log law,and it is minimal between Y^(+)=50 and Y^(+)=95.The temperature for nanoparticle concentration φ=5%is higher than that for φ=0.1%,in boundary layers,for all studied nanofluids.However,it is established that the behavior is inverted from the value of Y^(+)=1 and the temperature for φ =0.1% is more important than the case of φ =5%.For turbulence intensity peak,this peak exists at Y^(+)=100 for v=4 m/s,Y^(+)=10 for v=0.4 m/s and Y^(+)=8 for v=0.04 m/s.

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional （3D） lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel （FH） curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.

Direct detection and measurement of wall shear stress using a filamentous bio-nanoparticle

The wall shear stress （WSS） that a moving fluid exerts on a surface affects many processes including those relating to vascular function. WSS plays an important role in normal physiology （e.g. angiogenesis） and affects the microvasculature＇s primary function of molecular transport. Points of fluctuating WSS show abnormalities in a number of diseases; however, there is no established technique for measuring WSS directly in physiological systems. All current methods rely on estimates obtained from measured velocity gradients in bulk flow data. In this work, we report a nanosensor that can directly measure WSS in microfluidic chambers with sub-micron spatial resolution by using a specific type of virus, the bacteriophage M13, which has been fluorescently labeled and anchored to a surface. It is demonstrated that the nanosensor can be calibrated and adapted for biological tissue, revealing WSS in micro-domains of cells that cannot be calculated accurately from bulk flow measurements. This method lends itself to a platform applicable to many applications in biology and microfluidics.

Effects of cartilaginous rings on airflow and particle transport through simplified and realistic models of human upper respiratory tracts

In the present study, computational fluid dynamics （CFD） is used to investigate inspiratory and expiratory airflow characteristics in the human upper respiratory tract for the purpose of identifying the probable locations of particle deposition and the wall injury. Computed tomography （CT） scan data was used to reconstruct a three dimensional respiratory tract from trachea to first generation bronchi. To compare, a simplified model of respiratory tract based on Weibel was also used in the study. The steady state results are obtained for an airflow rate of 45 L/min, corresponding to the heavy breathing condition. The velocity distribution, wall shear stress, static pressure and particle deposition are compared for inspiratory flows in simplified and realistic models and expiratory flows in realistic model only. The results show that the location of cartilaginous rings is susceptible to wall injury and local particle deposition.