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.

Relationship between wall shear stresses and streamwise vortices in turbulent flows over wavy boundaries

The relationship between wall shear stresses and near-wall streamwise vortices is investigated via a direct numerical simulation(DNS) of turbulent flows over a wavy boundary with traveling-wave motion. The results indicate that the wall shear stresses are still closely related to the near-wall streamwise vortices in the presence of a wave. The wave age and wave phase significantly affect the distribution of a two-point correlation coefficient between the wall shear stresses and streamwise vorticity. For the slow wave case of c/Um = 0.14, the correlation is attenuated above the leeward side while the distribution of correlation function is more elongated and also exhibits a larger vertical extent above the crest. With respect to the fast wave case of c/U_m=1.4, the distribution of the correlation function is recovered in a manner similar to that in the flat-wall case. In this case, the maximum correlation coefficient exhibits only slight differences at different wave phases while the vertical distribution of the correlation function depends on the wave phase.

Wall shear stress can improve prediction accuracy for transient ischemic attack

BACKGROUND Early prediction of transient ischemic attack (TIA) has important clinical value. To date, systematic studies on clinical, biochemical, and imaging indicators related to carotid atherosclerosis have been carried out to predict the occurrence of TIA. However, their prediction accuracy is limited. AIM To explore the role of combining wall shear stress (WSS) with conventional predictive indicators in improving the accuracy of TIA prediction. METHODS A total of 250 patients with atherosclerosis who underwent carotid ultrasonography at Naval Military Medical University Affiliated Gongli Hospital were recruited. Plaque location, plaque properties, stenosis rate, peak systolic velocity, and end diastolic velocity were measured and recorded. The WSS distribution map of the proximal and distal ends of the plaque shoulder was drawn using the shear stress quantitative analysis software, and the average values of WSS were recorded. The laboratory indicators of the subjects were recorded. The patients were followed for 4 years. Patients with TIA were included in a TIA group and the remaining patients were included in a control group. The clinical data, laboratory indicators, and ultrasound characteristics of the two groups were analyzed. Survival curves were plotted by the Kaplan-Meier method. Receiver operating characteristic curves were established to evaluate the accuracy of potential indicators in predicting TIA. Logistic regression model was used to establish combined prediction, and the accuracy of combined predictive indicators for TIA was explored.RESULTS The intraclass correlation coefficients of the WSS between the proximal and distal ends of the plaque shoulder were 0.976 and 0.993, respectively, which indicated an excellent agreement. At the end of the follow-up, 30 patients suffered TIA (TIA group) and 204 patients did not (control group). Hypertension (P = 0.037), diabetes (P = 0.026), homocysteine (Hcy)(P = 0.022), fasting blood glucose (P = 0.034), plaque properties (P = 0.000), luminal stenosis rate (P = 0.000), and proximal end WSS (P = 0.000) were independent influencing factors for TIA during follow-up. The accuracy of each indicator for predicting TIA individually was not high (area under the curve [AUC]< 0.9). The accuracy of the combined indicator including WSS (AUC = 0.944) was significantly higher than that of the combined indicator without WSS (AUC = 0.856) in predicting TIA (z = 2.177, P = 0.030). The sensitivity and specificity of the combined indicator including WSS were 86.67% and 92.16%, respectively. CONCLUSION WSS at plaque surface combined with hypertension, diabetes, Hcy, blood glucose, plaque properties, and stenosis rate can significantly improve the accuracy of predicting TIA.

Effects of Elasticity on Wall Shear Stress in Patient-Specific Aneurysm of Cerebral Artery

The behavior of wall shear stress (WSS) was previously reported in a deformable aneurysm model using fluid-structure interactions. However, these findings have not been validated. In the present study, we examined the effect of elasticity (i.e., deformation) on wall shear stress inside a cerebral aneurysm at the apex of a bifurcation using particle image velocimetry in vitro. The flow model simulated a human patient-specific aneurysm at the apex of the bifurcation of the middle cerebral artery. Flow characteristics by wall elasticity were examined for both elastic and non-deformable aneurysm models with pulsatile blood flow. The absolute temporally- and spatially-averaged WSS along the bleb wall was smaller in the elastic model than that in the non-deformable model. This small WSS may be related to attenuation of the WSS. Further, the WSS gradient had a finite value near the stagnation point of the aneurysm dome. Finally, the WSS gradient near the stagnation point was slightly smaller in the elastic model than that in the non-deformable model. These data suggest that elasticity of the aneurysm wall can affect the progression and rupture of aneurysms via hemodynamic stress.

The Effect of Near-Wall Vortices on Wall Shear Stress in Turbulent Boundary Layers

The objective of the present study is to explore the relation between the near-wall vortices and the shear stress on the wall in two-dimensional channel flows. A direct numerical simulation of an incompressible two-dimensional turbulent channel flow is performed with spectral method and the results are used to examine the relation between wall shear stress and near-wall vortices. The two-point correlation results indicate that the wall shear stress is associated with the vortices near the wall and the maximum correlation-value location of the near-wall vortices is obtained. The analysis of the instantaneous diagrams of fluctuation velocity vectors provides a further expression for the above conclusions. The results of this research provide a useful supplement for the control of turbulent boundary layers.

Converging Parallel Plate Flow Chambers for Studies on the Effect of the Spatial Gradient of Wall Shear Stress on Endothelial Cells

Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.

The Wall Shear Stress of a Pulsatile Blood Flow in a Patient Specific Stenotic Right Coronary Artery

A computer simulation of the blood flow in a patient specific atherosclerotic right coronary artery is carried out to study the blood flow pattern and the wall shear stress (WSS) distribution in the artery. Both temporal and special distribution patterns of the WSS of the non-Newtonian blood flow are presented and the regions on the lumen surface where the WSS is constantly lower than 1N/m2are identified.

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.

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.

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.

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.

THE EFFECTS OF PHYSIOLOGICAL FLOW WAVEFORM ON WALL SHEAR STRESS IN CAROTID BIFURCATION MODEL

Numerical models of carotid bifurcation were constructed using a combination of tuning-fork bifurcation and straight or curved common carotid. The different inlet velocity profiles of the common carotid were generated for Bloch flow waveform and Holdsworth flow waveform, respectively. The effects of the different flow waveform for the common carotid on Wall Shear Stress （WSS） and Oscillatory Shear Index （OSI） of carotid bifurcation were studied by CFD method. The results show that the physiological flow waveform of curved common carotid has a significant effect on OSI. In particular, the OSI on the outer walls of carotid sinus and external carotid becomes higher in the inward-curved common carotid for Holdsworth flow waveform. But, in both cases of low WSS and high OSI, the effects of flow waveforms are smaller than those of the curved common carotid. The study reveals that the exact knowledge of the physiological flow waveform, vascular geometry and inlet velocity profile is important for hemodynamic numerical simulation of artery bifurcation.

Non-invasive assessment of intracranial wall shear stress using high-resolution magnetic resonance imaging in combination with computational fluid dynamics technique

In vivo studies on association between wall shear stress(WSS)and intracranial plaque are deficient.Based on the three-dimensional T1-weighted high-resolution magnetic resonance imaging(3DT1 HR-MRI)data of patients with low-grade stenotic(<50%)atherosclerotic middle cerebral artery(MCA)and subjects with normal MCA,we built a three-dimensional reconstructed WSS model by computational fluid dynamics(CFD)technique.Three-dimensional registration of the CFD model to the HR-MRI was performed with projections based on the resolution and thickness of the images.The relationships between the Wss at each side of the vessel wall and plaque location were analyzed.A total of 94 MCA plaques from 43 patients and 50 normal MCAs were analyzed.In the normal MCAs,WSS was lower at the ventral-inferior wall than at the dorsal-superior wall(proximal segment,p<0.001;middle segment,p<0.001)and lower at the inner wall than at the outer wall of the MCA curve(p<0.001).In atherosclerotic MCAs,similar low Wss regions were observed where plaques developed.The WSS ratio of the ventral-inferior wall to the dorsal-superior wall in atherosclerotic MCAs was lower than that in normal MCAs(p=0.002).The WSS_(inmer-outer)ratio in atherosclerotic MCAs was lower than that in normal MCAs(p=0.002).Low WSS was associated with MCA atherosclerosis formation and occurred mainly at the ventral inferior wall,which was anatomically opposite the orifices of penetrating arteries,and at the inner wall of the MCA curve.Overall,the results were well consistent with the low WSS theory in atherosclerosis formation.The reconstructed WSS model is a promising novel method for assessing an individualized vascular profile once validated by further studies.

Impact of an External Magnetic Field on the Shear Stresses Exerted by Blood Flowing in a Large Vessel

The aim of this paper is to provide an advanced analysis of the shear stresses exerted on vessel walls by the flowing blood, when a limb or the whole body, or a vessel prosthesis, a scaffold… is placed in an external static magnetic field B0. This type of situation could occur in several biomedical applications, such as magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering, mechanotransduction studies… Since blood is a conducting fluid, its charged particles are deviated by the Hall effect, and the equations of motion include the Lorentz force. Consequently, the velocity profile is no longer axisymmetric, and the velocity gradients at the wall vary all around the vessel. To illustrate this idea, we expand the exact solution given by Gold (1962) for the stationary flow of blood in a rigid vessel with an insulating wall in the presence of an external static magnetic field: the analytical expressions for the velocity gradients are provided and evaluated near the wall. We demonstrate that the derivative of the longitudinal velocity with respect to the radial coordinate is preponderant when compared to the θ-derivative, and that elevated values of B0 would be required to induce some noteworthy influence on the shear stresses at the vessel wall.

Investigation on Cracking of Concrete Shear Wall under Exceeded Temperature Differences Rate

In situ, the changes of temperature, deformation, and stressing of steel bar of C40 reinforced concrete shear wall were measured, respectively. The results are obvious that the temperature change of climate is one of the most effective factors which could lead the concrete shear wall to cracking at earlier age. The temperature differences between inside and outside concrete shear wall are so large that the concrete will gain larger shrinkage. This larger shrinkage which is caused by the temperature reducing ratio will gain the strained action of head, end and reinforced steel bar of concrete shear wall. This action can lead to tensile stress on the surface and inside concrete shear wall. If the tensile stress would exceed the pull strength of concrete, the concrete shear wall would crack and cause deterioration. Thus, the enhancing curing of concrete shear wall in suit at earlier age, and controlling temperature reducing ratio and deform caused by shrinkage, will be available treatments which control occurring and developing of cracking on concrete shear wall.