Wall Shear Stress Values Research Articles

Investigation on the differences of hemodynamics in normal common carotid, subclavian, and common femoral arteries using the vector flow technique.

To investigate the feasibility of the vector flow imaging (V Flow) technique to measure peripheral arterial hemodynamic parameters, including wall shear stress (WSS) and turbulence index (Tur) in healthy adults, and compare the results in different arteries. Fifty-two healthy adult volunteers were recruited in this study. The maximum and mean values of WSS, and the Tur values at early-systole, mid-systole, late-systole, and early diastole for total 156 normal peripheral arteries [common carotid arteries (CCA), subclavian arteries (SCA), and common femoral arteries (CFA)] were assessed using the V Flow technique. The mean WSS values for CCA, SCA, and CFA were (1.66 ± 0.68) Pa, (0.62 ± 0.30) Pa, and (0.56 ± 0.27) Pa, respectively. The mean Tur values for CCA, SCA, and CFA were (0.46 ± 1.09%), (20.7 ± 9.06%), and (24.63 ± 17.66%), respectively. The CCA and SCA, as well as the CCA and CFA, showed statistically significant differences in the mean WSS and the mean Tur (P < 0.01). The mean Tur values had a negative correlation with the mean WSS; the correlation coefficient between log(Tur) and WSS is -0.69 (P < 0.05). V Flow technique is a simple, practical, and feasible quantitative imaging approach for assessing WSS and Tur in peripheral arteries. It has the potential to be a useful tool for evaluating atherosclerotic plaques in peripheral arteries. The results provide a new quantitative foundation for future investigations into diverse arterial hemodynamic parameters.

Numerical simulation of flow resistance characteristics in a rod bundle channel under rolling conditions

Flow resistance characteristics in a 3 × 3 rod bundle channel under rolling motion are investigated by numerical simulation to overcome the limitation of experimental conditions and measurement methods. Severe rolling conditions are selected to make up for the lack of test range. The local parameters, including flow field, temperature field and wall shear stress are given to analyze the influence mechanism of the rolling motion on friction resistance of the rod bundle channel. Under rolling conditions, the absolute value of flow rate does not influence the fluctuation amplitude of frictional pressure drop when inlet flow rate does not fluctuate. Additional pressure drop is the main factor affecting the fluctuation amplitude of frictional pressure drop under rolling conditions. When the rolling motion becomes severe, the velocity deviation increases, while it has no obvious influence on velocity peak value within cross section. Increasing the flow rate weakens the effect of rolling motion on axial velocity distribution. The variation of flow rate does not affect the magnitude and distribution of radial velocity, and the radial secondary flow intensity is mainly determined by the intensity of rolling motion. Different from velocity distribution, the wall shear stress distribution is obviously affected by rolling motion and is unconnected with flow rate, while the flow rate affects the relative value of wall shear stress. Under the same rolling parameters, the variation range of boundary layer thickness increases with decreasing flow rate, which leads to an increase in the relative variation range of wall shear stress with decreasing flow rate.

Fluid-structure interaction study of bio-magnetic fluid in a wavy bifurcated channel with elastic walls

As a result of its wide range of applications, FSI has grabbed the attention of researchers and scientists. In this study we consider an incompressible, laminar fluid flowing through the bifurcated channel. The wavy walls of the channel are considered elastic. Moreover, a magnetic field is applied towards the axial direction of the flow. Using a two-way fluid-structure interaction, an Arbitrary Lagrangian-Eulerian (ALE) formulation is used for coupling the problem. The problem is discretized using P2 and P1 finite element methods to approximate the displacement, pressure, and velocity. The linearized system of equations is solved using Newton’s iterative scheme. The analysis is carried out for the Reynolds number and Hartman number. The ranges of the studied parameters are Reynolds number 300≤Re≤1000 and Hartmann number 0≤Ha≤10. The hemodynamic effects on the bifurcated channel and elastic walls are calculated using velocity, pressure, wall shear stresses (WSS), and loads at the walls. The study shows there is an increase in boundary load as the values of the Hartman number increase hence WSS increases. On the other hand, an increase in the Reynolds number increases the resistance forces hence velocity and WSS decrease. Also, numerical values of WSS for rigid and elastic walls are calculated. Studies showed that WSS decreases for the FSI case when compare to CFD (computational fluid dynamic) case.

P068 Computational fluid dynamic study in Obstructive Sleep Apnea patients

Abstract Introduction Obstructive sleep apnea (OSA) is a common disorder which may need surgery to widen the airway. However, the success rate of surgery is variable. Thus, it is necessary to predict the outcome of the surgery preoperatively. The purpose of this study is to evaluate the mechanical parameter of upper airway airflow in OSA patients using computational fluid dynamics (CFD) method. Method We conducted a study on the patients with snoring, underwent the full night polysomnograpny (PSG) and paranasal sinus computed tomography(CT). The patients with past history of previous trauma or surgery were excluded. Three-demensional reconstructions of the upper airway were created in the medical imaging software Mimics 16.0 using paranasal CT. The reconstructions extended from nasopharynx to hypopharynx. Steady-state, turbulent, inspiratory airflow simulations were conducted in Fluent 17.0 with following boundary conditions The mechanical parameters (wall shear stress, pressure, plane velocity) were calculated in the three levels of nasopharynx, retropalatal, retrolingual area. Results The maximum wall shear stress values were shown at the retropalatal plane in all patients. There is a tendency for the wall shear stress value of the retropalatal area to increase as the AHI increases. The maximum velocity values were shown at the retropalatal plane in all patients. The maximum pressure values were shown at the nasopharynx plane in all patients. Conclusion the maximum wall shear stress values were shown at the retropalatal plane and the wall shear stress value of the retropalatal area increased as the AHI increased. Thus, the palatal surgery might help the OSA patients.

Influence of morphological parameters on hemodynamics in internal carotid artery bifurcation aneurysms

Recent advancements in medical imaging techniques have enabled the accurate identification of unruptured intracranial aneurysms. To facilitate a proper patient management strategy, it is important to develop suitable mathematical models for their rupture prediction. To this end, the development of high-fidelity computational fluid dynamics (CFD) simulations with patient-specific boundary conditions will be useful in providing reliable hemodynamic parameters. In recent review articles, researchers have pointed out that, among several clinical and image-based indicators, morphological parameters, such as aspect ratio (AR) and size ratio (SR) of the aneurysm, correlated consistently with the rupture mechanism. However, it is not clear how these morphological indicators influence the hemodynamics-based CFD predictions. In the present work, the effect of these top-ranked morphological parameters on aneurysm hemodynamics and rupture prediction is investigated. Three patient-specific models have been used for analysis with the patient-specific inlet boundary conditions. We found that with an increase in AR and SR, the maximum value of wall shear stress (WSS) near the aneurysm neck is increased. Oscillatory shear index and relative residence time values are also increased with an increase in AR and SR. Furthermore, it was observed that an aneurysm with a multilobed structure shows complex flow, low WSS, and higher residence time over the secondary lobe. The turbulent kinetic energy and vorticity near the aneurysm neck are also increased with an increase in AR and SR.

Geometry-Based Computational Fluid Dynamic Model for Predicting the Biological Behavior of Bone Tissue Engineering Scaffolds.

The use of biocompatible and biodegradable porous scaffolds produced via additive manufacturing is one of the most common approaches in tissue engineering. The geometric design of tissue engineering scaffolds (e.g., pore size, pore shape, and pore distribution) has a significant impact on their biological behavior. Fluid flow dynamics are important for understanding blood flow through a porous structure, as they determine the transport of nutrients and oxygen to cells and the flushing of toxic waste. The aim of this study is to investigate the impact of the scaffold architecture, pore size and distribution on its biological performance using Computational Fluid Dynamics (CFD). Different blood flow velocities (BFV) induce wall shear stresses (WSS) on cells. WSS values above 30 mPa are detrimental to their growth. In this study, two scaffold designs were considered: rectangular scaffolds with uniform square pores (300, 350, and 450 µm), and anatomically designed circular scaffolds with a bone-like structure and pore size gradient (476–979 µm). The anatomically designed scaffolds provided the best fluid flow conditions, suggesting a 24.21% improvement in the biological performance compared to the rectangular scaffolds. The numerical observations are aligned with those of previously reported biological studies.

CFD simulations of respiratory airflow in human upper airways response to walking and running for oral breathing condition

Walking and running are common types of physical activities that people do in day to day living, to improve health and physical fitness or for recreation. During a physical activity, rate and depth of breathing increase because working muscles need extra oxygen in order to produce energy. In this study, computational fluid dynamics (CFD) simulations were used to investigate respiratory airflow dynamics in human upper airways response to walking and running for oral breathing. The numerical simulations were done in a realistic CT-scan airway model using ANAYS Fluent 19.0 software. Flow fields were analysed numerically and flow patterns were investigated in the airway model during inspiration and expiration response to walking and running. The axial velocity distributions and secondary flow patterns for the two respiratory phases were analysed response to the two physical activities at different cross-sections of the airway model. The maximum velocity, wall pressure and wall shear stress values for running were respectively 3.2, 9.4 and 5.9 times higher than that of walking during inspiration. The mixing of flow streamlines was observed to be higher during running than walking because of more significant turbulence. More skewed flows at airway curvatures were observed at inspiration than expiration. The results of this study supported the fact that running is a more intense activity than walking from a respiratory dynamics point of view.

An agent-based model of vibration-induced intimal hyperplasia.

Acute exposure to hand-arm transmitted vibrations (HAVs) may decrease the wall shear stress (WSS) exerted by the blood flow on the arterial endothelium. In the case of chronic exposure to HAVs, these WSS changes can lead to arterial growth and remodeling potentially induced by an intimal hyperplasia phenomenon. Accordingly, we implemented an agent-based model (ABM) that captures the hemodynamics-driven and mechanoregulated cellular mechanisms involved in vibration-induced intimal hyperplasia. Our ABM was combined with flow loop experiments that investigated the WSS-modulated secretion of the platelet-derived growth factor BB (PDGF-BB) by the endothelial cells. The ABM rules parameters were then identified and calibrated using our experimental findings and literature data. The model was able to replicate the basal state (no vibration) as well as predict a 30% stenosis resulting from a chronic drop of WSS values mimicking exposure to vibration during a timeframe of 10 years. The study of the influence of different WSS-modulated phenomena on the model showed that the magnitude of stenosis largely depends on the migratory effects of PDGF-BB and the mitogenic effects of Transforming Growth Factor [Formula: see text] on the Smooth Muscle Cells. The results also proved that the fall in circumferential stress due to arterial layer thickening to a great extent accounts for the degradation of the Extracellular Matrix in the media.

Numerical investigation of different viscosity models on pulsatile blood flow of thoracic aortic aneurysm (TAA) in a patient-specific model

Aortic aneurysm is one of the most common aortic diseases that can lead to unfortunate consequences. Numerical simulations have an important role in the prediction of the aftereffects of vascular diseases including aneurysm. In this research, numerical simulation of pulsatile blood flow is performed for a 3-dimensional patient-specific model of a thoracic aortic aneurysm (TAA). Since the choice of blood viscosity model may have a significant impact on the simulation results, the effects of four non-Newtonian models of blood viscosity namely Carreau, Casson, Herschel-Bulkley, power low, and the Newtonian model on the wall shear stress (WSS) distribution, shear rate, and oscillatory shear index (OSI) have been analyzed. Simulation results showed that all the non-Newtonian and Newtonian models generally, predict similar patterns for blood flow and shear rate. At high flow rates in the cardiac cycle, the WSS value for all the models are similar to each other except for the power-law model due to the shear thinning behavior. All models predict high values of OSI on the inner wall of the ascending aorta and broad areas of the inner wall of the aneurysm sac. However, the Newtonian model predicts the OSI less than the non-Newtonian models in some areas of the aneurysm sac. Results indicated that the Newtonian model generally can predict the hemodynamic parameters of the blood flow similar to the non-Newtonian but for more precise analysis and to predict the regions prone to rupture and atherosclerosis, choosing a proper non-Newtonian model is recommended.

Temperature Variation with Hemodynamic Effect Simulation on Wall Shear Stress in Fusiform Cerebral Aneurysm

A cerebral aneurysm is the dilation of an arterial wall and mostly occurs at the weak point in the arterial circulation in the brain. Approximately 85% of aneurysms are in the anterior circulation, predominately at junctions, or bifurcations along the circle of Willis. Several studies have been conducted by researchers to analyse the blood flow characteristic and flow on the aneurysmal wall, however, there are small numbers of research focus on the fusiform aneurysm and the effect of temperature on the blood flow inside the aneurysm. Thus, this study aims to analyse the body temperature effect on hemodynamic parameters in the fusiform aneurysm. Three different models of the fusiform aneurysm based on patient-specific geometries have been developed and simulated. The computational Fluid Dynamics (CFD) method was imposed in this study to analyse the effect of hemodynamic variables on the different body temperatures by analysing the Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI) at the fusiform aneurysmal wall. The result shows that the WSS values fluctuate with the temperature variations and were observed lowest low at the anterior fusiform aneurysm. The OSI indicates similar results for each physiological condition with the variation of temperature. The high value of WSS and low value of OSI increase the possibility of an aneurysmal wall being ruptured.

Research on the effect of visceral artery Aneurysm's cardiac morphological variation on hemodynamic situation based on time-resolved CT-scan and computational fluid dynamics

Background and ObjectiveMuscular arteries and related aneurysms keep deforming during the cardiac cycle. However, current patient-specific computational fluid dynamics (CFD) analyses of aneurysms are usually based on individual cardiac phase images. The cardiac deformation and displacement characteristics of muscle arteries and aneurysms, as well as their impact on CFD results, have not been adequately explored. The present study tried to illustrate the cardiac morphological variation of visceral muscular arteries (VMAs) & aneurysms (VAAs) and evaluate its influence on the hemodynamic situation at lesion locations. MethodsFour-dimensional computed tomography angiogram (4D-CTA) images of six patients with VAAs were acquired. Medical image registration is used to capture cardiac variations of VMAs. The steady-state CFD simulation is performed on twelve different time-phase geometries. Deformation, displacement, wall shear stress (WSS), velocity, and pressure values at pathological locations are compared to illustrate the deforming characteristics of VAAs and their influence on CFD simulation results. ResultsThe deformation and displacement characteristics of lesion locations for six specific patients show a pulsatile pattern. Maximum displacements are always less than 4 mm. The ratio fluctuations of endovascular cavity volume and vascular inner wall surface area, which were employed to depict cardiac deformation, are always less than 20%. According to CFD simulations based on deformed VMAs, WSS has a larger coefficient of variation (COV) than velocity and pressure. Except for one patient's WSS, the COVs of different hemodynamic parameters obtained from simulation results are always less than 10%. ConclusionsBased on 4D-CTA images, we confirmed that cardiovascular circulation has a periodic impact on the morphologic characteristics of VMAs. A wave that has extended throughout the studied region is observed. It has a dominant influence on the displacement of VMAs. According to CFD results, the influence of the VMAs' deformation and displacement on different hemodynamic parameters is distinct. The variance in WSS is more prominent compared to pressure and velocity. On most occasions, the influence of the VMAs’ periodic deformation and displacement on simulation results is insignificant. However, the variant simulation results induced by deforming VMAs cannot be simply ignored.

Hemodynamic changes after intracranial aneurysm growth.

For accurate risk assessment of unruptured intracranial aneurysms, it is important to understand the underlying mechanisms that lead to rupture. It is known that hemodynamic anomalies contribute to aneurysm growth and rupture, and that growing aneurysms carry higher rupture risks. However, it is unknown how growth affects hemodynamic characteristics. In this study, the authors assessed how hemodynamic characteristics change over the course of aneurysm growth. The authors included patients with observed aneurysm growth on longitudinal MRA in the period between 2012 and 2016. Patient-specific vascular models were created from baseline and follow-up images. Subsequently, intraaneurysmal hemodynamic characteristics were computed using computational fluid dynamics. The authors computed the normalized wall shear stress, oscillatory shear index, and low shear area to quantify hemodynamic characteristics. Differences between baseline and follow-up measurements were analyzed using paired t-tests. Twenty-five patients with a total of 31 aneurysms were included. The aneurysm volume increased by a median (IQR) of 26 (9-39) mm3 after a mean follow-up period of 4 (range 0.4-10.9) years. The median wall shear stress decreased significantly after growth. Other hemodynamic parameters did not change significantly, although large individual changes with large variability were observed. Hemodynamic characteristics change considerably after aneurysm growth. On average, wall shear stress values decrease after growth, but there is a large variability in hemodynamic changes between aneurysms.

Quantitative normal values of helical flow, flow jets and wall shear stress of healthy volunteers in the ascending aorta

Objectives4D flow MRI enables quantitative assessment of helical flow. We sought to generate normal values and elucidate changes of helical flow (duration, volume, length, velocities and rotational direction) and flow jet (displacement, flow angle) as well as wall shear stress (WSS).MethodsWe assessed the temporal helical existence (THEX), maximum helical volume (HVmax), accumulated helical volume (HVacc), accumulated helical volume length (HVLacc), maximum forward velocity (maxVfor), maximum circumferential velocity (maxVcirc), rotational direction (RD) and maximum wall shear stress (WSS) as reported elsewhere using the software tool Bloodline in 86 healthy volunteers (46 females, mean age 41 ± 13 years).ResultsWSS decreased by 42.1% and maxVfor by 55.7% across age. There was no link between age and gender regarding the other parameters.ConclusionThis study provides age-dependent normal values regarding WSS and maxVfor and age- and gender-independent normal values regarding THEX, HVmax, HVacc, HVLacc, RD and maxVcirc.Key Points• 4D flow provides numerous new parameters; therefore, normal values are mandatory.• Wall shear stress decreases over age.• Maximum helical forward velocity decreases over age.

A mathematical model for biomechanical behavior of the aortic arch.

The aortic arch plays a significant role in homeostatic mechanisms to retain blood pressure at stable balance in the cardiovascular system. Therefore, the objective is to estimate and identify cardiovascular illness imposed by the abnormal blood hemodynamic domain. In this regard, hemodynamic forces are monitored by the baroreflex of the artery wall. Therefore, these receptors quickly detect the abnormal stress magnitudes in the aortic arterial wall. The present study presents a 3D aortic arch model extracted by a Computerized tomography scan. Also, the numerical solution was carried out by ANSYS 2020 R1 in view of Fluid-Structure Interaction After that, we found wall shear stress (WSS), pressure, and velocity in the fluid domain. Also, the normal stress was analyzed to determine the aortic arch baroreflex location in the solid range. In this regard, higher WSS values are measured at the supra-aortic branches going out the aortic arch that reached 42.5 Pa. Also, higher normal stress happened at the aortic root and the supra-aortic branches and reached approximately 200 kPa at peak systole.

Fluid‐Structure Interaction Study of Coronary Artery Disease Biomechanics

Coronary artery disease (CAD) kills 1 in 7 in the United States. Atherosclerosis and thrombosis are both disease states that are impacted by biomechanical conditions in the blood vessels. Platelets and vascular endothelial cells are known to respond to their mechanical environments, which can be altered around a coronary stenosis. Certain pertinent mechanical parameters, such as vascular wall shear stress and strain, can be difficult or impossible to measure directly in vivo.Computational fluid dynamics (CFD) models and Fluid‐Structure Interaction (FSI) models are often used to assess coronary artery biomechanics. In this study, we developed three FSI models based on the computed tomography data from a patient: a normal model, a severe stenosis model with a 71% diameter occlusion (which would be a candidate for intervention), and a mild stenosis model (50% diameter occlusion, which would not be considered clinically severe). Our hypothesis was that the high‐resolution FSI model could reveal small changes in coronary biomechanics at the cellular level (microscopic scale), which may be used as a biomarker/indicator for endothelial cell and platelet activation at the early stage of disease development. FSI simulations were conducted in COMSOL Multiphysics. Time‐dependent velocity and pressure boundary conditions were applied at the inlet and outlet of the fluid domain, respectively. A five‐parameter Mooney‐Rivlin hyperelastic material model was used to model the material properties of the artery. A time‐dependent pressure boundary condition was applied to the outside of the vessel, mimicking squeezing of the cardiac muscle in areas of myocardial bridging. In the region of interest, a spatial resolution of less than 40 µm was achieved. This is comparable to the size of vascular endothelial cells (which can range in size from 20‐100 µm), allowing us to capture hemodynamic and solid mechanical behavior at the cellular level. In the normal geometry, wall shear stress (WSS) values peaked at 1.51 Pa. In the 71% stenosis throat, transient WSS could reach 200 Pa, while in the 50% stenosis throat, the maximum WSS was less than 5 Pa. In the recirculation zone of the 71% stenosis, WSS peaked at 4.66 Pa, while in the recirculation zone of the 50% stenosis WSS reduced to 0.83 Pa, which is pathologically low. Time‐averaged wall shear stress (TAWSS) was 0.62+0.002 Pa (average + standard error) in the normal model, 1.60+0.004 Pa in the 50% stenosis model, and 7.47+0.017 Pa in the 71% stenosis model. Time‐averaged wall shear stress gradient (TAWSSG) was 0.018+6.25*10‐5 N/m in the normal model, 0.150+3.4*10‐4 N/m in the 50% stenosis model, and 0.970+0.002 N/m in the 71% stenosis model. Radial strain in the normal, 71% stenosis throat, 50% stenosis throat, 71% recirculation zone, and 50% recirculation zone peaked at 7.5%, 4.0%, 6.3%, 0.5%, and 5.1% respectively, and the circumferential strain peaked at 8.9%, 4.4%, 6.6%, 0.6%, and 4.2% respectively. In summary, we were able to develop mesoscopic FSI models that can provide microscopic hemodynamic information at the cellular level. Such information can be used in the in vitro models to study biomechanical pathways associated with coronary artery atherosclerosis and thrombosis; it may also be used as biomarkers at the early stage of atherosclerosis development.

A New Method for Quantifying Abdominal Aortic Wall Shear Stress Using Phase Contrast Magnetic Resonance Imaging and the Womersley Solution.

Wall shear stress (WSS) is an important mediator of cardiovascular pathologies and there is a need for its reliable evaluation as a potential prognostic indicator. The purpose of this work was to develop a method that quantifies WSS from two-dimensional (2D) phase contrast magnetic resonance (PCMR) imaging derived flow waveforms, apply this method to PCMR data acquired in the abdominal aorta of healthy volunteers, and to compare PCMR-derived WSS values to values predicted from a computational fluid dynamics (CFD) simulation. The method uses PCMR-derived flow versus time waveforms constrained by the Womersley solution for pulsatile flow in a cylindrical tube. The method was evaluated for sensitivity to input parameters, intrastudy repeatability and was compared with results from a patient-specific CFD simulation. 2D-PCMR data were acquired in the aortas of healthy men (n = 12) and women (n = 15) and time-averaged WSS (TAWSS) was compared. Agreement was observed when comparing TAWSS between CFD and the PCMR flow-based method with a correlation coefficient of 0.88 (CFD: 15.0 ± 1.9 versus MRI: 13.5 ± 2.4 dyn/cm2) though comparison of WSS values between the PCMR-based method and CFD predictions indicate that the PCMR method underestimated instantaneous WSS by 3.7 ± 7.6 dyn/cm2. We found no significant difference in TAWSS magnitude between the sexes; 8.19 ± 2.25 versus 8.07 ± 1.71 dyn/cm2, p = 0.16 for men and women, respectively.

Fluid–Structure Interaction Model for Assessing Aneurysm Initiation at the Circle of Willis

Abstract Hemodynamics associated with the arteries of the circle of Willis (CoW) is analyzed to identify possible cerebral aneurysm initiation locations using computational methods. A numerical fluid–structure interaction model is developed using an idealized geometry with the linear elastic, isotropic arterial wall. Blood flow is assumed to be laminar, incompressible, and modeled using Navier–Stokes equations, non-Newtonian viscosity, and sinusoidal boundary conditions. Available analytical and experimental results are used for the validation of the model. The highest wall shear stress (WSS) and von Mises stress (VMS) are identified for understanding the most vulnerable sites. The WSS distribution in the entire CoW region shows that ACoA junction has the highest value and risk of aneurysm initiation. The flow patterns created due to the geometrical features of the CoW seem to be the significant factor in the distribution of WSS. It is noticed that a decrease in wall elasticity will reduce the magnitude of WSS, both the temporal and spatial averaged value. The wall weakening effects are more pronounced for the posterior communicating artery. The wall weakening creates changes in core velocity and WSS. Changes in Von Mises stress are also noticed due to wall weakening effects. Highly localized VMS is noticed at ACoA and could possess a higher risk for aneurysm initiation and rupture. Despite the simplifications involved in developing the fluid–structure interaction model, this work demonstrates the critical locations at the CoW region regarding aneurysm initiation.

Maximum Wall Stress on a Smooth Flat Plate Under Planar Jet Impingement

Abstract This paper investigates the maximum wall shear stress value τmax and its location xmax as measured on a smooth flat plate impinged upon by a normal planar jet. τmax and xmax are found to be closely related to the stagnation pressure Ps and the half-width of the mean wall pressure profile bpw. The measurements were made by two different techniques: a Stanton probe and oil film interferometry. The maximum wall shear stress location xmax is found to be independent of the jet Reynolds number. At a small nozzle-to-plate distance H≲6 Djet, xmax is related to the jet slot width as xmax≈1.1Djet. At a large nozzle-to-plate distance H≳6 Djet, the maximum wall shear stress location is related to the mean wall pressure half-width as xmax≈1.4 bpw. A new Reynolds number, referred to as the stagnation Reynolds number, is defined as Res=def2bpwPs/ρ/ν, where ρ is the fluid density and ν is the kinematic viscosity. The maximum wall shear stress is found to be strongly influenced by the stagnation Reynolds number, and the dependence as measured by Stanton probes is approximated by a power law of τmax/Ps≈0.38/Res0.38. The solution of the laminar flow equations in the Appendix gives an alternate relation for τmax, which is in better agreement with the oil film interferometry measurements. Dimensional analysis is performed to gain insight into the empirical findings.

INVESTIGATION OF FLOW IN AN IDEALIZED CURVED ARTERY: COMPARATIVE STUDY USING CFD AND FSI WITH NEWTONIAN AND NON-NEWTONIAN FLUIDS

Artery curvatures, where disturbed flow patterns are expected, are preferred sites of formation of atherosclerosis. Experimental studies have shown that low and oscillating wall shear stress (WSS) plays an important role in the development and progression of atherosclerosis. Accurate estimation of these biomechanical parameters is important to assess the risk of atherosclerosis formation. The coupled effects of non-Newtonian behavior of blood and artery wall flexibility for the transient blood flow through an idealized curved coronary artery are investigated using computational fluid dynamics (CFD) as well as fluid–structure interaction (FSI) simulations. The choice of fluid model, Carreau and Newtonian, was found to impact the time averaged and minimum WSS values. The effects of wall deformation on time averaged wall shear tress were negligible. However, a comparison of temporal minima of WSS along the curvature showed significant variations between CFD and FSI simulations. Since low WSS values are crucial in the prediction of atherosclerosis development, it is concluded that both the non-Newtonian behavior of blood and the wall flexibility should be considered for computational studies.

WSSNet: Aortic Wall Shear Stress Estimation Using Deep Learning on 4D Flow MRI.

Wall shear stress (WSS) is an important contributor to vessel wall remodeling and atherosclerosis. However, image-based WSS estimation from 4D Flow MRI underestimates true WSS values, and the accuracy is dependent on spatial resolution, which is limited in 4D Flow MRI. To address this, we present a deep learning algorithm (WSSNet) to estimate WSS trained on aortic computational fluid dynamics (CFD) simulations. The 3D CFD velocity and coordinate point clouds were resampled into a 2D template of 48 × 93 points at two inward distances (randomly varied from 0.3 to 2.0 mm) from the vessel surface (“velocity sheets”). The algorithm was trained on 37 patient-specific geometries and velocity sheets. Results from 6 validation and test cases showed high accuracy against CFD WSS (mean absolute error 0.55 ± 0.60 Pa, relative error 4.34 ± 4.14%, 0.92 ± 0.05 Pearson correlation) and noisy synthetic 4D Flow MRI at 2.4 mm resolution (mean absolute error 0.99 ± 0.91 Pa, relative error 7.13 ± 6.27%, and 0.79 ± 0.10 Pearson correlation). Furthermore, the method was applied on in vivo 4D Flow MRI cases, effectively estimating WSS from standard clinical images. Compared with the existing parabolic fitting method, WSSNet estimates showed 2–3 × higher values, closer to CFD, and a Pearson correlation of 0.68 ± 0.12. This approach, considering both geometric and velocity information from the image, is capable of estimating spatiotemporal WSS with varying image resolution, and is more accurate than existing methods while still preserving the correct WSS pattern distribution.