Wall Shear Stress Distribution Research Articles

Distribution of wall shear stress for a bubbly flow in rod assembly

The work is devoted to the experimental study of the wall shear stress in the vertical assembly of rods in a square arrangement for a bubble flow. The measurements were carried out using the electrodiffusion technique. The data obtained during the experiment show that the void fraction has a significant effect on the flow structure near the walls of the rods. The change in wall shear stress with distance from the spacer grid does not occur monotonously, in contrast to the single-phase case.

Analysis of hemodynamic changes from aneurysm inception to large sizes.

While previous studies have identified many risk factors for the progression and rupture of cerebral aneurysms, the changes in aneurysm flow characteristics during its evolution are not fully understood. This work analyzes the changes in the aneurysm hemodynamic environment from its initial development to later stages when the aneurysm has substantially enlarged. A total of 88 aneurysms at four locations were studied with image based computational fluid dynamics (CFD). Two synthetic sequences representing the aneurysm geometry at three earlier stages were generated by shrinking the aneurysm sac while keeping the neck fixed or shrinking the neck simultaneously. The flow conditions were then quantitatively compared between these two modes of evolution. As aneurysms enlarged, the inflow rate increased in growing neck sequences, but decreased in fixed neck sequences. The inflow jet became more concentrated in both sequences. The mean aneurysm flow velocity and wall shear stress decreased in both sequences, but they decreased faster in enlarging aneurysms if the neck was fixed. Additionally, the intra-aneurysmal flows became more complex and more unstable, wall shear stress distribution became more oscillatory, and the area under low wall shear stress increased for both sequences. The evolution of flow characteristics of aneurysms with fixed and growing necks are different. The observed trends suggest that fixed neck aneurysms may evolve towards a flow environment characteristic of stable aneurysms faster than aneurysms with growing necks, which could also evolve towards a more disfavorable environment.

Numerical investigation of patient-specific thoracic aortic aneurysms and comparison with normal subject via computational fluid dynamics (CFD).

Vascular hemodynamics play an important role in cardiovascular diseases. This work aimed to investigate the effects of an increase in ascending aortic diameter (AAD) on hemodynamics throughout a cardiac cycle for real patients. In this study, two scans of thoracic aortic aneurysm (TAA) subject with different AADs (42.94mm and 48.01mm) and a scan of a normal subject (19.81mm) were analyzed to assess the effects of hemodynamics on the progression of TAA with the same flow rate. Real-patient aortic geometries were scanned by computed tomography angiography (CTA), and steady and pulsatile flow conditions were used to simulate real patient aortic geometries. Aortic arches were obtained from routine clinical scans. Computational fluid dynamics (CFD) simulations were performed with in vivo boundary conditions, and 3D Navier-Stokes equations were solved by a UDF (user-defined function) code defining a real cardiac cycle of one patient using Fourier series (FS). Wall shear stress (WSS) and pressure distributions were presented from normal subject to TAA cases. The results show that during the peak systolic phase pressure load increased by 18.56% from normal subject to TAA case 1 and by 23.8% from normal subject to TAA case 2 in the aneurysm region. It is concluded that although overall WSS increased in aneurysm cases but was low in dilatation areas. As a result, abnormal changes in WSS and higher pressure load may lead to rupture and risk of further dilatation. CFD simulations were highly effective to guide clinical predictions and assess the progress of aneurysm regions in case of early surgical intervention. Graphical abstract.

Flow organisation in laterally unconfined Rayleigh–Bénard turbulence

Abstract

Structure of stationary gas slug in an annular channel

Experimental study of liquid flow structure around a stationary gas slug in an annular channel was performed. The channel consisted of two concentric pipes with the diameters of 32 and 10 mm. Slug was produced in a downward liquid flow in an annular channel. Wall shear stress distribution was measured in both walls of the channel using an electrodiffusional technique. It was shown that the shape of the slug in the annular channel differs significantly from that in a circular pipe. The distribution of wall shear stress along the slug was presented for different angular positions in the channel.

Study of Extracted Geometry Effect on Patient-Specific Cerebral Aneurysm Model with Different Threshold Coefficient (Cthres)

The recent diagnostic assessment of cerebrovascular disease makes use of computational fluid dynamics (CFD) to quantify blood flow and determine the hemodynamics factors contributing to the disease from patient-specific models. However, compliant and anatomical patient-specific geometries are generally reconstructed from the medical images with different threshold values subjectively. Therefore, this paper tends to present the effect of extracted geometry with different threshold coefficient, Cthres by using a patient-specific cerebral aneurysm model. A set of medical images, digital subtraction angiography (DSA) images from the real patient diagnosed with internal carotid artery (ICA) aneurysm was obtained. The threshold value used to extract the patient-specific cerebral aneurysm geometry was calculated by using a simple threshold determination method. Several threshold coefficients, Cthres such as 0.2, 0.3, 0.4, 0.5 and 0.6 were employed in the image segmentation creating three-dimensional (3D) realistic arterial geometries that were then used for CFD simulation. As a result, we obtained that the volume of patient-specific cerebral aneurysm geometry decreases as the threshold coefficient, Cthres increases. There is dislocation of artery attached to the ICA aneurysm geometry occurred at a high threshold coefficient, Cthres. Besides, the physical changes also bring remarkable physiological effect on the wall shear stress (WSS) distribution and velocity flow field at patient-specific cerebral aneurysm geometry reconstructed with different threshold coefficient, Cthres.

Effects of different positions of intravascular stent implantation in stenosed vessels on in-stent restenosis: An experimental and numerical simulation study

Percutaneous coronary intervention (PCI) has been widely used in the treatment of atherosclerosis, while in-stent restenosis (ISR) has not been completely resolved. Studies have shown that changes in intravascular mechanical environment are related to ISR. Hence, an in-depth understanding of the effects of stent intervention on vascular mechanics is important for clinically optimizing stent implantation and relieving ISR. Nine rabbits with stenotic carotid artery were collected by balloon injury. Intravascular stents were implanted into different longitudinal positions (proximal, middle and distal relative to the stenotic area) of the stenotic vessels for numerical simulations. Optical coherence tomography (OCT) scanning was performed to reconstruct the three-dimensional configuration of the stented carotid artery and blood flow velocity waveforms were collected by Doppler ultrasound. The numerical simulations were performed through direct solution of Naiver-Stokes equation in ANSYS. Results showed that the distributions of time-averaged wall shear stress (TAWSS), oscillating shear index (OSI) and relative residual time (RRT) in near-end segment were distinctively different from other regions of the stent which considered to promote restenosis for all three models. Spearman rank-correlation analysis showed a significant correlation between hemodynamic descriptors and the stent longitudinal positions (rTAWSS = -0.718, rOSI = 0.898, rRRT = 0.818, p < 0.01). Histology results of the near-end segment showed neointima thickening deepened with the longitudinal positions of stent which was consistent with the numerical simulations. The results suggest that stent implantation can promote restenosis at the near-end segment. As the stenting position moves to distal end, the impact on ISR is more significant.

Computational fluid dynamics of internal mammary artery-left anterior descending artery anastomoses.

The aim of this study was to elucidate the remodelling of the internal mammary artery (IMA)-left anterior descending artery anastomosis and compare 2 different anastomosis techniques (end-to-side versus side-to-side) using computational fluid dynamics. This study included 9 patients. Computed tomography (CT) angiography was performed immediately after coronary artery bypass grafting (CABG) and at 3-6 months later. The computational fluid dynamics models were made using the CT data. The pulsatile 3-dimensional blood flow was achieved with the finite volume method to evaluate the postoperative morphological and haemodynamic changes at the anastomosis in each patient. Flow velocity distribution, wall shear stress (WSS) and its fluctuation oscillatory shear index were measured. No early or mid-term graft occlusion was observed in the study series. In the side-to-side anastomosis, pouch formation at the distal end of IMA caused a vortex flow with low WSS immediately after CABG. However, at 3-6 months after surgery, this pouch disappeared. As a result, the laminar straight flow with uniform WSS distribution was achieved inside the anastomosis. In the end-to-side anastomosis, the anastomosis shape was remodelled, resulting in a laminar flow pattern with uniform WSS distribution. A patchy high oscillatory shear index was detected at the IMA wall on the top of anastomosis in either anastomosis techniques immediately after the surgery, but it disappeared at 3-6 months after surgery. Regardless of the anastomosis technique used, a successful remodelling of the IMA-left anterior descending artery anastomosis shape was achieved a few months after surgery, resulting in a straightforward flow streamline, with uniform WSS distribution and minimal oscillatory shear index.

Evaluation of magnetic resonance angiography as a possible alternative to rotational angiography or computed tomography angiography for assessing cerebrovascular computational fluid dynamics.

The aim of this study was to conduct a flow experiment using a cerebrovascular phantom and investigate whether magnetic resonance angiography (MRA) could replace three-dimensional rotational angiography (RA) and computed tomography angiography (CTA) to construct vascular models for computational fluid dynamics (CFD). We performed MRA and 3D cine phase-contrast (PC) MR imaging with a silicone cerebrovascular phantom of an internal carotid artery-posterior communicating artery aneurysm with blood-mimicking fluid, and controlled flow with a flowmeter. We also obtained RA and CTA data for the phantom. Four analysts constructed vascular models based on the three different modalities. These 12 constructed models used flow information based on 3D cine PC MR imaging for CFD. We compared RA-, CTA-, MRA-based CFD results using the micro-CT-based CFD result as the criterion standard to investigate whether MRA-based CFD was not inferior to RA- or CTA-based CFD. We also analyzed the inter-analyst variability. Wall shear stress (WSS) distributions and streamlines of RA- or MRA-based CFD and those of micro-CT-based CFD were similar, but the vascular models and WSS values were different. Accuracy in measurements of blood vessel diameter, cross-sectional maximum velocity, and spatially averaged WSS was the highest for RA-based CFD, followed by MRA-based and CTA-based CFD using micro-CT-based CFD result as the reference. Except maximum velocity from CTA, all other parameters had good inter-analyst agreement using different modalities. The results demonstrated that non-invasive MRA can be used for cerebrovascular CFD models with good inter-analyst agreements.

High Wall Shear Stress Is Related to Atherosclerotic Plaque Rupture in the Aortic Arch of Patients with Cardiovascular Disease: A Study with Computational Fluid Dynamics Model and Non-Obstructive General Angioscopy.

Aims: Wall shear stress (WSS) has been considered a major determinant of aortic atherosclerosis. Recently, non-obstructive general angioscopy (NOGA) was developed to visualize various atherosclerotic pathologies, including in vivo ruptured plaque (RP) in the aorta. However, the relationship between aortic RP and WSS distribution within the aortic wall is unclear. This study aimed to investigate the relationship between aortic NOGA-derived RP and the stereographic distribution of WSS by computational fluid dynamics (CFD) modeling using three-dimensional computed tomography (3D-CT) angiography. Methods: We investigated 45 consecutive patients who underwent 3D-CT before coronary angiography and NOGA during coronary angiography. WSS in the aortic arch was measured by CFD analysis based on the finite element method using uniform inlet and outlet flow conditions. Aortic RP was detected by NOGA. Results: Patients with a distinct RP showed a significantly higher maximum WSS value in the aortic arch than those without aortic RP (56.2±30.6 Pa vs 36.2±19.8 Pa, p =0.017), no significant difference was noted in the mean WSS between those with and without aortic RP. In a multivariate logistic regression analysis, the presence of a maximum WSS value more than a specific value was a significant predictor of aortic RP (odds ratio 7.21, 95% confidence interval 1.78-37.1, p =0.005). Conclusions: Aortic RP detected by NOGA was strongly associated with a higher maximum WSS in the aortic arch derived by CFD using 3D-CT. The maximum WSS value may have an important role in the underlying mechanism of not only aortic atherosclerosis, but also aortic RP.

Blood flow simulations in the pulmonary bifurcation in relation to adult patients with repaired tetralogy of Fallot

Understanding the haemodynamic environment of the pulmonary bifurcation is important in adults with repaired conotruncal congenital heart disease. In these patients, dysfunction of the pulmonary valve and narrowing of the branch pulmonary arteries are common and can have serious clinical consequences. The aim of this study was to numerically investigate the underlying blood flow characteristics in the pulmonary trunk under a range of simplified conditions. For that, an in-depth analysis was conducted in idealised two-dimensional geometries that facilitate parametric investigation of healthy and abnormal conditions. Subtle variations in morphology influenced the haemodynamic environment and wall shear stress distribution. The pressure in the left pulmonary artery was generally higher than that in the right and main arteries, but was markedly reduced in the presence of a local stenosis. Different downstream pressure conditions altered the branch flow ratio, from 50:50% to more realistic 60:40% ratios in the right and left pulmonary artery, respectively. Despite some simplifications, this study highlights some previously undocumented aspects of the flow in bifurcating geometries, by clarifying the role of the stagnation point location on wall shear stress and differential branch pressures. In addition, measurements of the mean pressure ratios in the pulmonary bifurcation are discussed in the context of a new haemodynamic index which could potentially contribute to the assessment of left pulmonary artery stenosis in tetralogy of Fallot patients. Further studies are required to confirm the results in patient-specific models with personalised physiological flow conditions.

Hemodynamic Data Assimilation in a\xa0Subject-specific Circle of Willis Geometry

PurposeThe anatomy of the circle of Willis (CoW), the brain’s main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations.MethodsTo the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF).ResultsQuantitative evaluation shows a considerable reduction (up to 90%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone.ConclusionThis study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.

Computational modelling for the spiral flow in umbilical arteries with different systole/diastole flow velocity ratios

The systole/diastole (S/D) flow velocity ratios in umbilical arteries (UAs) have been used to assess the health status of the feto-placental circulation, yet its connection to the morphology of UAs, specifically its coiling pattern remains unclear. Spiral flow induces unbalanced wall shear stress (WSS) distribution in UAs, and may contribute to the uneven arterial wall thickness, and the chirality. In this paper, we use a 3D computational fluid dynamics (CFD) technique to quantify the wall shear stress (WSS) in UA models of two configurations, i.e. at 0.17 and 0.50 spirals per centimeter, to represent normo- and hyper-coiling, respectively. For CFD simulations we use two different S/D ratios (3.02 and 5.70) revealed from the ultrasonography waveforms of a normal and an intrauterine growth restriction (IUGR) case. We found that more coils in the UA model enhanced WSS throughout a cardiac cycle (up to 24%) with the same inflow condition. In addition, time-averaged WSS are generally increased and more uneven in the hyper-coiling model. We suggest that the large WSS difference between the peak systole and end diastole (62% higher in the IURG case than the normal case) may induce uneven stenosis distribution at UAs, and contribute to UA chirality.

An Improved Immersed Boundary Method for Simulating Flow Hydrodynamics in Streams with Complex Terrains

Three-dimensional (3D) computational fluid dynamic (CFD) simulations have gained substantial popularity in recent years for stream flow modelling. The complex terrain in streams is usually represented by a 3D mesh conforming to the terrain geometry. Such terrain-conforming meshes are time-consuming to generate. In this work, an immersed boundary method is developed in an existing terrain-conforming CFD model named U2RANS as an alternative, in which terrains are represented implicitly in the Cartesian background mesh. An improved two-layer wall function is proposed in the framework of the k-ε turbulence model, with the aim of producing accurate and smooth wall shear stress distribution and paving the way for future model development on sediment transport and scour modeling. The improvement overcomes the inherent discontinuity and nonlinearity of the two-layer velocity profile, which causes error in the estimation of shear velocity. The new algorithm utilizes a distance control on the image point in immersed boundary method and a modification of velocity prediction in the laminar layer. The improved immersed boundary method is tested with 1D, 2D, and 3D cases, and comparisons with flume experiments show promising results.

How patient-specific do internal carotid artery inflow rates need to be for computational fluid dynamics of cerebral aneurysms?

BackgroundComputational fluid dynamics (CFD) has become a popular tool for studying ‘patient-specific’ blood flow dynamics in cerebral aneurysms; however, rarely are the inflow boundary conditions patient-specific. We aimed to test...

Hemodynamic conditions that favor bleb formation in cerebral aneurysms

BackgroundAlthough it is generally believed that blebs represent weaker spots in the walls of intracranial aneurysms (IAs), it is largely unknown which aneurysm characteristics favor their development.ObjectiveTo investigate possible associations...

Formation of Vortices in Idealised Branching Vessels: A CFD Benchmark Study.

Atherosclerosis preferentially occurs near the junction of branching vessels, where blood recirculation tends to occur (Malek et al. in J Am Med Assoc 282(21):2035-2042, 1999, https://doi.org/10.1001/jama.282.21.2035 ). For decades, CFD has been used to predict flow patterns such as separation and recirculation zones in hemodynamic models, but those predictions have rarely been validated with experimental data. In the context of verification and validation (V&V), we first conduct a CFD benchmark calculation that reproduces the vortex detection experiments of Karino and Goldsmith (1980) with idealised branching blood vessels (Karino and Goldsmith in Trans. Am. Soc. Artif. Internal Organs 26:500-506, 1980). The critical conditions for the formation of recirculation vortices, the so-called critical Reynolds numbers, are the main parameters for comparison with the experimental data to demonstrate the credibility of the CFD workflow. We then characterise the wall shear stresses and develop a surrogate model for the size of formed vortices. An automated parametric study generating more than 12,000 CFD simulations was performed, sweeping the geometries and flow conditions found in the experiments by Karino and Goldsmith. The flow conditions were restricted to steady-state laminar flow, with a range of inflow Reynolds numbers up to 350, with various flow ratios between the main branch outlet and side branch outlet. The side branch diameter was scaled relative to the main branch diameter, ranging from 1.05/3 to 3/3; and the branching angles ranged in size from [Formula: see text] to [Formula: see text]. Recirculation vortices were detected by the inversion of the velocity vector at certain locations, as well as by the inversion of the wall shear stress (WSS) vector. The CFD simulations demonstrated good agreement with the experimental data on the critical Reynolds numbers. The spatial distributions of WSS on each branch were analysed to identify potential regions of disease. Once a vortex is formed, the size of the vortex increases by the square root of the Reynolds number. The CFD data was fitted to a surrogate model that accurately predicts the vortex size without the need to run computationally more expensive CFD simulations. This benchmark study validates the CFD simulation of vortex detection in idealised branching vessels under comprehensive flow conditions. This work also proposes a surrogate model for the size of the vortex, which could reduce the computational requirements in the studies related to branching vessels and complex vascular systems.

Numerical study of bifurcation blood flows using three different non-Newtonian constitutive models

In this work, a variational multiscale finite element formulation is used to study bifurcation flows of non-Newtonian fluids, using a representative simplified Carotid Artery geometry. In particular, the flow pattern and wall shear stress (WSS) computed using power-law, Cross, and Carreau–Yasuda models, are assessed. First, the formulation is validated by contrasting simulations of a benchmark test for bifurcation flows reported in the literature. After that, a study of blood flow through the carotid artery is presented. Hemodynamics conditions aimed to describe the flow behavior from diastole to systole of the cardiac cycle for healthy arteries and two specific conditions (60% carotid stenosis due to atherosclerosis and 20% increased bifurcation angle due to aging), are specifically analyzed. For each condition, the hemodynamics present different velocity fields that lead to distinctive distribution of WSS enable us to classified three regions, depending on their magnitude: low-WSS, medium-WSS and high-WSS. Results show that power-law flows predict lower wall shear stresses, especially in sections where geometry concentrates stresses, compared to those predicted using Cross and Carreau–Yasuda models. Overall, low-WSS are usually present in zones where stenosis develops even in healthy arteries, however, both geometries lead to a decrease of WSS magnitude in low-WSS regions, increasing the risk factor associated with plaque building.

Enhanced wall shear stress prevents obstruction by astrocytes in ventricular catheters.

The treatment of hydrocephalus often involves the placement of a shunt catheter into the cerebrospinal ventricular space, though such ventricular catheters often fail by tissue obstruction. While diverse cell types contribute to the obstruction, astrocytes are believed to contribute to late catheter failure that can occur months after shunt insertion. Using in vitro microfluidic cultures of astrocytes, we show that applied fluid shear stress leads to a decrease of cell confluency and the loss of their typical stellate cell morphology. Furthermore, we show that astrocytes exposed to moderate shear stress for an extended period of time are detached more easily upon suddenly imposed high fluid shear stress. In light of these findings and examining the range of values of wall shear stress in a typical ventricular catheter through computational fluid dynamics (CFD) simulation, we find that the typical geometry of ventricular catheters has low wall shear stress zones that can favour the growth and adhesion of astrocytes, thus promoting obstruction. Using high-precision direct flow visualization and CFD simulations, we discover that the catheter flow can be formulated as a network of Poiseuille flows. Based on this observation, we leverage a Poiseuille network model to optimize ventricular catheter design such that the distribution of wall shear stress is above a critical threshold to minimize astrocyte adhesion and growth. Using this approach, we also suggest a novel design principle that not only optimizes the wall shear stress distribution but also eliminates a stagnation zone with low wall shear stress, which is common to current ventricular catheters.

Experimental Assessment of Two Non-Contrast MRI Sequences Used for Computational Fluid Dynamics: Investigation of Consistency Between Techniques

PurposeRecent studies have noted a degree of variance between the geometries segmented by different groups from 3D medical images that are used in computational fluid dynamics (CFD) simulations of patient-specific cardiovascular systems. The aim of this study was to determine if the applied sequence of magnetic resonance imaging (MRI) also introduced observable variance in CFD results.MethodsUsing a series of phantoms MR images of vessels of known diameter were assessed for the time-of-flight and multi-echo data image combination sequences. Following this, patient images of arterio-venous fistulas were acquired using the same sequences. Comparisons of geometry were made using the phantom and patient images, and of wall shear stress quantities using the CFD results from the patient images.ResultsPhantom images showed deviations in diameter between 0 and 15% between the sequences, depending on vessel diameter. Patient images showed different geometrical features such as narrowings that were not present on both sequences. Distributions of wall shear stress (WSS) quantities differed from simulations between the geometries obtained from the sequences.ConclusionIn conclusion, choosing different MRI sequences resulted in slightly different geometries of the same anatomy, which led to compounded errors in WSS quantities from CFD simulation.