Wall Shear Stress Vector Research Articles

Theory for electrodiffusional wall shear stress measurement by directionally sensitive twin semicircular probe

This study investigates the theoretical aspects of mass transport at the surface of a twin semicircular electrodiffusion probe tailored to measure the magnitude and direction of near-wall fluid flows. A critical aspect of this research is the development of a theoretical framework that facilitates experimental measurements by analytically relating measured electric currents to the wall shear stress vector. Central to the study is the derivation of analytical expressions for the mass transfer coefficients of the front and rear segments of the probe, which are essential for quantifying near-wall hydrodynamics. Validation of these analytical relations is achieved through numerical solutions of the convection–diffusion equation, providing a robust confirmation of the underlying theory. A comprehensive procedure for experimental data processing is proposed, taking into account both frontal and reverse flow conditions across the probe. In addition, a sensitivity analysis of the twin semicircular probe is performed. This analysis focuses on the response of current ratios to changes in the flow direction, an aspect critical to understanding the operational performance of the probe. The results of this analysis are compared to the characteristics of two-segment strip probes, highlighting the distinct sensitivity nuances of the twin semicircular probe. Our findings provide insight into the optimal application of this probe in various fluid dynamics scenarios.

Dynamic Wall Shear Stress Measurement Using Event-Based 3D Particle Tracking

We describe the implementation of a 3d Lagrangian particle tracking (LPT) system based on event-based vision (EBV) sensors and demonstrate its application for the near-wall characterization of a turbulent boundary layer (TBL) in air. The viscous sublayer of the TBL is illuminated by a thin light sheet that grazes the surface of a glass window inserted into the flat wall of the wind tunnel wall. The data simultaneously captured by three synchronized EBV-cameras is used to reconstruct the 3d particle tracks within 0.4 mm of the wall on a field of view of 12.0 mm by 7.5 mm. The velocity and position of particles within the viscous sub-layer permit the estimation of the local, unsteady wall shear stress vector under the assumption of linearity between particle velocity and wall shear stress. Thereby, 2d distributions and higher order statistics of the unsteady wall shear stress are obtained. The systematic underestimation of the spanwise shear stress fluctuation can be explained on the basis of DNS data; a methodology for its mitigation is proposed. The employed EBV hardware coupled with suited LPT algorithms provide data quality on par with currently used, considerably more expensive, high-speed framing cameras.

Evaluation of the shrinkage process of a neck remnant after stent-coil treatment of a cerebral aneurysm using silent magnetic resonance angiography and computational fluid dynamics analysis: illustrative case.

Silent magnetic resonance angiography (MRA) mitigates metal artifacts, facilitating clear visualization of neck remnants after stent and coil embolization of cerebral aneurysms. This study aims to scrutinize hemodynamics at the neck remnant by employing silent MRA and computational fluid dynamics. The authors longitudinally tracked images of a partially thrombosed anterior communicating artery aneurysm's neck remnant, which had been treated with stent-assisted coil embolization, using silent MRA over a decade. Computational fluid dynamics delineated the neck remnant's reduction process, evaluating hemodynamic parameters such as flow rate, wall shear stress magnitude and vector, and streamlines. The neck remnant exhibited diminishing surface area, volume, neck size, dome depth, and aspect ratio. Its reduction correlated with a decline in the flow rate ratio of the remnant dome to the inflow parent artery. Analysis delineated regions within the contracting neck remnant characterized by consistently low average wall shear stress magnitude and variation, accompanied by notable variations in wall shear stress vector directionality. Evaluation of neck remnants after stent-coil embolization is possible through silent MRA and computational fluid dynamics. Predicting the neck remnant reduction may be achievable through hemodynamic parameter analysis.

Abstract TMP4: Computational Fluid Dynamics Analysis Offers Novel Preoperative Insights for Unruptured Cerebral Aneurysms - Predicting Aneurysm Wall Thinning and Thickening -

Objective: The preoperative identification of thin-walled regions (TIWRs) and thick-walled regions (TKWRs) in cerebral aneurysms can contribute to enhancing surgical safety. Our recent computational fluid dynamics (CFD) analysis of cerebral aneurysms has demonstrated that the wall shear stress vector cycle variation (WSSVV) and the oscillatory shear index (OSI) can potentially predict TIWRs and TKWRs. This study aims to validate the accuracy of using WSSVV and the OSI to identify these areas and to report on their effectiveness in actual surgeries. Methods: Our cohort comprised 42 patients who underwent cerebral aneurysm clipping surgery at our hospital from January 2019 to September 2022. CFD analysis was performed using Hemoscope. We defined suspected TIWRs as blue regions and suspected TKWRs as red regions on both color maps. We evaluated the positive predictive value (PPV) by comparing these preoperative suspected areas with actual thin and thick areas determined intraoperatively under surgical microscopic observation. Results: Of the 42 patients, 15 were male and 27 were female. The average age was 63 years, and the average aneurysm size was 5.9 mm. The location of the aneurysms was the middle cerebral artery in 18 cases, the internal carotid artery in 15 cases, the anterior communicating artery in 8 cases, and the basilar artery in 1 case. WSSVV yielded a PPV of 83% for TIWRs and a PPV of 78% for TKWRs. In comparison, the OSI demonstrated a PPV of 77% for TIWRs and 76% for TKWRs. Spearman's rank correlation analysis revealed a strong correlation between WSSVV and the OSI; the correlation coefficient was 0.883 (p-value < 0.001). Conclusions: CFD analysis of unruptured cerebral aneurysms could be used to predict TIWRs and TKWRs using both WSSVV and the OSI with an accuracy of approximately 80%. The preoperative evaluation of the wall condition using CFD analysis appears to be highly reliable and is likely to contribute to the safety of cerebral aneurysm surgery.

Predicting Morphological Changes to Vessel Walls Adjacent to Unruptured Cerebral Aneurysms Using Computational Fluid Dynamics.

Objective This study compared intraoperative findings with preoperative computed tomography angiography (CTA) and computational fluid dynamics (CFD) analysis of perianeurysmal findings for the indication of possible vessel wall thinning. Materials and Methods Participants comprised 38 patients with unruptured middle cerebral artery aneurysms treated by surgical clipping at our hospital between May 2020 and April 2021. We defined parent artery radiation sign (PARS) as the presence of each of the following three findings in CFD analysis based on preoperative CTA: (1) impingement of the stream line on the outer parent vessel wall of the aneurysm; (2) radiation of wall shear stress vectors outwards from the same site; and (3) increased wall pressure compared with the surrounding area. CFD analysis showing PARS was compared with intraoperative findings. Results In all nine cases with PARS, no morphological abnormalities were found in the same area on CTA. However, intraoperative findings showed thinning of the parent artery wall in one of the nine cases and formation of a very small mass in three cases, differing from CTA findings. All nine patients underwent additional clipping and/or wrapping and coating at the site of PARS. Conclusion Detecting thinning of the vessel wall or the presence of a microaneurysm may be difficult in endovascular therapy, which is based on the visualization of the vessel lumen. CFD analysis suggests the necessity of confirming findings for the vessel wall around an aneurysm by direct manipulation, as the presence of PARS may indicate partial thinning of the vessel wall or formation of a microaneurysm.

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

AbstractIn 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.

Longitudinal wall shear stress evaluation using centerline projection approach in the numerical simulations of the patient-based carotid artery

In this numerical study, areas of the carotid bifurcation and of a distal stenosis in the internal carotid artery are closely observed to evaluate the patient’s current risks of ischemic stroke. An indicator for the vessel wall defects is the stress exerted by blood on the vessel tissue, typically expressed by the amplitude of the wall shear stress vector (WSS) and its oscillatory shear index. To detect negative shear stresses corresponding with reversal flow, we perform orientation-based shear evaluation. We investigate the longitudinal component of the wall shear vector, where tangential vectors aligned longitudinally with the vessel are necessary. However, resulting from imaging segmentation resolution of patients’ computed tomography angiography scans and stenotic regions, the geometry model’s mesh is non-smooth on its surface areas and the automatically generated tangential vector field is discontinuous and multi-directional, making an interpretation of our orientation-based risk indicators unreliable. We improve the evaluation of longitudinal shear stress by applying the projection of the vessel’s centerline to the surface to construct smooth tangential field aligned longitudinally with the vessel. We validate our approach for the longitudinal WSS component and the corresponding oscillatory index by comparing them to results obtained using automatically generated tangents in both rigid and elastic vessel modeling and to amplitude-based indicators. We present the major benefit of our longitudinal WSS evaluation based on its directionality for the cardiovascular risk assessment, which is the detection of negative WSS indicating persistent reversal or transverse flow. This is impossible in the case of the amplitude-based WSS.

Divergence of the normalized wall shear stress as an effective computational template of low-density lipoprotein polarization at the arterial blood-vessel wall interface

Background and ObjectiveNear-wall transport of low-density lipoproteins (LDL) in arteries plays a relevant role in the initiation of atherosclerosis. Although it can be modelled in silico by coupling the Navier–Stokes equations with the 3D advection-diffusion (AD) equation, the associated computational cost is high. As wall shear stress (WSS) represents a first-order approximation of the near-wall velocity in arteries, we aimed at identifying computationally convenient WSS-based quantities to infer LDL near-wall transport based on the underlying near-wall hemodynamics in five models of three human arterial districts (aorta, carotid bifurcations, coronary arteries). The simulated LDL transport and its WSS-based surrogates were qualitatively compared with in vivo longitudinal measurements of wall thickness growth on the coronary artery models. MethodsNumerical simulations of blood flow coupled with AD equations for LDL transport and blood-wall transfer were performed. The co-localization of the simulated LDL concentration polarization patterns with luminal surface areas characterized by low cycle-average WSS, near-wall flow stagnation and WSS attracting patterns was quantitatively assessed by the similarity index (SI). In detail, the latter two represent features of the WSS topological skeleton, obtained respectively through the Lagrangian tracking of surface-born particles, and the Eulerian analysis of the divergence of the normalized cycle-average WSS vector field. ResultsConvergence of the solution of the AD problem required the simulation of 3 (coronary artery) to 10 (aorta) additional cardiac cycles with respect to the Navier-Stokes problem. Co-localization results underlined that WSS topological skeleton features indicating near-wall flow stagnation and WSS attracting patterns identified LDL concentration polarization profiles more effectively than low WSS, as indicated by higher SI values (SI range: 0.17–0.50 for low WSS; 0.24–0.57 for WSS topological skeleton features). Moreover, the correspondence between the simulated LDL uptake and WSS-based quantities profiles with the in vivo measured wall thickness growth in coronary arteries appears promising. ConclusionsThe recently introduced Eulerian approach for identifying WSS attracting patterns from the divergence of normalized WSS provides a computationally affordable template of the LDL polarization at the arterial blood-wall interface without simulating the AD problem. It thus candidates as an effective biomechanical tool for elucidating the mechanistic link amongst LDL transfer at the arterial blood-wall interface, WSS and atherogenesis.

Vortex formation and associated aneurysmogenic transverse rotational shear stress near the apex of wide-angle cerebral bifurcations.

Aneurysm formation preferentially occurs at the site of wide-angle cerebral arterial bifurcations, which were recently shown to have a high longitudinal positive wall shear stress (WSS) gradient that promotes aneurysm formation. The authors sought to explore the other components of the hemodynamic environment that are altered with increasing bifurcation angle in the apical region and the effects of these components on WSS patterns on the vessel wall that may modulate aneurysm genesis and progression. Parametric models of symmetrical and asymmetrical bifurcations were created with increasing bifurcation angles (45°-240°), and 3D rotational angiography models of 13 middle cerebral artery (MCA) bifurcations (7 aneurysmal, 6 controls) were analyzed using computational fluid dynamics. For aneurysmal bifurcations, the aneurysm was digitally removed to uncover hemodynamics at the apex. WSS vectors along cross-sectional planes distal to the bifurcation apex were decomposed as orthogonal projections to the cut plane into longitudinal and transverse (tangential to the cross-sectional plane) components. Transverse rotational WSS (TRWSS) and TRWSS gradients (TRWSSGs) were sampled and evaluated at the apex and immediately distal from the apex. In parametric models, increased bifurcation angle was associated with transverse flow vortex formation with emergence of an associated apical high TRWSS with highly aneurysmogenic positive TRWSSGs. While TRWSS decayed rapidly away from the apex in narrow-angle bifurcations, it remained greatly elevated for many radii downstream in aneurysm-prone wider bifurcations. In asymmetrical bifurcations, TRWSS was higher on the aneurysm-prone daughter vessel associated with the wider angle. Patient-derived models with aneurysmal bifurcations had wider angles (149.33° ± 12.56° vs 98.17° ± 8.67°, p < 0.001), with significantly higher maximum TRWSS (1.37 ± 0.67 vs 0.48 ± 0.23 Pa, p = 0.01) and TRWSSG (1.78 ± 0.92 vs 0.76 ± 0.50 Pa/mm, p = 0.03) compared to control nonaneurysmal bifurcations. Wider vascular bifurcations are associated with a novel and to the authors' knowledge previously undescribed transverse component rotational wall shear stress associated with a positive (aneurysmogenic) spatial gradient. The resulting hemodynamic insult, demonstrated in both parametric models and patient-based anatomy, is noted to decay rapidly away from the protection of the medial pad in healthy narrow-angle bifurcations but remain elevated distally downstream of wide-angle aneurysm-prone bifurcations. This TRWSS serves as a new contribution to the hemodynamic environment favoring aneurysm formation and progression at wide cerebral bifurcations and may have clinical implications favoring interventions that reduce bifurcation angle.

Significance of aortoseptal angle anomalies to left ventricular hemodynamics and subaortic stenosis: A numerical study

Discrete subaortic stenosis (DSS) is an obstructive cardiac disease caused by a membranous lesion in the left ventricular (LV) outflow tract (LVOT). Although its etiology is unknown, the higher prevalence of DSS in LVOT anatomies featuring a steep aortoseptal angle (AoSA) suggests a potential role for hemodynamics. Therefore, the objective of this study was to quantify the impact of AoSA steepening on the LV three-dimensional (3D) hemodynamic stress environment. A 3D LV model reconstructed from cardiac cine-magnetic resonance imaging was connected to four LVOT geometrical variations spanning the clinical AoSA range (115°-160°). LV hemodynamic stresses were characterized in terms of cycle-averaged pressure, temporal shear magnitude (TSM), and oscillatory shear index. The wall shear stress (WSS) topological skeleton was further analyzed by computing the scaled divergence of the WSS vector field. AoSA steepening caused an increasingly perturbed subaortic flow marked by LVOT flow skewness and complex 3D secondary flow patterns. These disturbances generated WSS overloads (>45% increase in TSM vs. 160° model) on the inferior LVOT wall, and increased WSS contraction (>66% decrease in WSS divergence vs. 160° model) in regions prone to DSS membrane formation. AoSA steepening generated substantial hemodynamic stress abnormalities in LVOT regions prone to DSS formation. Further studies are needed to assess the possible impact of such mechanical abnormalities on the tissue and cellular responses.

Hemodynamic factor evaluation using computational fluid dynamics analysis for de novo bleb formation in unruptured intracranial aneurysms

BackgroundAlthough bleb formation increases the risk of rupture of intracranial aneurysms, previous computational fluid dynamic (CFD) studies have been unable to identify robust causative hemodynamic factors, due to the morphological differences of prebleb aneurysm models and a small number of aneurysms with de novo bleb formation. This study investigated the influences of differences in the aneurysm-models and identify causative hemodynamic factors for de novo bleb formation.Materials and methodsCFD analysis was conducted on three aneurysm models, actual prebleb, postbleb, and virtual prebleb models of two unruptured aneurysms with de novo bleb formation. A new multipoint method was introduced in this study. We evenly distributed points with a 0.5-mm distance on the aneurysm surface of the actual prebleb models (146 and 152 points in the individual aneurysm, respectively), and we statistically compared hemodynamics at the points in the areas with and without bleb formation (19 and 279 points, respectively).ResultsVisually, blebs formed on an aneurysm surface area with similar hemodynamic characteristics in the actual and virtual prebleb models. Statistical analysis using the multipoint method revealed that the de novo bleb formation area was significantly correlated with high pressure (p < 0.001), low wall shear stress (WSS) (p < 0.001), and the center of divergent WSS vectors (p = 0.025).ConclusionsDe novo bleb formation in intracranial aneurysms may occur in areas associated with the combination of high pressure, low WSS, and the center of divergent WSS vectors. The multipoint method is useful for statistical analysis of hemodynamics in a limited number of aneurysms.

A learning-based approach for solving shear stress vector distribution from shear-sensitive liquid crystal coating images

A learning-based approach for solving wall shear stresses from Shear-Sensitive Liquid Crystal Coating (SSLCC) color images is presented in this paper. The approach is able to learn and establish the mapping relationship between the SSLCC color-change responses in different observation directions and the shear stress vectors, and then uses the mapping relationship to solve wall shear stress vectors from SSLCC color images. Experimental results show that the proposed approach can solve wall shear stress vectors using two or more SSLCC images, and even using only one image for symmetrical flow field. The accuracy of the approach using four or more observations is found to be comparable to that of the traditional multi-view Gauss curve fitting approach; the accuracy is slightly reduced when using two or fewer observations. The computational efficiency is significantly improved when compared with the traditional Gauss curve fitting approach, and the wall shear stress vectors can be solved in nearly real time. The learning-based approach has no strict requirements on illumination direction and observation directions and is therefore more flexible to use in practical wind tunnel measurement when compared with traditional liquid crystal-based methods.

Wall Shear Stress Topological Skeleton Analysis in Cardiovascular Flows: Methods and Applications

A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, and unstable/stable manifolds, consisting of contraction/expansion regions linking fixed points. Such an interest arises from its ability to reflect the presence of near-wall hemodynamic features associated with the onset and progression of vascular diseases. Over the years, Lagrangian-based and Eulerian-based post-processing techniques have been proposed aiming at identifying the topological skeleton features of the WSS. Here, the theoretical and methodological bases supporting the Lagrangian- and Eulerian-based methods currently used in the literature are reported and discussed, highlighting their application to cardiovascular flows. The final aim is to promote the use of WSS topological skeleton analysis in hemodynamic applications and to encourage its application in future mechanobiology studies in order to increase the chance of elucidating the mechanistic links between blood flow disturbances, vascular disease, and clinical observations.

Quantification of Oscillatory Shear Stress from Reciprocating CSF Motion on 4D Flow Imaging.

Oscillatory shear stress could not be directly measured in consideration of direction, although cerebrospinal fluid has repetitive movements synchronized with heartbeat. Our aim was to evaluate the important of oscillatory shear stress in the cerebral aqueduct and foramen magnum in idiopathic normal pressure hydrocephalus by comparing it with wall shear stress and the oscillatory shear index in patients with idiopathic normal pressure hydrocephalus. By means of the 4D flow application, oscillatory shear stress, wall shear stress, and the oscillatory shear index were measured in 41 patients with idiopathic normal pressure hydrocephalus, 23 with co-occurrence of idiopathic normal pressure hydrocephalus and Alzheimer-type dementia, and 9 age-matched controls. These shear stress parameters at the cerebral aqueduct were compared with apertures and stroke volumes at the foramen of Magendie and cerebral aqueduct. Two wall shear stress magnitude peaks during a heartbeat were changed to periodic oscillation by converting oscillatory shear stress. The mean oscillatory shear stress amplitude and time-averaged wall shear stress values at the dorsal and ventral regions of the cerebral aqueduct in the idiopathic normal pressure hydrocephalus groups were significantly higher than those in controls. Furthermore, those at the ventral region of the cerebral aqueduct in the idiopathic normal pressure hydrocephalus group were also significantly higher than those in the co-occurrence of idiopathic normal pressure hydrocephalus with Alzheimer-type dementia group. The oscillatory shear stress amplitude at the dorsal region of the cerebral aqueduct was significantly associated with foramen of Magendie diameters, whereas it was strongly associated with the stroke volume at the upper end of the cerebral aqueduct rather than that at the foramen of Magendie. Oscillatory shear stress, which reflects wall shear stress vector changes better than the conventional wall shear stress magnitude and the oscillatory shear index, can be directly measured on 4D flow MR imaging. Oscillatory shear stress at the cerebral aqueduct was considerably higher in patients with idiopathic normal pressure hydrocephalus.

Endothelial cells do not align with the mean wall shear stress vector.

The alignment of arterial endothelial cells (ECs) with the mean wall shear stress (WSS) vector is the prototypical example of their responsiveness to flow. However, evidence for this behaviour rests on experiments where many WSS metrics had the same orientation or where they were incompletely characterized. In the present study, we tested the phenomenon more rigorously. Aortic ECs were cultured in cylindrical wells on the platform of an orbital shaker. In this system, orientation would differ depending on the WSS metric to which the cells aligned. Variation in flow features and hence in possible orientations was further enhanced by altering the viscosity of the medium. Orientation of endothelial nuclei was compared with WSS characteristics obtained by computational fluid dynamics. At low mean WSS magnitudes, ECs aligned with the modal WSS vector, while at high mean WSS magnitudes they aligned so as to minimize the shear acting across their long axis (transverse WSS). Their failure to align with the mean WSS vector implies that other aspects of endothelial behaviour attributed to this metric require re-examination. The evolution of a mechanism for minimizing transverse WSS is consistent with it having detrimental effects on the cells and with its putative role in atherogenesis.

The Story of Wall Shear Stress in Coronary Artery Atherosclerosis: Biochemical Transport and Mechanotransduction.

Coronary artery atherosclerosis is a local, multifactorial, complex disease, and the leading cause of death in the US. Complex interactions between biochemical transport and biomechanical forces influence disease growth. Wall shear stress (WSS) affects coronary artery atherosclerosis by inducing endothelial cell mechanotransduction and by controlling the near-wall transport processes involved in atherosclerosis. Each of these processes is controlled by WSS differently and therefore has complicated the interpretation of WSS in atherosclerosis. In this paper, we present a comprehensive theory for WSS in atherosclerosis. First, a short review of shear stress-mediated mechanotransduction in atherosclerosis was presented. Next, subject-specific computational fluid dynamics (CFD) simulations were performed in ten coronary artery models of diseased and healthy subjects. Biochemical-specific mass transport models were developed to study low-density lipoprotein, nitric oxide, adenosine triphosphate, oxygen, monocyte chemoattractant protein-1, and monocyte transport. The transport results were compared with WSS vectors and WSS Lagrangian coherent structures (WSS LCS). High WSS magnitude protected against atherosclerosis by increasing the production or flux of atheroprotective biochemicals and decreasing the near-wall localization of atherogenic biochemicals. Low WSS magnitude promoted atherosclerosis by increasing atherogenic biochemical localization. Finally, the attracting WSS LCS's role was more complex where it promoted or prevented atherosclerosis based on different biochemicals. We present a summary of the different pathways by which WSS influences coronary artery atherosclerosis and compare different mechanotransduction and biotransport mechanisms.

Wall Shear Stress Topological Skeleton Independently Predicts Long-Term Restenosis After Carotid Bifurcation Endarterectomy

Wall Shear Stress (WSS) topological skeleton, composed by fixed points and the manifolds linking them, reflects the presence of blood flow features associated to adverse vascular response. However, the influence of WSS topological skeleton on vascular pathophysiology is still underexplored. This study aimed to identify direct associations between the WSS topological skeleton and markers of vascular disease from real-world clinical longitudinal data of long-term restenosis after carotid endarterectomy (CEA). Personalized computational hemodynamic simulations were performed on a cohort of 13 carotid models pre-CEA and at 1 month after CEA. At 60 months after CEA, intima-media thickness (IMT) was measured to detect long-term restenosis. The analysis of the WSS topological skeleton was carried out by applying a Eulerian method based on the WSS vector field divergence. To provide objective thresholds for WSS topological skeleton quantitative analysis, a computational hemodynamic dataset of 46 ostensibly healthy carotid bifurcation models was considered. CEA interventions did not completely restore physiological WSS topological skeleton features. Significant associations emerged between IMT at 60 months follow-up and the exposure to (1) high temporal variation of WSS contraction/expansion (R2 = 0.51, p < 0.05), and (2) high fixed point residence times, weighted by WSS contraction/expansion strength (R2 = 0.53, p < 0.05). These WSS topological skeleton features were statistically independent from the exposure to low WSS, a previously reported predictor of long-term restenosis, therefore representing different hemodynamic stimuli and potentially impacting differently the vascular response. This study confirms the direct association between WSS topological skeleton and markers of vascular disease, contributing to elucidate the mechanistic link between flow disturbances and clinical observations of vascular lesions.

On the calibration-free two-component wall-shear-stress measurement technique using dual-layer hot-films.

The wall shear stress vector is an important quantity in fluid mechanics and is difficult to be measured. In this work, we first demonstrate that the directional sensitivity (sensitivity to yaw angle α) of a flush-mount hot-film sensor is cos1/3α using theoretical and experimental methods. Based on the directional sensitivity, a local two-component wall-shear-stress measurement technique is proposed using a pair of un-calibrated dual-layer hot-film sensors positioned perpendicular to each other. This technique use the heat fluxes transferred from the sensors to the fluid to determine both the magnitude and the direction of the wall shear stress so that a calibration is not required. Experimental results demonstrate that this technique is feasible when the angle between the stress and the centerline of the sensor is within ±15°. This valid angle range can be potentially increased if the two sensors are positioned with an angle larger than 90°.

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.

Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD, each mode evolves with a fixed frequency and therefore DMD modes represent physically meaningful structures that are ranked based on their dynamics. The application of DMD to patient-specific cardiovascular flow data is challenging. First, the input flow rate is unsteady and pulsatile. Second, the flow topology can change significantly in different phases of the cardiac cycle. Finally, blood flow in patient-specific diseased arteries is complex and often chaotic. The objective of this study was to overcome these challenges using our proposed multistage dynamic mode decomposition with control (mDMDc) method and use this technique to study patient-specific blood flow physics. The inlet flow rate was considered as the controller input to the systems. Blood flow data were divided into different stages based on the inlet flow waveform and DMD with control was applied to each stage. The system was augmented to consider both velocity and wall shear stress (WSS) vector data, and therefore study the interaction between the coherent structures in velocity and near-wall coherent structures in WSS. First, it was shown that DMD modes can exactly represent the analytical Womersley solution for incompressible pulsatile flow in tubes. Next, our method was applied to image-based coronary artery stenosis and cerebral aneurysm models where complex blood flow patterns are anticipated. The flow patterns were studied using the mDMDc modes and the reconstruction errors were reported. Our augmented mDMDc framework could capture coherent structures in velocity and WSS with a fewer number of modes compared to the traditional DMD approach and demonstrated a close connection between the velocity and WSS modes.