Characterization and estimation of turbulence-related wall shear stress in patient-specific pulsatile blood flow

Morphometric and Hemodynamic Analysis of the Compressed Iliac Vein

PURPOSE

To investigate the relationship between the morphological structure and hemodynamic properties of the compressed iliac vein and explore the reason for the formation of thrombosis in the compressed iliac vein.

MATERIALS AND METHODS

A total of 11 patients with iliac vein compression syndrome (IVCS) were included in this study, and their iliac veins were reconstructed in 3 dimensions (3D). The morphological structures of the iliac veins (confluence angle, degree of stenosis) were analyzed based on the 3D model. Variations in the hemodynamic properties of the iliac vein were investigated at 4 typical moments in one cardiac cycle, and the relationship between the different morphological configurations and the pressure difference was investigated.

RESULTS

In the region of the compressed iliac vein, the blood flow velocity is accelerated and the pressure changes abruptly accompanied by the increase in pressure difference. Higher time averaged wall shear stress (TAWSS) and lower relative residence time (RRT) appeared in stenosis regions of compressed iliac vein, while TAWSS was low and RRT was large near the stenosis position. There was a strong positive correlation between the degree of stenosis and the pressure difference (r=0.894), and a positive correlation between the confluence angle of the iliac vein and the pressure difference (r=0.638).

CONCLUSION

The morphological structure of the compressed iliac vein has an obvious influence on the hemodynamic surroundings; the pressure difference becomes larger when the degree of stenosis and the confluence angle increase. The iliac vein luminal areas with low TAWSS and high RRT near the compressed location can impede blood flow and lead to accumulation of blood components, which may increase the risk of thrombosis formation and should be fully considered in the treatment of IVCS.

Effect of turbulence and viscosity models on wall shear stress derived biomarkers for aorta simulations

Ascending aorta simulations provide insight into patient-specific hemodynamic conditions. Numerous studies have assessed fluid biomarkers which show a potential to aid clinicians in the diagnosis process. Unfortunately, there exists a large disparity in the computational methodology used to model turbulence and viscosity. Recognizing this disparity, some authors focused on analysing the influence of either the turbulence or viscosity models on the biomarkers in order to quantify the importance of these model choices. However, no analysis has yet been done on their combined effect. In order to fully understand and quantify the effect of the computational methodology, an assessment of the combined effect of turbulence and viscosity model choice was performed. Our results show that (1) non-Newtonian viscosity has greater impact (2.9-5.0%) on wall shear stress than Large Eddy Simulation turbulence modelling (0.1-1.4%), (2) the contribution of non-Newtonian viscosity is amplified when combined with a subgrid-scale turbulence model, (3) wall shear stress is underestimated when considering Newtonian viscosity by 2.9-5.0% and (4) cycle-to-cycle variability can impact the results as much as the numerical model if insufficient cycles are performed. These results demonstrate that, when assessing the effect of computational methodologies, the resultant combined effect of the different modelling assumptions differs from the aggregated effect of the isolated modifications. Accurate aortic flow modelling requires non-Newtonian viscosity and Large Eddy Simulation turbulence modelling.

Toward a Mesoscopic Modeling Approach of Magnetohydrodynamic Blood Flow in Pathological Vessels: A Comprehensive Review

The investigation of magnetohydrodynamic (MHD) blood flow within configurations that are pertinent to the human anatomy holds significant importance in the realm of scientific inquiry because of its practical implications within the medical field. This article presents an exhaustive appraisal of the diverse applications of magnetohydrodynamics and their computational modeling in biological contexts. These applications are classified into two categories: simple flow and pulsatile flow. An alternative approach of traditional CFD methods called Lattice Boltzmann Method (LBM), a mesoscopic method based on kinetic theory, is introduced to solve complex problems, such as hemodynamics. The results show that the flow velocity reduces considerably by increasing the magnetic field intensity, and the flow separation area is minimized by the increase of magnetic field strength. The LBM with BGK collision model has shown good results in terms of precision. Finally, this literature review has revealed a number of potential avenues for further research. Suggestions for future works are proposed accordingly.

Clinical Use of Blood Flow Analysis through 4D-Flow Imaging in Aortic Valve Disease

Bicuspid aortic valve (BAV), which affects 1% of the general population, results from the abnormal fusion of the cusps of the aortic valve. BAV can lead to the dilatation of the aorta, aortic coarctation, development of aortic stenosis (AS), and aortic regurgitation. Surgical intervention is usually recommended for patients with BAV and bicuspid aortopathy. This review aims to examine 4D-flow imaging as a tool in cardiac magnetic resonance imaging for assessing abnormal blood flow and its clinical application in BAV and AS. We present a historical clinical approach summarizing evidence of abnormal blood flow in aortic valve disease. We highlight how abnormal flow patterns can contribute to the development of aortic dilatation and novel flow-based biomarkers that can be used for a better understanding of the disease progression.

Analysis of Turbulence Effects in a Patient-Specific Aorta with Aortic Valve Stenosis

Blood flow in the aorta is often assumed laminar, however aortic valve pathologies may induce transition to turbulence and our understanding of turbulence effects is incomplete. The aim of the study was to provide a detailed analysis of turbulence effects in aortic valve stenosis (AVS).

METHODS

Large-eddy simulation (LES) of flow through a patient-specific aorta with AVS was conducted. Magnetic resonance imaging (MRI) was performed and used for geometric reconstruction and patient-specific boundary conditions. Computed velocity field was compared with 4D flow MRI to check qualitative and quantitative consistency. The effect of turbulence was evaluated in terms of fluctuating kinetic energy, turbulence-related wall shear stress (WSS) and energy loss.

RESULTS

Our analysis suggested that turbulence was induced by a combination of a high velocity jet impinging on the arterial wall and a dilated ascending aorta which provided sufficient space for turbulence to develop. Turbulent WSS contributed to 40% of the total WSS in the ascending aorta and 38% in the entire aorta. Viscous and turbulent irreversible energy losses accounted for 3.9 and 2.7% of the total stroke work, respectively.

CONCLUSIONS

This study demonstrates the importance of turbulence in assessing aortic haemodynamics in a patient with AVS. Neglecting the turbulent contribution to WSS could potentially result in a significant underestimation of the total WSS. Further work is warranted to extend the analysis to more AVS cases and patients with other aortic valve diseases.

Effect of non-Newtonian fluid rheology on an arterial bypass graft: A numerical investigation guided by constructal design

In post-operative scenarios of arterial graft surgeries to bypass coronary artery stenosis, fluid dynamics plays a crucial role. Problems such as intimal hyperplasia have been related to fluid dynamics and wall shear stresses near the graft junction. This study focused on the question of the use of Newtonian and non-Newtonian models to represent blood in this type of problem in order to capture important flow features, as well as an analysis of the performance of geometry from the view of Constructive Theory. The objective of this study was to investigate the effects rheology on the steady-state flow and on the performance of a system consisting of an idealized version of a partially obstructed coronary artery and bypass graft. The Constructal Design Method was employed with two degrees of freedom: the ratio between bypass and artery diameters and the junction angle at the bypass inlet. The flow problem was solved numerically using the Finite Volume Method with blood modeled employing the Carreau equation for viscosity. The Computational Fluid Dynamics model associated with the Sparse Grid method generated eighteen response surfaces, each representing a severe stenosis degree of 75% for specific combinations of rheological parameters, dimensionless viscosity ratio, Carreau number and flow index at two distinct Reynolds numbers of 150 and 250. There was a considerable dependence of the pressure drop on rheological parameters. For the two Reynolds numbers studied, the Newtonian case presented the lowest value of the dimensionless pressure drop, suggesting that the choice of applying Newtonian blood may underestimate the value of pressure drop in the system by about 12.4% (Re =150) and 7.8% (Re = 250). Even so, results demonstrated that non-Newtonian rheological parameters did not influence either the shape of the response surfaces or the optimum bypass geometry, which consisted of a diameter ratio of 1 and junction angle of 30°. However, the viscosity ratio and the flow index had the greatest impact on pressure drop, recirculation zones and wall shear stress. Rheological parameters also affected the recirculation zones downstream of stenosis, where intimal hyperplasia is more prevalent. Newtonian and most non-Newtonian results had similar wall shear stresses, except for the non-Newtonian case with high viscosity ratio. In the view of Constructal Design, the geometry of best performance was independent of the rheological model. However, rheology played an important role on pressure drop and flow dynamics, allowing the prediction of recirculation zones that were not captured by a Newtonian model.

Exploring the Relationships Between Hemodynamic Stresses in the Carotid Arteries

Background: Atherosclerosis manifests as a focal disease, often affecting areas with complex hemodynamics such as the carotid bifurcation. The magnitude and regularity of the hemodynamic shear stresses acting on the vessel wall are thought to generate risk patterns unique to each patient and play a role in the pathogenesis of atherosclerosis. The involvement of different expressions of shear stress in the pathogenesis of carotid atherosclerosis highlights the need to characterize and compare the differential impact of the various expressions of shear stress in the atherosclerotic carotid bifurcation. Therefore, the aim of this study is to characterize and compare hemodynamic wall shear stresses (WSS) in the carotid arteries of subjects with asymptomatic atherosclerotic plaques. Shear stresses were also compared against vessel diameter and bifurcation angle to examine the relationships with the geometry of the carotid bifurcation. Methods: 4D Flow MRI and contrast-enhanced MRA data were acquired for 245 subjects with atherosclerotic plaques of at least 2.7 mm in conjunction with the Swedish CArdioPulmonary bioImage Study (SCAPIS). Following automatic segmentation and geometric analysis, time-resolved WSS and near-wall turbulent kinetic energy (nwTKE) were derived from the 4D Flow data. Whole-cycle parameters including time-averaged WSS and nwTKE, and the oscillatory shear index (OSI) were calculated. Pairwise Spearman rank-correlation analyses were used to investigate relationships among the hemodynamic as well as geometric parameters. Results: One hundred and seventy nine subjects were successfully segmented using automated tools and subsequently geometric and hemodynamic analyses were performed. Temporally resolved WSS and nwTKE were strongly correlated, ρ = 0.64. Cycle-averaged WSS and nwTKE were moderately correlated, ρ = 0.57. Cycle-average nwTKE was weakly correlated to OSI (ρ = -0.273), revealing that nwTKE provides information about disturbed flow on the vessel wall that OSI does not. In this cohort, there was large inter-individual variation for both WSS and nwTKE. Both WSS and nwTKE varied most within the external carotid artery. WSS, nwTKE, and OSI were weakly correlated to vessel diameter and bifurcation angle. Conclusion: The turbulent and mean component of WSS were examined together in vivo for the first time, and a strong correlation was found between them. nwTKE presents the opportunity to quantify turbulent wall stresses in vivo and gain insight into the effects of disturbed flow on the vessel wall. Neither vessel diameter nor bifurcation angle were found to be strongly correlated to the turbulent or mean component of WSS in this cohort.

Model Verification and Error Sensitivity of Turbulence-Related Tensor Characteristics in Pulsatile Blood Flow Simulations

Model verification, validation, and uncertainty quantification are essential procedures to estimate errors within cardiovascular flow modeling, where acceptable confidence levels are needed for clinical reliability. While more turbulent-like studies are frequently observed within the biofluid community, practical modeling guidelines are scarce. Verification procedures determine the agreement between the conceptual model and its numerical solution by comparing for example, discretization and phase-averaging-related errors of specific output parameters. This computational fluid dynamics (CFD) study presents a comprehensive and practical verification approach for pulsatile turbulent-like blood flow predictions by considering the amplitude and shape of the turbulence-related tensor field using anisotropic invariant mapping. These procedures were demonstrated by investigating the Reynolds stress tensor characteristics in a patient-specific aortic coarctation model, focusing on modeling-related errors associated with the spatiotemporal resolution and phase-averaging sampling size. Findings in this work suggest that attention should also be put on reducing phase-averaging related errors, as these could easily outweigh the errors associated with the spatiotemporal resolution when including too few cardiac cycles. Also, substantially more cycles are likely needed than typically reported for these flow regimes to sufficiently converge the phase-instant tensor characteristics. Here, higher degrees of active fluctuating directions, especially of lower amplitudes, appeared to be the most sensitive turbulence characteristics.

Characterization of anisotropic turbulence behavior in pulsatile blood flow

Turbulent-like hemodynamics with prominent cycle-to-cycle flow variations have received increased attention as a potential stimulus for cardiovascular diseases. These turbulent conditions are typically evaluated in a statistical sense from single scalars extracted from ensemble-averaged tensors (such as the Reynolds stress tensor), limiting the amount of information that can be used for physical interpretations and quality assessments of numerical models. In this study, barycentric anisotropy invariant mapping was used to demonstrate an efficient and comprehensive approach to characterize turbulence-related tensor fields in patient-specific cardiovascular flows, obtained from scale-resolving large eddy simulations. These techniques were also used to analyze some common modeling compromises as well as MRI turbulence measurements through an idealized constriction. The proposed method found explicit sites of elevated turbulence anisotropy, including a broad but time-varying spectrum of characteristics over the flow deceleration phase, which was different for both the steady inflow and Reynolds-averaged Navier–Stokes modeling assumptions. Qualitatively, the MRI results showed overall expected post-stenotic turbulence characteristics, however, also with apparent regions of unrealizable or conceivably physically unrealistic conditions, including the highest turbulence intensity ranges. These findings suggest that more detailed studies of MRI-measured turbulence fields are needed, which hopefully can be assisted by more comprehensive evaluation tools such as the once described herein.

Non-periodicity of blood flow and its influence on wall shear stress in the carotid artery bifurcation: An in vivo measurement-based computational study

Although arterial blood flow is physiologically non-periodic under resting conditions, periodic flow assumption has been widely adopted in most hemodynamic studies. So far, it remains unclear how the non-periodicity of blood flow would influence local hemodynamic parameters, especially wall shear stress (WSS) that associates closely with endothelial function and vascular disease. In this study, numerical simulations of blood flows in sixteen normal carotid artery bifurcations were performed under measured non-periodic and averaged periodic flow conditions, respectively, with the obtained results being compared in terms of five typical WSS metrics (i.e., mean WSS (MWSS), time-averaged WSS (TAWSS), oscillatory shear index (OSI), transverse WSS (transWSS), and average temporal gradient of WSS (WSSTG)) in the atheroprone low-WSS regions. It was found that simplifying the physiologically non-periodic flow condition into a periodic one did not significantly alter the major features of WSS distribution, but resulted in underestimations of some WSS metrics. Specifically, the degree of underestimation was largest (27.2% ± 8.3%) for WSSTG, smallest (0.5% ± 0.4%) for MWSS, while moderate (5.1% ± 3.2% ~ 9.2% ± 4.1%) for other WSS metrics. Statistical analyses revealed that the cycle-to-cycle variability of flow velocity waveform (var-V) and the planarity of internal carotid artery correlated strongly with the periodic flow assumption-induced underestimations of WSS metrics. These findings suggest that taking the non-periodic characteristic of blood flow into consideration could be important for studying hemodynamics in arteries with a large var-V or specific morphological characteristics, especially when WSSTG is the main hemodynamic parameter of concern.