Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models

Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?

Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.

Proximal and Distal Occlusion of Complex Cerebral Aneurysms-Implications of Flow Modeling by Fluid-Structure Interaction Analysis

BACKGROUND

In complex cerebral aneurysms, adequate treatment by complete occlusion is not always possible. Partial occlusion by either proximal or distal occlusion is an alternative. However, the hemodynamic consequences of these partial occlusion options are often not easily predictable.

OBJECTIVE

To assess the feasibility of fluid-structure interaction (FSI) analysis to investigate the hemodynamic changes after partial occlusion in cerebral aneurysms.

METHODS

Two patients were analyzed. One was treated by proximal occlusion and 1 by distal occlusion. In both, flow replacement bypass surgery was performed. Three-dimensional models were constructed from magnetic resonance angiography (MRA) scans and used for FSI analysis. A comparative study was done for pre- and postoperative conditions. Postoperative thrombosis was modeled and analyzed for the distal occlusion. FSI results were compared to postoperative angiograms and computed tomography (CT)-scans.

RESULTS

Proximal occlusion resulted in reduction of velocity, wall shear stresses, and disappearance of helical flow patterns in the complete aneurysm. Distal occlusion showed a decrease of velocity and wall shear stress in the dome of the aneurysm. Results were validated against postoperative CT-scans and angiograms at 1-, 7-, and 9-mo follow-up. Addition of thrombus to the distal occlusion model showed no change in velocities and luminal pressure but resulted in decrease in wall tension.

CONCLUSION

This pilot study showed hemodynamic changes in 2 patients with proximal and distal occlusion of complex cerebral aneurysms. The FSI results were in line with the follow-up CT scans and angiograms and indicate the potential of FSI as a tool in patient-specific surgical interventions.

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.

Geometrically enhanced sensor surfaces for the selective capture of cell-like particles in a laminar flow field

Medical wires inserted into the blood stream of patients offer an attractive perspective to capture rare cells such as circulating tumor cells in vivo. A major challenge in such systems is to achieve an efficient interaction of the desired cells with the sensing surface and avoid those cells that simply flow by the wire without any contact while floating in a laminar flow field at some small distance to the sensor surface. We describe a new strategy to increase the interaction of cells or cell-like particles to such wire-shaped sensor surfaces both from an experimental and a theoretical point of view. For model experiments, we use cell-like particles that are flowing past the profile wire in a blood-like liquid stream. In the fluid dynamics simulations, this sensor is inserted into small capillaries. The influence of geometry and orientation of the wire with respect to the surrounding capillary onto the capture behavior is studied. Parameters, such as wire diameter, profile shape, wire torsion, and orientation of it with respect to the liquid stream, induce in some cases quite strong crossflows. These crossflows enhance the contact probability compared to a straight line wire of the same length by factors of up to about 80. A general model connecting the wire geometry with the crossflow intensity and the particle capture behavior is developed. Particle capture experiments demonstrate that the identified geometric factors can improve the capture of cell-like particles in laminar fluid flows and enhance the performance of such cell sensors.

An agent-based model of leukocyte transendothelial migration during atherogenesis

A vast amount of work has been dedicated to the effects of hemodynamics and cytokines on leukocyte adhesion and trans-endothelial migration (TEM) and subsequent accumulation of leukocyte-derived foam cells in the artery wall. However, a comprehensive mechanobiological model to capture these spatiotemporal events and predict the growth and remodeling of an atherosclerotic artery is still lacking. Here, we present a multiscale model of leukocyte TEM and plaque evolution in the left anterior descending (LAD) coronary artery. The approach integrates cellular behaviors via agent-based modeling (ABM) and hemodynamic effects via computational fluid dynamics (CFD). In this computational framework, the ABM implements the diffusion kinetics of key biological proteins, namely Low Density Lipoprotein (LDL), Tissue Necrosis Factor alpha (TNF-α), Interlukin-10 (IL-10) and Interlukin-1 beta (IL-1β), to predict chemotactic driven leukocyte migration into and within the artery wall. The ABM also considers wall shear stress (WSS) dependent leukocyte TEM and compensatory arterial remodeling obeying Glagov's phenomenon. Interestingly, using fully developed steady blood flow does not result in a representative number of leukocyte TEM as compared to pulsatile flow, whereas passing WSS at peak systole of the pulsatile flow waveform does. Moreover, using the model, we have found leukocyte TEM increases monotonically with decreases in luminal volume. At critical plaque shapes the WSS changes rapidly resulting in sudden increases in leukocyte TEM suggesting lumen volumes that will give rise to rapid plaque growth rates if left untreated. Overall this multi-scale and multi-physics approach appropriately captures and integrates the spatiotemporal events occurring at the cellular level in order to predict leukocyte transmigration and plaque evolution.

Modeling the Effect of Red Blood Cells Deformability on Blood Flow Conditions in Human Carotid Artery Bifurcation

The purpose of this work is to predict the effect of impaired red blood cells (RBCs) deformability on blood flow conditions in human carotid artery bifurcation. First, a blood viscosity model is developed that predicts the steady-state blood viscosity as a function of shear rate, plasma viscosity, and mechanical (and geometrical) properties of RBC's. Viscosity model is developed by modifying the well-known Krieger and Dougherty equation for monodisperse suspensions by using the dimensional analysis approach. With the approach, we manage to account for the microscopic properties of RBC's, such as their deformability, in the macroscopic behavior of blood via blood viscosity. In the second part of the paper, the deduced viscosity model is used to numerically predict blood flow conditions in human carotid artery bifurcation. Simulations are performed for different values of RBC's deformability and analyzed by investigating parameters, such as the temporal mean wall shear stress (WSS), oscillatory shear index (OSI), and mean temporal gradient of WSS. The analyses show that the decrease of RBC's deformability decrease the regions of low WSS (i.e., sites known to be prevalent at atherosclerosis-prone regions); increase, in average, the value of WSS along the artery; and decrease the areas of high OSI. These observations provide an insight into the influence of blood's microscopic properties, such as the deformability of RBC's, on hemodynamics in larger arteries and their influence on parameters that are known to play a role in the initiation and progression of atherosclerosis.

Numerical analysis of blood flow through an elliptic stenosis using large eddy simulation

The presence of a stenosis caused by the abnormal narrowing of the lumen in the artery tree can cause significant variations in flow parameters of blood. The original flow, which is believed to be laminar in most situations, may turn out to turbulent by the geometric perturbation created by the stenosis. Flow may evolve to fully turbulent or it may relaminarise back according to the intensity of the perturbation. This article reports the numerical simulation of flow through an eccentrically located asymmetric stenosis having elliptical cross section using computational fluid dynamics. Large eddy simulation technique using dynamic Smagorinsky sub-grid scale model is applied to capture the turbulent features of flow. Analysis is carried out for two situations: steady inflow as ideal condition and pulsatile inflow corresponding to the actual physiological condition in common carotid artery. The spatially varying pulsatile inflow waveforms are mathematically derived from instantaneous mass flow measurements available in the literature. Carreau viscosity model is used to estimate the effect of non-Newtonian nature of blood. The present simulations for steady and pulsatile conditions show that post-stenotic flow field undergoes transition to turbulence in all cases. The characteristics of mean and turbulent flow fields have been presented and discussed in detail.

The numerical analysis of non-Newtonian blood flow in human patient-specific left ventricle

Recently, various non-invasive tools such as the magnetic resonance image (MRI), ultrasound imaging (USI), computed tomography (CT), and the computational fluid dynamics (CFD) have been widely utilized to enhance our current understanding of the physiological parameters that affect the initiation and the progression of the cardiovascular diseases (CVDs) associated with heart failure (HF). In particular, the hemodynamics of left ventricle (LV) has attracted the attention of the researchers due to its significant role in the heart functionality. In this study, CFD owing its capability of predicting detailed flow field was adopted to model the blood flow in images-based patient-specific LV over cardiac cycle. In most published studies, the blood is modeled as Newtonian that is not entirely accurate as the blood viscosity varies with the shear rate in non-linear manner. In this paper, we studied the effect of Newtonian assumption on the degree of accuracy of intraventricular hemodynamics. In doing so, various non-Newtonian models and Newtonian model are used in the analysis of the intraventricular flow and the viscosity of the blood. Initially, we used the cardiac MRI images to reconstruct the time-resolved geometry of the patient-specific LV. After the unstructured mesh generation, the simulations were conducted in the CFD commercial solver FLUENT to analyze the intraventricular hemodynamic parameters. The findings indicate that the Newtonian assumption cannot adequately simulate the flow dynamic within the LV over the cardiac cycle, which can be attributed to the pulsatile and recirculation nature of the flow and the low blood shear rate.

Impact of bifurcation angle and other anatomical characteristics on blood flow - A computational study of non-stented and stented coronary arteries

The hemodynamic influence of vessel shape such as bifurcation angle is not fully understood with clinical and quantitative observations being equivocal. The aim of this study is to use computational modeling to study the hemodynamic effect of shape characteristics, in particular bifurcation angle (BA), for non-stented and stented coronary arteries. Nine bifurcations with angles of 40°, 60° and 80°, representative of ±1 SD of 101 asymptomatic computed tomography angiogram cases (average age 54±8 years; 57 females), were generated for (1) a non-stented idealized, (2) stented idealized, and (3) non-stented patient-specific geometry. Only the bifurcation angle was changed while the geometries were constant to eliminate flow effects induced by other vessel shape characteristics. The commercially available Biomatrix stent was used as a template and virtually inserted into each branch, simulating the T-stenting technique. Three patient-specific geometries with additional shape variation and ±2 SD BA variation (33°, 42° and 117°) were also computed. Computational fluid dynamics (CFD) analysis was performed for all 12 geometries to simulate physiological conditions, enabling the quantification of the hemodynamic stress distributions, including a threshold analysis of adversely low and high wall shear stress (WSS), low time-averaged WSS (TAWSS), high spatial WSS gradient (WSSG) and high Oscillatory Shear Index (OSI) area. The bifurcation angle had a minor impact on the areas of adverse hemodynamics in the idealized non-stented geometries, which fully disappeared once stented and was not apparent for patient geometries. High WSS regions were located close to the carina around peak-flow, and WSSG increased significantly after stenting for the idealized bifurcations. Additional shape variations affected the hemodynamic profiles, suggesting that BA alone has little effect on a patient׳s hemodynamic profile. Incoming flow angle, diameter and tortuosity appear to have stronger effects. This suggests that other bifurcation shape characteristics and stent placement/strategy may be more important than bifurcation angle in atherosclerotic disease development, progression, and stent outcome.

Analysis of non-Newtonian effects on Low-Density Lipoprotein accumulation in an artery

In this work, non-Newtonian effects on Low-Density Lipoprotein (LDL) transport across an artery are analyzed with a multi-layer model. Four rheological models (Carreau, Carreau-Yasuda, power-law and Newtonian) are used for the blood flow through the lumen. For the non-Newtonian cases, the arterial wall is modeled with a generalized momentum equation. Convection-diffusion equation is used for the LDL transport through the lumen, while Staverman-Kedem-Katchalsky, combined with porous media equations, are used for the LDL transport through the wall. Results are presented in terms of filtration velocity, Wall Shear Stresses (WSS) and concentration profiles. It is shown that non-Newtonian effects on mass transport are negligible for a healthy intramural pressure value. Non-Newtonian effects increase slightly with intramural pressure, but Newtonian assumption can still be considered reliable. Effects of arterial size are also analyzed, showing that Newtonian assumption can be considered valid for both medium and large arteries, in predicting LDL deposition. Finally, non-Newtonian effects are also analyzed for an aorta-common iliac bifurcation, showing that Newtonian assumption is valid for mass transport at low Reynolds numbers. At a high Reynolds number, it has been shown that a non-Newtonian fluid model can have more impact due to the presence of flow recirculation.

Low-density lipoprotein accumulation within a carotid artery with multilayer elastic porous wall: fluid-structure interaction and non-Newtonian considerations

Low-density lipoprotein (LDL), which is recognized as bad cholesterol, typically has been regarded as a main cause of atherosclerosis. LDL infiltration across arterial wall and subsequent formation of Ox-LDL could lead to atherogenesis. In the present study, combined effects of non-Newtonian fluid behavior and fluid-structure interaction (FSI) on LDL mass transfer inside an artery and through its multilayer arterial wall are examined numerically. Navier-Stokes equations for the blood flow inside the lumen and modified Darcy's model for the power-law fluid through the porous arterial wall are coupled with the equations of mass transfer to describe LDL distributions in various segments of the artery. In addition, the arterial wall is considered as a heterogeneous permeable elastic medium. Thus, elastodynamics equation is invoked to examine effects of different wall elasticity on LDL distribution in the artery. Findings suggest that non-Newtonian behavior of filtrated plasma within the wall enhances LDL accumulation meaningfully. Moreover, results demonstrate that at high blood pressure and due to the wall elasticity, endothelium pores expand, which cause significant variations on endothelium physiological properties in a way that lead to higher LDL accumulation. Additionally, results describe that under hypertension, by increasing angular strain, endothelial junctions especially at leaky sites expand more dramatic for the high elastic model, which in turn causes higher LDL accumulation across the intima layer and elevates atherogenesis risk.

The Impact of Blood Rheology on Drug Transport in Stented Arteries: Steady Simulations

BACKGROUND AND METHODS

It is important to ensure that blood flow is modelled accurately in numerical studies of arteries featuring drug-eluting stents due to the significant proportion of drug transport from the stent into the arterial wall which is flow-mediated. Modelling blood is complicated, however, by variations in blood rheological behaviour between individuals, blood's complex near-wall behaviour, and the large number of rheological models which have been proposed. In this study, a series of steady-state computational fluid dynamics analyses were performed in which the traditional Newtonian model was compared against a range of non-Newtonian models. The impact of these rheological models was elucidated through comparisons of haemodynamic flow details and drug transport behaviour at various blood flow rates.

RESULTS

Recirculation lengths were found to reduce by as much as 24% with the inclusion of a non-Newtonian rheological model. Another model possessing the viscosity and density of blood plasma was also implemented to account for near-wall red blood cell losses and yielded recirculation length increases of up to 59%. However, the deviation from the average drug concentration in the tissue obtained with the Newtonian model was observed to be less than 5% in all cases except one. Despite the small sensitivity to the effects of viscosity variations, the spatial distribution of drug matter in the tissue was found to be significantly affected by rheological model selection.

CONCLUSIONS/SIGNIFICANCE

These results may be used to guide blood rheological model selection in future numerical studies. The clinical significance of these results is that they convey that the magnitude of drug uptake in stent-based drug delivery is relatively insensitive to individual variations in blood rheology. Furthermore, the finding that flow separation regions formed downstream of the stent struts diminish drug uptake may be of interest to device designers.

Effect of anticoagulant treatment in deep vein thrombosis: A patient-specific computational fluid dynamics study

A methodology that might help physicians to establish a diagnostic and treatment tailored for each specific patient with a pathological thrombus is presented. A realistic model for the geometry of a popliteal vein with a thrombus just above the knee was reconstructed from in vivo computed tomography images acquired from one specific patient and then it was used to perform computational fluid dynamics (CFD) simulations. The wall shear stress (WSS) response to the administration of anticoagulant drugs and the influence of viscosity on the shape of the velocity distribution were investigated. Both a Newtonian and a non-Newtonian viscosity model were implemented for different blood flow rates in the range 3-7 cm(3)/s. The effect of anticoagulants on the blood was simulated by setting three different levels of viscosity in the Newtonian model (μ/μ∞=0.60, 0.80 and 1 with μ∞=3.45×10(-3) Pas). A reduction of μ by a given amount always led to a more modest reduction, typically by a factor of two, of the resulting WSS levels. Moreover, for a given flow rate the calculation with the non-Newtonian viscosity model yielded WSS levels between 20% and 40% larger than those obtained in the corresponding Newtonian fluid simulation. It was also found that blood moves slowly in the region between the thrombus and the vein wall, a fact that will favor the growth of the thrombotic mass. Both the mean WSS levels and the degree of sluggishness of the blood flow can be described by functions of the Reynolds number.

FDA's nozzle numerical simulation challenge: non-Newtonian fluid effects and blood damage

Data from FDA's nozzle challenge-a study to assess the suitability of simulating fluid flow in an idealized medical device-is used to validate the simulations obtained from a numerical, finite-differences code. Various physiological indicators are computed and compared with experimental data from three different laboratories, getting a very good agreement. Special care is taken with the derivation of blood damage (hemolysis). The paper is focused on the laminar regime, in order to investigate non-Newtonian effects (non-constant fluid viscosity). The code can deal with these effects with just a small extra computational cost, improving Newtonian estimations up to a ten percent. The relevance of non-Newtonian effects for hemolysis parameters is discussed.

Near-infrared transillumination back scattering sounding--new method to assess brain microcirculation in patients with chronic carotid artery stenosis

Purpose

The purpose of the study was to assess the responses of pial artery pulsation (cc-TQ) and subarachnoid width (sas-TQ) to acetazolamide challenge in patients with chronic carotid artery stenosis and relate these responses to changes in peak systolic velocity (PSV), cerebral blood flow (CBF), cerebral blood volume (CBV), mean transit time (MTT) and time to peak response (TTP).

Methods

Fifteen patients with carotid artery stenosis ≥90% on the ipsilateral side and <50% on the contralateral side were enrolled into the study. PSV was assessed using colour-coded duplex sonography, CBF, CBV, MTT and TTP with perfusion computed tomography, cc-TQ and sas-TQ with near-infrared transillumination/backscattering sounding (NIR-T/BSS).

Results

Based on the ipsilateral/contralateral cc-TQ ratio after acetazolamide challenge two groups of patients were distinguished: the first group with a ratio ≥1 and the second with a ratio <1. In the second group increases in CBF and CBV after the acetazolamide test were significantly higher in both hemispheres (ipsilateral: +33.0%±8.1% vs. +15.3%±4.4% and +26.3%±6.6% vs. +14.3%±5.1%; contralateral: +26.8%±7.0% vs. +17.6%±5.6% and +20.0%±7.3% vs. +10.0%±3.7%, respectively), cc-TQ was significantly higher only on the ipsilateral side (+37.3%±9.3% vs. +26.6%±8.6%) and the decrease in sas-TQ was less pronounced on the ipsilateral side (−0.7%±1.5% vs. −10.2%±1.5%), in comparison with the first group. The changes in sas-TQ following the acetazolamide test were consistent with the changes in TTP.

Conclusions

The ipsilateral/contralateral cc-TQ ratio following acetazolamide challenge may be used to distinguish patient groups characterized by different haemodynamic parameters. Further research on a larger group of patients is warranted.

SIMULATION OF PULSATILE BLOOD FLOW THROUGH STENOTIC ARTERY CONSIDERING DIFFERENT BLOOD RHEOLOGIES: COMPARISON OF 3D AND 2D-AXISYMMETRIC MODELS

Hemodynamic factors such as velocity distribution, pressure gradient and wall shear stress are thought to play an important role in the prognosis of symptomatic carotid occlusion. Although there are many studies about modeling the blood flow behavior in carotid, hemodynamic characteristics of blood flow in a stenosed carotid artery is still debatable. In this study a three-dimensional (3D) model of a symmetric stenosed common carotid artery (CCA) is developed and the simulation results of it are compared to the experimental data where subsequent agreement is confirmed. To study the accuracy of two-dimensional (2D) axisymmetric model, the result of it is compared to the result of the 3D model. Two non-Newtonian rheological models, namely Carreau and modified Power-law, as well as Newtonian model are used to realize the hemodynamical differences of 2D-axisymmetric and 3D models in pulsatile blood flow. Comparing the 3D simulated results with 2D-axisymmetric modeling results that were published in recent years indicates that the assumption of 2D-axisymmetric model cannot adequately predict the velocity profiles even for a symmetric stenotic artery. Although a symmetric stenotic artery is considered, the results indicate a nonsymmetric flow in poststenosis region that is detected by the presence of extensive secondary flows particularly at diastole. The existence of secondary flows that can only be detected in 3D modeling is the main reason for the differences in hemodynamic factors in 3D and 2D results.

The quantification of hemodynamic parameters downstream of a Gianturco Zenith stent wire using newtonian and non-newtonian analog fluids in a pulsatile flow environment

Although deployed in the vasculature to expand vessel diameter and improve blood flow, protruding stent struts can create complex flow environments associated with flow separation and oscillating shear gradients. Given the association between magnitude and direction of wall shear stress (WSS) and endothelial phenotype expression, accurate representation of stent-induced flow patterns is critical if we are to predict sites susceptible to intimal hyperplasia. Despite the number of stents approved for clinical use, quantification on the alteration of hemodynamic flow parameters associated with the Gianturco Z-stent is limited in the literature. In using experimental and computational models to quantify strut-induced flow, the majority of past work has assumed blood or representative analogs to behave as Newtonian fluids. However, recent studies have challenged the validity of this assumption. We present here the experimental quantification of flow through a Gianturco Z-stent wire in representative Newtonian and non-Newtonian blood analog environments using particle image velocimetry (PIV). Fluid analogs were circulated through a closed flow loop at physiologically appropriate flow rates whereupon PIV snapshots were acquired downstream of the wire housed in an acrylic tube with a diameter characteristic of the carotid artery. Hemodynamic parameters including WSS, oscillatory shear index (OSI), and Reynolds shear stresses (RSS) were measured. Our findings show that the introduction of the stent wire altered downstream hemodynamic parameters through a reduction in WSS and increases in OSI and RSS from nonstented flow. The Newtonian analog solution of glycerol and water underestimated WSS while increasing the spatial coverage of flow reversal and oscillatory shear compared to a non-Newtonian fluid of glycerol, water, and xanthan gum. Peak RSS were increased with the Newtonian fluid, although peak values were similar upon a doubling of flow rate. The introduction of the stent wire promoted the development of flow patterns that are susceptible to intimal hyperplasia using both Newtonian and non-Newtonian analogs, although the magnitude of sites affected downstream was appreciably related to the rheological behavior of the analog. While the assumption of linear viscous behavior is often appropriate in quantifying flow in the largest arteries of the vasculature, the results presented here suggest this assumption overestimates sites susceptible to hyperplasia and restenosis in flow characterized by low and oscillatory shear.