Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses

The flow field near a venous needle in hemodialysis: a computational study

The vascular access used in hemodialysis can suffer from numerous complications, which may lead to failure of the access, patient morbidity, and significant costs. The flow field in the region of the venous needle may be a source of damaging hemodynamics and hence adverse effects on the fistula. In this study, the venous needle flow has been considered, using three-dimensional computational methods. Four scenarios where the venous needle flow could potentially influence dialysis treatment outcome were identified and examined: Variation of the needle placement angle (10°, 20°, 30°), variation of the blood flow rate settings (200, 300, 400 mL/min), variation of the needle depth (top, middle, bottom), and the inclusion of a back eye in the needle design. The presence of the needle has significant effect on the flow field, with different scenarios having varying influence. In general, wall shear stresses were elevated above normal physiological values, and increased presence of areas of low velocity and recirculation-indicating increased likelihood of intimal hyperplasia development-were found. Computational results showed that the presence of the venous needle in a hemodialysis fistula leads to abnormal and potentially damaging flow conditions and that optimization of needle parameters could aid in the reduction of vascular access complications. Results indicate shallow needle angles and lower blood flow rates may minimize vessel damage.

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure-flow waveforms

In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

Direct observation of von Willebrand factor elongation and fiber formation on collagen during acute whole blood exposure to pathological flow

OBJECTIVE

In severe stenosis, von Willebrand factor (vWF) experiences millisecond exposures to pathological wall shear rates (γ(w)). We sought to evaluate the deposition of vWF onto collagen surfaces under flow in these environments.

METHODS AND RESULTS

Distinct from viscometry experiments that last many seconds, we deployed microfluidic devices for single-pass perfusion of whole blood or platelet-free plasma over fibrillar type 1 collagen (<50 ms transit time) at pathological γ(w) or spatial wall shear rate gradients (grad γ(w)). Using fluorescent anti-vWF, long thick vWF fibers (>20 μm) bound to collagen were visualized at constant γ(w)>30000 s(-1) during perfusion of platelet-free plasma, a process enhanced by EDTA. Rapid acceleration or deceleration of EDTA platelet-free plasma at grad γ(w)=±1.1×10(5) to ±4.3×10(7) s(-1)/cm did not promote vWF deposition. At 19400 s(-1), EDTA blood perfusion resulted in rolling vWF-platelet nets, although blood perfusion (normal Ca(2+)) generated large vWF/platelet deposits that repeatedly embolized and were blocked by anti-glycoprotein Ib or the α(IIb)β(3) inhibitor GR144053 and did not require grad γ(w). Blood perfusion at venous shear rate (200 s(-1)) produced a stable platelet deposit that was a substrate for massive but unstable vWF-platelet aggregates when flow was increased to 7800 s(-1).

CONCLUSIONS

Triggered by collagen and enhanced by platelet glycoprotein Ib and α(IIb)β(3), vWF fiber formation occurred during acute exposures to pathological γ(w) and did not require gradients in wall shear rate.

Mechanical action of the blood onto atheromatous plaques: influence of the stenosis shape and morphology

The vulnerability of atheromatous plaques in the carotid artery may be related to several factors, the most important being the degree of severity of the endoluminal stenosis and the thickness of the fibrous cap. It has recently been shown that the plaque length can also affect the mechanical response significantly. However, in their study on the effect of the plaque length, the authors did not consider the variations of the plaque morphology and the shape irregularities that may exist independently of the plaque length. These aspects are developed in this paper. The mechanical interactions between the blood flow and an atheromatous plaque are studied through a numerical model considering fluid-structure interaction. The simulation is achieved using the arbitrary Lagrangian-Eulerian scheme in the COMSOL TM commercial finite element package. The stenosis severity and the plaque length are, respectively, set to 45% and 15 mm. Different shapes of the stenosis are modelled, considering irregularities made of several bumps over the plaque. The resulting flow patterns, wall shear stresses, plaque deformations and stresses in the fibrous cap reveal that the effects of the blood flow are amplified if the slope upstream stenosis is steep or if the plaque morphology is irregular with bumps. More specifically, the maximum stress in the fibrous cap is 50% larger for a steep slope than for a gentle slope. These results offer new perspectives for considering the shape of plaques in the evaluation of the vulnerability.

Particle depositions and related hemodynamic parameters in the multiple stenosed right coronary artery

BACKGROUND

Blood flow analysis of the human right coronary artery (RCA) has been carried out to investigate the effects of serial stenosis on coronary hemodynamics. A 3-D model of a serial stenosed RCA was reconstructed based on multislice computerized tomography images.

METHODS

A velocity waveform in the proximal RCA and a pressure waveform in the distal RCA of a patient with a severe stenosis were acquired with a catheter delivered wire probe and applied as boundary conditions. The numerical analysis examines closely the effect of a multiple serial stenosis on the hemodynamic characteristics such as flow separation, wall shear stress (WSS) and particle depositions.

RESULTS AND CONCLUSIONS

Energy loss associated with such flow expansion after each constriction will be large and consequently the pressure drop will be higher. Overall pressure drop increased from 1700 Pa (12.75 mmHg) at the end diastole to 11000 Pa (82.5 mmHg) at the peak systole. At the peak systole the WSS values reached 110 Pa in the stenosis with 28% diameter reduction and 210 Pa in the stenosis with 54% diameter reduction, which is high enough to damage the endothelial cells. However at the end of one cardiac cycle a percent of 1.4% (15 from 1063 particles release at the inlet section) remain inside the stenosed RCA.

A numerical parametric study of the mechanical action of pulsatile blood flow onto axisymmetric stenosed arteries

In the present paper, a fluid-structure interaction model is developed, questioning how the mechanical action of the blood onto an atheromatous plaque is affected by the length and the severity of the stenosis. An axisymmetric model is considered. The fluid is assumed Newtonian. The plaque is modelled as a heterogeneous hyperelastic anisotropic solid composed of the arterial wall, the lipid core and the fibrous cap. Transient velocity and pressure conditions of actual pulsatile blood flow are prescribed. The simulation is achieved using the Arbitrary Lagrangian Eulerian scheme in the COMSOL commercial Finite Element package. The results reveal different types of behavior in function of the length (denoted L) and severity (denoted S) of the stenosis. Whereas large plaques (L>10 mm) are mostly deformed under the action of the blood pressure, it appears that shorter plaques (L<10 mm) are significantly affected by the shear stresses. The shear stresses tend to deform the plaque by pinching it. This effect is called: "the pinching effect". It has an essential influence on the mechanical response of the plaque. For two plaques having the same radius severity S=45%, the maximum stress in the fibrous cap is 50% larger for the short plaque (L=5 mm) than for a larger plaque (L=10 mm), and the maximum wall shear stress is increased by 100%. Provided that they are confirmed by experimental investigations, these results may offer some new perspectives for understanding the vulnerability of short plaques.

Multiscale systems biology and physics of thrombosis under flow

Blood clotting under hemodynamic conditions involves numerous multiscale interactions from the molecular scale to macroscopic vessel and systemic circulation scales. Transmission of shear forces to platelet receptors such as GPIbα, P-selectin, α(2)β(1), and α(2b)β(3) controls adhesion dynamics. These forces also drive membrane tether formation, cellular deformation, and mechanosignaling in blood cells. Blood flow results in red blood cell (RBC) drift towards the center of the vessel along with a near-wall plasma layer enriched with platelets. RBC motions also dramatically enhance platelet dispersion. Trajectories of individual platelets near a thrombotic deposit dictate capture-activation-arrest dynamics as these newly arriving platelets are exposed to chemical gradients of ADP, thromboxane, and thrombin within a micron-scale boundary layer formed around the deposit. If shear forces are sufficiently elevated (>50 dyne/cm(2)), the largest polymers of von Willebrand Factor may elongate with concomitant shear-induced platelet activation. Finally, thrombin generation enhances platelet recruitment and clot strength via fibrin polymerization. By combination of coarse-graining, continuum, and stochastic algorithms, the numerical simulation of the growth rate, composition, and occlusive/embolic potential of a thrombus now spans multiscale phenomena. These simulations accommodate particular flow geometries, blood phenotype, pharmacological regimen, and reactive surfaces to help predict disease risk or response to therapy.

Upregulation of SDF-1 is associated with atherosclerosis lesions induced by LDL concentration polarization

Previous numerical simulations on low-density lipoprotein (LDL) concentration polarization in the arterial system indicated that LDL concentration polarization might play an important role in the genesis and development of atherosclerosis. To date, no in vivo experiments have examined this question directly, and the molecular mechanisms are unknown. In this study, ten rabbits were treated with gel-silica loop to develop a defined local stenosis in the straight segment of the left carotid artery. Both numerical simulation and experiment measurements showed that the concentration of LDL was about 35% higher at the blood/arterial wall interface than in the lumen on the distal side of the stenosis. Atherosclerotic lesions with abundant lipid deposits were observed and stromal derived factor-1 (SDF-1) was detected at the distal end of the stenosis, while the straight segment was plaque-free. In vitro studies demonstrated that LDL-induced SDF-1 expression in endothelial cells and increased monocyte adhesion to endothelial cells in a dose-dependent manner. The adhesion was suppressed when endothelial cells were pretreated with SDF-1 antibody. These results suggested LDL concentration polarization contributed to the localization of atherosclerosis and to the expression of SDF-1. In turn, SDF-1 facilitated plaque formation.

Simulation of haemodynamic flow in head and neck cancer chemotherapy

Background

In recent years, intra arterial chemotherapy has become an important component in head and neck cancer treatment. However, therapy success can vary significantly and consistent treatment guidelines are missing. The purpose of this study was to create a computer simulation of the chemical agent injection in the head and neck arteries to investigate the distribution and concentration of the chemical.

Methods

Realistic three dimensional patient specific geometry was created from image scan data. Pulsatile blood flow, turbulence, the chemical agent injection via a catheter, and the mixture between blood and the chemical were then simulated through the arterial network by computational fluid dynamics software.

Results

The results show a consistent chemical distribution throughout all the arteries and this is ineffective. In addition, due to high wall shear stress and turbulence at the inner bifurcation wall, serious complications during the treatment could occur, for instance haemolysis or thrombosis.

Conclusions

The modelled catheter position is insufficient to provide a high chemical agent concentration in the desired tumour feeding artery, which is vital for therapy success.

Intracranial collateralization determines hemodynamic forces for carotid plaque disruption

INTRODUCTION

Percent diameter reduction provides an imperfect assessment of the risk for stroke from carotid atheroembolism. Stroke associated with atherosclerotic carotid stenosis commonly results from plaque disruption brought about by hemodynamic shear stress and Bernoulli forces. The aim of the present study was to predict the effect of incomplete intracranial collateralization through the circle of Willis (COW) on disruptive hemodynamic forces acting on carotid plaques.

METHODS

A simple circuit model of the major pathways and collaterals that form and supply the COW was developed. We modeled the intra- and extracranial arterial circuits from standard anatomic references, and the pressure-flow relationships within these conduits from standard fluid mechanics. The pressure drop caused by (laminar and turbulent) flow along the internal carotid artery path was then computed. Carotid circulation to the brain was classified as being with or without collateral connections through the COW, and the extracranial carotid circuit as being with or without severe stenosis. The pressure drop was computed for each scenario. Finally, a linear circuit model was used to compute brain blood flow in the presence/absence of a disconnected COW.

RESULTS

Pressure drop across a carotid artery stenosis increased as the flow rate within the carotid conduit increased. Poststenotic turbulence from a sudden expansion distal to the stenosis resulted in an additional pressure drop. Despite the stenosis, mean brain blood flow was sustained at 4.15 mL/s bilaterally. In the presence of an intact (collateralized) COW, this was achieved by enhanced flow in the contralateral (normal) carotid artery. However, in a disconnected COW, this was achieved by sustained systolic and enhanced diastolic flow through the stenosed artery. For a similar degree of stenosis, flow and velocity across the plaque was much higher when the COW was disconnected compared with an intact COW. Furthermore, the pressure drop across a similar stenosis was significantly higher with a disconnected COW compared with an intact COW.

CONCLUSIONS

Incomplete intracranial collateralization through the COW results in increased flow rates and velocities, and therefore large pressure drops across a carotid artery stenosis. This exerts large disruptive shear stress on the plaque compared with patients with an intact COW. Percent diameter reduction provides an inaccurate assessment of risk for atheroembolic stroke. An assessment of carotid flow rates, flow velocities, and the intracranial collateral circulation may add independent information to refine the estimation of stroke risk in patients with asymptomatic carotid atherosclerosis.

Large eddy simulation of a stenosed artery using a femoral artery pulsatile flow profile

Computational fluid dynamics simulation of stenosed arteries allows the analysis of quantities including wall shear stress, velocity, and pressure; detailed in vivo measurement is difficult yet the analysis of the fluid dynamics related to stenosis is important in understanding the likely causes and ongoing effects on the integrity of the vessel. In this study, a three-dimensional Large Eddy Simulation is conducted of a 50% occluded vessel, with a typical femoral artery profile used as the transient inlet conditions. The fluid is assumed to be homogenous, Newtonian and incompressible and the walls are assumed rigid. The stenosis is axisymmetric, however the three-dimensional study allows for a flow field that is not axisymmetric and results show significant three-dimensionality. High values of wall shear stress and oscillatory values of wall shear stress (varying in both space time) are observed. The results of the study give insight into the time-varying flow structures for a mildly stenosed artery and indicate that three-dimensional simulations may be important to gain a complete understanding of the flow field.

Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions

Shear stress plays a pivotal role in pathogenesis of coronary heart disease. The spatial and temporal variation in hemodynamics of blood flow, especially shear stress, is dominated by the vessel geometry. The goal of the present study was to investigate the effect of 2D and 3D geometries on the numerical modeling of coronary blood flow and shear stress distribution. We developed physiologically realistic 2D and 3D models (with similar geometries) of the human left coronary artery under normal and stenosis conditions (30%, 60%, and 80%) using PROE (WF 3). Transient blood flows in these models were solved using laminar and turbulent (k-ω) models using a computational fluid dynamics solver, FLUENT (v6.3.26). As the stenosis severity increased, both models predicted a similar pattern of increased shear stress at the stenosis throat, and in recirculation zones formed downstream of the stenosis. The 2D model estimated a peak shear stress value of 0.91, 2.58, 5.21, and 10.09 Pa at the throat location under normal, 30%, 60%, and 80% stenosis severity. The peak shear stress values at the same location estimated by the 3D model were 1.41, 2.56, 3.15, and 13.31 Pa, respectively. The 2D model underestimated the shear stress distribution inside the recirculation zone compared with that of 3D model. The shear stress estimation between the models diverged as the stenosis severity increased. Hence, the 2D model could be sufficient for analyzing coronary blood flow under normal conditions, but under disease conditions (especially 80% stenosis) the 3D model was more suitable.

A simple fluid-structure coupling algorithm for the study of the anastomotic mechanics of vascular grafts

Vascular anastomoses constitute a main factor in poor graft performance due to mismatches in distensibility between the host artery and the graft. This work aims at computational fluid-structure investigations of proximal and distal anastomoses of vein grafts and synthetic grafts. Finite element and finite volume models were developed and coupled with a user-defined algorithm. Emphasis was placed on the simplicity of the coupling algorithm. An artery and vein graft showed a larger dilation mismatch than an artery and synthetic graft. The vein graft distended nearly twice as much as the artery while the synthetic graft displayed only approximately half the arterial dilation. For the vein graft, luminal mismatching was aggravated by development of an anastomotic pseudo-stenosis. While this study focused on end-to-end anastomoses as a vehicle for developing the coupling algorithm, it may serve as useful point of departure for further investigations such as other anastomotic configurations, refined modelling of sutures and fully transient behaviour.

Coupled fluid-wall modelling of steady flow in stenotic carotid arteries

Arterial stenoses may cause critical blood flow and wall conditions leading to clinical complications. In this paper computational models of stenotic carotid arteries are proposed and the vessel wall collapse phenomenon is studied. The models are based on fluid-structure interactions (FSI) between blood and the arterial walls. Coupled finite element and computational fluid dynamics methods are used to simultaneously solve for stress and displacement in the solid, and for pressure, velocity and shear stress in the fluid domain. Results show high wall shear stress at the stenosis throat and low (negative) values accompanied by disturbed flow patterns downstream of the stenosis. The wall circumferential stress varies abruptly from tensile to compressive along the stenosis with high stress concentration on the plaque shoulders showing regions of possible plaque rupture. Wall compression and collapse are observed for severe cases. Post-stenotic collapse of the arterial wall occurs for stenotic severity as low as 50%, with the assumption that a given amount of blood flow needs to pass the stenotic artery; whereas if constant pressure drop should be maintained across a constriction, then collapse happens at severity of 75% and above. The former assumption is based on the requirement of adequate blood supply to the downstream organs/tissue, while the latter stems from the fact that the pumping mechanism of the body has a limited capacity in regulating blood pressure, in case a stenosis appears in the vasculature.

Atheromas feel the pressure: biomechanical stress and atherosclerosis

Atherosclerosis, a chronic vascular disease, is the underlying cause of over half the deaths in the United States each year. Variations in local vascular hemodynamics predispose select sites in the vasculature to atherosclerosis, and the atherosclerotic lesions, in turn alter the biomechanical functioning of the local microenvironment, the consequences of which are not well understood on a molecular level. Further progress in the field of atherosclerosis will require an understanding of the relationship between biomechanics, the tissue microenvironment, and the cellular and molecular response to these factors. This review summarizes this field, particularly within the context of the vascular smooth muscle cell.

Acquisition of 3-D arterial geometries and integration with computational fluid dynamics

A system for acquisition of 3-D arterial ultrasound geometries and integration with computational fluid dynamics (CFD) is described. The 3-D ultrasound is based on freehand B-mode imaging with positional information obtained using an optical tracking system. A processing chain was established, allowing acquisition of cardiac-gated 3-D data and segmentation of arterial geometries using a manual method and a semi-automated method, 3D meshing and CFD. The use of CFD allowed visualization of flow streamlines, 2-D velocity contours and 3-D wall shear stress. Three-dimensional positional accuracy was 0.17-1.8mm, precision was 0.06-0.47mm and volume accuracy was 4.4-15%. Patients with disease and volunteers were scanned, with data collection from one or more of the carotid bifurcation, femoral bifurcation and abdominal aorta. An initial comparison between a manual segmentation method and a semi-automated method suggested some advantages to the semi-automated method, including reduced operator time and the production of smooth surfaces suitable for CFD, but at the expense of over-smoothing in the diseased region. There were considerable difficulties with artefacts and poor image quality, resulting in 3-D geometry data that was unsuitable for CFD. These artefacts were exacerbated in disease, which may mean that future effort, in the integration of 3-D arterial geometry and CFD for clinical use, may best be served using alternative 3-D imaging modalities such as magnetic resonance imaging and computed tomography.

Numerical simulation of pulsatile turbulent flow in tapering stenosed arteries

Purpose

The purpose of this paper is to investigate the geometric effects and pulsatile characteristics during the stenotic flows in tapering arteries.

Design/methodology/approach

The low Reynolds number k − ω turbulence model is applied to describe the stenotic flows in the tapering arteries in this paper. The results are divided into two sections. The first section characterizes the geometric effects on the turbulent flow under steady condition. The second section illustrates the key physiological parameters including the pressure drop and wall stress during the periodic cycle of the pulsatile flow in the arteries.

Findings

The tapering and stenoses severity intensify the turbulent flow and stretch the recirculation zones in the turbulent arterial flow. The wall shear stress, pressure drop and velocity vary most intensively at the peak phase during the periodic cycle of the pulsatile turbulent flow.

Originality/value

This paper provides a comprehensive understanding of the spatial‐temporal fluid dynamics involved in turbulent and transitional arterial flow with stenoses. The low Reynolds number k − ω turbulence model method is applied for the analyses of the geometric effects on the arterial flow and fluid feature during the periodic cycle.

Fluid—structure interaction in axially symmetric models of abdominal aortic aneurysms

Abdominal aortic aneurysm disease progression is probably influenced by tissue stresses and blood flow conditions and so accurate estimation of these will increase understanding of the disease and may lead to improved clinical practice. In this work the blood flow and tissue stresses in axially symmetric aneurysms are calculated using a complete fluid—structure interaction as a benchmark for calculating the error introduced by simpler calculations: rigid walled for the blood flow, homogeneous pressure for the tissue stress, as well as one-way-coupled interactions. The error in the peak von Mises stress in a homogeneous pressure calculation compared with a fluid—structure interaction calculation was less than 3.5 per cent for aneurysm diameters up to 7 cm. The error in the mean wall shear stress, in a rigid-walled calculation compared with a fluid—structure interaction calculation, varied from 30 per cent to 60 per cent with increasing aneurysm diameter. These results suggest that incorporation of the fluid—structure interaction is unnecessary for purely mechanical modelling, with the aim of evaluating the current rupture probability. However, for more complex biological modelling, perhaps with the aim of predicting the progress of the disease, where accurate estimation of the wall shear stress is essential, some form of fluid—structure interaction is necessary.