Unsteady stenosis flow prediction: a comparative study of non-Newtonian models with operator splitting scheme

Effect of rheological models on pulsatile hemodynamics in a multiply afflicted descending human aortic network

In the cardiovascular diseased (CVD) conditions, it is essential to choose a suitable rheological model for capturing the correct physics behind the hemodynamic in the multiply afflicted diseased arterial network. This study investigates the effect of blood rheology on hemodynamics in a blood vessel with abdominal aortic aneurysm (AAA) and right internal iliac stenosis (RIIAS). A model with AAA and RIIAS is reconstructed from a human subject's computed tomography (CT) data. Localized mesh generation and pulsatile inflow condition are considered. Non-Newtonian models such as the Power-law, Carreau, Cross, and Herschel Berkley models are used in simulations. The outcome from a validated computational model is compared with the Newtonian model to identify the suitable model for dealing with pathological complications under consideration. The capabilities and significance of various rheological models are also examined via Wall Pressure (WP), Wall Shear Stress (WSS), velocity, Global non-Newtonian importance factor (IG), Vorticity Streamlines, and Swirling Strength. It is noted that during the entire cardiac cycle, the IG factor of the cross model is found to be relatively more significant. Power Law depicts larger IG factor during peak systole and early diastole. Also, the cross model depicts larger WSS, WPS, swirling strength distribution and vorticity during the peak systolic and diastolic phases It is noted that IG ∼0.02 is an appropriate non-Newtonian blood activity cut-off value in the descending abdominal artery having AAA and RIIAS. The critical important WSS values are in the range of 0-9 Pa which is stated in WSS contour plot.

Prediction of Hemodynamic-Related Hemolysis in Carotid Stenosis and Aiding in Treatment Planning and Risk Stratification Using Computational Fluid Dynamics

Atherosclerosis affects human health in many ways, leading to disability or premature death due to ischemic heart disease, stroke, or limb ischemia. Poststenotic blood flow disruption may also play an essential role in artery wall impairment linked with hemolysis related to shear stress. The maximum shear stress in the atherosclerotic plaque area is the main parameter determining hemolysis risk. In our work, a 3D internal carotid artery model was built from CT scans performed on patients qualified for percutaneous angioplasty due to its symptomatic stenosis. The obtained stenosis geometries were used to conduct a series of computer simulations to identify critical parameters corresponding to the increase in shear stress in the arteries. Stenosis shape parameters responsible for the increase in shear stress were determined. The effect of changes in the carotid artery size, length, and degree of narrowing on the change in maximum shear stress was demonstrated. Then, a correlation for the quick initial diagnosis of atherosclerotic stenoses regarding the risk of hemolysis was developed. The developed relationship for rapid hemolysis risk assessment uses information from typical non-invasive tests for treated patients. Practical guidelines have been developed regarding which stenosis shape parameters pose a risk of hemolysis, which may be adapted in medical practice.

Hemolysis of red blood cells in blood vessels modeled via computational fluid dynamics

The research aims to verify the universal relationship between vessel shape and the risk of hemolysis using a rheological model of blood reflecting the physiological processes related to blood for any blood vessel. Blood is a multi-component fluid, the rheology of which depends on many factors, such as the concentration of red blood cells and local shear stress, which significantly affect the process of hemolysis. Blood rheology models used so far cannot be used for all flows and geometries. Therefore, a new rheology model has been introduced suitable for modeling hemolytic flows observed in arteries with atherosclerotic lesions in the in vivo environment. The previously presented model also has advantages in modeling local viscosity in stenosis. Geometries of the blood vessels from computed tomography scans and simplified models of the actual arteries observed during medical procedures were used in the calculations. Population Balance Based Rheology model predicts the concentration of single, deagglomerated red blood cells and the concentration and size of red blood cell agglomerates, which affect blood rheology and hemolysis. Based on the simulations carried out, a correlation was found between the shape of the vessel cavity and the risk of hemolysis. Presented results can be used in the future to create a correlation between the shape of the atherosclerotic lesions and the risk of hemolysis in the blood to make an initial risk assessment for a given patient.

Vertebral artery hypoplasia as an independent risk factor of posterior circulation atherosclerosis and ischemic stroke

ABSTRACT

Vertebral artery hypoplasia (VAH) is a frequent anatomical variation of vertebral arteries, with emerging evidence suggesting that it contributes to posterior circulation ischemia. However, the relationship between VAH and ischemic stroke remains unknown. Hence, this study aimed to determine the prevalence of VAH in patients diagnosed with acute ischemic stroke who were followed up in a neurology clinic and to determine if it can potentially be a risk factor for atherosclerotic stenosis in vertebrobasilar circulation.This retrospective study included 609 patients diagnosed with acute ischemic stroke between January 1, 2019 and January 1, 2020. Demographic of patients, risk factors, radiological and clinical characteristics were evaluated.Posterior circulation was very common in patients with VAH, and the most common locations of atherosclerotic stenosis were V1 and V4 segments of the vertebral artery and the middle segment of basilar artery. Analysis of the risk factors for atherosclerotic stenosis in patients with posterior circulation acute ischemic stroke suggested that VAH was an independent risk factor.Findings of the study suggest that VAH pre-disposes atherosclerotic stenosis in vertebrobasilar circulation, although its mechanism remains unknown. Hemodynamic parameters associated with atherosclerosis could not be measured in vivo. Thus, to better understand the underlying mechanism, conducting studies that examine blood flow parameters with high-resolution magnetic resonance angiography in patients diagnosed with acute cerebral ischemia patients with VAH is warranted.

Effects of different non-Newtonian models on unsteady blood flow hemodynamics in patient-specific arterial models with in-vivo validation

The aim of this study is to demonstrate the implications of using different blood rheological models in the simulation of blood flow dynamics in atherosclerotic coronary arteries. Computational fluid dynamics simulation was performed using three-dimensional (3D) patient-specific models of diseased left anterior descending (LAD) coronary arteries with varying degrees of stenosis severity. The three-dimensional arterial models were reconstructed from 3D quantitative coronary angiography, and input flow conditions were prescribed with blood flow conditions measured in-vivo. Different blood viscosity models were used for the simulations, and they include Newtonian and also non-Newtonian models such as Bingham, Carreau, Carreau-Yasuda, Casson, modified Casson, Cross, modified Cross, simplified Cross, Herschel Bulkley, Kuang-Luo (K-L), PowellErying, modified PowellErying, Power-law, Quemada and Walburn-Schneck models. Results from this study show that the time-averaged velocity at the centre of the arteries produced in the CFD simulations that uses the Carreau, modified Casson or Quemada blood viscosity models corresponded exceptionally well with the clinical measurements regardless of stenosis severities and hence, highlights the usefulness of these models to determine the potential determinants of blood vessel wall integrity such as dynamic blood viscosity, blood velocity and wall shear stress.

EFFECT OF STENOSIS SEVERITY ON SHEAR-INDUCED DIFFUSION OF RED BLOOD CELLS IN CORONARY ARTERIES

In large blood vessels, migration of red blood cells (RBCs) affects the concentration of platelets and the transport of oxygen to the arterial endothelial cells. In this work, we investigate the locations where hydrodynamic diffusion of RBCs occurs and the effects of stenosis severity on shear-induced diffusion (SID) of RBCs, concentration distribution and wall shear stress (WSS). For the first time, multiphase mixture theory approach with Phillips shear-induced diffusive flux model coupled with Quemada non-Newtonian viscosity model has been applied to numerically simulate the RBCs macroscopic behavior in four different degrees of stenosis (DOS) geometries, viz., 30%, 50%, 70% and 85%. Considering SID of RBCs, the calculated average WSS increased by 77.70% which emphasises the importance of SID in predicting hemodynamic parameters. At the stenosis throat, it was observed that 85% DOS model had the lowest concentration of RBCs near the wall and highest concentration at the center. For the stenosis models with 70% and 85% DOS, the RBC lumen wall concentration at the distal section of stenosis becomes inhomogeneous with the maximum fluctuation of 1.568%. Finally, the wall regions with low WSS and low RBC concentrations correlate well with the atherosclerosis sites observed clinically.

Variations in pulsatile flow around stenosed microchannel depending on viscosity

In studying blood flow in the vessels, the characteristics of non-Newtonian fluid are important, considering the role of viscosity in rheology. Stenosis, which is an abnormal narrowing of the vessel, has an influence on flow behavior. Therefore, analysis of blood flow in stenosed vessels is essential. However, most of them exist as simulation outcomes. In this study, non-Newtonian fluid was observed in stenosed microchannels under the pulsatile flow condition. A polydimethylsiloxane channel with 60% stenosis was fabricated by combining an optic fiber and a petri dish, resembling a mold. Three types of samples were prepared by changing the concentrations of xanthan gum, which induces a shear thinning effect (phosphate buffered saline (PBS) solution as the Newtonian fluid and two non-Newtonian fluids mimicking normal blood and highly viscous blood analog). The viscosity of the samples was measured using a Y-shaped microfluidic viscometer. Thereafter, velocity profiles were analyzed under the pulsatile flow condition using the micro-particle image velocimetry (PIV) method. For the Newtonian fluid, the streamline was skewed more to the wall of the channel. The velocity profile of the non-Newtonian fluid was generally blunter than that of the Newtonian fluid. A highly oscillating wall shear stress (WSS) during the pulsatile phase may be attributed to such a bluntness of flow under the same wall shear rate condition with the Newtonian fluid. In addition, a highly viscous flow contributes to the variation in the WSS after passing through the stenosed structures. A similar tendency was observed in simulation results. Such a variation in the WSS was associated with plaque instability or rupture and damage of the tissue layer. These results, related to the influence on the damage to the endothelium or stenotic lesion, may help clinicians understand relevant mechanisms.

COUPLE STRESS FLUID MODEL FOR PULSATILE FLOW OF BLOOD IN A POROUS TAPERED ARTERIAL STENOSIS UNDER MAGNETIC FIELD AND PERIODIC BODY ACCELERATION

In this paper, a magnetic and non-Newtonian fluid model for pulsatile flow of blood with periodic body acceleration has been investigated by adopting Laplace transform and finite Hankel transform. A closed form of analytic solution is obtained for physiologically important quantities such as velocity profile, flow rate, wall shear stress and flow resistance. Effects of different physical parameters reflecting couple stress parameter, Darcy number, Hartman number, tapering angle (divergent tapered tube or convergent tapered tube), shape stenosis parameter and amplitude of periodic acceleration on wall shear stress and flow resistance have been emphasized. For any value of taper angle ([Formula: see text]) and stenotic height ([Formula: see text]), it is pertinent to point out here that the wall shear stress is less in the case of flow through the asymmetric stenosed tube as compared to the case of flow through the symmetric stenosed tube when one is in the up-stream of flow region, but it is of opposite behavior as one moves in the down-stream of flow region. It is important to note that the flow resistance increases significantly and more nonlinearly with the increase in the axial distance in the case of flow through a converging tapered artery with stenosis as compared to that of the same flow through a stenosed artery. The size of trapping bolus becomes larger for the flow of couple stress fluid through a converging tapered arterial stenosis than that of the same flow through a stenosed artery. Another important result is that as compared to the case of Newtonian fluid, the couple stress fluid behaviour plays a key role in increasing the size of trapping bolus. This investigation puts forward important observations that the asymmetric nature of stenosis considered plays a predominant role in reducing the flow resistance in the case of diseased blood vessel and the flow resistance is higher for the case of couple stress fluid than that of Newtonian fluid. Finally, some applications of the present model have been briefly discussed.

WALL SHEAR STRESS AND OSCILLATORY SHEAR INDEX DISTRIBUTION IN CAROTID ARTERY WITH VARYING DEGREE OF STENOSIS: A HEMODYNAMIC STUDY

A significant proportion of cerebral stroke is a consequence of the arterial stenotic plaque rupture causing local thrombosis or distal embolization. The formation and subsequent rupture of the plaque depends on wall shear stress (WSS) and oscillatory shear index (OSI). The purpose of the present study was to understand the effect of hemodynamics on the spatial and temporal variations of WSS and OSI using realistic models with varying degree of carotid artery stenosis (DOS). Multiple CT volumes were obtained from subjects in the carotid bifurcation zone and the 3D models were generated. A finite volume-based computational fluid dynamics (CFD) method was utilized to understand the hemodynamics in pulsatile flow conditions. It was observed that high stenosis models occupied a large value of normalized WSS in the internal carotid artery (ICA) whereas they had smaller values of normalized WSS in the common carotid artery (CCA). For clinical use, the authors recommend using the spatial average value of oscillatory shear rather than the maximum value for an accurate knowledge about the severity of stenosis. The resultant vorticity changes the direction of spin after the bifurcation zone. Additionally, we propose the use of limiting streamlines as a novel and convenient method to identify the disturbed flow regions that are prone to atherogenesis.

NUMERICAL SIMULATION OF TRANSIENT BLOOD FLOW THROUGH THE LEFT CORONARY ARTERY WITH VARYING DEGREES OF BIFURCATION ANGLES

Atherosclerosis is a cardiovascular condition that can occur in any part of the vascular system. Especially, it can exist in bifurcated arteries such as the left and right coronary arteries, abdominal aortic bifurcation or carotid artery bifurcation. In our study, we examine the left coronary artery as an exemplification using wall shear stress (WSS) and wall pressure gradient (WPG). Then, we attempt to find the relationship between bifurcated arterial geometry and hemodynamics. Computational fluid dynamics (CFD) is a common technique applied to characterize blood flow accurately and assist us to gain an insight of atherosclerosis. In this paper, we used CFD as the computational hemodynamics analysis technique to examine flow through the left coronary artery that has variable angular bifurcation. Our results demonstrated that the region of low WSS area and magnitudes of maximum WPG increases with the angles of bifurcation. Such hemodynamic condition resulting from the large bifurcation angles has an effect on atherogenesis and is worthy of investigation for better understanding of atherosclerosis.

Computational evaluation of smoothed particle hydrodynamics for implementing blood flow modelling through CT reconstructed arteries

Simulation of blood flow in a stenosed artery using Smoothed Particle Hydrodynamics (SPH) is a new research field, which is a particle-based method and different from the traditional continuum modelling technique such as Computational Fluid Dynamics (CFD). Both techniques harness parallel computing to process hemodynamics of cardiovascular structures. The objective of this study is to develop and test a new robust method for comparison of arterial flow velocity contours by SPH with the well-established CFD technique, and the implementation of SPH in computed tomography (CT) reconstructed arteries. The new method was developed based on three-dimensional (3D) straight and curved arterial models of millimeter range with a 25% stenosis in the middle section. In this study, we employed 1,000 to 13,000 particles to study how the number of particles influences SPH versus CFD deviation for blood-flow velocity distribution. Because further increasing the particle density has a diminishing effect on this deviation, we have determined a critical particle density of 1.45 particles/mm2 based on Reynolds number (Re = 200) at the inlet for an arterial flow simulation. Using this critical value of particle density can avoid unnecessarily big computational expenses that have no further effect on simulation accuracy. We have particularly shown that the SPH method has a big potential to be used in the virtual surgery system, such as to simulate the interaction between blood flow and the CT reconstructed vessels, especially those with stenosis or plaque when encountering vasculopathy, and for employing the simulation results output in clinical surgical procedures.

Numerical Investigation of Oxygenated and Deoxygenated Blood Flow through a Tapered Stenosed Arteries in Magnetic Field

Current paper is focused on transient modeling of blood flow through a tapered stenosed arteries surrounded a by solenoid under the presence of heat transfer. The oxygenated and deoxygenated blood are considered here by the Newtonian and Non-Newtonian fluid (power law and Carreau-Yasuda) models. The governing equations of bio magnetic fluid flow for an incompressible, laminar, homogeneous, non-Newtonian are solved by finite volume method with SIMPLE algorithm for structured grid. Both magnetization and electric current source terms are well thought-out in momentum and energy equations. The effects of fluid viscosity model, Hartmann number, and magnetic number on wall shear stress, shearing stress at the stenosis throat and maximum temperature of the system are investigated and are optimized. The current study results are in agreement with some of the existing findings in the literature and are useful in thermal and mechanical design of spatially varying magnets to control the drug delivery and biomagnetic fluid flows through tapered arteries.

High shear stress induces atherosclerotic vulnerable plaque formation through angiogenesis

Rupture of atherosclerotic plaques causing thrombosis is the main cause of acute coronary syndrome and ischemic strokes. Inhibition of thrombosis is one of the important tasks developing biomedical materials such as intravascular stents and vascular grafts. Shear stress (SS) influences the formation and development of atherosclerosis. The current review focuses on the vulnerable plaques observed in the high shear stress (HSS) regions, which localizes at the proximal region of the plaque intruding into the lumen. The vascular outward remodelling occurs in the HSS region for vascular compensation and that angiogenesis is a critical factor for HSS which induces atherosclerotic vulnerable plaque formation. These results greatly challenge the established belief that low shear stress is important for expansive remodelling, which provides a new perspective for preventing the transition of stable plaques to high-risk atherosclerotic lesions.

STUDY ON THE IMPACT OF STRAIGHT STENTS ON ARTERIES WITH DIFFERENT CURVATURES

Different stent structures lead to different deformations of blood vessels, such as different cross-sectional shapes, which further influence the blood flow patterns. In this paper, six non-commercial stents with different link structures called I-, C-, S-, U-, N- and W-types were considered. Their influences on arteries with five different curvatures (i.e., 0[Formula: see text], 15[Formula: see text], 30[Formula: see text], 45[Formula: see text] and 60[Formula: see text]) were studied using finite element method. Four indices including the maximum plastic strain of stents, the rate of expansion, the maximum von Mises stress and the ellipticity of arteries, were compared for all cases. The results showed that the S-type or U-type stents, with larger plastic strain and lower von Mises stress on the arteries, provided the optimal outcome. As the link structures became complex, the arterial expansion increased monotonically, while the ellipticity of arteries showed a decreasing tendency in the vessel models. The present study could be useful for the commercial design and clinic selection of a stent with different link structures for different curved arteries.

SURGICAL DECISION OF CORONARY ARTERY BYPASS GRAFTING FOR NORMAL LEFT ANTERIOR DESCENDING ARTERY (LAD) AND LAD WITH STENOSIS: SEQUENTIAL GRAFT OR NOT

Sequential graft was used frequently in clinical studies. In this study, the hemodynamic effect of one kind of sequential graft in two different conditions of the lesion was discussed and some recommendations on the surgical procedures were made. A patient-specific three-dimensional (3D) model of left anterior descending artery (LAD) was reconstructed. A moderate stenosis exist in the trunk of LAD between the first and the second diagonal branch (D1 and D2). Another 3D model without stenosis was also reconstructed based on the patient-specific model. Sequential graft and single graft were applied on these two 3D model. Thus four 3D models were built so that the hemodynamic effect of sequential graft can be discussed. The zero-dimensional (0D)/3D coupling method was used to perform the numerical simulation by coupling the 3D artery model with a 0D lumped parameter model of the cardiovascular system. The flow rates in the branches of LAD and the graft flow were calculated and illustrated in this paper. The wall shear stress (WSS) and oscillatory shear index (OSI) were also calculated and depicted. If the native LAD is stenosis, sequential graft should be applied for the short-term outcomes. Moreover, the long-term patency of the sequential graft applied on the stenosis LAD is good. The long-term patency of the single graft was bad. But the short-term outcomes are almost the same when LAD is not stenosis. If no stenosis exist in the native LAD, a graft with smaller diameter should be applied to improve the long-term patency.

INFLUENCE OF BIFURCATION DIAMETER ON THE VERTEBRAL ARTERY ORIGIN STENOSIS: A SIMULATION STUDY OF HEMODYNAMICS

The stenosis at the beginning segment of the vertebral artery accounts for the first risk of stroke in the posterior circulation. The extracranial vertebral arteries, especially the proximal ends, have been considered to be the predilection sites of stenosis or occlusion. From the perspective of hemodynamics, the mechanics of vertebral arteries stenosis is still unclear. In this paper, the formation of atherosclerosis in proximal end was concerned from the aspects of the effect of bifurcation diameter. Different models represent different bifurcation diameter. In order to find correlation between bifurcation diameter and WSS we build different models. Three idealized models with the vertebral artery diameter of [Formula: see text][Formula: see text]m (Model A1), [Formula: see text][Formula: see text]m (Model A2) and [Formula: see text][Formula: see text]m (Model A3) respectively and seven realistic models were analyzed by using computational fluid dynamics tools. The area of low wall shear stress (WSS, [Formula: see text] 1.5[Formula: see text]Pa) in the proximal end of vertebral artery extracted at the peak systole in the idealized models were 2.25[Formula: see text]e-7, 8.55[Formula: see text]e-7 and 1.61[Formula: see text]e-6[Formula: see text]m2, respectively. The area of low WSS on the vertebral artery origin of realistic models extracted at the peak systole were 0, 1.18[Formula: see text]e-09, 3.91[Formula: see text]e-07, 1.68[Formula: see text]e-07, 5.46[Formula: see text]e-06, 1.16[Formula: see text]e-06 and 2.25[Formula: see text]e-06[Formula: see text]m2, respectively. Moreover, the time-averaged WSSs of the three idealized models were 3.95, 3.56 and 3.19, respectively. The time-averaged WSSs of the realistic models were 6.28, 6.36, 4.48, 4.71, 3.59, 3.59 and 3.31[Formula: see text]Pa, respectively. With the increase of bifurcation diameter, the risk of endothelial dysfunction increases, and the same is to intimal hyperplasia.

MODELING AND HEMODYNAMIC SIMULATION OF HUMAN ARTERIAL STENOSIS VIA TRANSMISSION LINE MODEL

Arterial stenosis plays a key role in the development and formation of cardiovascular diseases. The effects of arterial stenosis on the global hemodynamic characteristics of human artery tree were studied based on a previously proposed transmission line model of 55 segment arterial tree. Different position, degree and length of the arterial stenosis were simulated to discuss the changes of blood pressure and flow waveform in human arterial tree. The stenosis degree of 50% to 90% were specified to represent a mild, moderate or severe stenosis. Three representative stenosis positions: aorta, carotid and iliac artery were selected. The stenosis length was specified to be 1[Formula: see text]cm to 4[Formula: see text]cm. The results of simulation were compared with the literature data. And ankle branchial index (ABI) was calculated to show its relationship with the stenosis position. The results showed that the influence of aorta stenosis on the blood pressure and flow waveforms of upstream artery is more obvious than those of downstream artery; branch artery stenosis has more influence on the blood pressure and flow waveforms of downstream artery than those of upstream artery. When the stenosis degree increased to 80%, the blood pressure and flow waveforms are affected significantly. The stenosis length causes a obvious change in the pressure and flow waveforms of stenosis inlet and outlet. The comparisons of literature and ABI demonstrated that the modeling method is a feasible tool to simulate and study the hemodynamics of the human artery stenosis.

MECHANICS OF BIOLOGICAL BLOOD FLOW ANALYSIS THROUGH CURVED ARTERY WITH STENOSIS

The viscous fluid model is considered in this article for the study of blood flow through an axis-symmetric stenosis with the effect of three distinct types of arteries i.e., diverging tapering arteries, converging tapering arteries and nontapered arteries. The Cauchy–Euler method has been used for the solution to velocity profile, resistance impedance to flow and the pressure gradient. The characteristics of viscous blood flow on velocity profile, impedance resistance to flow and pressure gradient have been discussed by plotting the graphs of various flow parameters and finally it is found that stenosis dominantes the curvature of curved artery.

VALIDATION OF LOSS-COEFFICIENT-BASED OUTLET BOUNDARY CONDITIONS FOR SIMULATING AORTIC FLOW

Flow in a polyurethane model of a human aorta, driven by a heart-lung machine, is analyzed experimentally and computationally for antegrade and retrograde perfusion. The purpose of the analysis is the validation of the previously proposed loss-coefficient-based outlet boundary condition for aortic branches. This model is claimed to be commonly applicable to different perfusion modes of the aorta, unlike the alternative straightforward constant-pressure outlet boundary condition. First, the antegrade perfusion is analyzed computationally and experimentally. This step delivers the loss-coefficients that are to be used in any other perfusion mode of the aorta. Subsequently, a retrograde perfusion is applied to the same aorta, where the flow rates at the outlets of the aortic branches are measured and predicted by applying the loss-coefficient-based outlet boundary conditions. A very good agreement of the predictions with the measurements is observed. The predictions delivered by the standard constant-pressure outlet boundary condition are observed, on the contrary, to be highly in error. Thus, the advocated loss-coefficient-based outlet boundary condition is experimentally validated. It is shown that it is applicable to different perfusion modes with a quite good accuracy, which is much higher compared to the straightforward constant-pressure outlet boundary condition.

FSI SIMULATION OF A HEALTHY CORONARY BIFURCATION FOR STUDYING THE MECHANICAL STIMULI OF ENDOTHELIAL CELLS UNDER DIFFERENT PHYSIOLOGICAL CONDITIONS

Atherosclerosis is a world-spread and well-known disease. This disease strongly relates to the endothelial cells (ECs) function. Normally, the endothelial cells align in the flow direction in the atheroprotected sites; however, in the case of atheroprone sites these cells orient randomly. The mechanical stimuli such as wall shear stress and strains could determine the morphology and function of the endothelial cells. In the present study, we numerically simulated the left main coronary artery (LCA) and its branches to left anterior descending (LAD) and left circumflex coronary (LCX) artery using fluid–structure interaction (FSI) modeling. The results were presented as longitudinal and circumferential strains of ECs as well as wall shear stress. Wide ranges of heart rate, cardiac motion, systolic and diastolic pressures were considered and their effects on mechanical stimuli were described in detail. The results showed that these factors could greatly influence the risk of atherosclerosis and the location of atherosclerotic lesions.

RUPTURE MODEL OF INTRACRANIAL SACCULAR ANEURYSMS DUE TO HYPERTENSION

The risk of rupture of intracranial saccular aneurysms is one of the leading dilemmas for patients and neurologists. Although the probability of rupture is small, the consequences of rupture are usually fatal or crippling, and a concern for the patient is whether or not to treat an existing aneurysm. In this paper, an idealized model of saccular aneurysms with assumed Fung material behavior was investigated for rupture potential when the stresses exceeded the maximum wall strength of the aneurysm wall. Numerical simulations used various levels of blood pressure, from normal to hypertensive, in order to determine correlations of aneurysm size and risk of rupture. Results showed that hypertensive individuals harboring cerebral aneurysms with a size of at least 6 mm are at risk.

A comparative study of three speckle reducing methods for intima-media thickness ultrasound images

BACKGROUND

Ultrasonic evaluation of intima-media thickness (IMT) is an early marker of assessing the development of atherosclerosis and determining cardiovascular risk. To attain the best possible diagnosis, it is essential that medical images be clear, sharp and without noise and artifacts.

OBJECTIVES

Comparison of speckle reducing anisotropic diffusion (SRAD), discrete (DTD) and continuum topological derivative (CTD) on B-mode ultrasound images of common carotid and brachial arteries throughout the cardiac cycle.

PATIENTS AND METHODS

In a cross-sectional design, an examination was performed on forty-two human subjects with a mean age of 44 ± 6 years from April 2013 to June 2013. This study was approved by the ethics committees of Kashan University of Medical Sciences and Beheshti Hospital. An ultrasonic examination of common carotid and brachial arteries of forty-two human subjects was performed. The program was designed in MATLAB software to extract consecutive B-mode images and apply region of interest (ROI) on the IMT of the common carotid and brachial arteries. Then, three different noise reduction filters with the Canny edge detection were used in ROI separately. Finally, the program measured the image quality metrics.

RESULTS

According to values of eleven different image quality metrics (mentioned in the main text), there was a significant difference between CTD, DTD and SRAD filters with the Canny edge detection status in the common carotid and brachial arteries throughout the cardiac cycle (all P values < 0.001). For example, peak signal to noise ratios (PSNR) using CTD, DTD and SRAD filters were 95.43 ± 0.64, 88.86 ± 0.82 and 73.02 ± 0.20 in common carotid and 96.39 ± 1.25, 92.58 ± 0.11 and 88.27 ± 0.63 in brachial arteries, respectively (both P values < 0.001).

CONCLUSIONS

By measuring image quality metrics, this study showed that DTD and CTD filters with the Canny edge detection respectively, are better than SRAD filter with the Canny detection for speckle suppression and details preservation in both arteries in the ultrasound images.

MODELING OF ILIAC ARTERY ANEURYSM USING FLUID–STRUCTURE INTERACTION

The aneurysm of iliac artery is a rare entity and there are few computational models that have studied the disease. In this study, we have presented the flow patterns in the aneurysmal artery using Fluid–structure interaction method. The blood was assumed Newotonian, pulsatile, laminar, incompressible, and homogenous. The geometry of the model was made based on CT images of clinical cases. Using the computational method, we have obtained the velocity and pressure contours, shear rates and vortices for the healthy and aneurysmal artery. The results show that a pressure maximum was found at the midpoint of the dilation. The vortices are formed in the aneurysmal area26 and shear rates do not change much. However, the rate increased in the neck of aneurysms. Furthermore, the aneurysm with bigger dilation tend to rupture due to more shear rates in the neck and the velocity at peak systole decreases in the aneurysmal area due to increase of the artery diameter. We have compared our results with some available relevant clinical data in discussion section.

THE INFLUENCE OF HEMODYNAMICS ON THE ULCERATION PLAQUES OF CAROTID ARTERY STENOSIS

The further rupture of atherosclerotic ulceration plaque is one of the main triggers of the carotid ischemic stroke. However, the abnormal hemodynamics is not well addressed yet. A lesion-based computational fluid dynamic (CFD) analysis is proposed to investigate the complex hemodynamic change of the ulceration plaque that prevails in patients. The 3D models including eight groups of ulcerations (six groups with single ulceration and two groups with two consecutive ulcerations), were reconstructed based on the computer tomography (CT) images, and the tetrahedral grid was taken to mesh the models with the appropriate numbers. After setting the boundary conditions, numerical simulation was carried out to analyze the pulsatile blood flow in the models. The complex flow in the vicinity of the ulcerations directly leads to a significant effect on the distribution of the wall shear stress (WSS). WSS is respectively from 3.29 to 35.41 Pa at the upstream, from 11.90 to 41.85 Pa at the downstream ulceration, and 18.60 and 30.60 Pa in the area between the two consecutive ulcerations. The rupture from these regions could cause the further rupture of ulceration plaques, particularly at the downstream ulceration and the area between the two consecutive ulcerations. The twisting and the curling of the flow at the ulcerations can lead to thrombosis which may break free later and go through the downstream stenosis by the effect of the flow. The different degrees of WSS in downstream and upstream ulcerations will damage the ulceration on the plaque because of pulling and stretching forces at the ulcerations. Furthermore, high wall shear stress gradient (WSSG) also increases the risk of the further rupture. Our study gives a better understanding in the further rupture mechanism of ulceration plaques and provides the information of the location of thrombosis after aggravated rupturing, which can be referred by surgeons to improve the surgical planning.

MODELING OF SUPERIOR MESENTERIC ARTERY ANEURYSM USING FLUID–STRUCTURE INTERACTION

The aim of this study was to model the blood flow and predict related hemodynamics characteristics in healthy superior mesenteric artery (SMA) and saccular aneurysm cases. A fluid–structure interaction (FSI) method was performed, using an arbitrary Langrangian–Eulerian mesh. The computational mesh was generated using anatomical data from available human computed tomography (CT)-images. Combining constitution and momentum equations, projection method, the discretized resultant equation were numerically solved for velocity, pressure, shear stress and vortices for healthy/aneurysmal artery. The results including velocity contours, pressure contours, shear rate values, and vortices were obtained and analyzed for three main steps including peak systole, diastole, and end of cardiac cycle. Profiles show the varying velocity and pressure for a pulsatile flow input before and after aneurysms. They also show the formation of single or multiple vortices at aneurysmal area and decrease of wall shear stress with aneurysm enlargement. Furthermore, shear rate values at the neck of aneurysms exceed throughout the entire cardiac cycle. The outcome of the computational analysis is then compared to information available on pressure, vortices and wall shear stress from some clinical findings.

NUMERICAL SIMULATION OF HEMODYNAMICS IN PORTAL VEIN WITH THROMBOSIS BY COMPUTATIONAL FLUID DYNAMICS

Portal vein thrombosis (PVT) is an important complication that is associated with cirrhotic portal hypertension. The etiology is as yet unclear but could be closely related to the hemodynamics of the portal vein system. This paper investigated the hemodynamics in the portal vein model, both with and without thrombosis, as well as the effect of obstructions on the hemodynamics of the portal vein system using the computational fluid dynamics (CFD) method. PVT can probably develop in the inlets of the portal vein as well as the left/right branches of the portal vein because the distribution of wall shear stress satisfies the conditions for PVT formation based upon the simulation of the hemodynamics in the normal portal vein model. According to the above results, geometric models for a portal vein with a thrombus were constructed and the influence of different degrees (26%, 39%, 53% and 64%) of obstructions was studied. In the model with the maximum obstruction (64% blocked), the maximum velocity of portal vein (PV) increased up to twice than in the model without thrombosis, and the maximum wall shear stress of PV in the model with thrombosis (64% blocked) increased up to 9.4 Pa, whereas it was only 1.9 Pa in the model without thrombosis (nearly one fifth of the maximum wall shear stress). Excessive wall shear stress may cause mechanical damage to the blood vessels and induce physiological changes.

Computational fluid dynamics in coronary artery disease

Computational fluid dynamics (CFD) is a widely used method in mechanical engineering to solve complex problems by analysing fluid flow, heat transfer, and associated phenomena by using computer simulations. In recent years, CFD has been increasingly used in biomedical research of coronary artery disease because of its high performance hardware and software. CFD techniques have been applied to study cardiovascular haemodynamics through simulation tools to predict the behaviour of circulatory blood flow in the human body. CFD simulation based on 3D luminal reconstructions can be used to analyse the local flow fields and flow profiling due to changes of coronary artery geometry, thus, identifying risk factors for development and progression of coronary artery disease. This review aims to provide an overview of the CFD applications in coronary artery disease, including biomechanics of atherosclerotic plaques, plaque progression and rupture; regional haemodynamics relative to plaque location and composition. A critical appraisal is given to a more recently developed application, fractional flow reserve based on CFD computation with regard to its diagnostic accuracy in the detection of haemodynamically significant coronary artery disease.

ENDOTHELIAL MECHANOTRANSDUCTION MECHANISMS FOR VASCULAR PHYSIOLOGY AND ATHEROSCLEROSIS

Vascular physiology and disease progression, such as atherosclerosis, are mediated by hemodynamic force generated from blood flow. The hemodynamic force exerts on vascular endothelial cells (ECs), which could perceive the mechanical signals and transmit them into cell interior by multiple potential shear sensors, collectively known as mechanotransduction. However, we do not understand completely how these shear-sensitive components orchestrate physiological and atherosclerotic responses to shear stress. In this review, we provide an overview of biomechanical mechanisms underlying vascular physiology and atherosclerotic progression. Additionally, we summarize current evidences to illustrate that atherosclerotic lesions preferentially develop in arterial regions experiencing disturbance in blood flow, during which endothelial dysfunction is the initial event of atherosclerosis, inflammation plays dominant roles in atherosclerotic progression, and angiogenesis emerges as compensatory explanation for atherosclerotic plaque rupture. Especially in the presence of systemic risk factors (e.g., hyperlipidaemia, hypertension and hyperglycemia), the synergy between these systemic risk factors with hemodynamic factors aggravates atherosclerosis by co-stimulating some of these biomechanical events. Given the hemodynamic environment of vasculature, understanding how the rapid shear-mediated signaling, particularly in combination with systemic risk factors, contribute to atherosclerotic progression through endothelial dysfunction, inflammation and angiogenesis helps to elucidate the role for atherogenic shear stress in specifically localizing atherosclerotic lesions in arterial regions with disturbed flow.

SWIRLING FLOW CAN SUPPRESS MONOCYTES ADHESION IN END-TO-END ARTERIAL ANASTOMOSIS

To test the hypothesis that the monocytes adhesion would be suppressed by intentionally inducing swirling flow in end-to-end arterial anastomosis to inhibit the flow disturbance, the comparing experimental and numerical investigation under both normal flow condition and swirling flow condition were executed, in which the sudden expanded tube and U-937 cells were used. The numerical results reveal that, comparing to normal flow, the swirling flow could reduce the size of flow disturbed zones and enhance the wall shear stress (WSS) in the closed downstream of sudden expanded tube. The experimental results show that there are disturbed flow zones in the sudden expanded tube, where the adhesion number of U-937 cells is larger than other zones. More importantly, comparing to the normal flow, the swirling flow could reduce the adhesion of U-937 cells, in which the adhesion number become smaller with the increasing of the swirling intensity. Therefore, the present study suggests that intentionally introducing swirling flow in end-to-end arterial anastomosis may be a solution to solve the problem of intimal hyperplasia (IH) by suppressing the flow disturbance and restraining the adhesion of monocytes to keep the favorably unimpeded flow.

NUMERICAL STUDY ON THE EFFECTS OF THE NUMBER AND GEOMETRIES OF DRUG-ELUTING STENT LINKS ON THE DRUG CONCENTRATION

The paper investigated the effects of the link numbers and geometries of drug-eluting stents (DESs) on the hemodynamics and the distribution of drug concentration, and the final results could be used as a guide for the optimization of DES design. Four 3D virtual stents with different numbers and geometries of links were modeled and numerically studied with respect to the distribution of wall shear stress (WSS) and drug concentration. Results have showed (1) The geometries of links have big impact on the distribution of WSS regions and the uniform drug concentration distribution on the vascular wall, but little effect on the mean drug concentration on the vascular wall; the S-shaped link stents had less low-WSS regions and the reason is that the flow direction was considered in the design of this type of stents. (2) The drug concentration distribution on the vascular wall had remarkable difference from that in blood. (3) The 6S link stent had the least low-WSS regions and with high and uniformly distributed drug concentration, so this type of stent was concluded to be the best design in four stents. Overall, it is not reliable to use the drug concentration in blood to deduce the drug concentration on the vascular wall. In DES design, the configuration of links should be, as much as possible, in line with the blood flow direction, so it can decrease the low-WSS regions. Meanwhile, in order to get more uniformly distributed drug on the vascular wall, the distribution of drug on the stent surface should be taken into account. Additionally, because of the increment of contact area between the stents and vascular wall, the drug concentration on the vascular wall increased with the number of links.

NUMERICAL STUDY OF BIDIRECTIONAL GLENN WITH UNILATERAL PULMONARY ARTERY STENOSIS

Purpose: Hypoplastic left heart syndrome (HLHS) is a congenital heart disease and is usually associated with pulmonary artery stenosis. The superior vena cava-to-pulmonary artery (bidirectional Glenn) shunt is used primarily as a staging procedure to the total cava-to-pulmonary connection for single-ventricle complex. When HLHS coexists with pulmonary artery stenosis, the surgeons then face a multiple problem. This leads to high demand of optimized structure of Glenn surgery. The objective of this article is to investigate the influence of various anastomotic structures and the direction of superior vena cava (SVC) in Glenn on hemodynamics under pulse inflow conditions and try to find an optimal structure of SVC in Glenn surgery with unilateral pulmonary artery stenosis.

Method: First, 3D patient-specific models were constructed from medical images of a HLHS patient before any surgery by using the commercial software Mimics, and another software Free-form was used to deform the reconstructed models in the computer. Four 3D patient-specific Glenn models were constructed: model-1 (normal Glenn), model-2 (lean the SVC back to the stenotic pulmonary artery), model-3 (lean the SVC towards the stenotic pulmonary artery), model-4 (add patch at junction of the SVC toward stenosis at pulmonary artery). Second, a lumped parameter model (LPM) was established to predict boundary conditions for computational fluid dynamics (CFD). In addition, numerical simulations were conducted using CFD through the finite volume method. Finally, hemodynamic parameters were obtained and evaluated.

Results: It was showed that model-4 have relatively balanced vena cava blood perfusion into the left pulmonary artery (LPA) and right pulmonary artery (RPA), this may be due to less helical flow and the patch at junction of the SVC. Near stenosis of pulmonary artery, model-4 performed with the higher wall shear stress (WSS), which would benefit endothelial cell function and gene expression. In addition, results showed that model-4 performed with the lower oscillatory shear index (OSI) and wall shear stress gradient (WSSG), which would decrease the opportunity of vascular intimal hyperplasia.

Conclusion: It is benefited that surgeons adds patch at junction of the SVC towards stenosis at pulmonary artery. These results can impact the surgical design and planning of the Glenn surgery with unilateral pulmonary artery stenosis.

BIOMIMETIC STRUCTURE DESIGN OF DRAGONFLY WING VENATION USING TOPOLOGY OPTIMIZATION METHOD

Scientists have carried out research for various biomimetic applications based on the dragonfly wings because of the superb flying skills and lightsome posture. The wings of dragonflies are mainly composed of veins and membranes, which give rise to the special characteristics of their wings that make dragonflies being supremely versatile, maneuverable fliers. Mimicking the dragonfly wing motion is of great technological interest from application's point of view. However, the major challenge is the biomimetic fabrication to replicate the wing motion due to the very complex nature of the wing venation of dragonfly wings. In this regard, the topology optimization method (TOM) is useful to simplify object's structure while retaining its mechanical properties. In this paper, TOM is employed to simplify and optimize the venation structure of dragonfly (Pantala flavescens Fabricius) wing that is captured by a 3D scanner and numerical reconfiguration. Combined with the material parameters obtained from nanoindentation testing, the quantitative models are established based on a finite element (FE) analysis and discussed in static range. The quantitative models are then compared with the square frame, staggered grid frame and hexagonal frame to examine the potentials of the biomimetic structure design for the fabrication of greenhouse roof.

RESEARCH ON THE DISTRIBUTION OF PRESSURE FIELD ON THE BASILAR MEMBRANE IN THE PASSIVE SPIRAL COCHLEA

The cochlea is the important auditory organ of the inner ear. It is responsible for transforming the acoustic signals into neural impulses that travel along the auditory nerve to the brain. The role of, perhaps, the most characteristic feature of the cochlea, its three-dimensional (3D) helical structure, has remained elusive. To address this problem, the present paper develops a 3D spiral cochlea mathematical model using orthogonal coordinate system. Based on the method of separation of variables and conformal transformation, equations of three cases for the velocity potential are derived to solve the steady flow problem of lymph in the cochlea. Then, the distribution of pressure field on the basilar membrane (BM) is obtained. By comparing the analytical results with FE analyses results, the derived formulas are demonstrated to be accurate and reliable. The conclusion can be drawn that the spiral shape and physical dimension of the cochlea have a significant influence on the distribution of pressure field. Interestingly, near the helicotrema, the velocity potential of the first case plays a leading role in pressure distribution on the BM. Therefore, it may enhance the vibration of BM and improve hearing ability in the low-frequency parts of human ears. The proposed model could provide an approach for further investigation of fluid-structure interaction problem in the cochlea.

INTIMAL HYPERPLASIA AND WALL SHEAR IN ARTERIAL BYPASS Y-GRAFTING AND CONSEQUENCE GRAFTING: A NUMERICAL STUDY

The progression of intimal hyperplasia is considered to be the main cause of bypass failure and is directly related to the individual blood rheology, local arterial geometry and placement of the junctions, graft diameter and graft surface characteristics as well as the degree of compliance. In this paper we use commercial computational fluid dynamics (CFD) ANSYS to examine under the correct physiological flow conditions the hemodynamic forces of composite bypass with internal mammary artery in Y-grafting and consequence grafting which is known to achieve high patency rate and highly recommended by clinicians. Particular emphasis is given here on the parameters that could initiate the development of intimal hyperplasia within these bypass configurations. The hemodynamic flow patterns between the consequence grafting and the composite Y-grafting are observed here to be different. Moreover, on both end-to-side and side-to-side configurations, the circulating flows are detected in the vicinity of the junction area, while the Dean flow vortexes are only observed on the end-to-side configuration. Likewise, the hemodynamic flow on the end-to-side configuration on the LCX of both 45° and 90° Y-grafting is found to be smoother than that of the junction on the LCA, regardless of the changing of anastomosis angles. The high WSS gradients are observed at the vicinity of the toe and on the bed of the junction, while the low WSS are presented at the distal of the stenosis and at the stagnation point. The clinical relevance of the results are presented and discussed with particular focus on the factors and the flow patterns that trigger the development of intimal hyperplasia.

SIMULATION OF CASSON FLUID FLOW AND HEAT TRANSPORT IN DIFFERENTLY SHAPED STENOSES

The present investigation deals with a mathematical model representing the response of heat transfer to blood streaming through the arteries under stenotic condition. The flowing blood is represented as the suspension of all erythrocytes assumed to be Casson fluid and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell (MAC) method. The necessary checking for numerical stability has been incorporated into the algorithm for better precision of the results computed. The quantitative analysis carried out finally includes the respective profiles of the flow-field and the temperature along with their individual distributions over the entire arterial segment as well. The key factors like the pressure drop, wall shear stress, flow separation, Nusselt number and streamlines are examined for qualitative insight into the blood flow and heat transport phenomena through arterial stenosis. In conformity with other several existing findings the present simulation predicts that the pressure drop and Nusselt number diminishes with increasing yield stress values, and significant enhancement in values of Nusselt number is observed with increasing severity of the stenosis. However, the effect of the shapes of the stenoses on flow separation cannot be ruled out from the present investigation.

WALL SHEAR STRESSES IN A FLUID–STRUCTURE INTERACTION MODEL OF PULSE WAVE PROPAGATION

In our prior paper, a fluid–structure interaction model of pulse wave propagation, called the elastic tube model, has been developed. The focus of this paper is wall shear stress (WSS) in this model and the effects of different parameters, including rigid walls, wall thickness, and internal radius. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic isotropic, and incompressible. A fluid–structure interaction scheme is constructed using a finite element method. The results demonstrate the elastic tube plays an important role in WSS distributions of wave propagation. It is shown that there is a time delay between the WSS waveforms at different locations in the elastic tube model while the time delay cannot be observed clearly in the rigid tube model. Compared with the elastic tube model, the increase of the wall thickness makes disturbed WSS distributions, however WSS values are increased greatly due to the decrease of the internal radius. The results indicate that the effects of different parameters on WSS distributions are significant. The proposed model gives valid results.

THE IMPACT OF THE NUMBER OF TEARS IN PATIENT-SPECIFIC STANFORD TYPE B AORTIC DISSECTING ANEURYSM: CFD SIMULATION

It is believed that the progression of Stanford type B aortic dissection is closely associated with vascular geometry and hemodynamic parameters. The hemodynamic differences owing to the presence of greater than two tears have not been explored. The focus of the present study is to investigate the impact of an additional re-entry tear on the flow, pressure and wall shear stress distribution in the dissected aorta. A 3D aorta model with one entry and one re-entry tear was generated from computed tomography (CT) angiographic images of a patient with Stanford Type B aortic dissection. To investigate the hemodynamic effect of more than two tear locations, an additional circular re-entry tear was added 24 mm above the original re-entry tear. Our simulation results showed that the presence of an additional re-entry tear provided an extra return path for blood back to the true lumen during systole, and an extra outflow path into the false lumen during diastole. The presence of this additional path led to a decrease in the false lumen pressure, particularly at the distal region. Meanwhile, the presence of this additional tear causes no significant difference on the time average wall shear stress (TAWSS) distribution except at regions adjacent to re-entry tear 2. Moderate and concentrated TAWSS was observed at the bottom region of this additional tear which may lead to further extension of the tear distally.

An investigation of dentinal fluid flow in dental pulp during food mastication: simulation of fluid-structure interaction

This study uses fluid-structure interaction (FSI) simulation to investigate the relationship between the dentinal fluid flow in the dental pulp of a tooth and the elastic modulus of masticated food particles and to investigate the effects of chewing rate on fluid flow in the dental pulp. Three-dimensional simulation models of a premolar tooth (enamel, dentine, pulp, periodontal ligament, cortical bone, and cancellous bone) and food particle were created. Food particles with elastic modulus of 2,000 and 10,000 MPa were used, respectively. The external displacement loading (5 μm) was gradually directed to the food particle surface for 1 and 0.1 s, respectively, to simulate the chewing of food particles. The displacement and stress on tooth structure and fluid flow in the dental pulp were selected as evaluation indices. The results show that masticating food with a high elastic modulus results in high stress and deformation in the tooth structure, causing faster dentinal fluid flow in the pulp in comparison with that obtained with soft food. In addition, fast chewing of hard food particles can induce faster fluid flow in the pulp, which may result in dental pain. FSI analysis is shown to be a useful tool for investigating dental biomechanics during food mastication. FSI simulation can be used to predict intrapulpal fluid flow in dental pulp; this information may provide the clinician with important concept in dental biomechanics during food mastication.

NUMERICAL SIMULATION ON THE EFFECTS OF DRUG-ELUTING STENTS WITH DIFFERENT LINKS ON HEMODYNAMICS AND DRUG CONCENTRATION DISTRIBUTION

The changes of hemodynamics and drug distribution caused by the implantation of drug-eluting stents (DES) have a significant influence on the in-stent restenosis. The present study numerically carried out a comparative study of hemodynamics and drug distribution using four different links of DES: Cordis BX velocity (Model A), Jostent flex (Model B), Sorin Carbostent (Model C), and DT-2 (Model D). The results showed that (1) low wall shear stress (WSS) distribution region spread widely in Model C (16.16%), with the least in Model B (10.35%); (2) Model C has relatively uniform drug concentration and causes of fewer low drug concentration region; and (3) Model A has the largest drug concentration, but also the most uneven distribution of drug. It was concluded that DES with circumferential links helps to improve in-stent restenosis as compared with that with longitudinal designs, and flexible links led to more uniformly and smoothly distributed blood flow than rigid links. However, the links with longitudinal designs had a better performance as drug release carrier than that with circumferential design. And if the links are too close together, the drug cannot be released effectively in the blood vessels. The current study helps to enhance our understanding of the performance of DES and provides assistance for optimal design and selection of DES.

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.

Timing and size of flow impingement in a giant intracranial aneurysm at the internal carotid artery

Flow impingement is regarded as a key factor for aneurysm formation and rupture. Wall shear stress (WSS) is often used to evaluate flow impingement even though WSS and impinging force are in two different directions; therefore, this raises an important question of whether using WSS for evaluation of flow impingement size is appropriate. Flow impinging behavior in a patient-specific model of a giant aneurysm (GA) at the internal carotid artery (ICA) was analyzed by computational fluid dynamics simulations. An Impingement Index (IMI) was used to evaluate the timing and size of flow impingement. In theory, the IMI is related to the WSS gradient, which is known to affect vascular biology of endothelial cells. Effect of non-Newtonian fluid, aneurysm size, and heart rate were also studied. Maximum WSS is found to be proportional to the IMI, but the area of high wall shear is not proportional to the size of impingement. A faster heart rate or larger aneurysm does not produce a larger impinging site, and the Newtonian assumption overestimates the size of impingement. Flow impingement at the dome occurs approximately 0.11 s after the peak of flow waveform is attained. This time delay also increases with aneurysm size and varies with heart rate and waveform.

Experimental and numerical study on the hemodynamics of stenosed carotid bifurcation

Numerical simulation is performed to demonstrate that hemodynamic factors are significant determinants for the development of a vascular pathology. Experimental measurements by particle image velocimetry are carried out to validate the credibility of the computational approach. We present a study for determining complex flow structures using the case of an anatomically realistic carotid bifurcation model that is reconstructed from medical imaging. A transparent silicone replica of the artery is developed for in-vitro flow measurement. The dynamic behaviours of blood through the vascular structure based on the numerical and experimental approaches show good agreement.

On the Relative Importance of Rheology for Image-Based CFD Models of the Carotid Bifurcation

Background: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. Method of Approach: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. Results: Sensitivity of WSS to the various rheological assumptions was roughly 1.0dyn∕cm2 or 8%, nearly seven times less than that due to geometric uncertainty (6.7dyn∕cm2 or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. Conclusions: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.

Spatial and phasic oscillation of non-Newtonian wall shear stress in human left coronary artery bifurcation: an insight to atherogenesis

OBJECTIVE

To investigate the wall shear stress oscillation in a normal human left coronary artery bifurcation computational model by applying non-Newtonian blood properties and phasic flow.

METHODS

The three-dimensional geometry of the investigated model included the left main coronary artery along with its two main branches, namely the left anterior descending and the left circumflex artery. For the computational analyses a pulsatile non-Newtonian flow was applied. To evaluate the cyclic variations in wall shear stress, six characteristic time-points of the cardiac cycle were selected. The non-Newtonian wall shear stress variation was compared with the Newtonian one.

RESULTS

The wall shear stress varied remarkably in time and space. The flow divider region encountered higher wall shear stress values than the lateral walls throughout the entire cardiac cycle. The wall shear stress exhibited remarkably lower and oscillatory values in systole as compared with that in diastole in the entire bifurcation region, especially in the lateral walls. Although the Newtonian wall shear stress experienced consistently lower values throughout the entire cardiac cycle than the non-Newtonian wall shear stress, the general pattern of lower wall shear stress values at the lateral walls, particularly during systole, was evident regardless of the blood properties.

CONCLUSIONS

The lateral walls of the bifurcation, where low and oscillating wall shear stress is observed, are more susceptible to atherosclerosis. The systolic period, rather than the diastolic one, favors the development and progression of atherosclerosis. The blood viscosity properties do not seem to qualitatively affect the spatial and temporal distribution of the wall shear stress.

Unsteady viscous flow model on moving the domain through a stenotic artery

An unsteady Navier-Stokes (N-S) solver based on the method of operator splitting and artificial compressibility has been studied for the moving boundary problem to simulate blood flow through a compliant vessel. Galerkin finite element analysis is used to discretize the governing equations. The model has been applied to a time-varying computational domain (two-dimensional tube) as a test case for validation. Consideration has been given to retaining the space conservation property. The same code is then applied to a hypothetical critical high-pressure gradient over a short length of blood vessel based on the spring and dashpot model. The governing equation for the blood vessel is based on two-dimensional dynamic thin-shell theory that takes into account the curvature of the stenotic portion of the vessel. Progressing the solution towards steady state is considered, as the main objective is to show the viability of the current technique for fluid/structure interactions. Preliminary results of the wall velocity and displacement based on steady state prediction agree well with data in the literature. Results, such as the streamlines, wall pressures and wall shear stress depict the possible progression of arterial disease.