Finite Element Modeling and Simulation of Arteries in the Human Arm to Study the Aortic Pulse Wave Propagation

AbstractFinite modelling and simulation of the arterial network in the human arm has been presented in this paper with an objective to study the aortic pulse wave propagation. In the biomedical domain, it becomes extremely essential to understand the propagation of the aortic pulse along the arterial network, to get a better insight about the functioning of the cardiovascular system. This would assist in haemodynamic measurements, diagnosing disorders and visualizing the effect of medical treatment. The fluid structure interaction has been simulated using COMSOL Multiphysics 4.4 with an objective to obtain the pressure, velocity profile of the aortic pulse and wall shear stresses at the ascending aorta, carotid, brachial, interosseous, ulnar and radial artery. The arterial walls are considered flexible and pulsatile pressure pulse has been used as boundary condition. The validity of the finite element simulation has been supported by comparing the numerical results to the standard published results

PIV-based Investigation of Hemodynamic Factors in Diseased Carotid Artery Bifurcations with Varying Plaque Geometries

Ischemic stroke is often a consequence of complications due to clot formation (i.e. thrombosis) at the site of an atherosclerotic plaque developed in the internal carotid artery. Hemodynamic factors, such as shear-stress forces and flow disturbances, can facilitate the key mechanisms of thrombosis. Atherosclerotic plaques can differ in the severity of stenosis (narrowing), in eccentricity (symmetry), as well as inclusion of ulceration (wall roughness). Therefore, in terms of clinical significance, it is important to investigate how the local hemodynamics of the carotid artery is mediated by the geometry of plaque. Knowledge of thrombosis-associated hemodynamics may provide a basis to introduce advanced clinical diagnostic indices that reflect the increased probability of thrombosis and thus assist with better estimation of stroke risk, which is otherwise primarily assessed based on the degree of narrowing of the lumen. A stereoscopic particle image velocimetry (stereo-PIV) system was configured to obtain instantaneous full-field velocity measurements in life-sized carotid artery models. Extraction of the central-plane and volumetric features of the flow revealed the complexity of the stenotic carotid flow, which increased with increasing stenosis severity and changed with the symmetry of the plaque. Evaluation of the energy content of two models of the stenosed carotid bifurcation provided insight on the expected level of flow instabilities with potential clinical implications. Studies in a comprehensive family of eight models ranging from disease-free to severely stenosed (30%, 50%, 70% diameter reduction) and with two types of plaque symmetry (concentric or eccentric), as well as a single ulcerated stenosed model, clearly demonstrated the significance of plaque geometry in marked alteration of the levels and patterns of downstream flow disturbances and shear stress. Plaque eccentricity and ulceration resulted in enhanced flow disturbances. In addition, shear-stress patterns in those models with eccentric stenosis were suggestive of increased thrombosis potential at the post-stenotic recirculation zone compared to their concentric counterpart plaques

Mathematical Modelling of Blood Flow through a Tapered Overlapping Stenosed Artery with Variable Viscosity

This paper presents a theoretical study of blood flow through a tapered and overlapping stenosed artery under the action of an externally applied magnetic field. The fluid (blood) medium is assumed to be porous in nature. The variable viscosity of blood depending on hematocrit (percentage volume of erythrocytes) is taken into account in order to improve resemblance to the real situation. The governing equation for laminar, incompressible and Newtonian fluid subject to the boundary conditions is solved by using a well known Frobenius method. The analytical expressions for velocity component, volumetric flow rate, wall shear stress and pressure gradient are obtained. The numerical values are extracted from these analytical expressions and are presented graphically. It is observed that the influence of hematocrit, magnetic field and the shape of artery have important impact on the velocity profile, pressure gradient and wall shear stress. Moreover, the effect of primary stenosis on the secondary one has been significantly observed

Non-Newtonian coupled field analysis of blood flow in normal and stenosed carotid artery with varying haemodynamic parameters

Atherosclerosis is a chronic disease affecting millions worldwide by leading to heart attack and stroke. It usually develops in regions with disturbed flow like the carotid artery, aorta, and coronary arteries. The major cause of atherosclerosis development is the deposition of lipids under the endothelial layer of the artery leading to plaque build-up. Also, evidence that the plaque formation occurs mainly near the bifurcations or curvatures had led to the hypothesis that irregular flow conditions plays a major role in development and progression of atherosclerosis. In vivo and in vitro studies at the cellular level and macroscopic levels shows the importance of understanding the local haemodynamics in atherosclerosis prone regions. Although diagnostic techniques such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) provides detailed anatomic information non-invasively, local haemodynamics can be studied at patient specific models using computational techniques like Computational Fluid Dynamics (CFD) and Fluid Structure Interaction (FSI). Therefore, it is very important to reconstruct anatomical models using CT or MRI images to gain accurate results in CFD or FSI analysis. The flow behaviour in large arteries is complex and it is influenced by the elasticity of the artery. Apart from this, the blood pressure changes during day to day activities. This interesting phenomenon of variation of blood pressure is studied by numerical simulation of blood flow in the normal and stenosed carotid artery. In this work, a three-dimensional (3D) Fluid Structure Interaction (FSI) study was carried out for a normal and stenosed patient specific carotid artery models. By considering physiological conditions, first the normal and then with hypertension disease, haemodynamic parameters were evaluated to better understand the genesis and progression of atherosclerotic plaques in the carotid artery bifurcation. Two-way FSI was performed by applying a fully implicit second-order backward Euler differencing scheme using commercial software ANSYS and ANSYS CFX (version 19.0). Arbitrary Lagrangian–Eulerian (ALE) formulation was employed to calculate the arterial response by using the temporal blood response. Due to arterial bifurcation, obvious velocity reduction and backflow formation were observed which decreased shear stress and made it oscillatory at the starting point of the internal carotid artery near the carotid sinus, which resulted in low shear stress. Oscillatory shear index (OSI) signifies oscillatory behaviour of artery wall shear stress. Comparison of the results of this study with those in the published literature showed that the regions with low wall shear stress and with OSI value greater than 0.3 pose potential risk to the development of plaques. It was observed that haemodynamics of the carotid artery was very much affected by the geometry and flow conditions. Furthermore, regions of relatively low wall shear stress were observed post stenosis, which is a known cause of plaque development and progression. The results were compared between Newtonian and Carreau – Yasuda blood viscosity models. Critical haemodynamic parameters such as wall shear stress (WSS) and Oscillatory Shear Index (OSI) were examined. Simulated hemodynamic parameters were able to capture the disturbed flow conditions in a normal and a stenosed carotid artery bifurcation, which play an important role in the development of local atherosclerotic plaques. Computational simulations based on diagnostic tools such as Ultrasound might help improving diagnostic and treatment management of carotid atherosclerosis

The effects of gravitational acceleration on micropolar fluid model of blood flow in a bifurcated stenosed artery

Gravity is a fundamental force regulating the cardiovascular system in our body. However not many previous studies on bio-fluids take into consideration of the variation of gravitational acceleration. Besides, the geometry of the bifurcated artery is chosen to be investigated since it is significant in human cardiovascular networking, where stenoses tend to form around branching junctions. Blood flow in the segment of artery is assumed to be axisymmetric, unsteady, laminar, fully developed, and two-dimensional. This research investigates the effects of gravity on micropolar fluid model of blood flow along a bifurcated artery segment which consists of a single stenosis at the parent branch. Meanwhile, to proceed with this study, blood is initially modelled as Newtonian fluid and micropolar fluid respectively in a straight stenosed artery segment. Then, the effects of gravity on Newtonian blood flow in bifurcated artery are explored. Here, a non-dimensional parameter G is introduced to describe the condition of gravity, where G is directly proportional to gravitational acceleration. The governing equations are solved numerically using the explicit finite difference method with prescribed condition of pressure and the computational algorithms are developed in Matlab software. Generally, with consideration of gravity variation, increment of gravitational acceleration causes decrement of axial velocity and increment of wall shear stress. Thus the consideration of gravity term in fluid model is necessary so that results obtained are closer to realistic conditions. Further, flow abnormalities are noticed at the branching junction from graphs of wall shear stress. This can be a crucial cause of stenosis overlapping and restenosis, which means that the structures of artery is significant in influencing blood flow patterns

Hemodynamics analysis for cosine shaped stenoses to blood flow behavior

The Study of flow over stenoses have been investigated by many researchers. In these cases, the more realistic the models are, the higher the acceptability of the results. For this study, a very common shape of stenosis, that is modified cosine, are modeled. Newtonian and non-Newtonian blood flow along with the pulsatile flow conditions was used. The results show that tendency for recirculation to occur reduces as the stenosis expands in the longitudinal direction. On the other hand, higher tendency for recirculation of blood is observed if the stenosis expands in the transverse direction. The wall shear stress is observed to decrease as the stenosis expands in the longitudinal direction but no significant changes is observed if the stenosis expands in the other direction. Similar patterns of flow are observed for both Newtonian & non-Newtonian flow condition but the non-Newtonian flow tends to produce higher WSS

Numerical and experimental haemodynamic studies of stenotic coronary arteries

Dissertação de mestrado integrado em Engenharia Biomédica (área de especialização em Biomateriais, Reabilitação e Biomecânica)Cardiovascular diseases remain the most frequent cause of mortality worldwide and constitute a major healthcare challenge. Among them, coronary artery disease causes nearly half of the deaths and, thus it is of great interest to better understand its development and effects. This disease is characterized by the narrowing (stenosis) of coronary arteries due to plaque deposition at the arterial wall, a pathological process known as atherosclerosis. This dissertation aimed to study the hemodynamics in stenotic coronary arteries, in order to get a deeper understanding of the effects of this pathology on the blood flow behavior. For this purpose, both numerical and experimental studies were conducted using idealized models. The numerical research was carried out using Ansys® software by means of computational fluid dynamics which applies the finite volume method. The experimental approach was performed using a high-speed video microscopy system, to visualize and investigate the blood flow in the in vitro stenotic biomodels. Initially, the influence of roughness in flow visualizations was studied, and the best biomodel was the one printed with the lowest resolution having been, therefore, the selected to perform the hemodynamic studies. To compare those results with numerical data, the flow was set to be laminar and stationary and the fluid was considered Newtonian. In general, the numerical and experimental results were in good agreement, not only in the prediction of the flow behavior with the appearance of recirculation zones in the post-stenotic section, but also in the velocity profiles. In a posterior phase, a pulsatile inlet condition was applied to compare the use of laminar and turbulent assumptions, using the SST k- model. The results obtained allowed to conclude that the second one is more appropriate to simulate the blood flow. Subsequently, the main differences in hemodynamics were examined considering blood as a Newtonian and non-Newtonian fluid (Carreau model). For these models, the differences were very slight in terms of velocity fields, but more significant for the wall shear stress measurements, with the Newtonian model predicting lower values. The remaining simulations were performed using the Carreau model and a transient inlet flow, having observed an increase in the velocities and wall shear stress values with the degree of stenosis, which is associated with a greater risk of thrombosis.As doenças cardiovasculares continuam a ser a causa mais frequente de mortalidade em todo o mundo e constituem um grande desafio para a saúde. Entre elas, a doença arterial coronariana causa quase metade das mortes e, portanto, é de enorme interesse entender melhor o seu desenvolvimento e efeitos. Esta doença é caracterizada pelo estreitamento (estenose) das artérias coronárias devido à deposição de placas na parede arterial, um processo patológico conhecido como aterosclerose. Esta dissertação teve como objetivo estudar a hemodinâmica nas artérias coronárias estenóticas, a fim de obter uma compreensão mais profunda dos efeitos desta patologia no comportamento do fluxo sanguíneo. Para tal, foram realizados estudos numéricos e experimentais, utilizando modelos idealizados. A investigação numérica foi realizada no software Ansys®, através da dinâmica computacional dos fluidos, que aplica o método dos volumes finitos. A abordagem experimental foi realizada utilizando um sistema de microscopia de vídeo de alta velocidade, para visualizar e investigar o fluxo sanguíneo nos biomodelos estenóticos in vitro. Inicialmente, estudou-se a influência da rugosidade nas visualizações do escoamento, e o melhor biomodelo foi o impresso com menor resolução tendo sido, portanto, o selecionado para a realização dos estudos hemodinâmicos. Para comparar esses resultados com dados numéricos, o escoamento foi definido como laminar e estacionário e o fluído foi considerado Newtoniano. Em geral, os resultados numéricos e experimentais foram concordantes, não só na previsão do comportamento do fluxo com aparecimento de zonas de recirculação na zona pós-estenótica, mas também nos perfis de velocidade. Numa fase posterior, foi aplicada uma condição de entrada pulsátil para comparar o uso de simulações de natureza laminar e turbulenta, usando o modelo SST k-. Os resultados obtidos permitiram concluir que a segunda é mais apropriado para simular o fluxo sanguíneo. Posteriormente, foram examinadas as principais diferenças hemodinâmicas, considerando o sangue como fluído Newtoniano e não-Newtoniano (modelo de Carreau). Para estes modelos, as diferenças foram muito pequenas nos perfis de velocidade, mas mais significativas nas tensões de corte na parede medidas, com o modelo Newtoniano a prever valores mais baixos. As restantes simulações foram realizadas usando o modelo de Carreau e um escoamento de entrada transiente, tendo-se observado um aumento dos valores das velocidades e da tensão de corte na parede com o grau de estenose, o que está associado a um maior risco de trombose

Computational Assessment of Fluid Flow in Stenotic Arteries: Application in Targeted Drug Therapy

Blood flow dynamics are crucial in the development and progression of cardiovascular diseases. Computational modeling of blood circulation in arteries is vital for understanding disease symptoms and enhancing treatments. Aneurysms, stenoses, and atherosclerosis can change blood flow characteristics, leading to serious healthcomplications due to abnormal blood flow patterns and high wall shear stresses (WWS). Simulating these changes can help in detecting cardiovascular diseases early and managing them effectively. The commencement of the dissertation involves an effort to create a model of the 2D shape of a non-uniform artery wall that has a restricted segment, using a segmented function, which includes an obstruction of approximately 40%. The blood flow in the body follows a rhythmic pressure gradient that imitates the heart’s systolic and diastolic phases. Because blood behaves like a non-Newtonian fluid in certain situations, the Casson model for non-Newtonian fluids is used to account for the yield stress resulting from the formation of red blood cell aggregates at low shear rates. The Navier-Stokes equations, which describe incompressible and unsteady fluid flow, are expanded to include the non-Newtonian behavior of blood flow in radial coordinates. This is accomplished by including a temperature equation. To analyze the impact of stenosis over the flow, drug delivery agents such as copper (Cu) and alumina (Al2O3) nanoparticles with a concentration of about 0.03% are used. The concept of magnetohydrodynamics (MHD) involves applying a magnetic field to blood flow in an artery, taking into account the Hall current, to deliver magnetic drug carriers to a specific location within the bloodstream. The simulation of blood flow begins from a state of rest with zero velocity and temperature, using initial conditions to simplify the mathematical modeling process. On the symmetry axis, a zero radial gradient condition is applied to both velocity and temperature, while no-slip conditions are applied to the arterial wall. The complexity of the governing partial differential equations is removed by nondimensionalizing them. There are two cases to consider: the first case involves disregarding the long wavelength approach, which remains open issue for future consideration. The alternative scenario involves presenting the acquired dimensionless PDEs through the long-wavelength approximation and then applying a radial coordinate transformation to simplify them even further. Afterward, MATLAB software is utilized to execute the 2D explicit forward time central space (FTCS) differentiation method. Momentum and thermal analysis were done for blood, Cublood nanofluid, and Cu-Al2O3-blood hybrid nanofluid, along with wall shear stress (WWS) and local Nusselt number (Nulocal) evaluation.We proceed to revise the last batch of dimensional partial differential equations (PDEs) describing the behavior of non-Newtonian Cu-Al2O3-blood by incorporating magnetohydrodynamic (MHD) effects. Our approach involves converting the PDEs into a Reynolds-averaged Navier Stokes equation (RANS), which employs Reynolds averaging to account for turbulence in the mean flow. This is achieved by decomposing the flow variables into average and perturbed components. The equations for fluid dynamics include turbulent forces caused by eddy shear and molecular turbulence. These forces are accounted for using Boussinesq’s eddy-viscosity hypothesis, which is based on the average flow of the fluid. Additionally, the Zero-equation turbulence model, which is also called the algebraic turbulence model, is utilized by combining the principles of Prandtl mixing length and Boussinesq approximation. Turbulent flow is considered unsteady and fully developed, and flow properties are also modified using the Prandtl mixing length model with the laminar and turbulent effect contribution. The subsequent step involves making these equations nondimensional and then utilizing radial coordinate transformations. The resulting set of dimensionless partial differential equations that consists of Reynold and turbulent Prandtl numbers are then simulated using FTCS methodology. Additionally, the effect of various emerging parameters is analyzed through a graphical representation of the momentum equation for high Reynold numbers (Re = 42000, 46000). The last analysis involved flow momentum and pressure for the laminar flow scenario by considering blood as a Newtonian fluid. Using AutoCAD software, a 3D constricted artery with a 70% elliptical shaped stenosis was created. To proceed further, an ideal mesh was created using OpenFOAM’s blockMesh and snappyHexMesh tools. The simulation for laminar and incompressible flow has been conducted using the coFoam solver, which guarantees the convergence of the simulation at Courant number ≈ 0.2 < 1. Two different scenarios have been taken into account for the velocity inlet. Firstly, a parabolic velocity profile was used with a maximum inlet velocity of 0.003m/s. The outlet velocity was set to zero gradient and the inlet pressure was also set to zero. Secondly, we used a constant inlet velocity of 0.0137m/s for laminar flow with a Reynolds number of 200. We graphically analyzed the momentum and pressure of the fluid both at the center of the stricture and throughout the constriction arterial segment for both inlet velocity conditions

Analysis of Flow Fields in a Flexible Tube with Periodic Constriction

Numerical techniques based on pressure-velocity formulation have been adopted to solve approximately, the governing equations for viscous flows through a tube (simulating an artery) with a periodic constriction. The effect of the constriction as well as the rigid of the tube, on the flow characteristics, and its consequences for arterial disease is the focus of this investigation. The unsteady incompressible Navier-Stokes equations are solved by using the finite-difference technique in staggered grid distribution. The haemodynamic factors like wall shear stress, pressure and velocity are analyzed through their graphical representations. Maximum resistance is attained in case of rigid stenosed tube rather than the flexible one. The main result is to contribute that the recirculating region is larger in case of a rigid tube than that of flexible one