Haemodynamics analysis of carotid artery stenosis and carotid artery stenting

Carotid stenosis is a local narrowing of the carotid artery, and is usually found in the internal carotid artery. The presence of a high-degree stenosis in a carotid artery may provoke transition from laminar to turbulent flow during part of the cardiac cycle. Turbulence in blood flow can influence haemodynamic parameters such as velocity profiles, shear stress and pressure, which are important in wall remodelling. Patients with severe stenosis could be treated with a minimally invasive clinical procedure, carotid artery stenting (CAS). Although CAS has been widely adopted in clinical practice, the complication of in-stent restenosis (ISR) has been reported after CAS. The incidence of ISR is influenced by stent characteristics and vessel geometry, and correlates strongly with regions of neointimal hyperplasia (NH). Therefore, the main purpose of this study is to provide more insights into the haemodynamics in stenosed carotid artery and in post-CAS geometries via computational simulation. The first part of the thesis presents a computational study on flow features in a stenotic carotid artery bifurcation using two computational approaches, large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) incorporating the Shear Stress Transport model with the γ-Reθ transition (SST-Tran) models. The computed flow patterns are compared with those measured with particle image velocimetry (PIV). The results show that both SST-Tran and LES can predict the PIV results reasonably well, but LES is more accurate especially at locations distal to the stenosis where flow is highly disturbed. The second part of the thesis is to determine how stent strut design may influence the development of ISR at the carotid artery bifurcation following CAS. Key parameters that can be indicative of ISR are obtained for different stent designs and compared; these include low and oscillating wall shear stress (WSS), high residence time, and wall stress. A computationally efficient methodology is employed to reproduce stent strut geometry. This method facilitates the accurate reconstruction of actual stent geometry and details of strut configuration and its inclusion in the fluid domain. Computational simulations for flow patterns and low-density lipoprotein (LDL) transport are carried out in order to investigate spatial and temporal variations of WSS and LDL accumulation in the stented carotid geometries. Furthermore, finite element (FE) analysis is performed to evaluate the wall stress distribution with different stent designs. The results reveal that the closed-cell stent design is more likely to create atheroprone and procoagulant flow conditions, causing larger area to be exposed to low wall shear stress (WSS), elevated oscillatory shear index, as well as to induce higher wall stress compared to the open-cell stent design. This study also demonstrates the suitability of SST-Tran and LES models in capturing the presence of complex flow patterns in post-stenotic region.Open Acces

A Theoretical Model for Blood Flow in Small Vessels

A two-fluid model consisting of a core region of suspension of all the erythrocytes (particles) in plasma (fluid) assumed to be a particle-fluid mixture and a peripheral layer of cell-free plasma (Newtonian fluid), has been proposed to represent blood flow in small diameter tubes. The analytical results obtained in the proposed model for effective viscosity, velocity profiles and flow rate have been evaluated numerically for various values of the parameters available from published works. Quantitative comparison has shown that present model suitability represents blood flow at hematocrit (less than or equal to 40%) and in vessels up to 70 micrometers in diameter. Using experimental values of the parameters, the flow rate for normal and diseased blood has been computed and compared with corresponding values obtained from a well known experimentally tested model in the literature

A Mathematical Model Of Blood Flow Of A Stenosed Artery In Variable Shape

In this theoretical study, a mathematical model is developed to carry out a systematic analysis of flow behaviour in a two-dimensional vessel (modeled as artery) with a locally variable shaped constriction. An artificial artery, which containing a viscous incompressible fluid that representing the flowing blood can be treated as inflexible vessel. The shape of the stenosis in the arterial lumen is chosen to be symmetric as well as asymmetric about the middle cross section is perpendicular to the axis of the vessel. The constricted vessel is resolved into a straight vessel and the entire resulting equations are solved by a numerical method with Reynolds number and ‘n’, a number giving the shape of the constriction as parameters. The impacts of these parameters on wall shear stress, pressure gradient and velocity have been analysed. It is found that the flow resistance decreases as the shape of a smooth stenosis changes and extreme resistance is attained for the symmetric stenosis. But the length of separation increases for the asymmetric constrictions and the oscillation in the shear layer appears earlier for asymmetric constriction than that in the case of symmetric constriction. The extreme resistance is attained for inflexible stenosed vessel rather than the flexible one

Numerical simulation of time-dependent non-Newtonian nano-pharmacodynamic transport phenomena in a tapered overlapping stenosed artery

Nanofluids are becoming increasingly popular in novel hematological treatments and also advanced nanoscale biomedical devices. Motivated by recent developments in this area, a theoretical and numerical study is described for unsteady pulsatile flow, heat and mass transport through a tapered stenosed artery in the presence of nanoparticles. An appropriate geometric expression is employed to simulate the overlapping stenosed arterial segment. The Sisko non-Newtonian model is employed for hemodynamic rheology. Buongiorno’s formulation is employed to model nanoscale effects. The two-dimensional non-linear, coupled equations are simplified for the case of mild stenosis. An explicit forward time central space (FTCS) finite difference scheme is employed to obtain a numerical solution of these equations. Validation of the computations is achieved with another numerical method, namely the variational finite element method (FEM). The effects of various emerging rheological, nanoscale and thermofluid parameters on flow and heat/mass characteristics of blood are shown via several plots and discussed in detail. The circulating regions inside the flow field are also investigated through instantaneous patterns of streamlines. The work is relevant to nanopharmacological transport phenomena, a new and exciting area of modern medical fluid dynamics which integrates coupled diffusion, viscous flow and nanoscale drug delivery mechanisms

Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative

This thesis investigates analytically the magnetohydrodynamics (MHD) transport of Newtonian and non-Newtonian fluids flows inside a circular channel. The flow was subjected to an external electric field for the Newtonian model and a uniform transverse magnetic field for all models. Pressure gradient or oscillating boundary condition was employed to drive the flow. In the first model Newtonian fluid flow without stenotic porous tube was considered and in the second model stenotic porous tube was taken into account. The third model is concerned with the temperature distribution and Nusselt number. The fourth model investigates the non-Newtonian second grade fluid velocity affected by the heat distribution and oscillating walls. Last model study the velocity, acceleration and flow rate of third grade non-Newtonian fluid flow in the porous tube. The non-linear governing equations were solved using the Caputo-Fabrizio time fractional order model without singular kernel. The analytical solutions were obtained using Laplace transform, finite Hankel transforms and Robotnov and Hartley’s functions. The velocity profiles obtained from various physiological parameters were graphically analyzed using Mathematica. Results were compared with those reported in the previous studies and good agreement were found. Fractional derivative and electric field are in direct relation whereas magnetic field and porosity are in inverse relation with respect to the velocity profile in Newtonian flow case. Meanwhile, fractional derivative and Womersely number are in direct relation whereas magnetic field, third grade parameter, frequency ratio and porosity are in inverse relation in third grade non-Newtonian flow case. In the case of second grade fluid, Prandtl number, fractional derivative and Grashof number are in direct relation whereas second grade parameter and magnetic field are in inverse relation. The fluid flow model can be regulated by applying a sufficiently strong magnetic field

Computational fluid dynamic simulation of two-fluid non-newtonian nanohemodynamics through a diseased artery with a stenosis and aneurysm

This article presents a two-dimensional theoretical study of hemodynamics through a diseased permeable artery with a mild stenosis and an aneurysm present. The effect of metallic nanoparticles on the blood flow is considered, motivated by drug delivery (pharmacology) applications. Two different models are adopted to mimic non-Newtonian characteristics of the blood flow; the Casson (viscoplastic) fluid model is deployed in the core region and the Sisko (viscoelastic) fluid model employed in the peripheral (porous) region. The revised Buongiorno two-component nanofluid model is utilized for nanoscale effects. The blood is considered to contain a homogenous suspension of nanoparticles. The governing equations are derived by extending the Navier-Stokes equations with linear Boussinesq approximation (which simulates both heat and mass transfer). Natural (free) double-diffusive convection is considered to simulate the dual influence of thermal and solutal buoyancy forces. The conservation equations are normalized by employing appropriate non-dimensional variables. The transformed equations are solved numerically using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A comprehensive mesh-independence study is included. The effect of selected parameters (thermophoresis, Brownian motion, Grashof number, thermo-solutal buoyancy ratio, Sisko parameter ratio and permeability parameter) on velocity, temperature, nanoparticle concentration 2 and hemodynamic pressure have been calculated for two clinically important cases of arteries with a stenosis and an aneurysm. Skin-friction coefficient, Nusselt number, volumetric flow rate and resistance impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing thermal buoyancy parameter i.e. Grashof number (Gr), the nanoparticle concentration and temperature decrease whereas velocity increases with an increment in Brownian motion parameter (Nb). Furthermore, velocity decreases in the peripheral porous region with elevation in the Sisko material ratio (m) and permeability parameter (k’). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in haematology

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

Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery : biomedical drug delivery simulation

Two-dimensional laminar hemodynamics through a diseased artery featuring an overlapped stenosis was simulated theoretically and computationally. This study presented a mathematical model for the unsteady blood flow with hybrid biocompatible nanoparticles (Silver and Gold) inspired by drug delivery applications. A modified Tiwari-Das volume fraction model was adopted for nanoscale effects. Motivated by the magnetohemodynamics effects, a uniform magnetic field was applied in the radial direction to the blood flow. For realistic blood behavior, Reynolds’ viscosity model was applied in the formulation to represent the temperature dependency of blood. Fourier’s heat conduction law was assumed, and heat generation effects were included. Therefore, the governing equations were an extension of the Navier-Stokes equations with magneto-hydrodynamic body force included. The two-dimensional governing equations were transformed and normalized with appropriate variables, and the mild stenotic approximation was implemented. The strongly nonlinear nature of the resulting dimensionless boundary value problem required a robust numerical method, and therefore the FTCS algorithm was deployed. Validation of solutions for the particular case of constant viscosity and non-magnetic blood flow was included. Using clinically realistic hemodynamic data, comprehensive solutions were presented for silver, and silver-gold hybrid mediated blood flow. A comparison between silver and hybrid nanofluid was also included, emphasizing the use of hybrid nanoparticles for minimizing the hemodynamics. Enhancement in magnetic parameter decelerated the axial blood flow in stenotic region. Colored streamline plots for blood, silver nano-doped blood, and hybrid nano-doped blood were also presented. The simulations were relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial disease

Investigation of blood cells migration in large stenosed artery

Atherosclerosis is one of the main diseases responsible for the high global mortality rate involving heart and blood vessel disorders. The build-up of fatty materials in the inner wall of the human artery prevents sufficient oxygen and nutrients reaching the organs of the body. Atherosclerosis is a chronic, long term condition, which develops and progresses over time; however, the disease does not present any symptoms until an advanced stage is reached, which results in potential permanent debility and sometimes sudden death. This thesis is concerned with the progression of atherosclerosis in an artery with mild stenosis that has resulted in a 30% reduction in its diameter. To this end, data on the low wall shear stress has been correlated with the atherosclerotic prone region. In a stenosed artery, this region corresponds to the separation zone that is formed distal to the lumen reduction. Atherosclerosis is a complex phenomenon, and not only involves wall shear stress, but also cellular interactions. Previous research has shown that even in the absence of wall biological effects, the blood cell distribution is strongly influenced by the hydrodynamics of the fluid. The mechanisms of blood cell distribution and the dynamic behaviour of the blood flow were investigated by developing a physical model of the stenosed artery, and by using particles to represent the presence of the blood cells. Particle Image Velocimetry system was employed and the size of particles were the 10μm and 20μm.The flow field was characterised and the particle distribution was measured. The characteristics of steady flow in the stenosed artery at Reynolds numbers of 250 and 320 revealed the importance of fluid inertia and the shear gradient distal to stenosis. Unequal distribution of the particles modelling the blood cells was observed, as more particles occupied the recirculation zones than the high shear region and central jet. The particle migration was found to depend on the particle size, particle concentration and fluid flow rates. The results suggested that the presence of similar effects in the real human arterial system may be significant to the progression of atherosclerotic plaques. At lower Reynolds number of 130, a particle depleted layer was observed at the wall region. In physiological flow the cell free layer will prevent the transport of oxygen and nitrogen oxide (NO) to the muscle tissues. A numerical method was used to simulate the flow characteristics measured in the experiment. The numerical results revealed the importance of the hydrodynamic mechanism of particle migration. Drag and lift forces were found to affect the residence time of particles in the recirculation region. The findings of this work have suggested that for a complex geometry like a large stenosed artery at physiological flow rates, hydrodynamic forces are important in cell migration in the flow separation zone. Even without biological forces, the cells migrate to the low wall shear stress region. For computational dynamics studies, this study has demonstrated the need for higher-order modelling at the cellular level in order to establish the particle migration mechanisms

Computational study of pulmonary flow patterns after repair of transposition of great arteries

Patients that undergo the arterial switch operation (ASO) to repair transposition of great arteries (TGA) can develop abnormal pulmonary trunk morphology with significant long-term complications. In this study, cardiovascular magnetic resonance was combined with computational fluid dynamics to investigate the impact of the postoperative layout on the pulmonary flow patterns. Three ASO patients were analyzed and compared to a volunteer control. Results showed the presence of anomalous shear layer instabilities, vortical and helical structures, and turbulent-like states in all patients, particularly as a consequence of the unnatural curvature of the pulmonary bifurcation. Streamlined, mostly laminar flow was instead found in the healthy subject. These findings shed light on the correlation between the post-ASO anatomy and the presence of altered flow features, and may be useful to improve surgical planning as well as the long-term care of TGA patients.Postprint (author's final draft