Generalized power-law model of magnetohydrodynamic blood flow in an inclined stenosed artery with body acceleration

This thesis focuses on the development of a mathematical model to investigate the effect of magnetic field and body acceleration on blood flow characteristics, heat and mass transfer from a stenosed artery, a condition due to the abnormal narrowing of a blood vessel. The arterial segment is assumed to be a cylindrical tube in an inclined position with oscillating boundary condition and the stenosis taking the shape of a cosine function. The momentum equation is based on the generalized power law model which is expected to handle the variations in blood rheology as blood flows through a different-sized vessel, with the index n 1 and n = 0 describing the shear-thinning, shear-thickening and Newtonian fluid respectively. The full governing equations comprising the generalized power-law equation, heat and mass equations are non-linear partial differential equations whose numerical procedure involves the discretization of the equations using the Marker and Cell (MAC) method, where pressure along the tube is calculated iteratively using the Successive-Over-Relaxation (SOR) technique. The results have been compared and validated with existing results in certain limiting cases. New results in terms of pressure, streamlines, heat and mass distribution are obtained for various parameter values of each of the external body forces. Specifically, for a stenosis with 48% occlusion, separation is seen to occur for Newtonian fluids at Re = 1000 and this region can be seen to increase in the case of shear thickening fluids, while the shear-thinning fluid is shown to be free of separation region. Moreover, blood velocity, wall shear stress and pressure drop decrease with increase n, while heat and mass transfer increase. It is also demonstrated through the simulations that under the influence of magnetic field, the velocity in the centre of the artery and the separation region are reduced with a sufficient strength of magnetic field, depending on the severity of stenosis. For a 75% and 84% occlusion, the separation zones entirely disappear with magnetic strength 8 and 12 Tesla respectively, while the pressure drop, wall shear stress, heat and mass transfer increase. On the other hand, increasing periodic body acceleration leads to increase velocity and the pressure drop while reducing heat and mass transfer. Inclination angle increases the velocity and wall shear stress but decreases the pressure drop and heat and mass transfer. Based on the results, patients with blood vessel disease are advised not to do a high-intensity exercise; it can put extra strain on the heart leading to a risk in chest pain or even cardiac arrest. Regular exercise and suitable intensity of magnetic field could enhance vascular health

Momputational analysis of MHD blood flow through a stenosed artery in the presence of body acceleration and chemical reaction

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyThe unsteady, laminar and two-dimensional pulsatile flow of both, Newtonian and non Newtonian chemically reacting blood in an axisymmetric stenosed artery subject to body ac celeration and magnetic fields were studied. In the case of non-Newtonian blood, heat transfer was taken into consideration. The combined effects of body acceleration, magnetic fields and chemical reaction on blood flow were considered. The non-Newtonian model was chosen to suit the Herschel-Bulkley fluid characteristics. The non-dimensional governing equations were solved using the explicit finite difference method and executed using MATLAB package. The solutions showing the velocity, temper ature and concentration profiles were illustrated. The effects of Reynolds number, Hartman number, Schmidt number, Eckert number and Peclet number were examined. Additionally, the effects of stenosis and body acceleration on blood flow were explored. The study found that, body acceleration, magnetic fields and stenosis affect the normal flow of blood. Body acceleration was observed to have more effect on blood flow than the mag netic fields and stenosis. Furthermore, as the key findings of the study, it was noticed that the combined effect of stenosis, body acceleration, magnetic field and chemical reaction, reduce the concentration profile of the blood flow and the blood flow velocity. It was also observed that, the axial velocity, concentration and skin friction, decrease with increasing stenotic height. The velocity on the other hand increased as the body acceleration increased. Furthermore, as the Hartman number increased, both the radial and axial velocities diminished. The higher the chemical reaction parameter was, the lower were the concentration profiles. For the non-Newtonian blood, the velocity profile diminished with increase in the Hartman number and increased with the body acceleration. The temperature profile was observed to rise by the increase of body acceleration and the Eckert number, while it diminished with the increase of the Peclet number. It was also found that, the concentration profile increased with the increase of the Soret number and decreased with the increase of the chemical reaction. It was further observed that the shear stress deviated more when the power law index, n > 1 than when n < 1

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

Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids

A theoretical study is conducted for magnetohydrodynamic pumping of electro-conductive couple stress physiological liquids (e.g. blood) through a two-dimensional ciliated channel. A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory. A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. A transverse static magnetic field is imposed transverse to the channel length. The Stokes’ couple stress (polar) rheological model is utilized to characterize the liquid. The normalized two-dimensional conservation equations for mass, longitudinal and transverse momentum are reduced with lubrication approximations (long wavelength and low Reynolds number assumptions) and feature a fourth order linear derivative in axial velocity representing couple stress contribution. A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame. No slip conditions are imposed at the channel walls. The emerging linearized boundary value problem is solved analytically, and expressions presented for axial (longitudinal) velocity, volumetric flow rate, shear stress function and pressure rise. The flow is effectively controlled by three geometric parameters, viz cilia eccentricity parameter, wave number and cilia length and two physical parameters, namely magnetohydrodynamic body force parameter and couple stress non-Newtonian parameter. Analytical solutions are numerically evaluated with MATLAB software. Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length, couple stress and magnetic parameters, with significant flattening of profiles with the latter two parameters. Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length, in the channel core region. Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width. The pressure-flow rate relationship is confirmed to be inversely linear and pumping, free pumping and augmented pumping zones are all examined. Bolus trapping is also analyzed. The study is relevant to MHD biomimetic blood pumps

Multiscale Fluid-Structure Interaction Models Development and Applications to the 3D Elements of a Human Cardiovascular System

Cardiovascular diseases (CVD) are the number one cause of death of humans in the United States and worldwide. Accurate, non-invasive, and cheaper diagnosis methods have always been on demand as cardiovascular monitoring increase in prevalence. The primary causes of the various forms of these CVDs are atherosclerosis and aneurysms in the blood vessels. Current noninvasive methods (i.e., statistical/medical) permit fairly accurate detection of the disease once clinical symptoms are suggestive of the existence of hemodynamic disorders. Therefore, the recent surge of hemodynamics models facilitated the prediction of cardiovascular conditions. The hemodynamic modeling of a human circulatory system involves varying levels of complexity which must be accounted for and resolved. Pulse-wave propagation effects and high aspect-ratio segments of the vasculature are represented using a quasi-one-dimensional (1D), non-steady, averaged over the cross-section models. However, these reduced 1D models do not account for the blood flow patterns (recirculation zones), vessel wall shear stresses and quantification of repetitive mechanical stresses which helps to predict a vessel life. Even a whole three-dimensional (3D) modeling of the vasculature is computationally intensive and do not fit the timeline of practical use. Thus the intertwining of a quasi 1D global vasculature model with a specific/risk-prone 3D local vessel ones is imperative. This research forms part of a multiphysics project that aims to improve the detailed understanding of the hemodynamics by investigating a computational model of fluid-structure interaction (FSI) of in vivo blood flow. First idealized computational a 3D FSI artery model is configured and executed in ANSYS Workbench, forming an implicit coupling of the blood flow and vessel walls. Then the thesis focuses on an approach developed to employ commercial tools rather than in-house mathematical models in achieving multiscale simulations. A robust algorithm is constructed to combine stabilization techniques to simultaneously overcome the added-mass effect in 3D FSI simulation and mathematical difficulties such as the assignment of boundary conditions at the interface between the 3D-1D coupling. Applications can be of numerical examples evaluating the change of hemodynamic parameters and diagnosis of an abdominal aneurysm, deep vein thrombosis, and bifurcation areas

The adomian decomposition method applied to blood flow through arteries in the presence of a magnetic field

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. February 16, 2015.The Adomian decomposition method is an effective procedure for the analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions, closure approximations, perturbation theory, or restrictive assumptions on stochasticity. Our aim here is to apply the Adomian decomposition method to steady two-dimensional blood flow through a constricted artery in the presence of a uniform transverse magnetic field. Blood flow is the study of measuring blood pressure and determining flow through arteries. Blood flow is assumed to be Newtonian and is governed by the equation of continuity and the momentum balanced equation (which are known as the Navier-Stokes equations). This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics and takes into account both magnetization and electrical conductivity of blood. We apply the Adomian decomposition method to the equations governing blood flow through arteries in the presence of an external transverse magnetic field. The results show that the e ect of a uniform external transverse magnetic field applied to blood flow through arteries favors the physiological condition of blood. The motion of blood in stenosed arteries can be regulated by applying a magnetic field externally and increasing/decreasing the intensity of the applied field

Shear-promoted drug encapsulation into red blood cells: a CFD model and μ-PIV analysis

The present work focuses on the main parameters that influence shear-promoted encapsulation of drugs into erythrocytes. A CFD model was built to investigate the fluid dynamics of a suspension of particles flowing in a commercial micro channel. Micro Particle Image Velocimetry (μ-PIV) allowed to take into account for the real properties of the red blood cell (RBC), thus having a deeper understanding of the process. Coupling these results with an analytical diffusion model, suitable working conditions were defined for different values of haematocrit

Investigation of vibrations at the skin surface caused by the flow disturbance in stenosed tubes

An occlusion in an artery (a stenosis) induces disturbances in the downstream flow and those disturbances produce mechanical waves that impinge on the vessel wall causing it to vibrate. These vibrations then travel through the soft tissues to the skin surface where they can be detected, thus providing a possible method for the non-invasive diagnosis of the underlying disease. Hence, in this study, the potential of measuring those disturbances was explored. Experiments were set-up to model the behaviour of carotid artery under different con-ditions. A 40:60 (by volume) glycerine-water solution was selected to simulate the vis-cosity of blood (approximately 4cP). A thin walled (250 μm - 350μm wall thickness) latex Penrose drain tube, with an external diameter of 6.35mm and a Young’s Modulus value of around 0.9MPa (for circumferential strains between 0.08 - 0.10), was used to mimic the carotid artery. Different severities (60%, 75% and 90% area reduction) of the stenoses, with a circular cross-section, were investigated. Two different types, axisym-metric and non-axisymmetric, were investigated to study the effects of asymmetry in the stenoses. The stenoses were 3D printed in an opaque VeroWhite material to mimic the occlusion. The stenosed artery was then embedded into a standardised neck phantom (filled with Parker Aquasonic 100 ultrasound gel) to mimic the soft tissues and the top of the phantom was sealed with a thin (50μm) polyurethane film (Platilon), with a stiffness value of approximately 21MPa, to simulate the skin. To detect the disturbance on the phantom surface, different equipment (including ac-celerometers, and a Laser Doppler Vibrometer [LDV]) were tested. The LDV proved to be the most reliable under all conditions and was chosen as the standard measurement method for all the phantom experiments. Having selected the appropriate materials and measurement techniques, the effects of flow rate, stenosis severity, stenosis symmetry and fluid viscosity were investigated. Both, steady and pulsatile flows were perfused through the phantom with flows ranging from 0-450ml/min for steady flow and 308-340ml/min for pulsatile flow. On modifying the viscosity of the fluid, it was seen that increasing the viscosity reduced the perturbations in the flow. This was expected due to the increased viscous forces in the flow, as the viscosity of the fluid increased. Furthermore, the experiments showed that, on increasing the flow rate, the stenosis severity, and/or introducing asymmetry in the stenosis, the post-stenotic perturbations in the flow were amplified and their zone of origin moved nearer to the stenosis. These features were confirmed by conducting bare tube experiments as well as some ultrasound scans in a modified phantom. On further investigation it was found that along with the positional dependence of these perturbations, their range of frequencies was increased with increasing flow rate, stenosis severity and/or stenosis asymmetry. In the phantom experiments the disturbances were barely detectable for an area reduc-tion of 60% and were weakly present at 75%. However, strong disturbances were seen for the highly (90%) stenosed tube. A possible cause of the unexpectedly small effect of the 75% stenosis was speculated to be the stenosis symmetry: in-vivo, atherosclerotic plaques are invariably not symmetrical. To show this, experiments were conducted with an asymmetric stenosis where higher level of disturbances were detected (even with the 75% stenosis severity), hence, emphasising the impact of stenosis symmetry. A preliminary computational simulation was also set-up to allow for future detailed modelling of the effects of changing the physical conditions on the signals arriving at the skin. The simulations (whose accuracy yet remains to be validated) showed similar effects of the increasing flow rates and the stenosis severity as the disturbances were amplified and moved nearer to the stenosis on increasing the value of either variable. Following this, an attempt was made to develop a fluid-structure interaction model to simulate the neck phantom and a sample simulation was set-up. This study developed a novel method for detecting the disturbances in the post-stenotic region, and the experimental results from this study suggest the feasibility of using LVD to infer the presence of a stenosis at an early stage before the symptoms are evident

In-Vitro and In-Silico Investigations of Alternative Surgical Techniques for Single Ventricular Disease

Single ventricle (SV) anomalies account for one-fourth of all cases of congenital Heart disease. The conventional second and third stage i.e. Comprehensive stage II and Fontan procedure of the existing three-staged surgical approach serving as a palliative treatment for this anomaly, entails multiple complications and achieves a survival rate of 50%. Hence, to reduce the morbidity and mortality rate associated with the second and third stages of the existing palliative procedure, the novel alternative techniques called “Hybrid Comprehensive Stage II” (HCSII), and a “Self-powered Fontan circulation” have been proposed. The goal of this research is to conduct in-vitro investigations to validate computational and clinical findings on these proposed novel surgical techniques. The research involves the development of a benchtop study of HCSII and self-powered Fontan circulation