Micropolar fluid flow through a stenosed bifurcated artery

The aim of this article is to investigate the blood flow in bifurcated artery with mild stenosis taking blood as a micropolar fluid. The arteries, forming bifurcation are taken to be symmetric and straight cylinders of finite length. The governing equations are non-dimensionalized and coordinate transformation is used to convert the irregular boundary to a regular boundary. The resulting system of equations is solved numerically using the finite difference method. The variation of velocity, microrotation, shear stress, flow rate and impedance near the flow divider with relevant physical parameters are presented graphically. It is found that, due to backflow and secondary flow, impedance and flow rate are perturbed largely at the apex. It is also seen that the microrotation changes it's sign from negative to positive for increase values of bifurcated angle and micropolar coupling number

Heat and Mass Transfer in Micropolar Model for Blood Flow Through a Stenotic Tapered Artery

Heat and mass transfer in blood flow through a tapered artery with mild stenosis is examined. The blood is considered to be an incompressible, micropolar fluid flowing through a vessel with nonsymmetric axial and symmetric radial axes. The geometry of the model takes into account the shape parameter, tapered angle and height of the stenosis.The variation in the shape parameter is used to describe the changes in the axial shape of the stenosis in the artery. The governing equations for the model, comprising the continuity, momentum, energy, and mass transfer equations are transformed and simplified under the assumption of mild stenosis. Analytical solutions for the equations are obtained. The effect of different parameters on temperature, concentration, velocity, resistance, shear stress, pressure drop, Nusselt number, and Sherwood number are presented in graphical form, analysed and discussed. It is discovered that the blood temperature increases as micropolar spin parameter or the particle size increases. Also, its concentration is slowed down with an increase in the micropolar parameter or coupling number. The temperature in the converging artery is higher than that of diverging artery when compared under the same conditions

3D model of generalized power law blood flow in a stenosed bifurcated artery

Numerical simulation of the behaviour of blood flow through a stenosed bifurcated artery with the presence of single mild stenosis at parent artery is investigated. The flow analysis applies the incompressible, steady, three-dimensional Navier-Stokes equations for non-Newtonian generalized power law fluids. Behaviour of blood flow is simulated numerically using COMSOL Multiphysics that based on finite element method. The results show the effect of severity of stenosis on flow characteristics such as axial velocity and its exhibit flow recirculation zone for analysis on streamlines pattern

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

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

Plaque Rupture Prediction in Human Arteries

According to the World Health Organisation (WHO), coronary artery disease (CAD) and stroke are the two leading causes of death globally, with more than 15.2 million deaths in 2016. In 2017, there were: 18,000 and 10,000 deaths in Australia due to CAD and cerebrovascular diseases, respectively. Atherosclerosis is the predominant cause for both coronary and cerebrovascular diseases with acute events usually caused by plaque rupture which releases thrombogenic material into the artery lumen leading to clot formation. Identification of the most at risk plaques for rupture, known as the ‘vulnerable plaque’, remains an important pursuit in the treatment of patients with CAD. The aim of this thesis was to model and simulate the nonlinear fluidstructure interaction (FSI) dynamics of atherosclerotic coronary arteries, based on clinical data, as a tool to recognise vulnerable locations and hence to predict the initiation of heart attack. This thesis consists of four peerreviewed journal papers, two published and two submitted for publication. • Paper 1: A dynamic, three-dimensional (3D), visco/hyperelastic, FSI model of an atherosclerotic coronary artery was developed via the finite element method (FEM) to examine the risk of high shear/von Mises stresses, incorporating: physiological pulsatile blood flow; tapered shape of the artery; viscoelasticity and hyperelasticity of the artery wall; effect of the motion of the heart; active artery muscle contraction; the lipid core inside the plaque; three layers of the artery wall; non-Newtonian characteristics of the blood flow; and micro-calcification. The paper has been published in the International Journal of Engineering Science (Q1; Impact Factor = 9.052; journal rank: 1 out of 88 in Multidisciplinary Engineering). • Paper 2: One of the highest risk locations of plaque growth and rupture initiation and hence occurrence of heart attack is the first main bifurcation of the left main (LM) coronary artery. Hence, this investigation aimed to analyse the nonlinear, three-dimensional biomechanics of the bifurcated, atherosclerotic LM coronary artery. The artery tree was modelled using FSI incorporating three-dimensionality, nonlinear geometric and material properties, asymmetry, viscosity, and hyperelasticity. The paper has been published in the International Journal of Engineering Science (Q1; Impact Factor = 9.052; journal rank: 1 out of 88 in Multidisciplinary Engineering) • Paper 3: Clinical data measurement was conducted at the Royal Adelaide Hospital (RAH) for two patients who underwent in vivo coronary angiography, optical coherence tomography (OCT) imaging, and electrocardiography (ECG). These clinically measured data were analysed using image processing techniques to obtain realistic geometries of the coronary arteries, heart motion measurements, and corresponding heart rate characteristics. A 3D FSI model was then developed using FEM, based on the measured clinical data for determination of high-risk locations. Validation of the model/simulations with clinical data was also performed. • Paper 4: In vivo OCT, ECG, angiography, and time-dependent blood pressure measurements were conducted for a patient at the RAH and the obtained data were analysed using image processing techniques. Fatigue-life and crack-analysis FEM models were developed and simulations were performed based on clinical obtained data for crack propagation, fatigue crack growth and plaque life analyses.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 201

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 Modeling of Cardiovascular Flows

Simulations of blood flow in the cardiovascular system offer investigative and predictive capabilities to augment current clinical tools. Using image-based modeling, the Navier-Stokes equations can be solved to obtain detailed 3-dimensional hemodynamics in patient-specific anatomical models. Relevant parameters such as wall shear stress and particle residence times can then be calculated from the 3D results and correlated with clinical data for treatment planning and device evaluation. Reduced-order models such as open or closed loop 0D lumped-parameter models can simulate the dynamic behavior of the circulatory system using an analogy to electrical circuits. When coupled to 3D simulations as boundary conditions, they produce physiologically realistic pressure and flow conditions in the 3D domain. We describe fundamentals and current state of the art of patient-specific, multi-scale computational modeling approaches applied to cardiovascular disease. These tools enable investigations of hemodynamics reflecting individual patients physiology, and we provide several illustrative case studies. These methods can supplement current clinical measurement and imaging capabilities and provide predictions of patient outcomes for surgical planning and risk stratification

Correlation between cardiovascular disease biomarkers and biochemical and physical milieu in complex vascular environments

La progressió de l'aterosclerosi i la trombosi en pacients amb risc de malaltia cardiovascular depèn en gran mesura de l'entorn únic a nivell físic i bioquímic cada individu. Característiques tals com l'arquitectura de la vasculatura, la composició bioquímica de la sang o el tipus de tractament defineixen el resultat de les intervencions cardiovasculars. La col•locació d'un stent o d'un bypass busca recuperar la permeabilitat del vas, però es veu limitada per la restenosis i la trombosi. El disseny de models multi-escala específics per a cada pacient pot ajudar a entendre la progressió d'aquests esdeveniments en tenir la capacitat per integrar les respostes cel•lulars microscòpiques en el context del flux macroscòpic i de les condicions estructurals. Aquests models poden proporcionar informació sobre com mitigar respostes adverses en funció de cada individu. Emprant mètodes in silico i in vitro prèviament validats, s'ha desenvolupat una plataforma de replicació arterial per reproduir bifurcacions vasculars coronàries i caròtides derivades d'imatges clíniques que s'han fet servir per generar arxius computacionals per a anàlisi in silico per una banda i per fabricar models arterials polimèrics biocompatibles per a anàlisis in vitro de l’altra. En paral•lel amb les simulacions de flux, els models físics van ser sembrats amb cèl•lules vasculars centrals en l'hemostàsia i la resposta a les lesions. Els models vasculars van ser exposats a fluxos fisiològics rellevants i a entorns urèmics, inflamatoris o anti-proliferatius. Després de la caracterització funcional dels models, el progrés de l'aterosclerosi i la trombosi es va quantificar a nivell local i es va correlacionar amb les característiques biològiques, químiques i físiques de l'entorn cel•lular. La quantitat de recirculació i la presència d'agents inflamatoris, productes químics anti proliferatius i de sèrum i soluts urèmics van ser crítics per a l'activació dels biomarcadors d'evolució d'aterosclerosi i trombosi . Plataformes integrades tals com la descrita en aquesta tesi podrien ser molt útils en una varietat de camps de la biomedicina. La plataforma pot ajudar els investigadors a respondre una sèrie de qüestions biològiques clínicament rellevants i té la capacitat de produir empelts vasculars bioimplantables en un futur pròxim.La progresión de la aterosclerosis y la trombosis en pacientes con riesgo de enfermedad cardiovascular depende en gran medida del entorno único a nivel físico y bioquímico de cada individuo. Características tales como la arquitectura de la vasculatura, composición bioquímica de la sangre o el tipo de tratamiento definen el resultado de las intervenciones cardiovasculares. La colocación de un stent o de un bypass busca recuperar la permeabilidad del vaso, pero se ve limitada por la restenosis y la trombosis. El diseño de modelos multi-escala específicos para cada paciente puede ayudar a entender la progresión de estos eventos al tener capacidad para integrar las respuestas celulares microscópicas en el contexto del flujo macroscópico y de las condiciones estructurales. Dichos modelos pueden proporcionar información sobre cómo mitigar respuestas adversas en función de cada individuo. Usando métodos in silico e in vitro previamente validados se ha desarrollado una plataforma de replicación arterial para reproducir bifurcaciones vasculares coronarias y carótidas derivadas de imágenes clínicas, que se han usado para generar archivos computacionales para análisis in silico por un lado y para fabricar modelos arteriales poliméricos biocompatibles para análisis in vitro por otro. En paralelo con las simulaciones de flujo, los modelos físicos fueron sembrados con células vasculares centrales en la hemostasia y la respuesta a las lesiones. Los modelos vasculares fueron expuestos a flujos fisiológicos relevantes y a entornos urémicos, inflamatorios o anti proliferativos. Tras la caracterización funcional de los modelos, el progreso de la aterosclerosis y la trombosis se cuantificó a nivel local y se correlacionó con las características biológicas, químicas y físicas del entorno celular. La cantidad de recirculación y la presencia de agentes inflamatorios, productos químicos anti proliferativos y de suero y solutos urémicos fueron críticos para la activación de los biomarcadores de evolución de aterosclerosis y trombosis. Plataformas integradas tales como la descrita en esta tesis podrían ser muy útiles en una variedad de campos de la biomedicina. La plataforma puede ayudar a los investigadores a responder una serie de cuestiones biológicas clínicamente relevantes y tiene la capacidad de producir injertos vasculares bioimplantables en un futuro próximo.Progression of atherosclerosis and thrombosis in patients at risk of cardiovascular disease depend heavily upon the unique physical and biochemical environment of each individual. Characteristics such as vessel architecture, biochemical composition of blood or type of treatment define the outcome of cardiovascular interventions. Stent placement and graft positioning seek to recover vessel patency, yet are limited by restenosis and thrombosis. Composite, patient-specific, multi-scale models able to integrate microscopic cellular responses in the context of relevant macroscopic flow and structural conditions may help understand the progression of these events, providing insight into how to mitigate adverse responses in specific settings and individuals. Based on previously validated in silico and in vitro methods, an arterial replication platform was developed. Vascular architectures from coronary and carotid bifurcations were derived from clinical imaging and used to generate conjoint computational meshing for in silico analysis and polymeric, biocompatible scaffolds for in vitro models. In parallel with three dimensional flow simulations, the geometrically-realistic constructs were seeded with vascular cells critical to vessel hemostasis and response to injury and exposed to relevant, physiologic flows and uremic, inflammatory or anti-proliferative conditions. Following functional characterization, in vitro surrogates of atherosclerotic and thrombogenic progression were locally quantified and correlated with the biological, chemical and physical characteristics of the cellular environment. The extent of recirculation and the presence of inflammatory agents, anti-proliferative chemicals and uremic serum and solutes were critical to the activation of atherosclerosis and thrombosis progression biomarkers. Integrated frameworks such as the one described in this thesis could be very useful in a range of biomedical fields. The platform may help researchers to answer an array of biological and clinically relevant questions and holds the capacity to cast bioimplantable vascular grafts in a close future

Power Law Nanofluid through Tapered Artery based on a ‎Consistent Couple Stress Theory

Based on couple stress theory, this study investigated non-Newtonian power-law nanofluid flows in converging, non-tapered, and diverging arteries. In addition to excluding gravity effects artery, geometry included mild stenosis. The momentum equation is solved via the Galerkin method, and the results are compared with experimental and classical findings. Although the power-law couple stress theory’s relations are first used in the analysis of non-Newtonian blood flow, the results of this theory are far more consistent with experimental results than classical results. Comparison of the results of the study of blood flow velocity profiles in a non-tapered artery without stenosis by the mentioned theory with experimental and classical theory results shows the difference in velocity at the center of the artery between the experimental results and the results of the classical theory is 36%, while this value has been reduced to 14% for the results of the couple stress theory. The variations in velocity profile with the power-law index (n=0.8 and n=0.85) and the dimensionless Darcy number (Da=10-10 and Da=10-7) in all three geometries indicated a flat velocity distribution with the increase in the power-law index while increasing the velocity profile with increased Darcy number. Mass transfer and energy equations are solved using the extended Kantorovich method. The solution convergence is evaluated, and the influence of parameters such as Prandtl number, Schmidt number, and dimensionless thermospheric and Brownian parameters on concentration and temperature profiles is obtained