Hemodynamics of Diseased Coronary Arteries

Cardiovascular diseases are one of the main causes of death worldwide. A common cardiovascular disease is atherosclerosis, caused by plaque deposition on the arterial wall which leads to the obstruction of the blood ow, known as stenosis. Atherosclerosis can form in any part of the arterial system but it may have serious consequences when located in one of the coronary arteries which supply blood to the heart. Plaque formation inside a coronary artery influences the flow behaviour and leads to the development of turbulence structures with physiological consequences, such as pressure drop. Percutaneous coronary intervention (PCI) is one of the most common treatments for coronary artery diseases (CADs). There are several benefits of PCI over other alternative methods for treatment of CADs including lower risks of complications and much shorter recovery period. However, it can result in thrombosis and in-stent restenosis, which are the major drawbacks of coronary stent placement in patients with CADs. It was shown that the likelihood of occurrence of restenosis and thrombosis is a function of the wall shear stress (WSS) distribution. The motivation for the research presented in this thesis is to develop an understanding of the hemodynamics of stenosed and stented coronary arteries with an ultimate goal of improving patient outcomes. This can only be achieved if the effect of stenoses and stents on the flow behaviour in arteries is well-characterised. Hence, in this thesis the relationship between the shape of stenosis, stent pattern, the downstream transitional ow behaviour, and the hemodynamic parameters is investigated. The research presented in this thesis is focused on the development of an in-depth understanding of the hemodynamics of diseased coronary arteries. Extensive pressure drop measurements, visualisation of the flow using particle image velocimetry (PIV), and computational modelling of the flow were conducted. Attention was mainly given to the stenosed and stented coronary arteries by investigating their influence on the flow behaviour, including velocity profile, pressure drop, time-averaged and -dependent WSS, and turbulent kinetic energy. The need for modelling the temporal geometric variations of the coronary arteries during a cardiac cycle for the investigation of the hemodynamics is discussed. Temporal geometric variations of the coronary arteries during a cardiac cycle are classified as a superposition of the changes in the position, curvature and torsion of the coronary artery and the variations in lumen cross-sectional shape due to distensible wall motion induced by the pulse pressure and/or contraction of the myocardium in a cardiac cycle. A sensitivity analysis was conducted to evaluate the effects of temporal geometric variations of the coronary arteries on the pressure drop and WSS. The results show that neglecting the effects of temporal geometric variations results in less than 5% deviation of the time-averaged pressure drop and WSS values. However, they lead to an approximately 20% deviation in the temporal geometric variations of hemodynamic parameters, such as time-dependent WSS. Based on the presented discussion, the temporal geometric variations of coronary arteries were not modelled in this thesis and the focus was on modelling the flow dynamics to develop an in-depth understanding of the ow features inside the stenosed and stented coronary arteries. In the next stage of the research, a model incorporating the plaque geometry, the pulsatile inlet ow and the induced turbulence in a stenosed coronary artery was developed and validated against numerical and experimental data. The transitional ow behaviour was quantified by investigation of the changes in the turbulent kinetic energy. The results suggest that there is a high risk of the formation of a secondary stenosis at a downstream distance of equal to 10 times the artery diameter in the regions to the side and downstream of the initial stenosis due to existence of the recirculation zones and low shear stresses. The applicability of the obtained results was tested with a patient-specific stenosed coronary artery model. Furthermore, for the non-invasive determination of the pressure drop in a stenosed artery model a mathematical model incorporating different physical parameters such as blood viscosity, artery length and diameter, ow rate and ow profile, and shape and degrees of stenosis, was developed. Extensive experimental pressure measurements were conducted for a wide range of degrees and shapes of stenosis to form a database in the process of the development of this equation. The validity of the developed relationship was also tested for the stenosed coronary artery models with the physiological flow profile of the left and right coronary arteries by comparing the pressure drop obtained from the developed equation and those from the experimental measurements. Moreover, the effect of artery curvature on the pressure drop and fractional ow reserve (FFR) wa investigated. The results show that neglecting the effect of artery curvature results in under-estimation of pressure drop by about 25{35%. The developed equation can determine the pressure drop inside a stenosed coronary artery using the measurement of the flow profle inside the artery as well as the images of the stenosed coronary artery. In order to develop an understanding of the hemodynamic performance of coronary stents, the effect of stent design on the hemodynamics of stented arteries was investigated experimentally and numerically. An innovative PIV technique was implemented for the visualisation of the entire ow and the investigation of WSS within the stent struts without covering the region of interest inside a stented coronary artery model. This novel technique was based on the construction of a transparent stented artery using silicone cast in one piece, instead of inserting a metal or non-metallic stent inside a cast artery model, which are translucent and distort the field of view. The results show that WSS is strongly dependent on the design of the stent. It was also shown that the likelihood of occurrence of restenosis is strongly dependent on strut depth and thickness, the distance between two consecutive struts, and the shape of the connector between the struts. This thesis provides an improved understanding of the hemodynamics of diseased coronary arteries with an ultimate goal of improving patient outcomes. The findings will provide a basis for improvement of the most common CAD diagnostic and treatment methods. Based on the results of this research, the susceptible regions for the formation of a new stenosis downstream of the initial stenosis can be determined. Identification of these locations, which are a function of different physical and geometrical parameters, such as shape, degree and eccentricity of the initial stenosis, can provide the necessary information for prevention of the distal propagation of stenoses. Furthermore, the equation developed to evaluate FFR non-invasively in this research can be used as a gatekeeper to prevent unnecessary FFR procedures for all patients. This will result in better patient outcomes and reduce costs related to unnecessary invasive FFR which will benefit the health system. In addition, the results of this study provide a better understanding of the effect of stents on the flow which can be used to improve stent designs.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 202

Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM.

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics

Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis.

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number

Dual Solutions for MHD Jeffery–Hamel Nano-Fluid Flow in Non-parallel Walls Using Predictor Homotopy Analysis Method

The main purpose of this study is to present dual solutions for the problem of magneto-hydrodynamic Jeffery–Hamel nano-fluid flow in non-parallel walls. To do so, we employ a new analytical technique, Predictor Homotopy Analysis Method (PHAM). This effective method is capable to calculate all branches of the multiple solutions simultaneously. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge-Kutta integration method illustrates the high accuracy for this technique. For the current problem, it is found that the multiple (dual) solutions exist for some values of governing parameters especially for the convergent channel cases (α = -1). The fluid in the non-parallel walls, divergent and convergent channels, is the drinking water containing different nanoparticles; Copper oxide (CuO), Copper (Cu) and Silver (Ag). The effects of nanoparticle volume fraction parameter (φ), Reynolds number (Re), magnetic parameter (Mn), and angle of the channel (α) as well as different types of nanoparticles on the flow characteristics are discussed

Transitional turbulent flow in a stenosed coronary artery with a physiological pulsatile flow

The turbulence in the blood flow, caused by plaque deposition on the arterial wall, increases by the combined effect of the complex plaque geometries and the pulsatile blood flow. The correlation between the plaque geometry, the pulsatile inlet flow and the induced turbulence in a constricted artery is investigated in this study. Pressure drop, flow velocity and wall shear stress are determined for stenosed coronary artery models with three different degrees of asymmetric stenosis and for different heart working conditions. A Computational Fluid Dynamics model, validated against experimental data published in the literature, was developed to simulate the blood pulsatile flow inside a stenosed coronary artery model. The transitional flow behaviour was quantified by investigation of the changes in the turbulence kinetic energy. It was shown that the separation starts from the side of the asymmetric stenosis and spreads to its opposite side further downstream. The results suggest that there is a high risk of the formation of a secondary stenosis at a downstream distance equal to 10- times of the artery diameter at the side and bottom regions of the first stenosis due to the existence of the recirculation zones and low shear stresses. Finally, a stenosed patient specific coronary artery model was employed to illustrate the applicability of the obtained results for real geometry models. The results of this study provide a good prediction of pressure drop and blood flow rate, which can be applied in the investigation of the heart muscle workout and the required heart power.N. Freidoonimehr, M. Arjomandi, N. Sedaghatizadeh, R. Chin, and A. Zande

Mathematical modelling of entropy generation in magnetized micropolar flow between co-rotating cylinders with internal heat generation

The present study investigates analytically the entropy generation in magnetized micropolar fluid flow in between two vertical concentric rotating cylinders of infinite length. The surface of the inner cylinder is heated while the surface of the outer cylinder is cooled. Internal heat generation (which arises in energy systems) is incorporated. The Eringen thermo-micropolar fluid model is used to simulate the micro-structural rheological flow characteristics in the annulus region. The flow is subjected to a constant, static, axial magnetic field. The surface of the inner cylinder is prescribed to be isothermal (constant temperature wall condition), whereas the surface of the outer cylinder was exposed to convection cooling. The conservation equations are normalized and closed-form solutions are obtained for the velocity, microrotation and temperature. These are thereafter utilized to derive the expressions for entropy generation number, Bejan number and total entropy generation rate. The effects of relevant thermo-physical parameters on the flow, heat and entropy generation rate are displayed graphically and interpreted at length. It is observed that the external magnetic force enhances the entropy production rate is minimum at the center point of the channel and maximum in the proximity of the inner cylinder. This causes more wear and tear at the surface of the inner cylinder. Greater Hartmann number also elevates microrotation values in the entire annulus region. The study is relevant to optimization of chemical engineering processes, nuclear engineering cooling systems and propulsion systems utilizing non-Newtonian fluids and magnetohydrodynamics

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers

Influence of Stefan blowing on nanofluid flow submerged in microorganisms with leading edge accretion or ablation

The unsteady forced convective boundary layer flow of viscous incompressible fluid containing both nanoparticles and gyrotactic microorganisms, from a flat surface with leading edge accretion (or ablation), is investigated theoretically. Utilizing appropriate similarity transformations for the velocity, temperature, nanoparticle volume fraction and motile microorganism density, the governing conservation equations are rendered into a system of coupled, nonlinear, similarity ordinary differential equations. These equations, subjected to imposed boundary conditions, are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in the MAPLE symbolic software. Good agreement between our computations and previous solutions is achieved. The effect of selected parameters on flow velocity, temperature, nano-particle volume fraction (concentration) and motile microorganism density function is investigated. Furthermore, tabular solutions are included for skin friction, wall heat transfer rate, nano-particle mass transfer rate and microorganism transfer rate. Applications of the study arise in advanced micro-flow devices to assess nanoparticle toxicity

Effect of degree of stenosis on the pulsatile flow pressure drop in a coronary artery

Artery blockage due to plaque formation affects the performance of the heart considerably. These plaques are formed inside an artery and forced the heart to work harder to feed the vessels and organs with oxygenated blood. In this study, the pressure drop of a pulsatile flow is calculated in diseased coronary arteries with different degrees of stenosis and for blood with different levels of blood viscosity. Pressure drop is much more significant at the severe degrees of stenosis (more than 60%) compared to the mild and moderate cases. The effect of changes in the level of blood viscosity on the pressure drop is more significant at early stages of atherosclerosis (mild degrees of stenosis). The comparison of the pressures measured before and after stenoses with the ones for healthy arteries is recommended to be used to estimate the severity of vessel constriction, which can be helpful in early detection of atherosclerosis via a non-invasive diagnostic procedure.N. Freidoonimehr, R. Chin, M. Arjomandi, and A. Zande