Computational investigation of two phase flow in artery bifurcation

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Κατσιγιάλου, Αικατερίνη
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In the present study a computational investigation of two phase flow in an artery bifurcation was contacted, using Computational Fluid Dynamics (CFD). In particular, we proposed an eulerian granular two phase model for the modeling of blood flow in an normal and a corresponding diseased left coronary artery bifurcation. Plasma was modeled as the continuous and liquid phase and Red Blood Cells (RBCs) as the granular and dispersed phase. The effect of the percentage of stenosis of 55%, 65% and 75% of a lesion type (1,0,1) of Medina Classification was investigated for the stage of rest and the stage of hyperemia. Also, the effect of the bifurcation angle from 50° to 70° and 90° was studied. A total number of 28 simulations were carried out. Results between single phase and two phase modeling of blood are compared in order to evaluate the proposed two phase model of blood flow. The geometric models of left coronary bifurcation were designed in the commercial program SolidWorks and the CFD simulations were carried out with the use of the commercial program Ansys Fluent (v16). In the first chapter, we present some basic biological knowledge about the cardiovascular system, the arteries and specifically coronary arteries, and the left coronary artery bifurcation. We also explain what atherosclerosis is and we discuss about significant hemodynamic factors that characterize the blood flow in left coronary artery bifurcation: the Wall Shear Stress (WSS) and the Fractional Flow Reserve (FFR). In the second chapter we can see the exact dimensions of the geometrical model of the ideal left coronary bifurcation that was created in SolidWorks. Also, we discuss about the Medina classification of coronary bifurcation lesions, and we explain the reason for selecting to study the type (1,0,1). Finally we can see the geometries of all created models. At the third chapter, we discuss the theory that was applied for the CFD investigation. First, we explain basic fluid dynamics that were used for single phase modeling of blood, and then we analyze the multiphase (two phase) modeling approach. The multiphase modeling approach was achieved using the eulerian granular model of Ansys' Fluent, considering plasma as continuous liquid and phase and RBCs as dispersed and granular phase. Then, we explain the meaning of the Reynolds Number, and we present the theory of k-ε dispersed turbulence model that was used in the case of multiphase modeling of blood flow at the stage of hyperemia. At the fourth chapter, we mention the assumptions that we made in order to solve our problem. We assumed blood as newtonian fluid in single phase modeling, and plasma phase also newtonian in the case of multiphase modeling. We also assumed homogenous, isotropic and rigid artery walls. The pressure at the bifurcation outlets, the left circumflex artery (LCX) and the left anterior descending artery (LAD), were assumed constant. Then, we mention the boundary conditions and the solution methods that were used. In the fifth chapter, we present the meshing methods that we used to grid our models. We used a patch confirming method of tetrahedrons with an inflation of the wall. Methods of measuring the quality of grid's elements, like orthogonal quality, skewness and aspect ratio are also presented. First we accomplish a good element quality and then we verify that the results of this study are independent of the mesh and element size, conducting a mesh independence study. At the sixth chapter, the results of the present study are represented. First we validate the methods used in this study. Then, results about the effect of the percentage of stenosis of left coronary artery bifurcation and the effect of the change in bifurcation angle are discussed. Results are represented comparatively between multiphase and single phase modeling of blood flow. Analysis was conducted for important hemodynamic factors of mass flow rate, velocity, pressure, WSS, FFR, RBCs granular temperature and RBCs volume fraction. These factors are also compared between the stages of rest and hyperemia. Finally further investigation is carried out using the k-ε turbulence model of Ansys' Fluent in single phase modeling of blood at the left coronary bifurcation at the stage of hyperemia. Concluding, in the seventh chapter, similarities are found between the two phase modeling of blood flow in left coronary artery and the single phase modeling. The percentage of stenosis above 55% in the diseased coronary bifurcation seems to play an important role in significant hemodynamic factors mentioned before, while the increase of bifurcation angle from 50° to 70° and to 90° for 75% stenosis does not affect our results. Results of the multiphase modeling of blood also indicate a good representation of blood's shear thinning property and Fareus-Lindqvist effect. Further experimental investigation is suggested to evaluate the precision of this result. Finally, for single phase modeling of blood in the artery bifurcation at the stage of hyperemia, a turbulence model may be necessary, as Reynolds Number is over 500. For this reason also, an experiment extent of this work is therefore suggested.
Two phase flow, Artery bifurcation, Atherosclerosis, Computational fluid dynamics (CFD)