A hemodynamic modelling of the blood circulation
Abstract
Description
A thesis Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER of SCIENCE in MATHEMATICS from Texas A&M University-Corpus Christi in Corpus Christi, Texas.
A mathematical model of the blood flow through an axisymmetric stenosis vessel was developed using the Navier-Stokes equations. A numerical approach has been used to analyze behavior of the blood flow because an analytical solution of such a problem is impossible. The method of finite elements was applied to find the velocity and the pressure of the blood flow in stenotic vessels of the cardio-vascular system. The solution of the Navier-Stokes equations was done using Matlab and COSMOL Multiphysics. The findings of the modeling demonstrated that velocity and wall shear stress significantly increase due to the stenosis in the part of the vessel that is blocking blood flow and that this increase depends on the size of the blockage. The modeling shows that increased velocity, vessel wall shear stress, and significant variations in blood pressure may lead to abnormality of the blood flow, which in turn may be a cause of the heart attacks or/and strokes. The analysis of this research has been compared with the existing results published in research papers. Future investigations of the effect of a more general boundary for a stenosis are planned.
Mathematics and Statistics
College of Science and Engineering
A mathematical model of the blood flow through an axisymmetric stenosis vessel was developed using the Navier-Stokes equations. A numerical approach has been used to analyze behavior of the blood flow because an analytical solution of such a problem is impossible. The method of finite elements was applied to find the velocity and the pressure of the blood flow in stenotic vessels of the cardio-vascular system. The solution of the Navier-Stokes equations was done using Matlab and COSMOL Multiphysics. The findings of the modeling demonstrated that velocity and wall shear stress significantly increase due to the stenosis in the part of the vessel that is blocking blood flow and that this increase depends on the size of the blockage. The modeling shows that increased velocity, vessel wall shear stress, and significant variations in blood pressure may lead to abnormality of the blood flow, which in turn may be a cause of the heart attacks or/and strokes. The analysis of this research has been compared with the existing results published in research papers. Future investigations of the effect of a more general boundary for a stenosis are planned.
Mathematics and Statistics
College of Science and Engineering