|
|
Blood flow modeling in arterial stenosis.
Matajová, Adéla ; Hron, Jaroslav (advisor) ; Dolejší, Vít (referee)
Arterial stenosis is a disease characterized by the buildup of a waxy substance inside the artery, which is associated with certain risks. It is difficult to eval- uate the severity of the stenosis, yet the diagnosis can become more accurate using computational fluid dynamics simulations. The present thesis introduces and applies the model of hemodynamics based on the Navier-Stokes equations, implemented in the FEniCS software employing the finite element method. The main focus lies on the prescription of the boundary condition at the outlet of the computational domain. The impact of the outlet boundary condition on medically significant quantities such as the wall shear stress is analyzed in a two- dimensional benchmark case. It appears that the right choice of the boundary condition is fundamental, in particular when vortices occur and propagate across the outlet boundary. The next part of the work is dedicated to the prescrip- tion of the outflow rate in the case of more than one outlet, corresponding to an artery branching inside the computational domain. The physically meaningful flux distribution is derived introducing Murray's law and its extension. Finally, the blood flow is simulated in a three-dimensional geometry of a patient-specific carotid artery. 1
|
|
|
Blood flow modeling in arterial stenosis.
Matajová, Adéla ; Hron, Jaroslav (advisor) ; Dolejší, Vít (referee)
Arterial stenosis is a disease characterized by the buildup of a waxy substance inside the artery, which is associated with certain risks. It is difficult to eval- uate the severity of the stenosis, yet the diagnosis can become more accurate using computational fluid dynamics simulations. The present thesis introduces and applies the model of hemodynamics based on the Navier-Stokes equations, implemented in the FEniCS software employing the finite element method. The main focus lies on the prescription of the boundary condition at the outlet of the computational domain. The impact of the outlet boundary condition on medically significant quantities such as the wall shear stress is analyzed in a two- dimensional benchmark case. It appears that the right choice of the boundary condition is fundamental, in particular when vortices occur and propagate across the outlet boundary. The next part of the work is dedicated to the prescrip- tion of the outflow rate in the case of more than one outlet, corresponding to an artery branching inside the computational domain. The physically meaningful flux distribution is derived introducing Murray's law and its extension. Finally, the blood flow is simulated in a three-dimensional geometry of a patient-specific carotid artery. 1
|
|
|
Mathematical analysis of bone and vascular remodelling model
Matajová, Adéla ; Maršík, František (advisor) ; Souček, Ondřej (referee)
Bone is a tissue that is constantly being renewed during the whole life. This complex biological process, controling among others adaptation to environ- mental loads, is called bone remodelling. It is due to this complexity that the process hasn't been fully biomechanically described yet. However, sev- eral mathematical models of bone remodelling have been conjectured, one of which we will introduce and analyze in this thesis. The model describes bone metabolism by five chemical equations. Using the biothermodynamical laws we will derive from these equations a system of ordinary differential equations. Then we will effectuate a qualitative analysis, while focusing on existence, uniqueness and stability of a stationary solution. Finally the im- pact of the mechanical loading on bone remodelling will be outlined.We will also mention the relation with vascular remodelling. 1
|
guest ::
RSS feed.