Hemodynamics in Ruptured Intracranial Aneurysms

Incidental detection of unruptured intracranial aneurysms (UIA) has increased in the recent years. There is a need in the clinical community to identify those that are prone to rupture and would require preventive treatment. Hemodynamics in cerebral blood vessels plays a key role in the lifetime cycle of intracranial aneurysms (IA). Understanding their initiation, growth, and rupture or stabilization may identify those hemodynamic features that lead to aneurysm instability and rupture. Modeling hemodynamics using computational fluid dynamics (CFD) could aid in understanding the processes in the development of IA. The neurosurgical approach during operation of IA allows direct visualization of the aneurysm sac and its sampling in many cases. Detailed analysis of the quality of the aneurysm wall under the microscope, together with histological assessment of the aneurysm wall and CFD modeling, can help in building complex knowledge on the relationship between the biology of the wall and hemodynamics. Detailed CFD analysis of the rupture point can further strengthen the association between hemodynamics and rupture. In this chapter we summarize current knowledge on CFD and intracranial aneurysms

Proudění biologických tekutin v reálných geometriích

1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary...1 Abstrakt: Časově závislé trojrozměrné proudění Newtonovské tekutiny je studováno v kontextu dvou bio- mechanických aplikací, proudění v mozkových výdutích a proudění ve stenotických cévách. V první části práce jsou výpočetní sítě, získané z medicínských zobrazovacích technik, použity na výpočet hemodynamických parametrů spojovaných s možností prasknutí mozkových výdutí. Hlavním výsledkem je výpočet ve dvaceti geometriích výdutí. Je ukázáno, že velikost výdutě hraje důležitější roli pro rozložení smykového napětí na stěnách než fakt, zda je výdut' prasklá nebo neprasklá. Druhá část práce je zaměřena na proudění ve stenotických chlopních. Je ukázáno, že metoda používaná v současnosti v lékařské praxi je založena na předpokladech, které jsou příliš omezující pro aplikace proudění krve v reálném případě. Je prezentován kompletní model mechaniky kontinua s fyziologicky relevantními okrajovými podmínkami a je ukázáno, že výsledky jsou konzistentní s naměřenými daty získanými z lite- ratury. Dále se zaměřujeme na získání tlakového pole z rychlostního pole. Prezentovaná metoda poskytuje přes- nější aproximaci tlaku než běžně používaná Poissonova rovnice pro tlak. Poslední kapitola práce se věnuje Nitscheho metodě pro slip okrajovou podmínku. Numerické výsledky jsou...Matematický ústav UKMathematical Institute of Charles UniversityFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Proudění biologických tekutin v reálných geometriích

1 Abstrakt: Časově závislé trojrozměrné proudění Newtonovské tekutiny je studováno v kontextu dvou bio- mechanických aplikací, proudění v mozkových výdutích a proudění ve stenotických cévách. V první části práce jsou výpočetní sítě, získané z medicínských zobrazovacích technik, použity na výpočet hemodynamických parametrů spojovaných s možností prasknutí mozkových výdutí. Hlavním výsledkem je výpočet ve dvaceti geometriích výdutí. Je ukázáno, že velikost výdutě hraje důležitější roli pro rozložení smykového napětí na stěnách než fakt, zda je výdut' prasklá nebo neprasklá. Druhá část práce je zaměřena na proudění ve stenotických chlopních. Je ukázáno, že metoda používaná v současnosti v lékařské praxi je založena na předpokladech, které jsou příliš omezující pro aplikace proudění krve v reálném případě. Je prezentován kompletní model mechaniky kontinua s fyziologicky relevantními okrajovými podmínkami a je ukázáno, že výsledky jsou konzistentní s naměřenými daty získanými z lite- ratury. Dále se zaměřujeme na získání tlakového pole z rychlostního pole. Prezentovaná metoda poskytuje přes- nější aproximaci tlaku než běžně používaná Poissonova rovnice pro tlak. Poslední kapitola práce se věnuje Nitscheho metodě pro slip okrajovou podmínku. Numerické výsledky jsou...1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary...Katedra geofyzikyDepartment of GeophysicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Flow of biological fluids in patient specific geometries

1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary..

Application of finite element method to real problems in hemodynamics.

The incompressible fluid flow around the geometries of cerebral artery aneurysms is studied in this thesis. The aneurysm is a local extension of a vessel. This disease is dangerous only in the case of rupture. Then the blood is released into the brain. The need of accurate computation of the velocity and pressure fields in this geometries is motivated exactly by the question which aneurysm has tendency to rupture. The finite element method (FEM) is used for the computation of the flow. A good domain discretization is one of the main step in FEM. Modern computed tomography is able to produce series of the two- dimensional images and it is necessary to create an appropriate three-dimensional model of the tissue. This thesis includes the description of the mesh generation and the ways to smooth and improve the meshes. In the theoretical part the equations of fluid flow are formulated. A suitability of a choice of boundary conditions is discussed. Weak formulation for the equations and its discretization are presented. In the practical part velocity and pressure fields are computed by the various finite elements. Wall shear stress which plays an important role in the evolution of an aneurysm is also computed on the introduced meshes. Comparison of mesh smoothing filters, used finite elements and used..

Mixed finite element method for the Poisson equation

Cílem této práce je implementovat smíšenou metodu konečných prvků na Poisso- novu rovnici a provést srovnání výsledků s klasickou metodou konečných prvků. Práce je rozdělena do dvou kapitol. V první kapitole jsou popsány prostory, které se vyskytují ve slabé formulaci Poissonovy rovnice a prostory, kterými je vhodné je aproximovat. Druhá kapitola se zabývá existencí řešení aproximovaných úloh spolu s jejich konvergencí. Hlavní částí této práce jsou grafy řešení obou metod a tabulky srovnávající chyby těchto řešení pro tři různé funkce. 1The aim of this bachelor thesis is the implementation of the mixed element method for the Poisson equation and the comparison with results of the classical finite element method. The thesis is divided into two chapters. In the first chapter there are descriptions of the spaces occurring in the weak formulation of the Poisson equation and descriptions of the spaces which are suitable to approach them. The second chapter studies the existence of the solutions of the approximated tasks and their convergence. The main part of this thesis are schemes of the solutions of both methods and the tables comparing errors of these solutions for three diferent functions. 1Department of Numerical MathematicsKatedra numerické matematikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Flow of biological fluids in patient specific geometries

1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary..

Application of finite element method to real problems in hemodynamics.

V této diplomové práci je studováno proudění nestlačitelných tekutin v geometriích mozkových cév postižených aneurysmatem. Aneurysma je lokální rozšíření tepny. Toto onemocnění je nebezpečné v případě, kdy dojde k prasknutí aneurysmatu a vylití krve do mozku. Potřeba výpočtu přesného rychlostního pole a zejména rozložení tlaku v geometriích cév postižených aneurysmatem je motivována právě otázkou, které aneurysma může být náchylné k prasknutí a je třeba je sledovat. K výpočtu proudění je použita metoda konečných prvků. Jedním z důležitých kroků při jejím použití je dobrá diskretizace oblasti. Moderní počítačová tomografie (CT) umožňuje pořizovat celé série prostorově navazujících rovinných snímků a je třeba na základě těchto dat vytvářet odpovídající třírozměrné modely tkání. Součástí práce je popis získání výpočetních sítí ze segmentace pořízené CT skenem, možností jejich zhlazení a úprav. V teoretické části jsou nejprve zformulovány použité rovnice včetně diskuze zadání vhodných okrajových podmínek až po nalezení slabé formulace úlohy a její diskretizace. V části pro numerické výsledky jsou uvedena spočtená rychlostní a tlaková pole pomocí různých konečných prvků a dopočteno je i smykové napětí na stěnách, které hraje důležitou roli při vzniku a vývoji aneurysma. Uvedena jsou srovnání přístupů...The incompressible fluid flow around the geometries of cerebral artery aneurysms is studied in this thesis. The aneurysm is a local extension of a vessel. This disease is dangerous only in the case of rupture. Then the blood is released into the brain. The need of accurate computation of the velocity and pressure fields in this geometries is motivated exactly by the question which aneurysm has tendency to rupture. The finite element method (FEM) is used for the computation of the flow. A good domain discretization is one of the main step in FEM. Modern computed tomography is able to produce series of the two- dimensional images and it is necessary to create an appropriate three-dimensional model of the tissue. This thesis includes the description of the mesh generation and the ways to smooth and improve the meshes. In the theoretical part the equations of fluid flow are formulated. A suitability of a choice of boundary conditions is discussed. Weak formulation for the equations and its discretization are presented. In the practical part velocity and pressure fields are computed by the various finite elements. Wall shear stress which plays an important role in the evolution of an aneurysm is also computed on the introduced meshes. Comparison of mesh smoothing filters, used finite elements and used...Matematický ústav UKMathematical Institute of Charles UniversityMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Application of finite element method to real problems in hemodynamics.

The incompressible fluid flow around the geometries of cerebral artery aneurysms is studied in this thesis. The aneurysm is a local extension of a vessel. This disease is dangerous only in the case of rupture. Then the blood is released into the brain. The need of accurate computation of the velocity and pressure fields in this geometries is motivated exactly by the question which aneurysm has tendency to rupture. The finite element method (FEM) is used for the computation of the flow. A good domain discretization is one of the main step in FEM. Modern computed tomography is able to produce series of the two- dimensional images and it is necessary to create an appropriate three-dimensional model of the tissue. This thesis includes the description of the mesh generation and the ways to smooth and improve the meshes. In the theoretical part the equations of fluid flow are formulated. A suitability of a choice of boundary conditions is discussed. Weak formulation for the equations and its discretization are presented. In the practical part velocity and pressure fields are computed by the various finite elements. Wall shear stress which plays an important role in the evolution of an aneurysm is also computed on the introduced meshes. Comparison of mesh smoothing filters, used finite elements and used..

A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions

International audienceWe consider flows of an incompressible Navier-Stokes fluid in a tubular domain with Navier's slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark. Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries