Immersed boundary method predictions of shear stresses for different flow topologies occuring in cerebral aneurysms

A volume-penalizing immersed boundary method is presented that facilitates the computation of incompressible fluid flow in complex flow domains. We apply this method to simulate the flow in cerebral aneurysms, and focus on the accuracy with which the flow field and the corresponding shear stress field are computed. The method is applied to laminar, incompressible flow in curved cylindrical vessels and in a model aneurysm. The time-dependent shear stress distributions over the vessel walls are visualized and interpreted in terms of the flow fields that develop. We compute shear stress levels at two different Reynolds numbers, corresponding to a steady and an unsteady flow. In the latter situation strong fluctuations in the shear stress are observed, that may be connected to raised risk-levels of aneurysm rupture

On the major role played by the curvature of intracranial aneurysms walls in determining their mechanical response, local hemodynamics, and rupture likelihood

The properties of intracranial aneurysms (IAs) walls are known to be driven by the underlying hemodynamics adjacent to the IA sac. Different pathways exist explaining the connections between hemodynamics and local tissue properties. The emergence of such theories is essential if one wishes to compute the mechanical response of a patient-specific IA wall and predict its rupture. Apart from the hemodynamics and tissue properties, one could assume that the mechanical response also depends on the local morphology, more specifically, the wall curvature, with larger values at highly-curved wall portions. Nonetheless, this contradicts observations of IA rupture sites more often found at the dome, where the curvature is lower. This seeming contradiction indicates a complex interaction between local hemodynamics, wall morphology, and mechanical response, which warrants further investigation. This was the main goal of this work. We accomplished this by analysing the stress and stretch fields in different regions of the wall for a sample of IAs, which have been classified based on particular local hemodynamics and local curvature. Pulsatile numerical simulations were performed using the one-way fluid-solid interaction strategy implemented in OpenFOAM (solids4foam toolbox). We found that the variable best correlated with regions of high stress and stretch was the wall curvature. Additionally, our data suggest a connection between the local curvature and local hemodynamics, indicating that the curvature is a property that could be used to assess both mechanical response and hemodynamic conditions, and, moreover, to suggest new metrics based on the curvature to predict the likelihood of rupture.Comment: Preprint submitted to Acta Biomaterialia, with 27 pages and 11 figure

Mathematical and Numerical Modeling of Healthy and Unhealthy Cerebral Arterial Tissues

Over the last two decades, we have witnessed an increasing application of mathematical models and numerical simulations for the study of the cardiovascular system. Indeed, both tools provide an important contribution to the analysis of the functioning of the different components of the cardiovascular system (i.e. heart, vessels and blood) and of their interactions either in physiological and pathological conditions. For this reason, reliable constitutive models for the cardiac, arterial and venous tissues as well as for the blood are an essential prerequisite for a number of different objectives that range from the improved diagnostic to the study of the onset and development of cardiovascular diseases (e.g atherosclerosis or aneurysms). This work focuses on the mathematical and numerical modeling of healthy and unhealthy cerebral arterial tissue. In particular, it presents a detailed analysis of different constitutive models for the arterial tissue by means of finite element numerical simulations of arterial wall mechanics and fluid-structure interaction problems occurring in hemodynamics. Hyperelastic isotropic and anisotropic constitutive laws are considered for the description of the passive mechanical behavior of the vessels. An anisotropic multi-mechanism model, specifically proposed for the cerebral arterial tissue, for which the activation of the collagen fibers occurs at finite strains is employed. Firstly, the constitutive laws are numerically validated by considering numerical simulations of static inflation tests on a cylindrical geometry representing a specimen of anterior cerebral artery. With this regard, the material parameters for the constitutive law are obtained from the data fitting of experimental measurements obtained on the same vessel. The constitutive models are critically discussed according to their capability of describing the physiogical highly nonlinear behavior of arteries and on other numerical aspects related to the computational simulation of arterial wall mechanics. Afterwards, simulations of the blood flow and vessel wall interactions are carried out on idealized blood vessels in order to analyze the influence of the modeling choice for the arterial wall on hemodynamic and mechanical quantities that are commonly considered as indicators of physiological or pathological conditions of arteries. We also consider the numerical simulations of unhealthy cerebral arterial tissues by taking into account the mechanical weakening of the vessel wall that occurs during early development stages of cerebral aneurysms by means of static inflation and FSI simulations. We employ both isotropic and anisotropic models study the effects of the mechanical degradation on hemodynamic and mechanical quantities of interest. The FSI simulations are carried out both on idealized geometries of blood vessels and on domains representing idealized and anatomically realistic cerebral aneurysms

A methodology for the derivation of unloaded abdominal aortic aneurysm geometry with experimental validation

In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 lm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5-8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment

COMPUTATIONAL INVESTIGATIONS OF RED BLOOD CELL MECHANICAL TRAUMA AND OF DISEASED RENAL ARTERY HEMODYNAMICS

In this work, Computational Fluid Dynamics (CFD) and Fluid Structure Interaction (FSI) methods were used to study two separate problems: red blood cell damage in flow and the hemodynamics of diseased renal arteries; specifically, those with renal artery stenoses or aneurysms.The study of red blood cell trauma was motivated by deficiencies in the current empirical models used for hemolysis estimation. Using CFD, classic hemolysis experiments performed in capillary tubes for laminar flow and a Couette viscometer for turbulent flow were re-examined. The results of the capillary tube simulations indicated that the extensional stresses present in the flow contributed to hemolysis, with a threshold value of approximately 3000 Pa for exposure times on the order of microseconds being indicative of hemolysis. In the turbulent Couette viscometer simulations, where experimental exposure times were five minutes, it was found that Kolmogorov Length Scales of the same order of magnitude as the size of a red blood cell were indicative of hemolysis, with some dependence on the median Kolmogorov Length Scale in the flow. The results of an inter-laboratory FDA study are also reported.Simulations of diseased renal arteries were also performed, which included simulations of stenoses and aneurysms of varying geometries. Initially, this work was done solely with CFD, however FSI was eventually incorporated into the renal artery aneurysm simulations. The results of this study indicate that the uncertain relationship between renal artery aneurysms and renin-dependent hypertension is possibly related to transient occlusions of the artery that occur when high pressure within the aneurysm causes the aneurysm and underlying vessel wall to deform into the blood strea

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements