Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure

Multiscale Fluid-Structure Interaction Models Development and Applications to the 3D Elements of a Human Cardiovascular System

Cardiovascular diseases (CVD) are the number one cause of death of humans in the United States and worldwide. Accurate, non-invasive, and cheaper diagnosis methods have always been on demand as cardiovascular monitoring increase in prevalence. The primary causes of the various forms of these CVDs are atherosclerosis and aneurysms in the blood vessels. Current noninvasive methods (i.e., statistical/medical) permit fairly accurate detection of the disease once clinical symptoms are suggestive of the existence of hemodynamic disorders. Therefore, the recent surge of hemodynamics models facilitated the prediction of cardiovascular conditions. The hemodynamic modeling of a human circulatory system involves varying levels of complexity which must be accounted for and resolved. Pulse-wave propagation effects and high aspect-ratio segments of the vasculature are represented using a quasi-one-dimensional (1D), non-steady, averaged over the cross-section models. However, these reduced 1D models do not account for the blood flow patterns (recirculation zones), vessel wall shear stresses and quantification of repetitive mechanical stresses which helps to predict a vessel life. Even a whole three-dimensional (3D) modeling of the vasculature is computationally intensive and do not fit the timeline of practical use. Thus the intertwining of a quasi 1D global vasculature model with a specific/risk-prone 3D local vessel ones is imperative. This research forms part of a multiphysics project that aims to improve the detailed understanding of the hemodynamics by investigating a computational model of fluid-structure interaction (FSI) of in vivo blood flow. First idealized computational a 3D FSI artery model is configured and executed in ANSYS Workbench, forming an implicit coupling of the blood flow and vessel walls. Then the thesis focuses on an approach developed to employ commercial tools rather than in-house mathematical models in achieving multiscale simulations. A robust algorithm is constructed to combine stabilization techniques to simultaneously overcome the added-mass effect in 3D FSI simulation and mathematical difficulties such as the assignment of boundary conditions at the interface between the 3D-1D coupling. Applications can be of numerical examples evaluating the change of hemodynamic parameters and diagnosis of an abdominal aneurysm, deep vein thrombosis, and bifurcation areas

Device Design for Inducing Aneurysm-Susceptible Flow Conditions Onto Endothelial Cells

Aneurysms are a deadly asymptomatic cardiovascular disease that may occur especially where there are bends and bifurcations in the cerebral vasculature. A region where these features are especially prominent is the Circle of Willis (COW) in the brain, where aneurysms are known to occur. In the carotid artery, which feeds into the COW, the Reynolds number of blood flow is typically around 200-500. Even with such a low Reynolds number, turbulent-like flow, or tortuous flow, can occur due to bends, bifurcations and highly pulsatile flow which lower the effective Reynolds number where tortuous flow can occur. Highly pulsatile flow is unsteady flow that is high in magnitude and changes over time. Endothelial cells (ECs) line the inner wall of the blood vessel and experience the friction force of blood flow. This work is focused on designing a device that can expose ECs to forces they would undergo in an aneurysm-susceptible site. This is accomplished by exposing ECs to physiologically relevant Wall Shear Stress (WSS) and vibrations simultaneously. Vibrations in the body occur due to flow separation at the vessel wall, which leads to pressure changes. These pressure changes induce vibrations onto ECs. The fluid flow in the designed Parallel Plate Flow Chamber (PPFC) is laminar to induce a predictable WSS onto the cells, while the vibrations will induce a rapid cyclical force to simulate pressure fluctuations that may occur in vivo. The aneurysm-susceptible flow will simulate a more turbulent-like flow in the carotid artery; higher maximum WSS (around 2.2 Pa) with vibrations. The aneurysm-protective flow will have a lower WSS maximum (around 0.5 Pa). The PPFC, made of polycarbonate, is small and light enough to be conveniently vibrated using an electromagnetic vibration stage. The PPFC can be driven by a syringe or peristaltic pump, allowing for either steady or transient waveforms. The PPFC’s fluid domain will not change upon vibration, isolating the effect of vibration on the cells. Also, two side-by-side glass slide slots were included to allow for both protein and mRNA quantification from the same experiment, increasing experimental efficiency and flow-related consistency between the two cell areas. Simulations using ANSYS Fluent verified the flow field and WSS waveform on the cells for the designed geometry for 3D and 2D cases, as well as verified equal WSS values throughout all areas of ECs. Then, Particle Image Velocimetry (PIV) was done to verify the predicted flow rate in the machined PPFC given a steady flow rate driven by a syringe pump. Preliminary cell experiments were performed in an incubator under flow and vibration conditions to demonstrate cell survivability

Numerical study of a thrombus migration risk in aneurysm after coil embolization in patient cases: FSI modelling

Purpose There are still many challenges for modelling a thrombus migration process in aneurysms. The main novelty of the present research lies in the modelling of aneurysm clot migration process in a realistic cerebral aneurysm, and the analysis of forces sufered by clots inside an aneurysm, through transient FSI simulations. Methods The blood fow has been modelled using a Womersley velocity profle, and following the Carreau viscosity model. Hyperelastic Ogden model has been used for clot and isotropic linear elastic model for the artery walls. The FSI coupled model was implemented in ANSYS® software. The hemodynamic forces sufered by the clot have been quantifed using eight diferent clot sizes and positions inside a real aneurysm. Results The obtained results have shown that it is almost impossible for clots adjacent to aneurysm walls, to leave the aneurysm. Nevertheless, in clots positioned in the centre of the aneurysm, there is a real risk of clot migration. The risk of migration of a typical post-coiling intervention clot in an aneurysm, in contact with the wall and occupying a signifcant percentage of its volume is very low in the case studied, even in the presence of abnormally intense events, associated with sneezes or impacts. Conclusions The proposed methodology allows evaluating the clot migration risk, vital for evaluating the progress after endovascular interventions, it is a step forward in the personalized medicine, patient follow-up, and helping the medical team deciding the optimal treatment.Universidade de Vigo/CISU

A novel framework for fluid/structure interaction in rapid subjectspecific simulations of blood flow in coronary artery bifurcations

Background/Aim. Practical difficulties, particularly long model development time, have limited the types and applicability of computational fluid dynamics simulations in numerical modeling of blood flow in serial manner. In these simulations, the most revealing flow parameters are the endothelial shear stress distribution and oscillatory shear index. The aim of this study was analyze their role in the diagnosis of the occurrence and prognosis of plaque development in coronary artery bifurcations. Methods. We developed a novel modeling technique for rapid cardiovascular hemodynamic simulations taking into account interactions between fluid domain (blood) and solid domain (artery wall). Two numerical models that represent the observed subdomains of an arbitrary patient-specific coronary artery bifurcation were created using multi-slice computed tomography (MSCT) coronagraphy and ultrasound measurements of blood velocity. Coronary flow using an in-house finite element solver PAK-FS was solved. Results. Overall behavior of coronary artery bifurcation during one cardiac cycle is described by: velocity, pressure, endothelial shear stress, oscillatory shear index, stress in arterial wall and nodal displacements. The places where (a) endothelial shear stress is less than 1.5, and (b) oscillatory shear index is very small (close or equal to 0) are prone to plaque genesis. Conclusion. Finite element simulation of fluid-structure interaction was used to investigate patient-specific flow dynamics and wall mechanics at coronary artery bifurcations. Simulation model revealed that lateral walls of the main branch and lateral walls distal to the carina are exposed to low endothelial shear stress which is a predilection site for development of atherosclerosis. This conclusion is confirmed by the low values of oscillatory shear index in those places

Geometry of the carotid bifurcation predicts its exposure to disturbed flow

BACKGROUND AND PURPOSE: That certain vessels might be at so-called geometric risk of atherosclerosis rests on assumptions of wide interindividual variations in disturbed flow and of a direct relationship between disturbed flow and lumen geometry. In testing these often-implicit assumptions, the present study aimed to determine whether investigations of local risk factors in atherosclerosis can indeed rely on surrogate geometric markers of disturbed flow. METHODS: Computational fluid dynamics simulations were performed on carotid bifurcation geometries derived from MRI of 25 young adults. Disturbed flow was quantified as the surface area exposed to low and oscillatory shear beyond objectively-defined thresholds. Interindividual variations in disturbed flow were contextualized with respect to effects of uncertainties in imaging and geometric reconstruction. Relationships between disturbed flow and various geometric factors were tested via multiple regression. RESULTS: Relatively wide variations in disturbed flow were observed among the 50 vessels. Multiple regression revealed a significant (P\u3c0.002) relationship between disturbed flow and both proximal area ratio (β≈0.5) and bifurcation tortuosity (β≈-0.4), but not bifurcation angle, planarity, or distal area ratio. These findings were shown to be insensitive to assumptions about the flow conditions and to the choice of disturbed flow indicator and threshold. CONCLUSIONS: Certain geometric features of the young adult carotid bifurcation are robust surrogate markers of its exposure to disturbed flow. It may therefore be reasonable to consider large-scale retrospective or prospective imaging studies of local risk factors for atherosclerosis without the need for time-consuming and expensive flow imaging or CFD studies. © 2008 American Heart Association, Inc

Transient Cardiovascular Hemodynamics In A Patient-Specific Arterial System

The ultimate goal of the present study is to aid in the development of tools to assist in the treatment of cardiovascular disease. Gaining an understanding of hemodynamic parameters for medical implants allow clinicians to have some patient-specific proposals for intervention planning. In the present study a full cardiovascular experimental phantom and digital phantom (CFD model) was fabricated to study: (1) the effects of local hemodynamics on global hemodynamics, (2) the effects of transition from bed-rest to upright position, and (3) transport of dye (drug delivery) in the arterial system. Computational three dimensional (3-D) models (designs A, B, and C) stents were also developed to study the effects of stent design on hemodynamic flow and the effects of drug deposition into the arterial wall. The experimental phantom used in the present study is the first system reported in literature to be used for hemodynamic assessment in static and orthostatic posture changes. Both the digital and experimental phantom proved to provide different magnitudes of wall shear and normal stresses in sections where previous studies have only analyzed single arteries. The dye mass concentration study for the digital and experimental cardiovascular phantom proved to be useful as a surrogate for medical drug dispersion. The dye mass concentration provided information such as transition time and drug trajectory paths. For the stent design CFD studies, hemodynamic results (wall shear stress (WSS), normal stress, and vorticity) were assessed to determine if simplified stented geometries can be used as a surrogate for patient-specific geometries and the role of stent design on flow. Substantial differences in hemodynamic parameters were found to exist which confirms the need for patient-specific modeling. For drug eluting stent studies, the total deposition time for the drug into the arterial wall was approximately 3.5 months