Link between deviations from Murray's Law and occurrence of low wall shear stress regions in the left coronary artery.

Murray developed two laws for the geometry of bifurcations in the circulatory system. Based on the principle of energy minimization, Murray found restrictions for the relation between the diameters and also between the angles of the branches. It is known that bifurcations are prone to the development of atherosclerosis, in regions associated to low wall shear stresses (WSS) and high oscillatory shear index (OSI). These indicators (size of low WSS regions, size of high OSI regions and size of high helicity regions) were evaluated in this work. All of them were normalized by the size of the outflow branches. The relation between Murray's laws and the size of low WSS regions was analysed in detail. It was found that the main factor leading to large regions of low WSS is the so called expansion ratio, a relation between the cross section areas of the outflow branches and the cross section area of the main branch. Large regions of low WSS appear for high expansion ratios. Furthermore, the size of low WSS regions is independent of the ratio between the diameters of the outflow branches. Since the expansion ratio in bifurcations following Murray's law is kept in a small range (1 and 1.25), all of them have regions of low WSS with similar size. However, the expansion ratio is not small enough to completely prevent regions with low WSS values and, therefore, Murray's law does not lead to atherosclerosis minimization. A study on the effect of the angulation of the bifurcation suggests that the Murray's law for the angles does not minimize the size of low WSS regions.

A review of computational methodologies to predict the fractional flow reserve in coronary arteries with stenosis.

Computational methodologies for predicting the fractional flow reserve (FFR) in coronary arteries with stenosis have gained significant attention due to their potential impact on healthcare outcomes. Coronary artery disease is a leading cause of mortality worldwide, prompting the need for accurate diagnostic and treatment approaches. The use of medical image-based anatomical vascular geometries in computational fluid dynamics (CFD) simulations to evaluate the hemodynamics has emerged as a promising tool in the medical field. This comprehensive review aims to explore the state-of-the-art computational methodologies focusing on the possible considerations. Key aspects include the rheology of blood, boundary conditions, fluid-structure interaction (FSI) between blood and the arterial wall, and multiscale modelling (MM) of stenosis. Through an in-depth analysis of the literature, the goal is to obtain an overview of the major achievements regarding non-invasive methods to compute FFR and to identify existing gaps and challenges that inform further advances in the field. This research has the major objective of improving the current diagnostic capabilities and enhancing patient care in the context of cardiovascular diseases.

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 suffered by clots inside an aneurysm, through transient FSI simulations. METHODS: The blood flow has been modelled using a Womersley velocity profile, 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 suffered by the clot have been quantified using eight different 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 significant 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.

FSI modeling on the effect of artery-aneurysm thickness and coil embolization in patient cases.

BACKGROUND AND OBJECTIVE: The attainment of a methodology to simulate the hemodynamic in patient-specific cerebral vessels with aneurysms is still a challenge. The novelty of this work is focused on the effect of coil embolization in a realistic cerebral aneurysm, according to the vessel wall thickness and aneurysm thickness, through transient FSI simulations. METHODS: The quality of the mesh for simulations was checked with a specific mesh convergence study; and the numerical methodology was validated using numerical research data of the literature. The model was implemented in ANSYS® software. The total deformation and equivalent stress evolution in the studied cases, before and after coil embolization, were compared. More than 20 different models were employed due to different arterial wall thickness and aneurysm wall thickness combinations. RESULTS: The obtained results have showed that deformation and stress values are highly influenced with the sac thickness. The thinner sac aneurysm thickness is, the greater deformation and stress are. The results after coil embolization process have highlighted that considering typical values of arterial wall thickness and aneurysm thickness 0.3 mm and 0.15 mm respectively, a deformation reduction around 50% and a stress reduction around 70% can be achieved. CONCLUSIONS: The proposed methodology is a step forward in the personalized medicine, quantifying the aneurysm rupture risk reduction, and helping the medical team in the preoperative planning, or to deciding the optimal treatment.

Role of the left coronary artery geometry configuration in atherosusceptibility: CFD simulations considering sPTT model for blood.

The achievement of clinically viable methodologies to simulate the hemodynamics in patient-specific coronary arteries is still a major challenge. Therefore, the novelty of this work is attained by the introduction of the viscoelastic property of blood in the numerical simulations, to study the role of the left coronary artery (LCA) geometry configuration in the atherosusceptibility. Apparently healthy patients were used and four different methodologies were tested. The methodology giving the most accurate results at the same time of having the lowest computational time is the one considering the viscoelastic property of blood and computational fluid dynamics. A Pearson correlation analysis was used to highlight relationships between geometric configuration and hemodynamic descriptors based on the simulated wall shear stress (WSS). The left main stem (LMS) has the greatest atherosusceptibility followed by the left anterior descending artery (LAD) since the relative residence time (RRT) average values are 3.81 and 3.70 Pa-1, respectively. The geometric parameters with relevant contribution to directional flow change are the cross-sectional areas, especially the one of LMS segment (ALMS), and the curvature of LMS segment. For LMS and LAD segments, when ALMS increases, blood flow disturbance (r = 0.81 in LMS and r = 0.74 in LAD) and atherosusceptibility (r = 0.84 in LMS and r = 0.85 in LAD) increases. When the LMS curvature decreases, the WSS magnitude (r = 0.80 in LMS and r = 0.83 in LAD) decreases, and disturbance (r=-0.80 in LMS and r=-0.91 in LAD) and atherosusceptibility (r=-0.74 in LMS and r=-0.74 in LAD) increases.

Correlation between geometric parameters of the left coronary artery and hemodynamic descriptors of atherosclerosis: FSI and statistical study.

The hemodynamics conditioned by coronary geometry may play an important role in the creation of a pro-atherogenic environment in specific locations of the coronary tree. The aim of this study is to identify how several geometric parameters of the left coronary artery - cross-section areas, proximal left anterior descending artery length, angles between the branches and the septum, curvature and tortuosity - can be related with hemodynamic descriptors, using a computational fluid-structure interaction method. It is widely accepted that the hemodynamic indicators play an important role in identifying possible pro-atherogenic locations. A statistical study, using Pearson correlation coefficient and P value, was performed for a population study of 8 normal human left coronary arteries presenting right-dominant circulation. Within the study cases, arteries with high caliber (r = 0.88), high angles LMS-LAD (r = 0.49), LAD-LCx (r = 0.57) and LAD-Septum (r = 0.52), and high tortuosity LMS-LCx (r = 0.63) were correlated with a hemodynamic behavior propitious to plaque formation in the left anterior descending artery. In contrast, high proximal left anterior descending artery length (r = -0.41), high angle LMS-LCx (r = -0.59), high tortuosity LMS-LAD (r = -0.56) and LAD-LCx (r = -0.55) and high curvature of LMS (r = -0.60) and LCx (r = -0.56) can lead to non-favorable hemodynamic conditions for atheroma formation. Graphical abstract.

The Impact of the Right Coronary Artery Geometric Parameters on Hemodynamic Performance.

PURPOSE: Coronary artery geometry can have a significant impact in the hemodynamic behavior of coronary blood flow, influencing atherosclerotic plaque formation. The present work focuses on, through a statistical study, the connection between several geometric parameters of the right coronary artery-ostium cross-sectional area, angles between the common trunk and the side-branches, tortuosity, curvature and cross-sectional area in each side-branch-and their influence on hemodynamic descriptors. Parameters such as low wall shear stress and local disturbed flow, which are associated with atherosclerosis formation, were analysed. METHODS: Computed tomography images of ten healthy individuals were selected to reconstruct in vivo three-dimensional models of right coronary arteries. Blood flow was simulated through a compliant model with realistic boundary conditions. Calculated hemodynamic descriptors values were correlated with the geometric parameters using the Pearson correlation coefficient (r) and the p value. RESULTS: The strongest correlations were found in the middle and distal segments of the right coronary artery. A decrease in the ostium area promotes a decrease in the WSS magnitude from the proximal to the distal segment (r = 0.82). Very strong correlations (r > 0.90) were achieved between geometric parameters (cross-sectional area, angle, tortuosity) of the right-ventricular branch and the wall shear stress magnitude in the middle and distal segments. CONCLUSIONS: Low values of tortuosity, smaller cross-sectional area and higher angle of the right-ventricular branch leads to a hemodynamic behavior more propitious to atherosclerosis formation, within the study cases. The right-ventricular branch seems to have the highest influence in the hemodynamic behavior of the right coronary artery.

Numerical study on the hemodynamics of patient-specific carotid bifurcation using a new mesh approach.

The definition of a suitable mesh to simulate blood flow in the human carotid bifurcation has been investigated. In this research, a novel mesh generation method is proposed: hexahedral cells at the center of the vessel and a fine grid of tetrahedral cells near the artery wall, in order to correctly simulate the large blood velocity gradients associated with specific locations. The selected numerical examples to show the pertinence of the novel generation method are supported by carotid ultrasound image data of a patient-specific case. Doppler systolic blood velocities measured during ultrasound examination are compared with simulated velocities using 4 different combinations of hexahedral and tetrahedral meshes and different fluid dynamic simulators. The Lin's test was applied to show the concordance of the results. Wall shear stress-based descriptors and localized normalized helicity descriptor emphasize the performance of the new method. Another feature is the reduced computation time required by the developed methodology. With the accurate combined mesh, different flow rate partitions, between the internal carotid artery and external carotid artery, were studied. The overall effect of the partitions is mainly in the blood flow patterns and in the hot-spot modulation of atherosclerosis-susceptible regions, rather than in their distribution along the bifurcation.

Numerical study of wall shear stress-based descriptors in the human left coronary artery.

The present work is about the application of wall shear stress descriptors - time averaged wall shear stress (TAWSS), oscillating shear index (OSI) and relative residence time (RRT) - to the study of blood flow in the left coronary artery (LCA). These descriptors aid the prediction of disturbed flow conditions in the vessels and play a significant role in the detection of potential zones of atherosclerosis development. Hemodynamic descriptors data were obtained, numerically, through ANSYS® software, for the LCA of a patient-specific geometry and for a 3D idealized model. Comparing both cases, the results are coherent, in terms of location and magnitude. Low TAWSS, high OSI and high RRT values are observed in the bifurcation - potential zone of atherosclerosis appearance. The dissimilarities observed in the TAWSS values, considering blood as a Newtonian or non-Newtonian fluid, releases the importance of the correct blood rheologic caracterization. Moreover, for a higher Reynolds number, the TAWSS values decrease in the bifurcation and along the LAD branch, increasing the probability of plaques deposition. Furthermore, for a stenotic LCA model, very low TAWSS and high RRT values in front and behind the stenosis are observed, indicating the probable extension, in the flow direction, of the lesion.