A study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions

Recent computational fluid dynamics (CFD) studies relate abnormal blood flow to rupture of cerebral aneurysms. However, it is still debated how to model blood flow with sufficient accuracy. Common assumptions made include Newtonian behaviour of blood, traction free outlet boundary conditions and inlet boundary conditions based on available literature. These assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature. However, the consequences of these assumptions have so far been inadequately addressed.     

Newtonian and non-Newtonian blood flow in coiled cerebral aneurysms

Endovascular coiling aims to isolate the aneurysm from blood circulation by altering hemodynamics inside the aneurysm and triggering blood coagulation. Computational fluid dynamics (CFD) techniques have the potential to predict the post-operative hemodynamics and to investigate the complex interaction between blood flow and coils. The purpose of this work is to study the influence of blood viscosity on hemodynamics in coiled aneurysms. Three image-based aneurysm models were used. Each case was virtually coiled with a packing density of around 30%. CFD simulations were performed in coiled and untreated aneurysm geometries using a Newtonian and a Non-Newtonian fluid models. Newtonian fluid slightly overestimates the intra-aneurysmal velocity inside the aneurysm before and after coiling. There were numerical differences between fluid models on velocity magnitudes in coiled simulations. Moreover, the non-Newtonian fluid model produces high viscosity (>0.007$>0.007$ [Pa s]) at aneurysm fundus after coiling. Nonetheless, these local differences and high-viscous regions were not sufficient to alter the main flow patterns and velocity magnitudes before and after coiling. To evaluate the influence of coiling on intra-aneurysmal hemodynamics, the assumption of a Newtonian fluid can be used.     

Stratification of a population of intracranial aneurysms using blood flow metrics

Indices of the intra-aneurysm hemodynamic environment have been proposed as potentially indicative of their longitudinal outcome. To be useful, the indices need to be used to stratify large study populations and tested against known outcomes. The first objective was to compile the diverse hemodynamic indices reported in the literature. Furthermore, as morphology is often the only patient-specific information available in large population studies, the second objective was to assess how the ranking of aneurysms in a population is affected by the use of steady flow simulation as an approximation to pulsatile flow simulation, even though the former is clearly non-physiological. Sixteen indices of aneurysmal hemodynamics reported in the literature were compiled and refined where needed. It was noted that, in the literature, these global indices of flow were always time-averaged over the cardiac cycle. Steady and pulsatile flow simulations were performed on a population of 198 patient-specific and 30 idealised aneurysm models. All proposed hemodynamic indices were estimated and compared between the two simulations. It was found that steady and pulsatile flow simulations had a strong linear dependence (r ≥ 0.99 for 14 indices; r ≥ 0.97 for 2 others) and rank the aneurysms in an almost identical fashion (ρ ≥ 0.99 for 14 indices; ρ ≥ 0.96 for other 2). When geometry is the only measured piece of information available, stratification of aneurysms based on hemodynamic indices reduces to being a physically grounded substitute for stratification of aneurysms based on morphology. Under such circumstances, steady flow simulations may be just as effective as pulsatile flow simulation for estimating most key indices currently reported in the literature.     

A reduced-order model for wall shear stress in abdominal aortic aneurysms by proper orthogonal decomposition

In this paper, we introduce a method to construct a Reduced-Order Model (ROM) to study the physiological flow and the Wall Shear Stress (WSS) conditions in Abdominal Aortic Aneurysms (AAA). We start the process by running a training case using Computational Fluid Dynamics (CFD) simulations with time-varying flow parameters, such that these parameters cover the range of parameters that we would like to consider in our ROM. We use the inflow angle as the variable parameter in the current study. Then we use the snapshot Proper Orthogonal Decomposition (POD) to construct the reduced-order bases, which are subsequently enhanced using a QR-factorization technique to satisfy the relevant fluid boundary conditions. The resulting ROM enables us to study the flow pattern and the WSS distribution over a range of system parameters computationally very efficiently. We have used this method to show how the WSS varies significantly for an AAA with a simplified geometry, over a range of inflow angles usually considered mild in clinical terms. We have validated the ROM results with CFD results. This approach enables comprehensive analysis of the model system across a range of inflow angles and frequencies without the need to re-compute the simulation for small changes.     

The effect of inlet waveforms on computational hemodynamics of patient-specific intracranial aneurysms

Due to the lack of patient-specific inlet flow waveform measurements, most computational fluid dynamics (CFD) simulations of intracranial aneurysms usually employ waveforms that are not patient-specific as inlet boundary conditions for the computational model. The current study examined how this assumption affects the predicted hemodynamics in patient-specific aneurysm geometries. We examined wall shear stress (WSS) and oscillatory shear index (OSI), the two most widely studied hemodynamic quantities that have been shown to predict aneurysm rupture, as well as maximal WSS (MWSS), energy loss (EL) and pressure loss coefficient (PLc). Sixteen pulsatile CFD simulations were carried out on four typical saccular aneurysms using 4 different waveforms and an identical inflow rate as inlet boundary conditions. Our results demonstrated that under the same mean inflow rate, different waveforms produced almost identical WSS distributions and WSS magnitudes, similar OSI distributions but drastically different OSI magnitudes. The OSI magnitude is correlated with the pulsatility index of the waveform. Furthermore, there is a linear relationship between aneurysm-averaged OSI values calculated from one waveform and those calculated from another waveform. In addition, different waveforms produced similar MWSS, EL and PLc in each aneurysm. In conclusion, inlet waveform has minimal effects on WSS, OSI distribution, MWSS, EL and PLc and a strong effect on OSI magnitude, but aneurysm-averaged OSI from different waveforms has a strong linear correlation with each other across different aneurysms, indicating that for the same aneurysm cohort, different waveforms can consistently stratify (rank) OSI of aneurysms.     

An approach to quantitative assessment of hemodynamic differences between unruptured and ruptured ophthalmic artery aneurysms

Background and purpose: Hemodynamic parameters are important in the pathogenesis, evolution and rupture of intracranial aneurysm. Energy loss (EL) has been applied for the rupture risk prediction of artery aneurysms recently. We proposed a new EL and further investigate its effects on the rupture of aneurysms. Materials and methods: Sixty-four patient-specific ophthalmic aneurysm datasets were divided into ruptured and unruptured groups based on their clinical history. Based on patient-specific 3D-DSA data, realistic models were retrospectively reconstructed and then analyzed by using computational fluid dynamic method. Results: The flow field feature EL in ruptured cases was significantly higher than that in unruptured cases. The average wall shear stress (WSS) and the maximum WSS in ruptured cases were higher than those in unruptured cases. Modified pressure loss coefficient (PLC_M) in ruptured cases was slight higher than that in unruptured cases but the difference has no statistical significance. Multivariate logistic regression analysis demonstrated flow field feature EL (p < 0.05) and the maximum WSS (p < 0.05) were the only independently significant variables to predict rupture of ophthalmic aneurysm. There were no differences in PLC_M, the maximum oscillatory shear index (OSI), the average OSI and AR between the two groups. Conclusion: Flow field feature EL may be a reliable factor to predict the rupture risk of aneurysms.     

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations.Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.     

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.     

Computational biomechanics of human brain with and without the inclusion of the body under different blast orientation

Three different human head models in a free space are exposed to blast waves coming from four different directions. The four head–neck–body models composed of model a, with the neck free in space; model b, with neck fixed at the bottom; and model c, with the neck attached to the body. The results show that the effect of the body can be ignored for the first milliseconds of the head–blast wave interactions. Also one can see that although most biomechanical responses of the brain have similar patterns in all models, the shear stresses are heavily increased after a few milliseconds in model b in which the head motion is obstructed by the fixed-neck boundary conditions. The free-floating head model results are closer to the attached-body model.