Non-Newtonian versus numerical rheology: Practical impact of shear-thinning on the prediction of stable and unstable flows in intracranial aneurysms

Toward a physiological model of vascular wall vibrations in the arteriovenous fistula

The mechanism behind hemodialysis arteriovenous fistula (AVF) failure remains poorly understood, despite previous efforts to correlate altered hemodynamics with vascular remodeling. We have recently demonstrated that transitional flow induces high-frequency vibrations in the AVF wall, albeit with a simplified model. This study addresses the key limitations of our original fluid-structure interaction (FSI) approach, aiming to evaluate the vibration response using a more realistic model. A 3D AVF geometry was generated from contrast-free MRI and high-fidelity FSI simulations were performed. Patient-specific inflow and pressure were incorporated, and a three-term Mooney-Rivlin model was fitted using experimental data. The viscoelastic effect of perivascular tissue was modeled with Robin boundary conditions. Prescribing pulsatile inflow and pressure resulted in a substantial increase in vein displacement ( + 400 %) and strain ( + 317 %), with a higher maximum spectral frequency becoming visible above -42 dB (from 200 to 500 Hz). Transitioning from Saint Venant-Kirchhoff to Mooney-Rivlin model led to displacement amplitudes exceeding 10 micrometers and had a substantial impact on strain ( + 116 %). Robin boundary conditions significantly damped high-frequency displacement ( - 60 %). Incorporating venous tissue properties increased vibrations by 91%, extending up to 700 Hz, with a maximum strain of 0.158. Notably, our results show localized, high levels of vibration at the inner curvature of the vein, a site known for experiencing pronounced remodeling. Our findings, consistent with experimental and clinical reports of bruits and thrills, underscore the significance of incorporating physiologically plausible modeling approaches to investigate the role of wall vibrations in AVF remodeling and failure.

On flow fluctuations in ruptured and unruptured intracranial aneurysms: resolved numerical study

Flow fluctuations have emerged as a promising hemodynamic metric for understanding of hemodynamics in intracranial aneurysms. Several investigations have reported flow instabilities using numerical tools. In this study, the occurrence of flow fluctuations is investigated using either Newtonian or non-Newtonian fluid models in five patient-specific intracranial aneurysms using high-resolution lattice Boltzmann simulation methods. Flow instabilities are quantified by computing power spectral density, proper orthogonal decomposition, and fluctuating kinetic energy of velocity fluctuations. Our simulations reveal substantial flow instabilities in two of the ruptured aneurysms, where the pulsatile inflow through the neck leads to hydrodynamic instability, particularly around the rupture position, throughout the entire cardiac cycle. In other monitoring points, the flow instability is primarily observed during the deceleration phase; typically, the fluctuations begin just after peak systole, gradually decay, and the flow returns to its original, laminar pulsatile state during diastole. Additionally, we assess the rheological impact on flow dynamics. The disparity between Newtonian and non-Newtonian outcomes remains minimal in unruptured aneurysms, with less than a 5% difference in key metrics. However, in ruptured cases, adopting a non-Newtonian model yields a substantial increase in the fluctuations within the aneurysm sac, with up to a 30% higher fluctuating kinetic energy compared to the Newtonian model. The study highlights the importance of using appropriate high-resolution simulations and non-Newtonian models to capture flow fluctuation characteristics that may be critical for assessing aneurysm rupture risk.

AnXplore: a comprehensive fluid-structure interaction study of 101 intracranial aneurysms

Advances in computational fluid dynamics continuously extend the comprehension of aneurysm growth and rupture, intending to assist physicians in devising effective treatment strategies. While most studies have first modelled intracranial aneurysm walls as fully rigid with a focus on understanding blood flow characteristics, some researchers further introduced Fluid-Structure Interaction (FSI) and reported notable haemodynamic alterations for a few aneurysm cases when considering wall compliance. In this work, we explore further this research direction by studying 101 intracranial sidewall aneurysms, emphasizing the differences between rigid and deformable-wall simulations. The proposed dataset along with simulation parameters are shared for the sake of reproducibility. A wide range of haemodynamic patterns has been statistically analyzed with a particular focus on the impact of the wall modelling choice. Notable deviations in flow characteristics and commonly employed risk indicators are reported, particularly with near-dome blood recirculations being significantly impacted by the pulsating dynamics of the walls. This leads to substantial fluctuations in the sac-averaged oscillatory shear index, ranging from -36% to +674% of the standard rigid-wall value. Going a step further, haemodynamics obtained when simulating a flow-diverter stent modelled in conjunction with FSI are showcased for the first time, revealing a 73% increase in systolic sac-average velocity for the compliant-wall setting compared to its rigid counterpart. This last finding demonstrates the decisive impact that FSI modelling can have in predicting treatment outcomes.

Flow-induced high frequency vascular wall vibrations in an arteriovenous fistula: a specific stimulus for stenosis development?

Hemodialysis is the lifeline for nearly three million end stage renal disease patients worldwide. Native arteriovenous fistula (AVF) is the preferred vascular access, but 40% fail within 1 year. We recently demonstrated that AVFs harbour transitional flows and the goal of the present study was to investigate whether the associated high-frequency pressure fluctuations could promote vibrations within the vascular wall. We acquired MRI images and flow rates immediately after surgery in one patient and generated a 3D patient-specific model. High-fidelity fluid structure interaction simulations revealed the presence of wall vibrations in distinct frequency bands up to 200 Hz and amplitude of 200 μm. A sensitivity analysis to assess the impact of flow rates, and vascular wall stiffness and thickness, changes that typically occur during AVF maturation, confirmed the robustness of the results. Interestingly, the vibrations were always predominant at the anastomosis floor and on the inner venous side, which correlates with typical stenotic regions. As studies seeking to correlate aberrant stresses and vascular remodelling have been largely inconclusive, the focal colocalization between vibrations and stenosis may suggest an unknown mechanobiological process between high-frequency mechanical stresses within the vascular wall and adverse vascular remodelling.

Standardized viscosity as a source of error in computational fluid dynamic simulations of cerebral aneurysms

BACKGROUND

Computational fluid dynamics (CFD) simulations are a powerful tool for studying cerebral aneurysms, capable of evaluating hemodynamics in a way that is infeasible with imaging alone. However, the difficulty of incorporating patient-specific information and inherent obstacles of in vivo validation have limited the clinical usefulness of CFD of cerebral aneurysms. In this work we investigate the effect of using standardized blood viscosity values in CFD simulations of cerebral aneurysms when compared to simulations of the same aneurysms using patient-specific viscosity values derived from hematocrit measurements.

PURPOSE

The objective of this work is to determine the level of error, on average, that is, caused by using standardized values of viscosity in CFD simulations of cerebral aneurysms. By quantifying this error, we demonstrate the need for incorporating patient-specific viscosity in future CFD investigations of cerebral aneurysms.

METHODS

CFD simulations of forty-one cerebral aneurysms were conducted using patient-specific boundary conditions. For each aneurysm two simulations were conducted, one utilizing patient-specific blood viscosity derived from hematocrit measurements and another using a standardized value for blood viscosity. Hemodynamic parameters such as wall shear stress (WSS), wall shear stress gradient (WSSG), and the oscillatory shear index (OSI) were calculated for each of the simulations for each aneurysm. Paired t-tests for differences in the time-averaged maps of these hemodynamic parameters between standardized and patient-specific viscosity simulations were conducted for each aneurysm. Bland-Altman analysis was used to examine the cohort-wide changes in the hemodynamic parameters. Subjects were broken into two groups, those with higher than standard viscosity and those with lower than standard viscosity. An unpaired t-test was used to compare the percent change in WSS, WSSG, and OSI between patient-specific and standardized viscosity simulations for the two cohorts. The percent changes in hemodynamic parameters were correlated against the direction and magnitude of percent change in viscosity, aneurysm size, and aneurysm location. For all t-tests, a Bonferroni-corrected significance level of 0.0167 was used.

RESULTS

63.2%, 41.5%, and 48.7% of aneurysms showed statistically significant differences between patient-specific and standardized viscosity simulations for WSS, WSSG, and OSI respectively. No statistically significant difference was found in the percent changes in WSS, WSSG, and OSI between the group with higher than standard viscosity and those with lower than standard viscosity, indicating an increase in viscosity can cause either an increase or decrease in each of the hemodynamic parameters. On a study-wide level no significant bias was found in either direction for WSS, WSSG, or OSI between the simulation groups due to the bidirectional effect of changing viscosity. No correlation was found between percent change of viscosity and percent change of WSS, WSSG, or OSI, meaning an after-the-fact correction for patient-specific viscosity is not feasible.

CONCLUSION

Standardizing viscosity values in CFD of cerebral aneurysms has a large and unpredictable impact on the calculated WSS, WSSG, and OSI when compared to CFD simulations of the same aneurysms using a patient-specific viscosity. We recommend implementing hematocrit-based patient-specific blood viscosity values for all CFD simulations of cerebral aneurysms.

A verified and validated moving domain computational fluid dynamics solver with applications to cardiovascular flows

Computational fluid dynamics (CFD) in combination with patient-specific medical images has been used to correlate flow phenotypes with disease initiation, progression and outcome, in search of a prospective clinical tool. A large number of CFD software packages are available, but are typically based on rigid domains and low-order finite volume methods, and are often implemented in massive low-level C++ libraries. Furthermore, only a handful of solvers have been appropriately verified and validated for their intended use. Our goal was to develop, verify and validate an open-source CFD solver for moving domains, with applications to cardiovascular flows. The solver is an extension of the CFD solver Oasis, which is based on the finite element method and implemented using the FEniCS open source framework. The new solver, named OasisMove, extends Oasis by expressing the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation, which is suitable for handling moving domains. For code verification we used the method of manufactured solutions for a moving 2D vortex problem, and for validation we compared our results against existing high-resolution simulations and laboratory experiments for two moving domain problems of varying complexity. Verification results showed that the L 2 error followed the theoretical convergence rates. The temporal accuracy was second-order, while the spatial accuracy was second- and third-order using ℙ 1 / ℙ 1 and ℙ 2 / ℙ 1 finite elements, respectively. Validation results showed good agreement with existing benchmark results, by reproducing lift and drag coefficients with less than 1% error, and demonstrating the solver's ability to capture vortex patterns in transitional and turbulent-like flow regimes. In conclusion, we have shown that OasisMove is an open-source, accurate and reliable solver for cardiovascular flows in moving domains.

Assessment of the flow-diverter efficacy for intracranial aneurysm treatment considering pre- and post-interventional hemodynamics

Endovascular treatment of intracranial aneurysms with flow diverters (FD) has become one of the most promising interventions. Due to its woven high-density structure they are particularly applicable for challenging lesions. Although several studies have already conducted realistic hemodynamic quantification of the FD efficacy, a comparison with morphologic post-interventional data is still missing. This study analyses the hemodynamics of ten intracranial aneurysm patients treated with a novel FD device. Based on pre- and post-interventional 3D digital subtraction angiography image data, patient-specific 3D models of both treatment states are generated applying open source threshold-based segmentation methods. Using a fast virtual stenting approach, the real stent positions available in the post-interventional data are virtually replicated and both treatment scenarios were characterized using image-based blood flow simulations. The results show FD-induced flow reductions at the ostium by a decrease in mean neck flow rate (51%), inflow concentration index (56%) and mean inflow velocity (53%). Intraluminal reductions in flow activity for time-averaged wall shear stress (47%) and kinetic energy (71%) are present as well. However, an intra-aneurysmal increase in flow pulsatility (16%) for the post-interventional cases can be observed. Patient-specific FD simulations demonstrate the desired flow redirection and activity reduction inside the aneurysm beneficial for thrombosis formation. Differences in the magnitude of hemodynamic reduction exist over the cardiac cycle which may be addressed in a clinical setting by anti-hypertensive treatment in selected cases.

Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation

The assumed rheological behavior of blood influences the hemodynamic characteristics of numerical blood flow simulations. Until now, alternative rheological specifications have been utilized, with uncertain implications for the results obtained. This work aims to group sixteen blood rheological models in homogeneous clusters, by exploiting data generated from numerical simulations on an idealized symmetrical arterial bifurcation. Blood flow is assumed to be pulsatile and is simulated using a commercial finite volume solver. An appropriate mesh convergence study is performed, and all results are collected at three different time instants throughout the cardiac cycle: at peak systole, early diastole, and late diastole. Six hemodynamic variables are computed: the time average wall shear stress, oscillatory shear index, relative residence time, global and local non-Newtonian importance factor, and non-Newtonian effect factor. The resulting data are analyzed using hierarchical agglomerative clustering algorithms, which constitute typical unsupervised classification methods. Interestingly, the rheological models can be partitioned into three homogeneous groups, whereas three specifications appear as outliers which do not belong in any partition. Our findings suggest that models which are defined in a similar manner from a mathematical perspective may behave substantially differently in terms of the data they produce. On the other hand, models characterized by different mathematical formulations may belong to the same statistical group (cluster) and can thus be considered interchangeably.

Hemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fields

Recent advances in diagnostic neuroradiological imaging, allowed the detection of unruptured intracranial aneurysms (IAs). The shape - irregular or multilobular - of the aneurysmal dome, is considered as a possible rupture risk factor, independently of the size, the location and patient medical background. Disturbed blood flow fields in particular is thought to play a key role in IAs progression. However, there is an absence of widely-used hemodynamic indices to quantify the extent of a multi-directional disturbed flow. We simulated blood flow in twelve patient-specific anterior circulation unruptured intracranial aneurysms with daughter blebs utilizing the spectral/hp element framework Nektar++. We simulated three cardiac cycles using a volumetric flow rate waveform while we considered blood as a Newtonian fluid. To investigate the multidirectionality of the blood flow fields, besides the time-averaged wall shear stress (TAWSS), we calculated the oscillatory shear index (OSI), the relative residence time (RRT) and the time-averaged cross flow index (TACFI). Our CFD simulations suggest that in the majority of our vascular models there is a formation of complex intrasaccular flow patterns, resulting to low and highly oscillating WSS, especially in the area of the daughter blebs. The existence of disturbed multi-directional blood flow fields is also evident by the distributions of the RRT and the TACFI. These findings further support the theory that IAs with daughter blebs are linked to a potentially increased rupture risk.

Hemodynamic Analysis Shows High Wall Shear Stress Is Associated with Intraoperatively Observed Thin Wall Regions of Intracranial Aneurysms

BACKGROUND

Studying the relationship between hemodynamics and local intracranial aneurysm (IA) pathobiology can help us understand the natural history of IA. We characterized the relationship between the IA wall appearance, using intraoperative imaging, and the hemodynamics from CFD simulations.

METHODS

Three-dimensional geometries of 15 IAs were constructed and used for CFD. Two-dimensional intraoperative images were subjected to wall classification using a machine learning approach, after which the wall type was mapped onto the 3D surface. IA wall regions included thick (white), normal (purple-crimson), and thin/translucent (red) regions. IA-wide and local statistical analyses were performed to assess the relationship between hemodynamics and wall type.

RESULTS

Thin regions of the IA sac had significantly higher WSS, Normalized WSS, WSS Divergence and Transverse WSS, compared to both normal and thick regions. Thicker regions tended to co-locate with significantly higher RRT than thin regions. These trends were observed on a local scale as well. Regression analysis showed a significant positive correlation between WSS and thin regions and a significant negative correlation between WSSD and thick regions.

CONCLUSION

Hemodynamic simulation results were associated with the intraoperatively observed IA wall type. We consistently found that elevated WSS and WSS_Norm were associated with thin regions of the IA wall rather than thick and normal regions.

Role of patient-specific blood properties in computational fluid dynamics simulation of flow diverter deployed cerebral aneurysms

BACKGROUND:

Hemodynamics and their clinical outcome of cerebral aneurysms treated with flow diverter (FD) stents have thus far been investigated using computational fluid dynamics (CFD) simulations. Although human blood is characterized as a non-Newtonian patientspecific fluid, non-patient-specific blood properties (PSBP) were applied in most extant studies.

OBJECTIVE:

To investigate the hemodynamic effects caused by PSBPs in aneurysms treated with FD stents.

METHODS:

We measured blood properties (density and viscosity) for 12 patients who underwent FD stent deployment. We conducted CFD simulations with the measured PSBPs and non-PSBPs quoted from previous studies. The average blood flow velocity and wall shear stress within the aneurysms were calculated and two simulation patterns were compared.

RESULTS:

The velocity and wall shear stress changed by 2.93% and 3.16% on average, respectively, without an FD stent deployed. Conversely, with the FD stents deployed, the change rates increased to 11.1% and 9.06% on average, respectively.

CONCLUSIONS:

The change in hemodynamic parameters if PSBPs are considered, may not be negligible when conducting CFD simulations of FD stent deployed aneurysms To obtain an adequate hemodynamic environment for cerebral aneurysms with FD stents deployed, it is recommended to use PSBPs for CFD simulations.

Disturbed flow's impact on cellular changes indicative of vascular aneurysm initiation, expansion, and rupture: A pathological and methodological review

Aneurysms are malformations within the arterial vasculature brought on by the structural breakdown of the microarchitecture of the vessel wall, with aneurysms posing serious health risks in the event of their rupture. Blood flow within vessels is generally laminar with high, unidirectional wall shear stressors that modulate vascular endothelial cell functionality and regulate vascular smooth muscle cells. However, altered vascular geometry induced by bifurcations, significant curvature, stenosis, or clinical interventions can alter the flow, generating low stressor disturbed flow patterns. Disturbed flow is associated with altered cellular morphology, upregulated expression of proteins modulating inflammation, decreased regulation of vascular permeability, degraded extracellular matrix, and heightened cellular apoptosis. The understanding of the effects disturbed flow has on the cellular cascades which initiate aneurysms and promote their subsequent growth can further elucidate the nature of this complex pathology. This review summarizes the current knowledge about the disturbed flow and its relation to aneurysm pathology, the methods used to investigate these relations, as well as how such knowledge has impacted clinical treatment methodologies. This information can contribute to the understanding of the development, growth, and rupture of aneurysms and help develop novel research and aneurysmal treatment techniques.

Simulation of intracranial hemodynamics by an efficient and accurate immersed boundary scheme

We use computational fluid dynamics (CFD) to simulate blood flow in intracranial aneurysms (IAs). Despite ongoing improvements in the accuracy and efficiency of body-fitted CFD solvers, generation of a high quality mesh appears as the bottleneck of the flow simulation and strongly affects the accuracy of the numerical solution. To overcome this drawback, we use an immersed boundary method. The proposed approach solves the incompressible Navier-Stokes equations on a rectangular (box) domain discretized using uniform Cartesian grid using the finite element method. The immersed object is represented by a set of points (Lagrangian points) located on the surface of the object. Grid local refinement is applied using an automated algorithm. We verify and validate the proposed method by comparing our numerical findings with published experimental results and analytical solutions. We demonstrate the applicability of the proposed scheme on patient-specific blood flow simulations in IAs.

Non-Newtonian Blood Modeling in Intracranial Aneurysm Hemodynamics: Impact on the Wall Shear Stress and Oscillatory Shear Index Metrics for Ruptured and Unruptured Cases

When simulating blood flow in intracranial aneurysms (IAs), the Newtonian model seems to be ubiquitous. However, analyzing the results from the few studies on this subject, the doubt remains on whether it is necessary to use non-Newtonian models in computational fluid dynamics (CFD) simulations of cerebral vascular flows. The objective of this study is to investigate whether different rheology models would influence the hemodynamic parameters related to the wall shear stress (WSS) for ruptured and unruptured IA cases, especially because ruptured aneurysms normally have morphological features, such as lobular regions and blebs, that could trigger non-Newtonian phenomena in the blood flow due to low shear rates. Using CFD in an open-source framework, we simulated four ruptured and four unruptured patient-specific aneurysms to assess the influence of the blood modeling on the main hemodynamic variables associated with aneurysm formation, growth, and rupture. Results for WSS and oscillatory shear index (OSI) and their metrics were obtained using Casson and Carreau-Yasuda non-Newtonian models and were compared with those obtained using the Newtonian model. We found that all differences between non-Newtonian and the Newtonian models were consistent among all cases irrespective of their rupture status. We further found that the WSS at peak systole is overestimated by more than 50% by using the non-Newtonian models, but its metrics based on time and surface averaged values are less affected-the maximum relative difference among the cases is 7% for the Casson model. On the other hand, the surface-averaged OSI is underestimated by more than 30% by the non-Newtonian models. These results suggest that it is recommended to investigate different blood rheology models in IAs simulations when specific parameters to characterize the flow are needed, such as peak-systole WSS and OSI.

The Rheology of the Carotid Sinus: A Path Toward Bioinspired Intervention

The association between blood viscosity and pathological conditions involving a number of organ systems is well known. However, how the body measures and maintains appropriate blood viscosity is not well-described. The literature endorsing the function of the carotid sinus as a site of baroreception can be traced back to some of the earliest descriptions of digital pressure on the neck producing a drop in blood delivery to the brain. For the last 30 years, improved computational fluid dynamic (CFD) simulations of blood flow within the carotid sinus have demonstrated a more nuanced understanding of the changes in the region as it relates to changes in conventional metrics of cardiovascular function, including blood pressure. We suggest that the unique flow patterns within the carotid sinus may make it an ideal site to transduce flow data that can, in turn, enable real-time measurement of blood viscosity. The recent characterization of the PIEZO receptor family in the sinus vessel wall may provide a biological basis for this characterization. When coupled with other biomarkers of cardiovascular performance and descriptions of the blood rheology unique to the sinus region, this represents a novel venue for bioinspired design that may enable end-users to manipulate and optimize blood flow.

Identification of intra-individual variation in intracranial arterial flow by MRI and the effect on computed hemodynamic descriptors

OBJECTIVES

To determine the intra-individual flow variation in serially acquired studies, and the influence of this variation on subsequent hemodynamic simulations using the inlet flow as a boundary condition. Author: Kindly check and confirm whether the corresponding authors are correctly identified.Confirmed.

MATERIALS AND METHODS

This prospective study included 51 patients (37 females and 14 males) with unruptured intracranial aneurysms who have received more than three times follow-up of 2D phase-contrast MR. The flow and velocity parameters were extracted to calculate the reproducibility and variation. Patient-specific computational fluid dynamics simulations were performed using the measured flows.

RESULTS

Intraclass correlation coefficients for mean and maximum velocity and flow parameters ranged from 0.77 to 0.90. A 10% CV of mean flow was identified. Variations of 10% in inlet flow resulted in hemodynamic changes including 41.41% of peak systolic wall shear stress; 39.13% of end-diastolic wall shear stress; 2.79% of low shear area at peak systole; 2.12% of low shear area at end diastole: 47.57% of time-averaged wall shear stress; and 0.17% of oscillatory shear index.

CONCLUSION

This study identified 10% of intra-individual mean flow variation on phase-contrast MR. Intra-individual flow variation resulted in a non-negligible variation in wall shear stress, but relatively small variation in low shear area in hemodynamic calculations.

Central moments multiple relaxation time LBM for hemodynamic simulations in intracranial aneurysms: An in-vitro validation study using PIV and PC-MRI

The lattice Boltzmann method (LBM) has recently emerged as an efficient alternative to classical Navier-Stokes solvers. This is particularly true for hemodynamics in complex geometries. However, in its most basic formulation, i.e. with the so-called single relaxation time (SRT) collision operator, it has been observed to have a limited stability domain in the Courant/Fourier space, strongly constraining the minimum time-step and grid size. The development of improved collision models such as the multiple relaxation time (MRT) operator in central moments space has tremendously widened the stability domain, while allowing to overcome a number of other well-documented artifacts, therefore opening the door for simulations over a wider range of grid and time-step sizes. The present work focuses on implementing and validating a specific collision operator, the central Hermite moments multiple relaxation time model with the full expansion of the equilibrium distribution function, to simulate blood flows in intracranial aneurysms. The study further proceeds with a validation of the numerical model through different test-cases and against experimental measurements obtained via stereoscopic particle image velocimetry (PIV) and phase-contrast magnetic resonance imaging (PC-MRI). For a patient-specific aneurysm both PIV and PC-MRI agree fairly well with the simulation. Finally, low-resolution simulations were shown to be able to capture blood flow information with sufficient accuracy, as demonstrated through both qualitative and quantitative analysis of the flow field while leading to strongly reduced computation times. For instance in the case of the patient-specific configuration, increasing the grid-size by a factor of two led to a reduction of computation time by a factor of 14 with very good similarity indices still ranging from 0.83 to 0.88.

Association between aneurysm hemodynamics and wall enhancement on 3D vessel wall MRI

OBJECTIVE

Aneurysm wall enhancement (AWE) on 3D vessel wall MRI (VWMRI) has been suggested as an imaging biomarker for intracranial aneurysms (IAs) at higher risk of rupture. While computational fluid dynamics (CFD) studies have been used to investigate the association between hemodynamic forces and rupture status of IAs, the role of hemodynamic forces in unruptured IAs with AWE is poorly understood. The authors investigated the role and implications of abnormal hemodynamics related to aneurysm pathophysiology in patients with AWE in unruptured IAs.

METHODS

Twenty-five patients who had undergone digital subtraction angiography (DSA) and VWMRI studies from September 2016 to September 2017 were included, resulting in 22 patients with 25 IAs, 9 with and 16 without AWE. High-resolution CFD models of hemodynamics were created from DSA images. Univariate and multivariate analyses were performed to investigate the association between AWE and conventional morphological and hemodynamic parameters. Normalized MRI signal intensity was quantified and quantitatively associated with wall shear stresses (WSSs) for the entire aneurysm sac, and in regions of low, intermediate, and high WSS.

RESULTS

The AWE group had lower WSS (p < 0.01) and sac-averaged velocity (p < 0.01) and larger aneurysm size (p < 0.001) and size ratio (p = 0.0251) than the non-AWE group. From multivariate analysis of both hemodynamic and morphological factors, only low WSS was found to be independently associated with AWE. Sac-averaged normalized MRI signal intensity correlated with WSS and was significantly different in regions of low WSS compared to regions of intermediate (p = 0.018) and high (p < 0.001) WSS.

CONCLUSIONS

The presence of AWE was associated with morphological and hemodynamic factors related to rupture risk. Low WSS was found to be an independent predictor of AWE. Our findings support the hypothesis that low WSS in IAs with AWE may indicate a growth and remodeling process that may predispose such aneurysms to rupture; however, a causality between the two cannot be established.

Associations between morphology and hemodynamics of intracranial aneurysms based on 4D flow and black-blood magnetic resonance imaging

Background

Previous studies have hypothesized that intracranial aneurysm (IA) morphology interacts with hemodynamic conditions. Magnetic resonance imaging (MRI) provides a single image modality solution for both morphological and hemodynamic measurements for IA. This study aimed to explore the interaction between the morphology and hemodynamics of IA using black-blood MRI (BB-MRI) and 4D flow MRI.

Methods

A total of 97 patients with unruptured IA were recruited for this study. The IA size, size ratio (SR), and minimum wall thickness (mWT) were measured using BB-MRI. Velocity, blood flow, pulsatility index (PI), and wall shear stress (WSS) were measured with 4D flow MRI. The relationship between hemodynamic parameters and morphological indices was investigated by linear regression analysis and unpaired two-sample t-test. To determine the independent interaction, multiple linear regression analysis was further performed.

Results

The findings showed that mWT was negatively correlated with IA size (r=-0.665, P<0.001). Maximum blood flow in IA (Flow_IA) was positively correlated with IA size (r=0.458, P<0.001). The average WSS (WSS_avg) was negatively correlated with IA size (r=-0.650, P<0.001). The relationships remained the same after the multivariate analysis was adjusted for hemodynamic, morphologic, and demographic confounding factors. The WSS_avg was positively correlated with mWT (r=0.528, P<0.001). In the unpaired two-sample t-test, mWT, WSS_avg, and Flow_IA were statistically significantly associated with the size and SR of IAs.

Conclusions

There is potential for BB-MRI and 4D flow MRI to provide morphological and hemodynamic information regarding IA. Blood flow, WSS, and mWT may serve as non-invasive biomarkers for IA assessments, and may contribute to a more comprehensive understanding of the mechanism of IA.

Numerical study on the energy cascade of pulsatile Newtonian and power-law flow models in an ICA bifurcation

The complex physics and biology underlying intracranial hemodynamics are yet to be fully revealed. A fully resolved direct numerical simulation (DNS) study has been performed to identify the intrinsic flow dynamics in an idealized carotid bifurcation model. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. We scrutinize the kinetic energy cascade (KEC) rates in the Fourier domain and the vortex structure of both fluid models and examine the impact of the power-law viscosity model. The flow intrinsically contains coherent structures which has frequencies corresponding to the boundary frequency, which could be associated with the regulation of endothelial cells. From the proposed comparative study, it is found that KEC rates and the vortex-identification are significantly influenced by the shear-thinning blood properties. Conclusively, from the obtained results, it is found that neglecting the non-Newtonian behavior could lead to underestimation of the hemodynamic parameters at low Reynolds number and overestimation of the hemodynamic parameters by increasing the Reynolds number. In addition, we provide physical insight and discussion onto the hemodynamics associated with endothelial dysfunction which plays significant role in the pathogenesis of intracranial aneurysms.

How patient specific are patient-specific computational models of cerebral aneurysms? An overview of sources of error and variability

Computational modeling of cerebral aneurysms, derived from clinical 3D angiography, has become widespread over the past 15 years. While such "image-based" or "patient-specific" models have shown promise for the assessment of rupture risk, much debate remains about their reliability in light of necessary modeling assumptions and incomplete or uncertain model input parameters derived from the clinic. The aims of this review were to walk through the various steps of this so-called patient-specific modeling pipeline and to highlight evidence supporting those steps that we can or cannot rely on. The relative importance of the different sources of error and variability on hemodynamic predictions is summarized, with recommendations to standardize for those that can be avoided and to pay closer attention those to that cannot.

A review on the reliability of hemodynamic modeling in intracranial aneurysms: why computational fluid dynamics alone cannot solve the equation

Computational blood flow modeling in intracranial aneurysms (IAs) has enormous potential for the assessment of highly resolved hemodynamics and derived wall stresses. This results in an improved knowledge in important research fields, such as rupture risk assessment and treatment optimization. However, due to the requirement of assumptions and simplifications, its applicability in a clinical context remains limited.This review article focuses on the main aspects along the interdisciplinary modeling chain and highlights the circumstance that computational fluid dynamics (CFD) simulations are embedded in a multiprocess workflow. These aspects include imaging-related steps, the setup of realistic hemodynamic simulations, and the analysis of multidimensional computational results. To condense the broad knowledge, specific recommendations are provided at the end of each subsection.Overall, various individual substudies exist in the literature that have evaluated relevant technical aspects. In this regard, the importance of precise vessel segmentations for the simulation outcome is emphasized. Furthermore, the accuracy of the computational model strongly depends on the specific research question. Additionally, standardization in the context of flow analysis is required to enable an objective comparison of research findings and to avoid confusion within the medical community. Finally, uncertainty quantification and validation studies should always accompany numerical investigations.In conclusion, this review aims for an improved awareness among physicians regarding potential sources of error in hemodynamic modeling for IAs. Although CFD is a powerful methodology, it cannot provide reliable information, if pre- and postsimulation steps are inaccurately carried out. From this, future studies can be critically evaluated and real benefits can be differentiated from results that have been acquired based on technically inaccurate procedures.

What does computational fluid dynamics tell us about intracranial aneurysms? A meta-analysis and critical review

Despite the plethora of published studies on intracranial aneurysms (IAs) hemodynamic using computational fluid dynamics (CFD), limited progress has been made towards understanding the complex physics and biology underlying IA pathophysiology. Guided by 1733 published papers, we review and discuss the contemporary IA hemodynamics paradigm established through two decades of IA CFD simulations. We have traced the historical origins of simplified CFD models which impede the progress of comprehending IA pathology. We also delve into the debate concerning the Newtonian fluid assumption used to represent blood flow computationally. We evidently demonstrate that the Newtonian assumption, used in almost 90% of studies, might be insufficient to describe IA hemodynamics. In addition, some fundamental properties of the Navier-Stokes equation are revisited in supplementary material to highlight some widely spread misconceptions regarding wall shear stress (WSS) and its derivatives. Conclusively, our study draws a roadmap for next-generation IA CFD models to help researchers investigate the pathophysiology of IAs.

A framework for automated and objective modification of tubular structures: Application to the internal carotid artery

Patient-specific medical image-based computational fluid dynamics has been widely used to reveal fundamental insight into mechanisms of cardiovascular disease, for instance, correlating morphology to adverse vascular remodeling. However, segmentation of medical images is laborious, error-prone, and a bottleneck in the development of large databases that are needed to capture the natural variability in morphology. Instead, idealized models, where morphological features are parameterized, have been used to investigate the correlation with flow features, but at the cost of limited understanding of the complexity of cardiovascular flows. To combine the advantages of both approaches, we developed a tool that preserves the patient-specificness inherent in medical images while allowing for parametric alteration of the morphology. In our open-source framework morphMan we convert the segmented surface to a Voronoi diagram, modify the diagram to change the morphological features of interest, and then convert back to a new surface. In this paper, we present algorithms for modifying bifurcation angles, location of branches, cross-sectional area, vessel curvature, shape of bends, and surface roughness. We show qualitative and quantitative validation of the algorithms, performing with an accuracy exceeding 97% in general, and proof-of-concept on combining the tool with computational fluid dynamics. By combining morphMan with appropriate clinical measurements, one could explore the morphological parameter space and resulting hemodynamic response using only a handful of segmented surfaces, effectively minimizing the main bottleneck in image-based computational fluid dynamics.

Inter-patient variations in flow boundary conditions at middle cerebral artery from 7T PC-MRI and influence on Computational Fluid Dynamics of intracranial aneurysms

BACKGROUND

Computational fluid dynamics(CFD) of intracranial aneurysms requires flow boundary conditions(BCs) as inputs. Patient-specific BCs are usually unavailable and substituted by literature-derived generic BCs. Therefore, we investigated inter-patient BC variations and their influence on middle cerebral artery aneurysmal hemodynamics.

METHOD

We retrospectively collected CT angiography and 7-T Phase-Contrast(PC)-MRI data from eight middle-cerebral-artery bifurcation aneurysms to reconstruct the geometry and measure the arterial flowrates, respectively. The coefficient of variation(CoV) was calculated for the inlet flowrate and the pulsatility index(PI). The outflow split estimated by Murray's law was compared with PC-MRI measurements. For each aneurysm, we performed seven simulations: "baseline" using PC-MRI-derived BCs and the other six with changing BCs to explore the influence of BC variations on hemodynamics.

RESULTS

From PC-MRI, the inlet flowrate was 1.94 ± 0.71 cm³/s(CoV = 36%) and PI was 0.37 ± 0.13(CoV = 34%). The outflow split estimated by Murray's law deviated by 15.3% compared to PC-MRI. Comparing to "baseline" models, ±36% variations in inlet flowrate caused -61% to +89% changes in time-averaged wall shear stress(WSS), -37% to +32% in normalized WSS(NWSS; by parent-artery), and -42% to +126% in oscillatory shear index(OSI). The ±34% variations in PI caused, -46% to +67% in OSI. Applying ±15% variations in outflow split led to inflow jet deflection and -41% to +52% changes in WSS, -41% to +47% in NWSS, and -44% to +144% in OSI.

CONCLUSION

Inflow rate and outflow split have a drastic impact on hemodynamics of intracranial aneurysms. Inlet waveform has a negligible impact on WSS and NWSS but major impact on OSI. CFD-based models need to consider such sensitivity.

Hemodynamics of Cerebral Aneurysms: Connecting Medical Imaging and Biomechanical Analysis

In the last two decades, numerous studies have conducted patient-specific computations of blood flow dynamics in cerebral aneurysms and reported correlations between various hemodynamic metrics and aneurysmal disease progression or treatment outcomes. Nevertheless, intra-aneurysmal flow analysis has not been adopted in current clinical practice, and hemodynamic factors usually are not considered in clinical decision making. This review presents the state of the art in cerebral aneurysm imaging and image-based modeling, discussing the advantages and limitations of each approach and focusing on the translational value of hemodynamic analysis. Combining imaging and modeling data obtained from different flow modalities can improve the accuracy and fidelity of resulting velocity fields and flow-derived factors that are thought to affect aneurysmal disease progression. It is expected that predictive models utilizing hemodynamic factors in combination with patient medical history and morphological data will outperform current risk scores and treatment guidelines. Possible future directions include novel approaches enabling data assimilation and multimodality analysis of cerebral aneurysm hemodynamics.

Numerical investigation of the effects of blood rheology and wall elasticity in abdominal aortic aneurysm under pulsatile flow conditions

BACKGROUND

Previous studies on aneurysm modeling have focused on the blood rheology and vessel elasticity separately. The combined effects of blood shear thinning properties and wall elasticity need to be revealed.

OBJECTIVE

To provide insights on how pulsatile hemodynamics vary with blood rheology and vessel elasticity for a developed abdominal aortic aneurysm (AAA).

METHOD

An Arbitrary Lagrangian-Eulerian fluid-solid interaction method is adopted with the Newtonian and the shear thinning Carreau constitutive models for the fluid with the linearly elastic and the hyperelastic Yeoh models for the vessel. Finite element based numerical solver is used to simulate the blood flow in the AAA.

RESULTS

Newtonian model overestimates the velocity values compared to the Carreau model and the difference in the velocity field increases as the shear rate decreases at the instances of the cardiac cycle. The rigid walled simulations display higher deviations in the velocity and wall shear stress with the fluid rheology. The risk indicators show that Newtonian assumption combined with the linearly elastic model may overlook degeneration risk of arterial tissue.

CONCLUSIONS

Newtonian assumption for the blood as well as modelling the arterial wall as linearly elastic lead to significant differences in oscillatory hemodynamic properties with respect to the use of Carreau fluid together with hyperelastic vessel model, even in large vessel aneurysms.

Automated and objective removal of bifurcation aneurysms: Incremental improvements, and validation against healthy controls

Abnormal hemodynamic stresses are thought to correlate with aneurysm initiation, growth, and rupture. We have previously investigated the role of wall shear stress (WSS) and WSS gradients (WSSG) in search for a mechanistic link to formation of sidewall aneurysms using an automated and objective tool for aneurysm removal and arterial reconstruction in combination with computational fluid dynamics (CFD). However, we warned against the use of the tool for bifurcation type aneurysms because of a potential unrealistic reconstruction of the apex. We hypothesized that inclusion of additional morphological features from the surrounding vasculature could overcome these constraints. We extended the previously published method for removal and reconstruction of the bifurcation vasculature based on diverging and converging points of the parent and daughter artery centerlines, to also include two new centerlines between the daughter vessels, one of them passed through the bifurcation center. Validation was performed by comparing the efficacy of the two algorithms, using ten healthy models of the internal carotid artery terminus as ground truth. Qualitative results showed that the bifurcation apexes became smoother relative to the original algorithm; more consistent with the reference models. This was reflected quantitatively by a reduced maximum distance between the reference and reconstructed surfaces, although not statistically significant. Furthermore, the modified algorithm also quantitatively improved CFD derived WSS and WSSG, especially the latter. In conclusion, the modified algorithm does not perfectly reconstruct the bifurcation apex, but provides an incremental improvement, especially important for the derived hemodynamic metrics of interest in vascular pathobiology.

The FDA nozzle benchmark: "In theory there is no difference between theory and practice, but in practice there is"

The utility of flow simulations relies on the robustness of computational fluid dynamics (CFD) solvers and reproducibility of results. The aim of this study was to validate the Oasis CFD solver against in vitro experimental measurements of jet breakdown location from the FDA nozzle benchmark at Reynolds number 3500, which is in the particularly challenging transitional regime. Simulations were performed on meshes consisting of 5, 10, 17, and 28 million (M) tetrahedra, with Δt  =  10^-5 seconds. The 5M and 10M simulation jets broke down in reasonable agreement with the experiments. However, the 17M and 28M simulation jets broke down further downstream. But which of our simulations are "correct"? From a theoretical point of view, they are all wrong because the jet should not break down in the absence of disturbances. The geometry is axisymmetric with no geometrical features that can generate angular velocities. A stable flow was supported by linear stability analysis. From a physical point of view, a finite amount of "noise" will always be present in experiments, which lowers transition point. To replicate noise numerically, we prescribed minor random angular velocities (approximately 0.31%), much smaller than the reported flow asymmetry (approximately 3%) and model accuracy (approximately 1%), at the inlet of the 17M simulation, which shifted the jet breakdown location closer to the measurements. Hence, the high-resolution simulations and "noise" experiment can potentially explain discrepancies in transition between sometimes "sterile" CFD and inherently noisy "ground truth" experiments. Thus, we have shown that numerical simulations can agree with experiments, but for the wrong reasons.

Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?

Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.

Real-World Variability in the Prediction of Intracranial Aneurysm Wall Shear Stress: The 2015 International Aneurysm CFD Challenge

Purpose

Image-based computational fluid dynamics (CFD) is widely used to predict intracranial aneurysm wall shear stress (WSS), particularly with the goal of improving rupture risk assessment. Nevertheless, concern has been expressed over the variability of predicted WSS and inconsistent associations with rupture. Previous challenges, and studies from individual groups, have focused on individual aspects of the image-based CFD pipeline. The aim of this Challenge was to quantify the total variability of the whole pipeline.

Methods

3D rotational angiography image volumes of five middle cerebral artery aneurysms were provided to participants, who were free to choose their segmentation methods, boundary conditions, and CFD solver and settings. Participants were asked to fill out a questionnaire about their solution strategies and experience with aneurysm CFD, and provide surface distributions of WSS magnitude, from which we objectively derived a variety of hemodynamic parameters.

Results

A total of 28 datasets were submitted, from 26 teams with varying levels of self-assessed experience. Wide variability of segmentations, CFD model extents, and inflow rates resulted in interquartile ranges of sac average WSS up to 56%, which reduced to < 30% after normalizing by parent artery WSS. Sac-maximum WSS and low shear area were more variable, while rank-ordering of cases by low or high shear showed only modest consensus among teams. Experience was not a significant predictor of variability.

Conclusions

Wide variability exists in the prediction of intracranial aneurysm WSS. While segmentation and CFD solver techniques may be difficult to standardize across groups, our findings suggest that some of the variability in image-based CFD could be reduced by establishing guidelines for model extents, inflow rates, and blood properties, and by encouraging the reporting of normalized hemodynamic parameters.

Influence of aging-induced flow waveform variation on hemodynamics in aneurysms present at the internal carotid artery: A computational model-based study

The variation of blood flow waveform in the internal carotid artery (ICA) with age is a well-documented hemodynamic phenomenon, but little is known about how such variation affects the characteristics of blood flow in aneurysms present in the region. In the study, hemodynamic simulations were conducted for 26 ICA aneurysms, with flow waveforms measured in the ICAs of young and older adults being used respectively to set the inflow boundary conditions. Obtained results showed that replacing the young-adult flow waveform with the older-adult one led to little changes (<10%) in simulated time-averaged wall shear stress (WSS), transient maximum WSS, relative residence time and trans-aneurysm pressure loss coefficient, but resulted in a marked increase (32.36 ± 17.24%) in oscillatory shear index (OSI). Frequency-domain wave analysis revealed that the progressive enhancement of low-frequency harmonics dominated the observed flow waveform variation with age and was a major factor contributing to the increase in OSI. Cross-sectional comparisons among the aneurysms further revealed that the degree of increase in OSI correlated positively with some specific morphological features of aneurysm, such as aspect ratio and size ratio. In summary, the study demonstrates that the variation in flow waveform with age augments the oscillation of WSS in ICA aneurysms, which underlies the importance of setting patient-specific boundary conditions in hemodynamic studies on cerebral aneurysms, especially those involving long-term patient follow-up or cross-sectional comparison among patients of different ages.

Validation of Patient-Specific Cerebral Blood Flow Simulation Using Transcranial Doppler Measurements

We present a validation study comparing results from a patient-specific lattice-Boltzmann simulation to transcranial Doppler (TCD) velocity measurements in four different planes of the middle cerebral artery (MCA). As part of the study, we compared simulations using a Newtonian and a Carreau-Yasuda rheology model. We also investigated the viability of using downscaled velocities to reduce the required resolution. Simulations with unscaled velocities predict the maximum flow velocity with an error of less than 9%, independent of the rheology model chosen. The accuracy of the simulation predictions worsens considerably when simulations are run at reduced velocity, as is for example the case when inflow velocities from healthy individuals are used on a vascular model of a stroke patient. Our results demonstrate the importance of using directly measured and patient-specific inflow velocities when simulating blood flow in MCAs. We conclude that localized TCD measurements together with predictive simulations can be used to obtain flow estimates with high fidelity over a larger region, and reduce the need for more invasive flow measurement procedures.

Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery

Flow instability has emerged as a new hemodynamic metric hypothesized to have potential value in assessing the rupture risk of cerebral aneurysms. However, diverse findings have been reported in the literature. In the present study, high-resolution hemodynamic simulations were performed retrospectively on 35 aneurysms (10 ruptured & 25 unruptured) located at the internal carotid artery (ICA). Simulated hemodynamic parameters were statistically compared between the ruptured and unruptured aneurysms, with emphasis on examining the correlation of flow instability with the status of aneurysm rupture. Pronounced flow instability was detected in 20% (2 out of 10) of the ruptured aneurysms, whereas in 44% (11 out of 25) of the unruptured aneurysms. Statistically, the flow instability metric (quantified by the temporally and spatially averaged fluctuating kinetic energy over the aneurysm sac) did not differ significantly between the ruptured and unruptured aneurysms. In contrast, low wall shear stress area (LSA) and pressure loss coefficient (PLC) exhibited significant correlations with the status of aneurysm rupture. In conclusion, the present study suggests that the presence of flow instability may not correlate closely with the status of aneurysm rupture, at least for ICA aneurysms. On the other hand, the retrospective nature of the study and the small sample size may have to some extent compromised the reliability of the conclusion, and therefore large-scale prospective studies would be needed to further address the issue.

Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations

BACKGROUND AND PURPOSE

Computational fluid dynamics simulations of neurovascular diseases are impacted by various modeling assumptions and uncertainties, including outlet boundary conditions. Many studies of intracranial aneurysms, for example, assume zero pressure at all outlets, often the default ("do-nothing") strategy, with no physiological basis. Others divide outflow according to the outlet diameters cubed, nominally based on the more physiological Murray's law but still susceptible to subjective choices about the segmented model extent. Here we demonstrate the limitations and impact of these outflow strategies, against a novel "splitting" method introduced here.

MATERIALS AND METHODS

With our method, the segmented lumen is split into its constituent bifurcations, where flow divisions are estimated locally using a power law. Together these provide the global outflow rate boundary conditions. The impact of outflow strategy on flow rates was tested for 70 cases of MCA aneurysm with 0D simulations. The impact on hemodynamic indices used for rupture status assessment was tested for 10 cases with 3D simulations.

RESULTS

Differences in flow rates among the various strategies were up to 70%, with a non-negligible impact on average and oscillatory wall shear stresses in some cases. Murray-law and splitting methods gave flow rates closest to physiological values reported in the literature; however, only the splitting method was insensitive to arbitrary truncation of the model extent.

CONCLUSIONS

Cerebrovascular simulations can depend strongly on the outflow strategy. The default zero-pressure method should be avoided in favor of Murray-law or splitting methods, the latter being released as an open-source tool to encourage the standardization of outflow strategies.