The Computational Fluid Dynamics Rupture Challenge 2013--Phase II: Variability of Hemodynamic Simulations in Two Intracranial Aneurysms.

With the increased availability of computational resources, the past decade has seen a rise in the use of computational fluid dynamics (CFD) for medical applications. There has been an increase in the application of CFD to attempt to predict the rupture of intracranial aneurysms, however, while many hemodynamic parameters can be obtained from these computations, to date, no consistent methodology for the prediction of the rupture has been identified. One particular challenge to CFD is that many factors contribute to its accuracy; the mesh resolution and spatial/temporal discretization can alone contribute to a variation in accuracy. This failure to identify the importance of these factors and identify a methodology for the prediction of ruptures has limited the acceptance of CFD among physicians for rupture prediction. The International CFD Rupture Challenge 2013 seeks to comment on the sensitivity of these various CFD assumptions to predict the rupture by undertaking a comparison of the rupture and blood-flow predictions from a wide range of independent participants utilizing a range of CFD approaches. Twenty-six groups from 15 countries took part in the challenge. Participants were provided with surface models of two intracranial aneurysms and asked to carry out the corresponding hemodynamics simulations, free to choose their own mesh, solver, and temporal discretization. They were requested to submit velocity and pressure predictions along the centerline and on specified planes. The first phase of the challenge, described in a separate paper, was aimed at predicting which of the two aneurysms had previously ruptured and where the rupture site was located. The second phase, described in this paper, aims to assess the variability of the solutions and the sensitivity to the modeling assumptions. Participants were free to choose boundary conditions in the first phase, whereas they were prescribed in the second phase but all other CFD modeling parameters were not prescribed. In order to compare the computational results of one representative group with experimental results, steady-flow measurements using particle image velocimetry (PIV) were carried out in a silicone model of one of the provided aneurysms. Approximately 80% of the participating groups generated similar results. Both velocity and pressure computations were in good agreement with each other for cycle-averaged and peak-systolic predictions. Most apparent "outliers" (results that stand out of the collective) were observed to have underestimated velocity levels compared to the majority of solutions, but nevertheless identified comparable flow structures. In only two cases, the results deviate by over 35% from the mean solution of all the participants. Results of steady CFD simulations of the representative group and PIV experiments were in good agreement. The study demonstrated that while a range of numerical schemes, mesh resolution, and solvers was used, similar flow predictions were observed in the majority of cases. To further validate the computational results, it is suggested that time-dependent measurements should be conducted in the future. However, it is recognized that this study does not include the biological aspects of the aneurysm, which needs to be considered to be able to more precisely identify the specific rupture risk of an intracranial aneurysm.

Variability of computational fluid dynamics solutions for pressure and flow in a giant aneurysm: the ASME 2012 Summer Bioengineering Conference CFD Challenge.

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

Correlation of flow complexity parameter with aneurysm rupture status.

Ruptured aneurysms are known to have complex flow patterns and concentrated inflow jet, but a quantifiable measure for the degree of flow complexity in patient-specific geometries has not been established. Previously, we proposed a flow complexity parameter that provides a quantitative description of the complexity of flow patterns through calculated curvature and torsion of the flow field. The purpose of the current study was to provide an analytic solution of the flow complexity parameter and assess a possible correlation with the rupture status of cerebral aneurysms by analyzing the parameter on five ruptured and five unruptured aneurysms from anterior communicating artery. We analyzed the flow complexity parameter in jet and non-jet regions in order to measure the concentration of the jet flow and the complexity of the non-jet flow. We found that on average, in a ruptured case the jet region is significantly less complex (4.5 times) than the jet region in an unruptured case, while the non-jet region is significantly more complex (3.5 times) than the non-jet region in an unruptured case. We also found a strong positive correlation of the non-jet complexity with dome volume in ruptured cases, but no correlation of jet complexity with dome volume. These findings suggest that a ruptured aneurysm has more than 4 times more concentrated inflow jet and more than 3 times more complex flow patterns in non-jet region than an unruptured aneurysm. This newly implemented kinematic parameter provides a measurable degree of complexity of flow patterns in cerebral aneurysms that can better assess aneurysm rupture risk.

Pulse wave velocity as a diagnostic index: The effect of wall thickness.

Vascular compliance is a major determinant of wave propagation within the vascular system, and hence the measurement of pulse wave velocity (PWV) is commonly used clinically as a method of detecting vascular stiffening. The accuracy of that assessment is important because vascular stiffening is a major risk factor for hypertension. PWV is usually measured by timing a pressure wave as it travels from the carotid artery to the femoral or radial artery and estimating the distance that it traveled in each case to obtain the required velocity. A major assumption on which this technique is based is that the vessel wall thickness h is negligibly small compared with the vessel radius a. The extent to which this assumption is satisfied in the cardiovascular system is not known because the ratio h/a varies widely across different regions of the vascular tree and under different pathological conditions. Using the PWV as a diagnostic test without knowing the effect of wall thickness on the measurement could lead to error when interpreting the PWV value as an index of vessel wall compliance. The aim of the present study was to extend the validity of the current practice of assessing wall stiffness by developing a method of analysis that goes beyond the assumption of a thin wall. We analyzed PWVs calculated with different wall models, depending on the ratio of wall thickness to vessel radius and the results showed that PWV is not reliable when it is estimated with the classic thin wall theory if the vessel wall is not around 25% of vessel radius. If the arterial wall is thicker than 25% of vessel radius, then the wave velocity calculated with the thin wall theory could be overestimated and in the clinical setting, this could lead to a false positive. For thicker walls, a thick wall model presented here should be considered to account for the stresses within the wall thickness that become dominant compared with the wall inertia.

(PEAK) WALL STRESS AS AN INDICATOR OF ABDOMINAL AORTIC ANEURYSM SEVERITY.

Abdominal aortic aneurysms, which consist of dilatations of the infra-renal aorta by at least 1.5 times of its normal diameter, are becoming a leading cause of death worldwide. Rupture often occurs unexpectedly, before a repair procedure is conducted. The AAA maximum diameter has been used as a clinical criterion to monitor AAA severity. However, assessment of AAA rupture risk requires knowledge of wall stress and wall strength at the potential rupture location. We conducted a study on 37 patient specific CT datasets to investigate the benefits of using peak wall stress instead of Dmax for AAA rupture severity. Correlation between PWS and 24 geometric indices and biomechanical factors was studied where eleven of them showed a statistically significant correlation with PWS. A Finite Element Analysis Rupture Index was used to conclude that the use of D max as a single predictor of AAA behavior and severity may be insufficient based on our patient population with a Dmax smaller than the 5.5 cm, clinically recommended repair threshold.

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.

Multiple Aneurysms AnaTomy CHallenge 2018 (MATCH): Phase I: Segmentation.

PURPOSE: Advanced morphology analysis and image-based hemodynamic simulations are increasingly used to assess the rupture risk of intracranial aneurysms (IAs). However, the accuracy of those results strongly depends on the quality of the vessel wall segmentation. METHODS: To evaluate state-of-the-art segmentation approaches, the Multiple Aneurysms AnaTomy CHallenge (MATCH) was announced. Participants carried out segmentation in three anonymized 3D DSA datasets (left and right anterior, posterior circulation) of a patient harboring five IAs. Qualitative and quantitative inter-group comparisons were carried out with respect to aneurysm volumes and ostia. Further, over- and undersegmentation were evaluated based on highly resolved 2D images. Finally, clinically relevant morphological parameters were calculated. RESULTS: Based on the contributions of 26 participating groups, the findings reveal that no consensus regarding segmentation software or underlying algorithms exists. Qualitative similarity of the aneurysm representations was obtained. However, inter-group differences occurred regarding the luminal surface quality, number of vessel branches considered, aneurysm volumes (up to 20%) and ostium surface areas (up to 30%). Further, a systematic oversegmentation of the 3D surfaces was observed with a difference of approximately 10% to the highly resolved 2D reference image. Particularly, the neck of the ruptured aneurysm was overrepresented by all groups except for one. Finally, morphology parameters (e.g., undulation and non-sphericity) varied up to 25%. CONCLUSIONS: MATCH provides an overview of segmentation methodologies for IAs and highlights the variability of surface reconstruction. Further, the study emphasizes the need for careful processing of initial segmentation results for a realistic assessment of clinically relevant morphological parameters.

Relationship between aneurysm occlusion and flow diverting device oversizing in a rabbit model.

BACKGROUND AND PURPOSE: Implanted, actual flow diverter pore density is thought to be strongly influenced by proper matching between the device size and parent artery diameter. The objective of this study was to characterize the correlation between device sizing, metal coverage, and the resultant occlusion of aneurysms following flow diverter treatment in a rabbit model. METHODS: Rabbit saccular aneurysms were treated with flow diverters (iso-sized to proximal parent artery, 0.5 mm oversized, or 1.0 mm oversized, respectively, n=6 for each group). Eight weeks after implantation, the angiographic degree of aneurysm occlusion was graded (complete, near-complete, or incomplete). The ostium of the explanted aneurysm covered with the flow diverter struts was photographed. Based on gross anatomic findings, the metal coverage and pore density at the ostium of the aneurysm were calculated and correlated with the degree of aneurysm occlusion. RESULTS: Angiographic results showed there were no statistically significant differences in aneurysm geometry and occlusion among groups. The mean parent artery diameter to flow diverter diameter ratio was higher in the 1.0 mm oversized group than in the other groups. Neither the percentage metal coverage nor the pore density showed statistically significant differences among groups. Aneurysm occlusion was inversely correlated with the ostium diameter, irrespective of the size of the device implanted. CONCLUSIONS: Device sizing alone does not predict resultant pore density or metal coverage following flow diverter implantation in the rabbit aneurysm model. Aneurysm occlusion was not impacted by either metal coverage or pore density, but was inversely correlated with the diameter of the ostium.

Computational fluid dynamics simulation of an anterior communicating artery ruptured during angiography.

We present a computational fluid dynamics (CFD) analysis of the hemodynamic environment of an anterior communicating artery that spontaneously ruptured immediately following three-dimensional rotational angiography. Subsequent digital subtraction angiography allowed for the localization of the point of rupture within the aneurysm dome. CFD analysis demonstrated a concentrated jet that impinged directly at the site of rupture. Peak systolic pressure and wall shear stress were both maximal near the rupture location.

Adaptive grid generation in a patient-specific cerebral aneurysm.

Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce computational time for patient-specific hemodynamics simulations, which are used to help assess the likelihood of aneurysm rupture using CFD calculated flow patterns.

Computational fluid dynamics simulation of an anterior communicating artery ruptured during angiography.

We present a computational fluid dynamics (CFD) analysis of the hemodynamic environment of an anterior communicating artery that spontaneously ruptured immediately following three-dimensional rotational angiography. Subsequent digital subtraction angiography allowed for the localization of the point of rupture within the aneurysm dome. CFD analysis demonstrated a concentrated jet that impinged directly at the site of rupture. Peak systolic pressure and wall shear stress were both maximal near the rupture location.

Grid convergence errors in hemodynamic solution of patient-specific cerebral aneurysms.

Computational fluid dynamics (CFD) has become a cutting-edge tool for investigating hemodynamic dysfunctions in the body. It has the potential to help physicians quantify in more detail the phenomena difficult to capture with in vivo imaging techniques. CFD simulations in anatomically realistic geometries pose challenges in generating accurate solutions due to the grid distortion that may occur when the grid is aligned with complex geometries. In addition, results obtained with computational methods should be trusted only after the solution has been verified on multiple high-quality grids. The objective of this study was to present a comprehensive solution verification of the intra-aneurysmal flow results obtained on different morphologies of patient-specific cerebral aneurysms. We chose five patient-specific brain aneurysm models with different dome morphologies and estimated the grid convergence errors for each model. The grid convergence errors were estimated with respect to an extrapolated solution based on the Richardson extrapolation method, which accounts for the degree of grid refinement. For four of the five models, calculated velocity, pressure, and wall shear stress values at six different spatial locations converged monotonically, with maximum uncertainty magnitudes ranging from 12% to 16% on the finest grids. Due to the geometric complexity of the fifth model, the grid convergence errors showed oscillatory behavior; therefore, each patient-specific model required its own grid convergence study to establish the accuracy of the analysis.