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 computati...

The non-invasive determination of the pressure (normal stress) in a flowing fluid has ramifications in a variety of important problems: the flow of blood in blood vessels, and flows taking place in inaccessible locations in complex internal geometries that occur in mechanical systems. In this paper we discuss a rigorous new mathematical procedure for the determination of the pressure (normal stress) field, from data for the velocity field that can be obtained through imaging procedures such as 4D Magnetic Resonance Imaging or Echocardiography. We then use the procedure to demonstrate its efficacy by considering flows in an idealized geometry with a symmetric and asymmetric obstruction. We delineate the superiority of the method with regard to the methods that are currently in place. In Part II of this two part paper, we study the loss of pressure and the dissipation that occurs due to the flow of blood across a diseased valve (the pressure loss being an important indicator of the extent of the valvular disease) as well as the flow taking place in a realistic cerebral aneurysm.

Hemodynamic parameters play a significant role in the development of cerebral aneurysms. Parameters such as wall shear stress (WSS) or velocity could change in time and may contribute to aneurysm growth and rupture. However, the hemodynamic changes at the rupture location remain unclear because it is difficult to obtain data prior to rupture. We analyzed a case of a ruptured middle cerebral artery (MCA) aneurysm for which we acquired imaging data at three time points, including at rupture. A patient with an observed MCA aneurysm was admitted to the emergency department with clinical symptoms of a subarachnoid hemorrhage. During three-dimensional (3D) digital subtraction angiography (DSA), the aneurysm ruptured again. Imaging data from two visits before rupture and this 3D DSA images at the moment of rupture were acquired, and computational fluid dynamic (CFD) simulations were performed. Results were used to describe the time-dependent changes of the hemodynamic variables associated with rupture. Time-dependent hemodynamic changes at the rupture location were characterized by decreased WSS and flow velocity magnitude. The impingement jet in the dome changed its position in time and the impingement area at follow-up moved near the rupture location. The results suggest that the increased WSS on the dome and increased low wall shear stress area (LSA) and decreased WSS on the daughter bleb with slower flow and slow vortex may be associated with rupture. CFD performed during the follow-up period may be part of diagnostic tools used to determine the risk of aneurysm rupture.

Computational fluid dynamics (CFD) has grown as a tool to help understand the hemodynamic properties related to the rupture of cerebral aneurysms. Few of these studies deal specifically with aneurysm growth and most only use a single time instance within the aneurysm growth history. The present retrospective study investigated four patient-specific aneurysms, once at initial diagnosis and then at follow-up, to analyze hemodynamic and morphological changes. Aneurysm geometries were segmented via the medical image processing software Mimics. The geometries were meshed and a computational fluid dynamics (CFD) analysis was performed using ANSYS. Results showed that major geometry bulk growth occurred in areas of low wall shear stress (WSS). Wall shape remodeling near neck impingement regions occurred in areas with large gradients of WSS and oscillatory shear index. This study found that growth occurred in areas where low WSS was accompanied by high velocity gradients between the aneurysm wall and large swirling flow structures. A new finding was that all cases showed an increase in kinetic energy from the first time point to the second, and this change in kinetic energy seems correlated to the change in aneurysm volume.

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