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.

Fusiform versus Saccular Intracranial Aneurysms-Hemodynamic Evaluation of the Pre-Aneurysmal, Pathological, and Post-Interventional State

Minimally-invasive therapies are well-established treatment methods for saccular intracranial aneurysms (SIAs). Knowledge concerning fusiform IAs (FIAs) is low, due to their wide and alternating lumen and their infrequent occurrence. However, FIAs carry risks like ischemia and thus require further in-depth investigation. Six patient-specific IAs, comprising three position-identical FIAs and SIAs, with the FIAs showing a non-typical FIA shape, were compared, respectively. For each model, a healthy counterpart and a treated version with a flow diverting stent were created. Eighteen time-dependent simulations were performed to analyze morphological and hemodynamic parameters focusing on the treatment effect (TE). The stent expansion is higher for FIAs than SIAs. For FIAs, the reduction in vorticity is higher (Δ35-75% case 2/3) and the reduction in the oscillatory velocity index is lower (Δ15-68% case 2/3). Velocity is reduced equally for FIAs and SIAs with a TE of 37-60% in FIAs and of 41-72% in SIAs. Time-averaged wall shear stress (TAWSS) is less reduced within FIAs than SIAs (Δ30-105%). Within this study, the positive TE of FDS deployed in FIAs is shown and a similarity in parameters found due to the non-typical FIA shape. Despite the higher stent expansion, velocity and vorticity are equally reduced compared to identically located SIAs.

Improving the accuracy of computational fluid dynamics simulations of coiled cerebral aneurysms using finite element modeling

Cerebral aneurysms are a serious clinical challenge, with ∼half resulting in death or disability. Treatment via endovascular coiling significantly reduces the chances of rupture, but the techniquehas failure rates of ∼20 %. This presents a pressing need to develop a method fordetermining optimal coildeploymentstrategies. Quantification of the hemodynamics of coiled aneurysms using computational fluid dynamics (CFD) has the potential to predict post-treatment outcomes, but representing the coil mass in CFD simulations remains a challenge. We use the Finite Element Method (FEM) for simulating patient-specific coil deployment for n = 4 ICA aneurysms for which 3D printed in vitro models were also generated, coiled, and scanned using ultra-high resolution synchrotron micro-CT. The physical and virtual coil geometries were voxelized onto a binary structured grid and porosity maps were generated for geometric comparison. The average binary accuracy score is 0.8623 and the average error in porosity map is 4.94 %. We then conduct patient-specific CFD simulations of the aneurysm hemodynamics using virtual coils geometries, micro-CT generated oil geometries, and using the porous medium method to represent the coil mass. Hemodynamic parameters including Neck Inflow Rate (Qneck) and Wall Shear Stress (WSS) were calculated for each of the CFD simulations. The average relative error in Qneck and WSS from CFD using FEM geometry were 6.6 % and 21.8 % respectively, while the error from CFD using a porous media approximation resulted in errors of 55.1 % and 36.3 % respectively; demonstrating a marked improvement in the accuracy of CFD simulations using FEM generated coil geometries.

Modeling the Mechanical Microenvironment of Coiled Cerebral Aneurysms

Successful occlusion of cerebral aneurysms using coil embolization is contingent upon stable thrombus formation, and the quality of the thrombus depends upon the biomechanical environment. The goal of this study was to investigate how coil embolization alters the mechanical micro-environment within the aneurysm dome. Inertialess particles were injected in three-dimensional, computational simulations of flow inside patient aneurysms using patient-specific boundary conditions. Coil embolization was simulated as a homogenous porous medium of known permeability and inertial constant. Lagrangian particle tracking was used to calculate the residence time and shear stress history for particles in the flow before and after treatment. The percentage of particles entering the aneurysm dome correlated with the neck surface area before and after treatment (pretreatment: R2 = 0.831, P < 0.001; post-treatment: R2 = 0.638, P < 0.001). There was an inverse relationship between the change in particles entering the dome and coil packing density (R2 = 0.600, P < 0.001). Following treatment, the particles with the longest residence times tended to remain within the dome even longer while accumulating lower shear stress. A significant correlation was observed between the treatment effect on residence time and the ratio of the neck surface area to porosity (R2 = 0.390, P = 0.007). The results of this study suggest that coil embolization triggers clot formation within the aneurysm dome via a low shear stress-mediated pathway. This hypothesis links independently observed findings from several benchtop and clinical studies, furthering our understanding of this treatment strategy.

Platelet Dynamics and Hemodynamics of Cerebral Aneurysms Treated with Flow-Diverting Stents

Flow-diverting stents (FDS) are used to treat cerebral aneurysms. They promote the formation of a stable thrombus within the aneurysmal sac and, if successful, isolate the aneurysmal dome from mechanical stresses to prevent rupture. Platelet activation, a mechanism necessary for thrombus formation, is known to respond to biomechanical stimuli, particularly to the platelets' residence time and shear stress exposure. Currently, there is no reliable method for predicting FDS treatment outcomes, either a priori or after the procedure. Eulerian computational fluid dynamic (CFD) studies of aneurysmal flow have searched for predictors of endovascular treatment outcome; however, the hemodynamics of thrombus formation cannot be fully understood without considering the platelets' trajectories and their mechanics-triggered activation. Lagrangian analysis of the fluid mechanics in the aneurysmal vasculature provides novel metrics by tracking the platelets' residence time (RT) and shear history (SH). Eulerian and Lagrangian parameters are compared for 19 patient-specific cases, both pre- and post-treatment, to assess the degree of change caused by the FDS and subsequent treatment efficacy.