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

Abstract

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.

Keywords: cerebral aneurysm; computational fluid dynamics; viscosity.

FIGURE 1

p-value from t-test on maps of time averaged well shear stress (WSS; above), well shear stress gradient (WSSG; middle), and oscillatory shear index (OSI) (below) between computational fluid dynamics (CFD) simulations of the same aneurysms using patient-specific and standardized values for viscosity plotted against the magnitude of the percent change in viscosity between simulations. The significance level is displayed with dashed red line. Linear regression and confidence interval shown in blue. Each subject is colored by aneurysm size. Shapes represent aneurysm location.

FIGURE 2

Bland–Altman plots comparing the differences in wall shear stress (WSS; top), WSS gradient (WSSG; middle), and oscillatory shear index (OSI; bottom) between standardized and patient-specific simulations, with each subject colored by the percent change in viscosity.

FIGURE 3

Percent change in wall shear stress (WSS), WSS gradient (WSSG), and oscillatory shear index (OSI) plotted against percent change in viscosity. Linear regression and confidence interval shown in blue. Each subject is colored by aneurysm size. Shapes represent aneurysm location.

FIGURE 4

Contour plots of wall shear stress (WSS) from the standardized and patient-specific viscosity simulations for patients 22, 39, and 41 with change in average WSS and viscosity tabulated above. A small decrease in viscosity leads to a visual indetectable but meaningful reduction in average WSS of 5.43%, while a large increase in viscosity leads to a small but visually detectable reduction in WSS of 4.11% for patient 41. Patient 39 displays a qualitatively different WSS distribution and 125.59% increase in average WSS from a large reduction in viscosity.