Abstract
BackgroundComputational modeling of cardiovascular flow is a growing and useful field, but such simulations usually require the researcher to guess the flow’s inlet and outlet conditions since they are difficult and expensive to measure. It is critical to determine the amount of uncertainty introduced by these assumptions in order to evaluate the degree to which cardiovascular flow simulations are accurate. Our work begins to address this question by examining the sensitivity of flow to several different assumed velocity inlet and outlet conditions in a patient-specific aorta model.MethodsWe examined the differences between plug flow, parabolic flow, linear shear flows, skewed cubic flow profiles, and Womersley flow at the inlet. Only the shape of the inlet velocity profile was varied—all other parameters were identical among these simulations. Secondary flow in the form of a counter-rotating pair of vortices was also added to parabolic axial flow to study its effect on the solution. In addition, we examined the differences between two-element Windkessel, three element Windkessel and the outflow boundary conditions. In these simulations, only the outlet boundary condition was varied.ResultsThe results show axial and in-plane velocities are considerably different close to the inlet for the cases with different inlet velocity profile shapes. However, the solutions are qualitatively similar beyond 1.75D, where D is the inlet diameter. This trend is also observed in other quantities such as pressure and wall shear stress. Normalized root-mean-square deviation, a measure of axial velocity magnitude differences between the different cases, generally decreases along the streamwise coordinate. The linear shear inlet velocity boundary condition and plug velocity boundary condition solution exhibit the highest time-averaged wall shear stress, approximately 8% higher than the parabolic inlet velocity boundary condition. Upstream of 1D from the inlet, adding secondary flow has a significant impact on temporal wall shear stress distributions. This is especially observable during diastole, when integrated wall shear stress magnitude varies about 26% between simulations with and without secondary flow. The results from the outlet boundary condition study show the Windkessel models differ from the outflow boundary condition by as much as 18% in terms of time-averaged wall shear stress. Furthermore, normalized root-mean-square deviation of axial velocity magnitude, a measure of deviation between Windkessel and the outflow boundary condition, increases along the streamwise coordinate indicating larger variations near outlets.ConclusionIt was found that the selection of inlet velocity conditions significantly affects only the flow region close to the inlet of the aorta. Beyond two diameters distal to the inlet, differences in flow solution are small. Although additional studies must be performed to verify this result, the data suggest that it is important to use patient-specific inlet conditions primarily if the researcher is concerned with the details of the flow very close to the inlet. Similarly, the selection of outlet conditions significantly affects the flow in the vicinity of the outlets. Upstream of five diameters proximal to the outlet, deviations between the outlet boundary conditions examined are insignificant. Although the inlet and outlet conditions only affect the flow significantly in their respective neighborhoods, our study indicates that outlet conditions influence a larger percentage of the solution domain.
Highlights
Computational modeling of cardiovascular flow is a growing and useful field, but such simulations usually require the researcher to guess the flow’s inlet and outlet conditions since they are difficult and expensive to measure
This work investigated the variation introduced into a simulation of aortic blood flow by choice of inlet and outlet boundary conditions
Outlet conditions prescribing a zero-diffusion flux with specified mass flow rate (ANSYS® Academic Research [Fluent], release 16.2, outflow boundary conditions, ANSYS, Inc.), two-element Windkessel, and the three-element Windkessel conditions were investigated. Both the two-element and the three-element Windkessel models don’t vary much near the inlet as seen from the time-averaged wall shear stress variations. Both the two-element and the three-element models differ from the outflow boundary condition by 0.3544 and 0.3571% respectively in terms of time-averaged wall shear stress integrated up to 1D
Summary
Computational modeling of cardiovascular flow is a growing and useful field, but such simulations usually require the researcher to guess the flow’s inlet and outlet conditions since they are difficult and expensive to measure. HeartFlow, Inc., Redwood City, California has developed a non-invasive CFD-based tool to identify lesions causing ischemia [8, 9] Another application of cardiovascular CFD is designing new surgical techniques and implantable medical devices [10, 11]. [10] designed a ‘virtual surgery’ for pediatric surgeons based on patient-specific images Their framework computed post-operative hemodynamics based on the virtual surgery, thereby aiding surgeons in surgical planning. Hemodynamic alterations are known to be a significant cause of ischemic disease progression [19] Owing to these uses and other promising applications, there is a substantial need for accurate modeling of cardiovascular flows
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