A reduced-order model for wall shear stress in abdominal aortic aneurysms by proper orthogonal decomposition

In this paper, we introduce a method to construct a Reduced-Order Model (ROM) to study the physiological flow and the Wall Shear Stress (WSS) conditions in Abdominal Aortic Aneurysms (AAA). We start the process by running a training case using Computational Fluid Dynamics (CFD) simulations with time-varying flow parameters, such that these parameters cover the range of parameters that we would like to consider in our ROM. We use the inflow angle as the variable parameter in the current study. Then we use the snapshot Proper Orthogonal Decomposition (POD) to construct the reduced-order bases, which are subsequently enhanced using a QR-factorization technique to satisfy the relevant fluid boundary conditions. The resulting ROM enables us to study the flow pattern and the WSS distribution over a range of system parameters computationally very efficiently. We have used this method to show how the WSS varies significantly for an AAA with a simplified geometry, over a range of inflow angles usually considered mild in clinical terms. We have validated the ROM results with CFD results. This approach enables comprehensive analysis of the model system across a range of inflow angles and frequencies without the need to re-compute the simulation for small changes.