Optimization-Based Geometry Correction Of Blood Flow CFD Simulations Using 4D-Flow Data

Abstract: 4D-flow is a powerful tool capable of capturing 3-dimensional, time-resolved flow measurements of blood flow in the body. Their current use is limited by resolution and scan times. A proposed solution is to use Simulation Based Imaging (SBI). This combines lower resolution 4D-flow scans with CFD simulations to improve resolution and reduce scan times. Previous work has focused on inlet and outlet conditions. This thesis explores the possibility of adding geometry correction to an optimization-based framework for SBI. Three different ways of deforming the mesh were implemented to explore geometry optimization. First finding the correct the diameter of a simple channel, second finding an initial rotation and translation error, and finally small boundary perturbations using Radial Basis Functions. The CFD simulations were performed using higher order finite element discretization. To compare the CFD simulations the MR images a forward function was used and the optimization was performed using gradients calculated using the adjoint method as well as finite differences. All three cases managed to correct the geometry errors both with and without noise in the MR-image, but the errors increased with increased noise levels. The results shows that all three approaches worked in 2D but was sensitive to noise and flow conditions. 4