Flow Reconstruction from 4D-Flow MRI Data
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The purpose of this work is to reconstruct blood flow from real 4D-flow MRI data in order to estimate relevant biomarkers that cannot be directly computed from the noisy data. In particular, wall shear stress (WSS) is a well-known biomarker for assessing the risk of rupture in aortic aneurysms. However, direct computation of WSS from 4D-flow MRI data is not usable in practice, due to noise. We propose to reconstruct flow in the aorta from 4D-flow MRI data using a sequential continuation method, without the need to resort to a lumped parameter modeling of the boundary conditions. Although this method was originally introduced for a steady problem, we adapt it here in a sequential manner. The method relies on consistent regularization techniques based on finite element stabilization. We also investigate how including noise variance in the cost function allows us to improve WSS estimations. The method is assessed by using real and synthetic 4D MRI data. In particular, the simulation of the MRI signal is generally performed by solving the Bloch equations in a Lagrangian framework, which requires simulating a large and uniformly distributed number of particles per cell. As a consequence, the Lagrangian formulation is computationally very expensive, especially for certain types of acquisition sequences that require an even larger number of particles to obtain accurate results. In this work, we instead simulate the signal emitted by proton spins in the body during a realistic MRI procedure by discretizing the Bloch equations in Eulerian formalism, using stabilized finite elements and an explicit time-stepping procedure.
