2023/05/04 by Bastian Zapf, Johannes Haubner, Zapf, Bastian +5 · 2 citations
Mathematics · #35D30 #35L02 #35Q49 #35Q93 #35R30 #49M05 #49M41 #49N45 #65D18 #65K10 #65M32 #65M50 #68T99 #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2305.03020
openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Patient specific brain mesh generation from MRI can be a time consuming task and require manual corrections, e.g., for meshing the ventricular system or defining subdomains. To address this issue, we consider an image registration approach. The idea is to use the registration of an input magnetic resonance image (MRI) to a respective target in order to obtain a new mesh from a template mesh. To obtain the transformation, we solve an optimization problem that is constrained by a linear hyperbolic transport equation. We use a higher-order discontinuous Galerkin finite element method for discretization and motivate the numerical upwind scheme and its limitations from the continuous weak space--time formulation of the transport equation. We present a numerical implementation that builds on the finite element packages FEniCS and dolfin-adjoint. To demonstrate the efficacy of the proposed approach, numerical results for the registration of an input to a target MRI of two distinct individuals are presented. Moreover, it is shown that the registration transforms a manually crafted input mesh into a new mesh for the target subject whilst preserving mesh quality. Challenges of the algorithm are discussed.