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 high-quality 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 show that, under a restrictive assumption, the numerical upwind scheme can be derived from the continuous weak formulation of the transport equation. We present a numerical implementation that builds on the established 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 with the complex cortical folding structure are discussed.

翻译：从MRI生成患者特定脑网格是一项耗时任务，且需要手动校正（例如对脑室系统进行网格划分或定义子域）。为解决此问题，我们考虑采用图像配准方法。其核心思想是利用输入磁共振图像（MRI）与对应目标的配准，从高质量模板网格中获得新网格。为获取变换，我们求解一个受线性双曲输运方程约束的优化问题。采用高阶间断伽辽金有限元方法进行离散化，并证明在约束假设下，数值迎风格式可从输运方程的连续弱形式推导得出。我们的数值实现基于成熟的有限元软件包FEniCS和dolfin-adjoint。为验证所提方法的有效性，展示了两个不同个体输入MRI与目标MRI配准的数值结果。此外，结果表明配准能在保持网格质量的同时，将人工构建的输入网格变换为目标对象的新网格。最后讨论了该算法在处理复杂皮层折叠结构时面临的挑战。