The reconstruction of cortical surfaces is a prerequisite for quantitative analyses of the cerebral cortex in magnetic resonance imaging (MRI). Existing segmentation-based methods separate the surface registration from the surface extraction, which is computationally inefficient and prone to distortions. We introduce Vox2Cortex-Flow (V2C-Flow), a deep mesh-deformation technique that learns a deformation field from a brain template to the cortical surfaces of an MRI scan. To this end, we present a geometric neural network that models the deformation-describing ordinary differential equation in a continuous manner. The network architecture comprises convolutional and graph-convolutional layers, which allows it to work with images and meshes at the same time. V2C-Flow is not only very fast, requiring less than two seconds to infer all four cortical surfaces, but also establishes vertex-wise correspondences to the template during reconstruction. In addition, V2C-Flow is the first approach for cortex reconstruction that models white matter and pial surfaces jointly, therefore avoiding intersections between them. Our comprehensive experiments on internal and external test data demonstrate that V2C-Flow results in cortical surfaces that are state-of-the-art in terms of accuracy. Moreover, we show that the established correspondences are more consistent than in FreeSurfer and that they can directly be utilized for cortex parcellation and group analyses of cortical thickness.

翻译：脑皮层表面重建是磁共振成像（MRI）中大脑皮层定量分析的前提条件。现有基于分割的方法将表面配准与表面提取分离，计算效率低且易产生形变。我们提出Vox2Cortex-Flow（V2C-Flow），这是一种深度网格变形技术，可学习从脑模板到MRI扫描皮层表面的变形场。为此，我们设计了一种几何神经网络，以连续方式建模描述变形的常微分方程。该网络架构包含卷积层和图卷积层，使其能同时处理图像和网格数据。V2C-Flow不仅速度极快（推理全部四个皮层表面仅需不到两秒），还能在重建过程中建立与模板的顶点级对应关系。此外，V2C-Flow是首个联合建模白质表面和软脑膜表面的皮层重建方法，从而避免两者之间的交叉。我们在内部和外部测试数据上的全面实验表明，V2C-Flow生成的皮层表面在精度上达到当前最优水平。同时，我们证明其建立的对应关系比FreeSurfer更一致，可直接用于皮层分割和皮层厚度的群体分析。