The goal of diffusion-weighted magnetic resonance imaging (DWI) is to infer the structural connectivity of an individual subject's brain in vivo. To statistically study the variability and differences between normal and abnormal brain connectomes, a mathematical model of the neural connections is required. In this paper, we represent the brain connectome as a Riemannian manifold, which allows us to model neural connections as geodesics. This leads to the challenging problem of estimating a Riemannian metric that is compatible with the DWI data, i.e., a metric such that the geodesic curves represent individual fiber tracts of the connectomics. We reduce this problem to that of solving a highly nonlinear set of partial differential equations (PDEs) and study the applicability of convolutional encoder-decoder neural networks (CEDNNs) for solving this geometrically motivated PDE. Our method achieves excellent performance in the alignment of geodesics with white matter pathways and tackles a long-standing issue in previous geodesic tractography methods: the inability to recover crossing fibers with high fidelity.

翻译：弥散加权磁共振成像（DWI）的目标是推断个体受试者大脑的结构连接性。为了统计研究正常与异常大脑连接组的变异性与差异，需要建立神经连接的数学模型。本文将大脑连接组表示为黎曼流形，从而将神经连接建模为测地线。这引出了一个具有挑战性的问题：估计与DWI数据兼容的黎曼度量，即使得测地曲线代表连接组学中单个纤维束的度量。我们将该问题简化为求解一组高度非线性的偏微分方程（PDE），并研究了卷积编码器-解码器神经网络（CEDNN）在求解这一几何驱动PDE中的适用性。所提出的方法在测地线与白质通路对齐方面取得了优异性能，并解决了此前测地线纤维束成像方法中长期存在的难题：无法高保真度地恢复交叉纤维。