Gahm Jin Kyu, Shi Yonggang
Laboratory of Neuro Imaging, USC Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, USA.
Med Image Comput Comput Assist Interv. 2016 Oct;9900:228-236. doi: 10.1007/978-3-319-46720-7_27. Epub 2016 Oct 2.
With the advance of human connectome research, there are great interests in computing diffeomorphic maps of brain surfaces with rich connectivity features. In this paper, we propose a novel framework for connectivity-driven surface mapping based on Riemannian metric optimization on surfaces (RMOS) in the Laplace-Beltrami (LB) embedding space. The mathematical foundation of our method is that we can use the pullback metric to define an isometry between surfaces for an arbitrary diffeomorphism, which in turn results in identical LB embeddings from the two surfaces. For connectivity-driven surface mapping, our goal is to compute a diffeomorphism that can match a set of connectivity features defined over anatomical surfaces. The proposed RMOS approach achieves this goal by iteratively optimizing the Riemannian metric on surfaces to match the connectivity features in the LB embedding space. At the core of our framework is an optimization approach that converts the cost function of connectivity features into a distance measure in the LB embedding space, and optimizes it using gradients of the LB eigen-system with respect to the Riemannian metric. We demonstrate our method on the mapping of thalamic surfaces according to connectivity to ten cortical regions, which we compute with the multi-shell diffusion imaging data from the Human Connectome Project (HCP). Comparisons with a state-of-the-art method show that the RMOS method can more effectively match anatomical features and detect thalamic atrophy due to normal aging.
随着人类连接组研究的进展，人们对计算具有丰富连接特征的脑表面微分同胚映射产生了浓厚兴趣。在本文中，我们基于拉普拉斯 - 贝尔特拉米（LB）嵌入空间中表面的黎曼度量优化（RMOS），提出了一种用于连接驱动表面映射的新框架。我们方法的数学基础是，对于任意微分同胚，我们可以使用回拉度量来定义表面之间的等距，这反过来会导致两个表面具有相同的LB嵌入。对于连接驱动的表面映射，我们的目标是计算一个能匹配在解剖表面上定义的一组连接特征的微分同胚。所提出的RMOS方法通过迭代优化表面上的黎曼度量以匹配LB嵌入空间中的连接特征来实现这一目标。我们框架的核心是一种优化方法，它将连接特征的成本函数转换为LB嵌入空间中的距离度量，并使用LB特征系统相对于黎曼度量的梯度对其进行优化。我们根据与十个皮质区域的连接性，在丘脑表面映射上展示了我们的方法，这是我们使用来自人类连接组计划（HCP）的多壳扩散成像数据计算得出的。与一种先进方法的比较表明，RMOS方法能够更有效地匹配解剖特征，并检测出由于正常衰老导致的丘脑萎缩。
