The structural network of the brain, or structural connectome, can be represented by fiber bundles generated by a variety of tractography methods. While such methods give qualitative insights into brain structure, there is controversy over whether they can provide quantitative information, especially at the population level. In order to enable population-level statistical analysis of the structural connectome, we propose representing a connectome as a Riemannian metric, which is a point on an infinite-dimensional manifold. We equip this manifold with the Ebin metric, a natural metric structure for this space, to get a Riemannian manifold along with its associated geometric properties. We then use this Riemannian framework to apply object-oriented statistical analysis to define an atlas as the Fr\'echet mean of a population of Riemannian metrics. This formulation ties into the existing framework for diffeomorphic construction of image atlases, allowing us to construct a multimodal atlas by simultaneously integrating complementary white matter structure details from DWMRI and cortical details from T1-weighted MRI. We illustrate our framework with 2D data examples of connectome registration and atlas formation. Finally, we build an example 3D multimodal atlas using T1 images and connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project.
翻译:大脑的结构网络,或结构连接体,可以用各种地形学方法生成的纤维捆绑来代表。虽然这些方法对大脑结构有质的洞察力,但对于它们能否提供定量信息,特别是在人口层面提供定量信息存在争议。为了能够对结构连接体进行人口层面的统计分析,我们提议将连接体作为列伊曼尼度量度仪,这是一个无限多维的点。我们用Ebin 度量仪,即这个空间的自然度量度结构,来为这个元件提供一个里伊曼尼方块及其相关的几何特性。我们随后利用里伊曼框架应用面向对象的统计分析来界定一个图集,作为里曼度量度的人群的Fr\'echet平均值。我们提议将这种配方与现有图集的变异形构建框架相联系,使我们能构建一个多式图集,同时将DWMRI的互补的白物质结构细节和T1加权MRI的螺旋性细节结合起来。我们用2D数据表来说明我们的框架,从T1号地图的连接点注册和数位集成成的人类图集图集的图集中,我们用T1号图集的2D-D-D-ROmmmmmmmmmmmmmmml 建立了一个模型的图集的图集的图集的模型,最后,我们用了一个模型做了一个示例。