CRCNS Research Proposal: Collaborative Research: The Space of Riemannian Metrics for the Statistical Analysis of the Human Connectome

人脑是最复杂的生物几何对象之一。人类连接组项目旨在提供来自健康成年人的无与伦比的神经功能和结构成像数据的汇编。来自900多名受试者的数据已经公布。人类连接计划提供的主要数据是弥散加权磁共振成像和功能磁共振成像。由于这个项目产生的数据量和复杂性，需要新的技术来分析、比较和表示这些数据，这是本提案中概述的研究的动机和推动力。这个合作项目有三个基本目标：(1)进一步发展几何统计的数学理论，特别是所有黎曼度量的无限维流形的作用；(2)为人脑连通性的统计研究开发实用工具；以及(3)展示所开发的技术的实用性，用于分割和分割丘脑和结构磁共振中看不到的皮质下灰质的其他亚区。这个项目将首次在无限维黎曼度量流形上发展统计技术。项目团队认为，黎曼度量的空间是分析人脑架构可变性的自然框架。扩散加权磁共振成像允许研究人员将单个人脑建模为具有轴突连接的黎曼流形，轴突连接是适当度量的测地线曲线。该团队将研究所有黎曼指标的空间，并开发基于几何统计的方法来分析整个人口。开发的技术的直接实际应用将是基于丘脑皮质连接的丘脑分割。丘脑的内部结构在标准的结构核磁共振中是不可见的，而是通过与皮质不同区域的连接来定义的。在这个项目中，研究人员将通过连接将皮质的功能分区投射到丘脑上，从而对丘脑进行分区。其目的是使用几何统计映射方法来产生单个患者丘脑的统计信息分区。主要的驱动力是最终改善作为治疗特发性震颤的脑深部刺激的结果，丘脑是主要的靶点。皮质下白质还与许多神经疾病有关，如缺血性血管疾病、亨廷顿氏症、多发性硬化症和艾滋病毒/艾滋病痴呆症。PI设想，为确定正常人群中白质的详细结构而开发的统计技术将对所有这些疾病产生影响。这个项目将提供新的分析工具来揭开人脑的奥秘。这个奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The human brain is one of the most complex biological geometrical objects. The Human Connectome Project aims to make available an unparalleled compilation of neural functional and structural imaging data from healthy adults. Data from over 900 subjects has already been released. The principal data provided by the Human Connectome Project are diffusion-weighted MRI and functional MRI. Due to the amount and complexity of the data generated in this project, new techniques to analyze, compare and represent these data are needed, which is the motivation and driving force for the research outlined in this proposal. This collaborative project has three fundamental goals: (1) to further develop the mathematical theory of geometrical statistics, in particular the role of the infinite-dimensional manifold of all Riemannian metrics; (2) to develop practical tools for the statistical study of the connectivity of the human brain; and (3) to demonstrate the utility of the developed techniques for the segmentation and parcellation of the thalamus and other subareas of the subcortical gray matter that are not visible in structural MRI. This project will develop for the first time statistical techniques on the infinite-dimensional manifold of Riemannian metrics. The project team believes that the space of Riemannian metrics is the natural framework for analyzing the variability of the architecture of the human brain. Diffusion-weighted MRI allows the investigators to model an individual human brain as a Riemannian manifold with axonal connections that are geodesic curves of an appropriate metric. The team will study the space of all Riemannian metrics and develop methods based on geometrical statistics for the analysis of the whole population. An immediate practical application of the techniques developed will be the parcellation of the thalamus based on thalamocortical connectivity. The internal architecture of the thalamus is not visible in standard structural MRI but rather is defined via the connections to the different areas of the cortex. In this project, the investigators will partition the thalamus by projecting the functional partition of the cortex onto the thalamus via the connectomics. The aim is to use geometric statistical mapping methods to produce a statistically informed partition of an individual patient's thalamus. The primary driving motivation is to eventually improve outcomes of deep brain stimulation as a therapy for essential tremor, in which the thalamus is the primary target. The subcortical white matter is also implicated in many neurological disorders, such as ischemic vascular disease, Huntington's, Multiple Sclerosis, and HIV/AIDS dementia. The PIs envision that the statistical techniques developed for qualifying the detailed architecture of the white matter in the normal population will have implications for all these diseases. This project will provide novel analytical tools to unravel the mysteries of the human brain.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.