III-CXT: Collaborative Research: Integrated Modeling and Learning of Multimodality Data across Subjects for Brain Disorder Study

成像技术的进步（例如磁共振成像）大大加速了大脑疾病的研究。迫切需要在大量人群中整合，索引和建模多模态数据，以便更详细地了解这个非常复杂的生物系统中的过程相互作用。当前最先进的计算和软件技术在多模态数据集成和建模以及跨人类受试者的不同神经成像数据集的集成分析方面存在不足。该提案的总体目标是开发一种新的，严格的框架，用于基于黎曼几何，多元单纯形样条和统计学习的多模态神经影像数据的集成建模和分析。这个跨学科的研究团队将为大脑成像数据的高级和综合分析设计一个基本框架。所有研究活动将围绕以下主题和目标：（1）探索基于三维流形黎曼几何的新理论工具，以发展一种新的规范体积模型（CVM），该模型提供个体大脑到实体单位球的体积映射，并在受试者之间进行精确匹配;（2）设计层次球面三变量单纯形样条函数，以高效、准确地实现多模态异构成像数据的紧凑表示、集成、索引和可视化，其可以通过基于分层样条体与拉格朗日动力学的集成的更高维物理空间中的细节层次匹配来进一步细化对象间配准;（三）设计新的统计学习和挖掘方法，以同时分析各种数据在广泛的空间和时间尺度和人类主题，以便在神经系统疾病研究中推断大脑功能的动力学。广泛的影响这项研究将有助于数据密集型的大脑研究，提供一个准确的，强大的，创新的科学方法，分析整合，统计建模，和定量分析的各种大脑成像数据。所提出的计算框架有可能应用于大脑研究的多个领域以及临床诊断。这项工作很可能会影响大量神经系统疾病患者，并为许多其他研究人员提供普遍接受的标准基础设施。研究所的研究工作将与一套互补的教育目标紧密结合，包括：（1）制定真正多学科科学教育的新战略;（2）加强现有课程;（3）研究生研究人员的博士培训;（4）为代表性不足的群体的学生开展辅导活动。

Advances in imaging technologies (Magnetic Resonance Imaging, for example) have significantly accelerated brain disorder studies. There is an urgent need to integrate, index and model multimodal data across a large population in order to discover a more detailed understanding about process interaction in this very complex biological system. Current state-of-the-art computational and software technologies fall short in multimodality data integration and modeling, and integrated analysis of diverse neuroimaging datasets across human subjects. The overall aim of this proposal is to develop a novel, rigorous framework for integrated modeling and analysis of multimodality neuroimaging data based on Riemannian geometry, multivariate simplex splines, and statistical learning. Intellectual Merits This interdisciplinary research team will design a fundamental framework for advanced and integrated analysis of brain imaging data. All research activities will address the following major themes and objectives: (1) To explore new theoretic tools based on Riemannian geometry of 3-manifolds for the development of a novel Canonical Volumetric Model (CVM) which provides volumetric mapping of individual brain to a solid unit sphere with accurate matching across subjects; (2) To design hierarchical spherical trivariate simplex splines for compact representation, integration, indexing and visualization of multimodality heterogeneous imaging data with high efficiency and accuracy, which can further refine the intersubject registration through level-of-detail matching in a higher dimensional physical space based on the integration of the hierarchical spline volume with Lagrangian dynamics; (3) To design new statistical learning and mining methods to analyze simultaneously the variety of data across the broad range of spatial and temporal scales and human subjects in order to infer the dynamics of brain functions in neurological disease studies. Broad Impacts This research will contribute to the data-intensive brain study by offering an accurate, robust, and innovative scientific approach for analytic integration, statistical modeling, and quantitative analysis of a variety of brain imaging data. The proposed computational framework has the potential to be applied across multiple areas of brain research as well as in clinical diagnosis. It is likely that this work will impact a large number of patients with neurological diseases and will provide a commonly accepted standard infrastructure for use by many other researchers. The PIs'' research endeavors will be tightly integrated with a complementary set of educational objectives, including: (1) the development of new strategies for truly multi-disciplinary science education; (2) the enhancement of the existing curricula; (3) the doctoral training of graduate researchers; (4) the implementation of mentoring activities for students from underrepresented groups.