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)大大加快了对大脑疾病的研究。迫切需要对大量人口中的多模式数据进行整合、索引和建模，以便更详细地了解这一非常复杂的生物系统中的过程相互作用。目前最先进的计算和软件技术在多模式数据集成和建模以及对人类受试者不同的神经成像数据集的集成分析方面存在不足。该建议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、多变量单纯形样条和统计学习的多模式神经成像数据的集成建模和分析。智力优势这个跨学科的研究团队将为高级和集成的大脑成像数据分析设计一个基本框架。所有研究活动将针对以下主要主题和目标：(1)探索基于三维流形的黎曼几何的新的理论工具，以开发一种新的正则体积模型(CVM)，该模型提供个体大脑到实体单位球体的体积映射，并实现跨对象的精确匹配；(2)设计分层球面三变量单纯形样条，用于高效、准确地紧凑地表示、集成、索引和可视化多模异质成像数据，它可以在基于分层样条体和拉格朗日动力学的基础上，通过更高维物理空间中的层次细节匹配来进一步精细化主体间配准；(3)设计新的统计学习和挖掘方法，同时分析广泛的时空尺度和人类受试者的各种数据，以推断神经疾病研究中脑功能的动态变化。广泛影响这项研究将为各种脑成像数据的分析集成、统计建模和定量分析提供准确、稳健和创新的科学方法，从而为数据密集型脑研究做出贡献。建议的计算框架具有在脑研究的多个领域以及临床诊断中应用的潜力。这项工作可能会影响大量患有神经疾病的患者，并将为许多其他研究人员提供一个普遍接受的标准基础设施。私人投资机构的研究工作将与一套相辅相成的教育目标紧密结合在一起，其中包括：(1)为真正的多学科科学教育制定新战略；(2)改进现有课程；(3)对研究生研究人员进行博士培训；(4)为代表人数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.