III: Small: Multi-modal Neuroimaging Data Fusion and Analysis with Harmonic Maps Under Designed Riemannian Metric

III：小：设计黎曼度量下的多模态神经影像数据融合与调和图分析

• 批准号: 1421165
• 负责人: Yalin Wang
• 金额: $ 41.81万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1421165&HistoricalAwards=false
• 关键词: III; Small; Multi; modal; Neuroimaging

The rapid development in acquiring multi-modal neuroimaging data provides exciting new opportunities to systematically characterize human brain structure, its relationship to cognition and behavior, and the contributions of genetic and environmental factors to individual differences in brain circuitry. To optimally use such rich multi-modal data, there is an urgent need for powerful computational frameworks to integrate and analyze multi-source data. The current practice usually combines available data features from different sources without considering the intrinsic geometry and biology structure relationship between data sources. Shape analysis based approach may serve as a bridge for a general and integrative approach to multi-model data fusion and analysis. Although numerous studies have been devoted to imaging data registration research, limited progress has been made to integrate different modality data with some physically nature and geometrically intrinsic structures. This proposal focuses on investigating and developing computational algorithms on harmonic map with prescribed Riemannian metric, and on producing theoretically sound and practically efficient solutions for general multi-modal data fusion and analysis problems. The work outlined in this proposal will have applications in a number of research fields, including (1) Shape Analysis, neuroimaging and medical imaging in general. The proposed research unifies and connects a variety of computational geometry techniques and tackles a few open problems making it an ideal framework for teaching concepts in shape analysis as well as providing students a broader context in which various components may fit together. The algorithms and tools developed in this project will have a direct impact on neuroimaging research. It may enable discovery of multi-modal imaging biomarkers for some neurodegenerative disease, such as Alzheimer's disease. Harmonic maps and their related methods have applications in many other fields, including medical imaging, computer vision, machine learning, computer graphics, and geometric modeling. The PI will make the software tools accessible to the society. This project will facilitate the development of new courses and laboratory infrastructure for neuroimaging research. It also provides a unique opportunity for students from computer science to learn neuroscience more efficiently. The funding will allow continuation of ongoing efforts to actively recruit and advise students from under-represented groups.An integrated research and education plan is outlined in this project to investigate and develop computational theorems and algorithms. The first goal is to develop a method to compute the harmonic map under a designed Riemannian metric between general surfaces. One key novelty is that the new method formulates multi-source information with a Riemannian metric and thus the multi-source fusion problem is converted to compute a surface harmonic map which is adapted to any designed Riemannian metric on the target surface. Next, a variational formulation that optimizes the diffeomorphic harmonic map via adjusting the Riemannian metric will be developed. The harmonic map guarantees that it has the global minimum deformation. It will be a practical way to optimize diffeomorphisms between surfaces and provide the flexibility to introduce general objective functions defined by other data sources. In addition, an algorithm for volumetric harmonic maps under a designed Riemannian metric and a set of novel multivariate geometry statistics for multi-source data analysis will be implemented. The framework explores multi-source data fusion with intrinsic geometry structures and the multivariate statistics may provide more sensitive, reliable and accessible brain imaging biomarkers for neuroimaging analysis. The anticipated outcomes of this research project are: (1) new computational algorithms on harmonic maps with significant applications in various fields, such as medical imaging, computer vision, machine learning, computer graphics and geometric modeling; (2) a practical software package with a rigorous mathematical foundation to analyze multi-modal data and produce sensitive and comprehensive multivariate imaging statistics. It will be tested on a large public neuroimaging dataset and evaluated by various classification tasks.

获取多模态神经成像数据的快速发展为系统地表征人脑结构、其与认知和行为的关系以及遗传和环境因素对脑回路个体差异的贡献提供了令人兴奋的新机会。为了优化使用如此丰富的多模态数据，迫切需要强大的计算框架来集成和分析多源数据。目前的实践通常结合了来自不同来源的可用数据特征，而没有考虑数据源之间内在的几何和生物结构关系。基于形状分析的方法可以作为一个桥梁的通用和综合的方法，多模型数据融合和分析。虽然大量的研究已经致力于成像数据配准的研究，有限的进展已经取得了不同的模态数据与一些物理性质和几何固有的结构。该提案的重点是研究和开发具有规定黎曼度量的调和映射的计算算法，并为一般的多模态数据融合和分析问题提供理论上合理和实际有效的解决方案。 本提案中概述的工作将在许多研究领域中应用，包括（1）形状分析，神经成像和医学成像。拟议的研究统一和连接各种计算几何技术，并解决了一些开放的问题，使其成为一个理想的框架，在形状分析教学概念，以及为学生提供更广泛的背景下，各种组件可能适合在一起。该项目开发的算法和工具将对神经影像学研究产生直接影响。它可能使发现多模态成像生物标志物的一些神经退行性疾病，如阿尔茨海默氏病。 调和映射及其相关方法在许多其他领域中有应用，包括医学成像、计算机视觉、机器学习、计算机图形学和几何建模。PI将使软件工具向社会开放。该项目将促进神经影像学研究的新课程和实验室基础设施的发展。它还为计算机科学专业的学生提供了一个独特的机会，可以更有效地学习神经科学。这笔资金将允许继续努力，积极招募和建议来自代表性不足的群体的学生。在这个项目中概述了一个综合的研究和教育计划，以调查和开发计算定理和算法。 第一个目标是发展一种方法来计算一般曲面之间的调和映射在一个设计的黎曼度量。一个关键的新奇是，新方法制定多源信息与黎曼度量，从而多源融合问题被转换为计算表面调和映射，这是适应于任何设计的黎曼度量的目标表面。 接下来，将开发通过调整黎曼度量来优化非纯调和映射的变分公式。调和映射保证它具有全局最小变形。这将是一个实用的方法来优化曲面之间的同构，并提供了灵活性，引入其他数据源定义的一般目标函数。 此外，一个算法的体积调和映射下设计的黎曼度量和一组新的多变量几何统计多源数据分析将实施。该框架探索了具有内在几何结构的多源数据融合，并且多元统计可以为神经成像分析提供更灵敏、可靠和可访问的脑成像生物标志物。该研究项目的预期成果是：（1）在医学成像、计算机视觉、机器学习、计算机图形学和几何建模等各个领域具有重要应用的谐波映射新计算算法;（2）具有严格数学基础的实用软件包，用于分析多模态数据并产生敏感和全面的多元成像统计。它将在一个大型公共神经成像数据集上进行测试，并通过各种分类任务进行评估。