Mathematical and Statistical Modeling and Methodology for Topics in Diffusion Tensor Imaging

扩散张量成像是一种非侵入性磁共振成像技术，可用于分析大脑复杂的神经元网络。目前，由于高水平的噪声，大脑连通性测量很复杂，很难验证。该项目旨在对测量中的噪声进行建模，并大幅提高科学和医学最终用户对大脑中的纤维束做出自信决定的能力。最终，该项目的目标是改进对阿尔茨海默病、创伤性脑损伤和多发性硬化症等脑部疾病和障碍的早期诊断工具。研究结果将有助于进一步发展扩散张量成像技术，使其成为一种可靠、实用的常规临床检查方法。研究人员拥有统计学、数学、成像物理、工程学和神经科学方面的专业知识，还在培训一个由年轻研究人员组成的跨学科团队，他们将通过定期会议、非参数统计和图像处理方面的研究生课程以及其他研究小组活动，获得对该项目的数学和神经科学方面的宝贵接触。该小组还计划激发K-12年级学生对如何使用“数学和统计”来理解大脑连接结构的兴趣。积分曲线是各种科学现象的自然模型，从大脑中的轴突纤维，到大气中的喷流，再到自动驾驶汽车的道路轮廓。传统上，它们被建模为在3D域中利用噪声观测的方向向量场上定义的方向分布函数的解。脑成像技术的进步现在可以提供高度复杂的方向信息，如纵向数据、由积分曲线构成的流形以及潜在轴突解剖的图形结构。使用这种增强的定向数据跟踪的单个积分曲线及其束提供了极大地增加我们对生物现象的理解的潜力，例如轴突纤维的结构完整性，并帮助选择在脑MRI中的最佳扫描方案。然而，基于新数据的单个积分曲线及其丛的统计性质的估计器还没有被很好地理解。在这个项目中，PI旨在为将复杂方向数据的3D-4D-6D场中的积分曲线估计与潜在的图形噪声结构联系起来提供坚实的理论基础，并应用新的方法来解决扩散张量成像(DTI)和高角分辨率扩散成像(HARDI)这两种脑MRI常用技术中的几个实际问题。具体地说，目标是(1)轴突纤维结构完整性的纵向建模，(2)建模和评估纤维束的不确定性，(3)在合理的扫描时间内搜索最佳扩散方向和贝壳数目，(4)均衡纤维跟踪表征方法，以及(5)得出数据采集协议的统计最优设计。该项目致力于提高DTI/HARDI不仅是一种可靠的神经科学研究工具，而且是一种用于常规临床应用的可靠和实用的成像技术。该奖项反映了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。

Diffusion tensor imaging is a non-invasive magnetic resonance imaging technology that can be used to analyze the complex neuronal network of the brain. Currently, brain connectivity measurements are complicated and are difficult to validate due to a high level of noise. This project aims to model the noise in measurements and substantially improve the ability of scientific and medical end-users to make confident decisions about fiber tracts in the brain. Ultimately, this project aspires to improve early diagnostic tools for brain diseases and disorders such as Alzheimer's disease, traumatic brain injury, and multiple sclerosis. The results of the research are expected to help further develop diffusion tensor imaging technology as a reliable and practical routine clinical procedure. The investigators, with expertise in statistics, mathematics, imaging physics, engineering, and neuroscience, are also training an interdisciplinary team of young researchers, who will gain valuable exposure to both mathematical and neuroscience aspects of this project through regular meetings, graduate courses in nonparametric statistics and image processing, and other research group activities. The group also plans to stimulate interest of K-12 students on how to use "math and stat" to understand brain wiring structures. Integral curves are natural models for a variety of scientific phenomena, from axonal fibers in the brain, to jet streams in the atmosphere, to road outlines for self-driving cars. Traditionally, they are modeled as solutions to the orientation distribution functions defined on fields of direction vectors that are observed with noise in a 3D domain. Advances in brain imaging technology can now provide highly complex directional information, such as longitudinal data, manifolds constructed out of integral curves, and graphic structures of the underlying axonal anatomy. Individual integral curves as well as their bundles traced using this enhanced directional data provide the potential to dramatically increase our understanding of biological phenomena such as the structural integrity of the axonal fibers and to assist in selecting an optimal scanning protocol in brain MRI. However, the estimators for the statistical properties of individual integral curves and their bundles based on the new data are not well understood. In this project, the PIs aim to provide a solid theoretical foundation for linking integral curve estimation in 3D-4D-6D fields of complex directional data with underlying graphical noise structures and to apply the new methodology to address several practical problems in diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI), technologies commonly used in brain MRI. Specifically, the goals are (1) longitudinal modeling of the structural integrity of the axonal fibers, (2) modeling and assessing the uncertainty of a bundle of fibers, (3) searching for optimal numbers of diffusion directions and shells within a reasonable scan time, (4) equalizing methods for the fiber tracking characterization, and (5) deriving statistically optimal designs for data acquisition protocols. This project strives to improve DTI/HARDI not only as a reliable neuroscience research tool but also as a reliable and practical imaging technique for routine clinical applications.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.