Statistical Representations and Algorithms for Brain Connectivity

图像样本的统计分析是一个极具挑战性的问题，因为这些数据的复杂性很高，而且数据量很大。目前的方法大多是临时的，这限制了分析的范围和质量。这项研究通过在更一般的对象数据分析框架内开发基于模型的统计方法，特别是用于分析函数值空间随机过程来解决这一问题。这样的数据在时空气候学研究和静息状态下的功能磁共振成像中都会遇到。后者用于无任务脑成像，以确定大脑连通性，是本研究的主要重点。一个关键的方面是，研究人员将每个大脑视为一个采样单位，并开发出统计方法，利用可用的整个大脑图像样本来推断共同的结构和连通性的变化。这些方法普遍适用于空间过程依赖结构的评估。研究人员既研究了针对给定空间过程实现的个人连通性的建模，也研究了人口层面的连通性。为了对个体建模，他们研究了随机协方差曲面及其性质，在协方差函数空间上采用了适当的度量。为了模拟人口连通性，研究人员开发了时空协方差的分解。对于所有提出的方法，他们都在研究理论、有效的计算实现以及对大脑和空间数据的应用。研究人员开发了大脑成像数据的高级统计方法。这类数据是许多人在功能性磁共振成像中常规收集的，而且规模庞大且复杂。他们的分析需要开发复杂的计算和统计工具，这是本研究的重点。然后，这些方法被应用于量化和比较个体和跨群体大脑不同部分的反复出现的连接模式。除了表征大脑的功能外，连接模式还可能包括早期病理指标，如痴呆症的早期迹象。调查人员还研究了新方法的更广泛的影响和适用性。

The statistical analysis of samples of images and in particular of fMRI brain images is a challenging problem, due to the high complexity of these data and their large size. Current methodology is mostly ad hoc, which limits the scope and quality of the analysis. This research addresses this situation by developing model-based statistical methodology, speci cally for the analysis of function-valued spatial stochastic processes, within a more general frame- work of object data analysis. Such data are encountered in spatio-temporal climatological studies and in resting state fMRI. The latter is used for task-free brain imaging in order to determine brain connectivity and is a main focus of this research. A key aspect is that the investigators view each brain as a sampling unit and develop statistical methods that utilize the entire sample of available brain images to infer common structures and variation in connectivity. The methods are generally applicable for the assessment of dependency structures for spatial processes. The investigators study both modeling of individual connectivity for a given realization of the spatial process, as well as connectivity at the population level. To model individuals, they investigate random covari- ance surfaces and their properties, adopting adequate metrics on the space of covariance functions. To model population connectivity, the investigators develop a decomposition for spatio-temporal covari- ance. For all proposed methods, they investigate theory, efficient computational implementations and applications to both brain and spatial data.The investigators develop advanced statistical methods for brain imaging data. Such data are routinely collected for many individuals in functional magnetic resonance imaging and are large and complex. Their analysis requires the development of sophisticated computational and statistical tools, which is the focus of this research. The methods are then applied to quantify and compare recurring patterns of connectivity of different parts of the brain for individuals and across populations. Besides characterizing the function of the brain, patterns of connectivity may include early indicators of pathology such as early signs of dementia. The investigators also study the broader impact and applicability of the new methodology.