Statistical Representations and Algorithms for Brain Connectivity

University Of California-Davis, Davis CA

Investigators

Abstract

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.