Statistical Analysis of Biomedical Imaging Data in Curved Space

DESCRIPTION (provided by applicant): Large-scale medical imaging studies have collected a rich set of ultra-high dimensional imaging data, behavioral data, and clinical data in order to better understand the progress of neuropsychiatric disorders, neurological dis- orders and stroke, normal brain development, diagnosis of colorectal cancer, osteoarthritis, and prostate cancer, among many others. However, the development of statistical and computational methods for the joint analysis of imaging and clinical data has fallen seriously behind the technological advances. Three common and important themes of these image data are (T1) ultra-high dimensional functional data with a multi-dimensional tensor struc- ture, (T2) complex geometric structures of human organs, and (T3) complex spatial correlation structures. To meet this critical and important challenge, we will establish a comprehensive statistical framework by addressing three methodological problems. First, there are few efficient and fast methods on modeling high-dimensional imaging data as piecewise smooth functions, while accounting for themes (T2) and (T3). Second, there are few efficient methods on the use of ultra-high dimensional tensor data to predict cognitive development and high- dimensional imaging data, while accounting for the themes (T1)-(T3). Third, little has been done on the analysis of imaging data from longitudinal twin studies. We will establish a comprehensive statistical framework to address these methodological problems. Specifically, we will develop a class of hierarchical functional process models, a class of functional tensor prediction process models, and a class of functional structural equation process mod- els. Scientifically, these new statistical methods are motivated by the analysis of a longitudinal neuroimaging database on early brain development in high-risk children from the Conte study. Our new methods can dramatically increase scientists' ability to better address important scientific questions associated with many imaging studies, particularly those for the Conte study. As these tools are being developed, they will be evaluated and refined through extensive Monte Carlo simulations and the Conte database. Companion software, which will pro- vide much needed analytic tools for the joint analysis of imaging and clinical data, will be disseminated to imaging researchers through ://www.nitrc.org/ and ://www.bios.unc.edu/research/bias.The proposed methodology will have wide applications in neuropsychiatric and neurodegenerative diseases, neurological disorders and stroke, and osteoarthritis, among others.