Bayesian Analysis of Neuroimage Data Using Gaussian Process Priors

Abstract

Magnetic Resonance Imaging (MRI) is a foundational tool for medical and academic research. Functional MRI (fMRI) and human brain research, for example, have become nearly synonymous phrases. MRI results in a dense, high-dimensional, highly correlated 3D or 4D datatype only digestible with concerted statistical effort. This dissertation focuses on developing new semiparametric Bayesian models and computational techniques to cope with some of the challenges that arise with fMRI data.

The first project (Chapter 2) presents a model designed to integrate presurgical fMRI data collected at two different spatial resolutions. Modern neuroradiologists use fMRI to map patient-specific functional neuroanatomy to assist in presurgical planning. This application requires a high degree of spatial precision, but in practice the fMRI signal-to-noise ratio decreases with increasing spatial resolution. To mitigate this issue, our collaborator collected functional scans of preoperative patients at high and low spatial resolutions. The data inherently exhibit different levels of noise and lack a common spatial support, rendering them difficult to combine in a straightforward manner. We solve this problem by modeling the mean image intensity function of both data sources using a Gaussian process and develop a scalable posterior computation algorithm based on Riemann manifold Hamiltonian Monte Carlo methods. We show in simulation our method enables more accurate inference on image mean intensity than single-resolution alternatives, and further illustrate our approach in analyses of preoperative patient images.

The second project (Chapter 3) is motivated by studies where heterogeneous latent imaging subgroup effects may be present in the study population. We propose a Bayesian semiparametric hierarchical model for image-on-scalar regression with subgroup detection. We model the mean intensity of imaging outcomes with a mixture of spatially varying coefficient (SVC) regression models, and take into account spatial dependence in the SVCs with Gaussian processes. Additional individual-level covariates are used to inform the mixing distribution via a logistic stick-breaking process prior. This class of prior admits individual-specific mixture weights and induces correlation in mixture component assignments between individuals with similar covariate profiles. We show through simulation our model can lead to superior clustering and feature estimation compared to common unsupervised methods. Further, we illustrate our method via analysis of resting-state fMRI data from the Autism Brain Imaging Data Exchange (ABIDE) study.

In the third project (Chapter 4), we address an important issue in neuroimaging research: improving spatial modeling of group-level effects of interest on the cortical surface. A state-of-the-art image preprocessing tool computes cross-subject alignment of cortical features by first mapping each hemisphere of the brain onto a sphere. Critically, this procedure enables a measure of great-circle distance between cortical points. Geodesic distances along the cortical surface are more biologically meaningful than the classically used Euclidean distance in 3D space. We propose a Bayesian spatially varying coefficient model for imaging outcome data observed at locations on a sphere, and use Gaussian processes to model the probability law governing the regression coefficient functions. We consider different approaches to approximate posterior inference with our model and compare performance against standard vertex-wise analyses. Finally, we illustrate our method in an analysis of fMRI task contrast data from a large cohort of children in the Adolescent Brain Cognitive Development (ABCD) study.