### Department of Biostatistics Seminar/Workshop Series

# Spatio-Temporal Mixed Effects Models for fMRI Data Analysis

## Hakmook Kang, PhD

### Center for Statistical Sciences, Brown University

### Thursday, February 17, 1:00-2:00pm, MRBIII Conference Room 1220

In this talk, we demonstrate that in order to accurately estimate the activation parameters in functional magnetic resonance imaging (fMRI) data, it is important to properly take into account the intrinsic spatial and temporal correlation. Standard approaches to fMRI analyses avoid specifying the spatio-temporal correlation because of the computational demand. One clever way to reduce the computational complexity is to transform the time series data into the frequency domain because the Fourier coefficients are approximately uncorrelated. The resulting spatio-spectral data has a block diagonal structure which is considerably simpler than the spatio-temporal data. Hence, we propose a spatio-spectral mixed effects model which (1.) accounts for variation in activation between voxels within a region of interest (ROI); (2.) gives a multi-scale spatial correlation structure that disentangles local correlation (within voxels in an ROI) and global correlation (between ROIs); and (3.) gives a covariance structure that greatly reduces computational burden. Building on existing theory on linear mixed effect models to conduct estimation and inference, we applied our model to fMRI data collected to estimate activation in pre-specified regions in the prefrontal cortex and to estimate the correlation structure in the brain network. The result is consistent with known neuroanatomy and supports the existence of a functional network among those regions associated with the experimental task.

This is joint work with H. Ombao, C. Linkletter (Brown Biostatistics), and D. Badre (Brown Cognitive, Linguistic, and Psychological Sciences).