fMRI-Kernel Regression: A Kernel-based Method for Pointwise Statistical Analysis of rs-fMRI for Population Studies

Due to the spontaneous nature of resting-state fMRI (rs-fMRI) signals, cross-subject comparison and therefore, group studies of rs-fMRI are challenging. Most existing group comparison methods use features extracted from the fMRI time series, such as connectivity features, independent component analysis (ICA), and functional connectivity density (FCD) methods. However, in group studies, especially in the case of spectrum disorders, distances to a single atlas or a representative subject do not fully reflect the differences between subjects that may lie on a multi-dimensional spectrum. Moreover, there may not exist an individual subject or even an average atlas in such cases that is representative of all subjects. Here we describe an approach that measures pairwise distances between the synchronized rs-fMRI signals of pairs of subjects instead of to a single reference point. We also present a method for fMRI data comparison that leverages this generated pairwise feature to establish a radial basis function kernel matrix. This kernel matrix is used in turn to perform kernel regression of rs-fMRI to a clinical variable such as a cognitive or neurophysiological performance score of interest. This method opens a new pointwise analysis paradigm for fMRI data. We demonstrate the application of this method by performing a pointwise analysis on the cortical surface using rs-fMRI data to identify cortical regions associated with variability in ADHD index. While pointwise analysis methods are common in anatomical studies such as cortical thickness analysis and voxel- and tensor-based morphometry and its variants, such a method is lacking for rs-fMRI and could improve the utility of rs-fMRI for group studies. The method presented in this paper is aimed at filling this gap.