Bayesian Spatiotemporal Modeling on Complex-Valued fMri Signals via Kernel Convolutions

Abstract

We propose a model‐based approach that combines Bayesian variable selection tools, a novel spatial kernel convolution structure, and autoregressive processes for detecting a subject's brain activation at the voxel level in complex‐valued functional magnetic resonance imaging (CV‐fMRI) data. A computationally efficient Markov chain Monte Carlo algorithm for posterior inference is developed by taking advantage of the dimension reduction of the kernel‐based structure. The proposed spatiotemporal model leads to more accurate posterior probability activation maps and less false positives than alternative spatial approaches based on Gaussian process models, and other complex‐valued models that do not incorporate spatial and/or temporal structure. This is illustrated in the analysis of simulated data and human task‐related CV‐fMRI data. In addition, we show that complex‐valued approaches dominate magnitude‐only approaches and that the kernel structure in our proposed model considerably improves sensitivity rates when detecting activation at the voxel level.

Denoising brain networks using a fixed mathematical phase change in independent component analysis of magnitude‐only fMRI data

“…Taking analyses of motor task‐related complex‐valued fMRI data as examples, 139% more contiguous motor‐related voxels were detected for the task‐related brain network as well as 331% more contiguous voxels were detected in the regions expected to be activated for the default mode network (DMN) in ICA of single‐subject data (Yu et al, 2015 ); 393% more contiguous and reasonable activations were extracted for the task‐related brain network and 301% for DMN in independent vector analysis of multiple‐subject data (Kuang, Lin, Gong, Cong, et al, 2017b ); and 178.7% more contiguous activations were detected in task‐related regions consisting of the left and right primary motor areas and the supplementary motor areas in tensor decomposition of multiple‐subject data (Kuang et al, 2020 ). These are consistent with the improved sensitivity and activation detection results obtained by model‐driven (Rowe, 2005 , 2009 ; Rowe & Logan, 2004 ; Yu et al, 2018 , 2022 ) and data‐driven (Arja et al, 2010 ; Calhoun & Adalı, 2012a ; Calhoun et al, 2002 ) methods for analyzing complex‐valued fMRI data, supporting the fact that fMRI phase contains biological information regarding the vasculature contained within voxels (Adrian et al, 2018 ; Feng et al, 2009 ; Yu et al, 2018 , 2022 ). The effectiveness of SSP denoising is also consistent with previous findings that the phase change of observed phase fMRI data has the capacity of accessing the voxel quality.…”