Hemodynamic Matrix Factorization for Functional Magnetic Resonance Imaging
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Neural activation causes a complex change in neurophysiological parameters of the cerebral blood flow (CBF). Functional magnetic resonance imaging (fMRI) measures one of these neurophysiological parameters, which is the blood oxygen level dependent (BOLD) response. The general linear model (GLM) used in fMRI task experiments relates activated brain areas to extrinsic task stimuli. The translation of task-induced neural activation into a hemodynamic response is approximated with a convolution model in the GLM design. There are major limitations to the GLM approach. First, the GLM approach does not model intrinsic brain activity. Second, the GLM assumes compliant task participation matching the stimulus timing and duration in the corresponding task. We propose hemodynamic matrix factorization (HMF), a data-driven approach to model intrinsic and extrinsic neural activation in fMRI. By contrast to the GLM, the HMF does not incorporate the original task design. The neural activation is a latent variable and estimated from fMRI data. Each component of the HMF consists of a neural activation time course and a spatial mapping. A linear filter translates neural activation time courses into BOLD responses. We apply our HMF to a motor localization task of an open source data cohort. We obtain neural activation time courses that correlate with the original block design of the task and whose corresponding spatial maps match individual areas of the sensory-motor cortex known to be activated by either foot, hand or tongue movement. We find HMF components whose neural activation time courses correlate with the visual cue timings presented at the beginning of each task block. HMF thus constitutes a novel tool to validate if the actual task execution of a subject matches the intended execution specified in the task design of fMRI experiments.