A Multivariate Approach to Estimate Complexity of FMRI Time Series

Modern functional brain imaging methods (e.g. functional magnetic resonance imaging, fMRI) produce large amounts of data. To adequately describe the underlying neural processes, data analysis methods are required that are capable to map changes of high-dimensional spatio-temporal patterns over time. In this paper, we introduce Multivariate Principal Subspace Entropy (MPSE), a multivariate entropy approach that estimates spatio-temporal complexity of fMRI time series. In a temporally sliding window, MPSE measures the differential entropy of an assumed multivariate Gaussian density, with parameters that are estimated based on low-dimensional principal subspace projections of fMRI images. First, we apply MPSE to simulated time series to test how reliably it can differentiate between state phases that differ only in their intrinsic dimensionality. Secondly, we apply MPSE to real-world fMRI data of subjects who were scanned during an emotional task. Our findings suggest that MPSE might be a valid descriptor of spatio-temporal complexity of brain states.