System identification and surrogate data analyses imply approximate Gaussianity and non-stationarity of resting-brain dynamics

Compared with model-based and phenomenological descriptions of the spatiotemporal dynamics of resting-brain activity, statistical characterizations of resting-state fMRI (rs-fMRI) data remain relatively underexplored. Some sophisticated analysis techniques, such as Mapper-based topological data analysis (TDA) and innovation-driven coactivation pattern analysis (iCAP), can distinguish real data from phase-randomized (PR) surrogates, suggesting that rs-fMRI data are not as simple as stationary Gaussian processes. However, the exact statistical properties that distinguish real rs-fMRI data from PR surrogates have not yet been determined. In this study, we conducted system identification analysis and surrogate data analysis to specify key statistical properties that allow TDA and iCAP to discriminate real rs-fMRI data from PR surrogates. We first analyzed rs-fMRI data concatenated across scans using autoregressive (AR) modeling and found that the scan-concatenated rs-fMRI data were weakly non-Gaussian. However, non-Gaussianity alone was insufficient to reproduce realistic TDA and iCAP results because of non-stationarity across scans. AR modeling of single-scan data revealed that rs-fMRI data were statistically indistinguishable from a Gaussian distribution within a single scan, although TDA and iCAP results still differed between the real data and PR surrogates. A new surrogate dataset designed to preserve non-stationarity successfully reproduced realistic TDA and iCAP results, suggesting that TDA and iCAP likely capture the non-stationarity of rs-fMRI data to distinguish it from PR surrogates. Together, these results indicate approximate Gaussianity and non-stationarity in rs-fMRI data, providing a data-driven and statistical characterization of resting-state brain activity that can serve as a quantitative reference for whole brain simulations and generative models.