Signatures of fractal temporal dependencies are correlated between MEG and fMRI

Long-range temporal dependencies (LRTD) are an important signature of computation in the brain. They were shown to be decreased by Alzheimer’s and increased by epilepsy. An established way of capturing the LRTDs is to use Hurst exponents, for which estimation various methodologies were proposed in different fields of study. In neuroscience, LRTDs have been measured in broad-band electro- and magnetoencephalography (E/MEG) [2] (Fig. 1h), amplitude envelopes of oscillations [1] (Fig. 1g), and functional Magnetic Resonance Imaging (fMRI) [3] (Fig. 1f) using several existing methods. Theoretical work suggests that there are many equivalent methods and advises using multiple methods on data [4]. Apart from the first work [1] - which shows nonrigorous agreement between Detrended Fluctuation Analysis (DFA) and spectral method (1/f) - subsequent work has been mostly restricted to using only a single method and a single data domain. We demonstrate that combining multiple methods can improve the inference and demonstrate how this improved methodology enables uncovering consistency between MEG and fMRI temporal dependencies across long timescales.
We developed a comprehensive framework for evaluating LRTD methods and applied them to MEG, fMRI, and EEG. In our framework, we evaluate the methods on simulated data with an autoregressive fractionally integrated moving average (ARFIMA) process (Fig. 1a,b) and colored noise. These simulations revealed that only three methods successfully identified the correct Hurst exponent: Detrended Fluctuation Analysis (DFA), spectral method (1/f), and wavelet method. The best approach established in simulations is to use the average between DFA and Wavelet Method (Fig. 1c,d) because their error is uncorrelated.
We applied the optimized procedure to MEG and fMRI data from the Human Connectome Project [6] and established optimal fitting ranges for each method. For MEG subjects, we show that exponents match between accurate methods, supporting the hypothesis of a mono-fractal amplitude envelope. Finally, we find a significant correlation between the MEG alpha envelope and fMRI (Fig. 1i). A similar albeit weaker correlation exists in MEG between broadband and alpha envelope exponents.
We will make our developed framework available to catalyze subsequent research. We extend the evidence for similar underlying dynamics of the MEG alpha envelope and fMRI in the time domain from evoked potentials [5] to long-range temporal correlations.