PSIICOS projection optimality for EEG and MEG based functional coupling detection

Abstract

Functional connectivity is crucial for cognitive processes in the healthy brain and serves as a marker for a range of neuropathological conditions. Non-invasive exploration of functional coupling using temporally resolved techniques such as MEG allows for a unique opportunity of exploring this fundamental brain mechanism in a reasonably ecological setting. The indirect nature of MEG measurements complicates the the estimation of functional coupling due to the spatial leakage effects. In previous work (Ossadtchi et al., 2018), we introduced PSIICOS, a method that for the first time allowed us to suppress the spatial leakage and yet retain information about functional networks whose nodes are coupled with close to zero or zero mutual phase lag. In this paper, we demonstrate analytically that the PSIICOS projection is optimal in achieving a controllable trade-off between suppressing mutual spatial leakage and retaining information about zero-phase coupled networks. We also derive an alternative solution using the regularization-based inverse of the mutual spatial leakage matrix and show its equivalence to the original PSIICOS. This approach allows us to incorporate the PSIICOS solution into the conventional source estimation framework. Instead of sources, the unknowns are the elementary networks and their activation timeseries are formalized by the corresponding source-space cross-spectral coefficients. Additionally, we outline potential avenues for future research to enhance functional coupling estimation and discuss alternative estimators that parallel the established source estimation approaches. Finally, we propose that the PSIICOS framework is well-suited for Bayesian techniques and offers a principled way to incorporate priors derived from structural connectivity.