Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources

Abstract

Magnetoencephalography (MEG) is a neuroimaging method ideally suited for non-invasive studies of brain dynamics. MEG's spatial resolution critically depends on the approach used to solve the ill-posed inverse problem in order to transform sensor signals into cortical activation maps. Over recent years non-globally optimized solutions based on the use of adaptive beamformers (BF) gained popularity.When operating in the environment with a small number of uncorrelated sources the BFs perform optimally and yield spatial super-resolution. However, the BFs are known to fail when dealing with correlated sources acting like poorly tuned spatial filters with low signal-to-noise ratio (SNR) of the output timeseries and often meaningless cortical maps of power distribution.This fact poses a serious limitation on the broader use of this promising technique especially since fundamental mechanisms of brain functioning, its inherent symmetry and task-based experimental paradigms result into a great deal of correlation in the activity of cortical sources. To cope with this problem, we developed a novel beamformer approach that preserves high spatial resolution in the environments with correlated sources.At the core of our method is a projection operation applied to the vectorized sensor-space covariance matrix. This projection does not remove the activity of the correlated sources from the sensor-space covariance matrix but rather selectively handles their contributions to the covariance matrix and creates a sufficiently accurate approximation of an ideal data covariance that could hypothetically be observed should these sources be uncorrelated. Since the projection operation is reciprocal to the PSIICOS method developed by us earlier (Ossadtchi et al. (2018)) we refer to the family of algorithms presented here as ReciPSIICOS.We asses the performance of the novel approach using realistically simulated MEG data and show its superior performance in comparison to the well established MNE and classical BF approaches. We have also applied our approach to the MEG datasets from the two experiments involving two different auditory tasks.The analysis of experimental MEG datasets showed that beamformers from ReciPSIICOS family, but not MNE and the classical BF, discovered the expected bilateral focal sources in the primary auditory cortex and detected motor cortex activity associated with the audio-motor task. Moreover, ReciPSI-ICOS beamformers yielded cortical activity estimates with amplitude an order of magnitude higher than that obtained with the classical BF, which indicates the severeness of the signal cancellation problem when applying classical beamformers to MEG signals generated by synchronous sources.

Testing covariance models for MEG source reconstruction of hippocampal activity

“…Solutions to this correlated source problem have been forthcoming for many years, with a wide variety of approaches published 24 – 31 . For a detailed history, Kuznetsova and colleagues provide a review of the literature within their own solution to the correlated source problem 31 .…”

“…Solutions to this correlated source problem have been forthcoming for many years, with a wide variety of approaches published 24 – 31 . For a detailed history, Kuznetsova and colleagues provide a review of the literature within their own solution to the correlated source problem 31 . One common approach is to collapse two distinct and hypothetically correlated sources into a single source 24 , 27 , the problem being that as these sources are now correlated a priori, and all solutions (regardless of the underlying physiology) will reflect this.…”

Ant Colony System Optimization for Spatiotemporal Modelling of Combined EEG and MEG Data

“…However, the BFs are known to fail when dealing with correlated sources acting like poorly tuned spatial filters with a low signal-to-noise ratio (SNR) of the output time series and often meaningless cortical maps of power distribution. To address this limitation, the authors of [ 23 ] developed a novel data covariance approach to supply robustness to the beamforming technique when operating in an environment with correlated sources. To reduce the impact of the low spatial resolution of MEG and EEG, the authors of [ 24 ] developed a unifying framework for quantifying the spatial fidelity of MEG/EEG source estimates.…”

Testing covariance models for MEG source reconstruction of hippocampal activity

“…Solutions to this correlated source problem have been forthcoming for many years, with a wide variety of approaches published [24][25][26][27][28][29][30][31] . For a detailed history, Kuznetsova and colleagues provide a review of the literature within their own solution to the correlated source problem 31 .…”

“…Solutions to this correlated source problem have been forthcoming for many years, with a wide variety of approaches published [24][25][26][27][28][29][30][31] . For a detailed history, Kuznetsova and colleagues provide a review of the literature within their own solution to the correlated source problem 31 . One common approach is to collapse two distinct and hypothetically correlated sources into a single source 24,27 , the problem being that as these sources are now correlated a priori, and all solutions (regardless of the underlying physiology) will reflect this.…”