New methods for solving the inverse MEG problem and assessing functional connectivity

The solution of the inverse problem involves finding the distribution of neuronal population activity across the cerebral cortex based on data recorded noninvasively using EEG and MEG. The inverse problem does not have a unique solution from a mathematical point of view, so its solution requires the use of various assumptions about the desired solution, as well as optimization methods. 

Another aspect of the analysis of cortical source activity is the assessment of the functional connectivity between them, defined through the constancy of phase delays in the synchronous activity of neuronal populations (e.g., through a cross-spectral function). An important limitation within this task is the volumetric conduction artifacts that generate false connectivity indices due to signal mixing. 
As previously shown (Hincapie et al., 2015), reconstructing cortical source activity and assessing their functional connectivity requires different regularization parameters, indicating that these tasks are antagonistic. Therefore, standard approaches in which the activity of the sources is initially estimated and then the same activity is used to calculate connectivity indices are not optimal.

The Center for Bioelectrical Interfaces research has developed the PSIICOS method (Ossadtchi et al., 2018) to estimate functional connectivity, particularly with small phase delays. This method uses a direct model-based projection operator and uses it to suppress the volume conductance artifact component of the cross-spectrum in the sensor space. After getting rid of volumetric conductivity artifacts, it is possible to consider pairs of nodes in the network as sources and solve the problem of functional connectivity estimation already in the source space in terms of multivariate regression.



Figure 1. The effect of PSIICOS projection on the characteristics of the direct model topographies. Ossadtchi, A., Altukhov, D., & Jerbi, K. (2018). Phase shift invariant imaging of coherent sources (PSIICOS) from MEG data. NeuroImage, 183, 950-971.

The reciprocal form of the described projection operator (ReciPSIICOS) (Kuznetsova et al., 2021) can be used to optimize inverse problem solutions using bimformers (beam shapers). The focality of the solutions obtained with bimformers is ensured by minimizing the filter output power, taking into account maintaining the maximum magnitude in the direction of the source being evaluated. A limitation of this approach is the assumption of cortical source activity independence, which may generate signal mutual suppression if the data are based on sources with correlated activity. The contribution of such sources is suppressed by the ReciPSIICOS projection, providing robustness of the solutions obtained using bimformers.



Fig. 2. Demonstration of the reconstruction of the activity of simulated sources by different methodsKuznetsova, A., Nurislamova, Y., & Ossadtchi, A. (2021). Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources. Neuroimage, 228, 117677.

Published articles on the project:

1. Ossadtchi, A., Altukhov, D., & Jerbi, K. (2018). Phase shift invariant imaging of coherent sources (PSIICOS) from MEG data.   NeuroImage   ,   183   , 950-971.
2. Kuznetsova, A., Nurislamova, Y., & Ossadtchi, A. (2021). Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources. Neuroimage, 228, 117677.