Functional brain connectivity analysis based on the solution of the inverse problem and on covariance analysis.

The Linearly Constrained Minimum Variance (LCMV) beamformer is one of the most accepted techniques used to estimate the solution of the inverse problem in functional brain dynamics studies, using magnetoencephalograms (MEG). However, since it is based on the assumption of uncorrelated brain sources, its performance decreases in the presence of correlated brain activity, compromising the accuracy of estimates of brain interactions. This problem has not stopped the use of the beamformer in techniques such as Dynamic Imaging of Coherent Sources (DICS), which estimates the functional brain dynamics in a more direct way than the LCMV, and with less computational cost. In this work it is proposed to use a modified version of the well known Minimum Norm Estimates (MNE) spatial filter to estimate the functional brain dynamics of highly correlated activity. This is achieved by using the filter to estimate the cross-spectral density matrices for the brain activity in the same way that DICS does with the LCMV beamformer. The MNE spatial filter is used as a basis because it is not affected by the presence of correlated brain activity. The results obtained from simulations shown that it is possible to estimate highly correlated brain interactions using the proposed method. However, additional methods and constraints need to be applied because of the distorted and weighted output characteristic of the MNE spatial filter. Methods such as the FOcal Undetermined System Solution (FOCUSS) and Singular Value Decomposition
Truncation (SVDT) are used to reduce the distorted output, while the estimation of brain dynamics is limited to cortical surface interactions to avoid weighted solutions.