The Role of Spectral Complexity in Connectivity Estimation

The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.

The Need for and Road to Hybrid Magnetoencephalography–Magnetic Resonance Imaging

This chapter addresses the need for hybrid magnetoencephalography (MEG) and magnetic resonance imaging (MRI) systems. The importance of combining MEG with MRI was realized early. The most important benefit of MEG over the widely available electroencephalography (EEG) is its ability to locate brain activity. To relate the location coordinates to individual anatomy, structural MRI is needed. In addition, structural MRI can help constrain the estimated source currents to the cortex, making the three-dimensional source volume a two-dimensional layer. Later, after the invention of functional MRI (fMRI), it was realized that the new kind of data could be used as additional information to help solve the MEG inverse problem. Thus, structural MRI benefits MEG data interpretation in three main ways: first, MEG localization results can be displayed on top of anatomical images; second, one obtains geometrical information for the analysis of the inverse problem, for example, in beamforming; third, a priori information regarding source locations will be more accurate. Since MEG and MRI are normally done separately, the two data sets have to be combined. This requires co-registration of the MEG and MRI coordinate systems.

An inversion method based on random sampling for real-time MEG neuroimaging

The MagnetoEncephaloGraphy (MEG) has gained great interest in neurorehabilitation training due to its high temporal resolution. The challenge is to localize the active regions of the brain in a fast and accurate way. In this paper we use an inversion method based on random spatial sampling to solve the real-time MEG inverse problem. Several numerical tests on synthetic but realistic data show that the method takes just a few hundredths of a second on a laptop to produce an accurate map of the electric activity inside the brain. Moreover, it requires very little memory storage. For these reasons the random sampling method is particularly attractive in real-time MEG applications.