A methodological framework for inverse-modeling of propagating cortical activity using MEG/EEG

Characterization of Second-Order Mixing Effects in Reconstructed Cross-Spectra of Random Neural Fields

Functional connectivity in electroencephalography (EEG) and magnetoencephalography (MEG) data is commonly assessed by using measures that are insensitive to instantaneously interacting sources and as such would not give rise to false positive interactions caused by instantaneous mixing of true source signals (first-order mixing). Recent studies, however, have drawn attention to the fact that such measures are still susceptible to instantaneous mixing from lagged sources (i.e. second-order mixing) and that this can lead to a large number of false positive interactions. In this study we relate first- and second-order mixing effects on the cross-spectra of reconstructed source activity to the properties of the resolution operators that are used for the reconstruction. We derive two identities that relate first- and second-order mixing effects to the transformation properties of measurement and source configurations and exploit them to establish several basic properties of signal mixing. First, we provide a characterization of the configurations that are maximally and minimally sensitive to second-order mixing. It turns out that second-order mixing effects are maximal when the measurement locations are far apart and the sources coincide with the measurement locations. Second, we provide a description of second-order mixing effects in the vicinity of the measurement locations in terms of the local geometry of the point-spread functions of the resolution operator. Third, we derive a version of Lagrange's identity for cross-talk functions that establishes the existence of a trade-off between the magnitude of first- and second-order mixing effects. It also shows that, whereas the magnitude of first-order mixing is determined by the inner product of cross-talk functions, the magnitude of second-order mixing is determined by a generalized cross-product of cross-talk functions (the wedge product) which leads to an intuitive geometric understanding of the trade-off. All results are derived within the general framework of random neural fields on cortical manifolds.

CiftiStorm pipeline: facilitating reproducible EEG/MEG source connectomics

We present CiftiStorm, an electrophysiological source imaging (ESI) pipeline incorporating recently developed methods to improve forward and inverse solutions. The CiftiStorm pipeline produces Human Connectome Project (HCP) and megconnectome-compliant outputs from dataset inputs with varying degrees of spatial resolution. The input data can range from low-sensor-density electroencephalogram (EEG) or magnetoencephalogram (MEG) recordings without structural magnetic resonance imaging (sMRI) to high-density EEG/MEG recordings with an HCP multimodal sMRI compliant protocol. CiftiStorm introduces a numerical quality control of the lead field and geometrical corrections to the head and source models for forward modeling. For the inverse modeling, we present a Bayesian estimation of the cross-spectrum of sources based on multiple priors. We facilitate ESI in the T1w/FSAverage32k high-resolution space obtained from individual sMRI. We validate this feature by comparing CiftiStorm outputs for EEG and MRI data from the Cuban Human Brain Mapping Project (CHBMP) acquired with technologies a decade before the HCP MEG and MRI standardized dataset.

Minimizing the distortions in electrophysiological source imaging of cortical oscillatory activity via Spectral Structured Sparse Bayesian Learning

Oscillatory processes at all spatial scales and on all frequencies underpin brain function. Electrophysiological Source Imaging (ESI) is the data-driven brain imaging modality that provides the inverse solutions to the source processes of the EEG, MEG, or ECoG data. This study aimed to carry out an ESI of the source cross-spectrum while controlling common distortions of the estimates. As with all ESI-related problems under realistic settings, the main obstacle we faced is a severely ill-conditioned and high-dimensional inverse problem. Therefore, we opted for Bayesian inverse solutions that posited a priori probabilities on the source process. Indeed, rigorously specifying both the likelihoods and a priori probabilities of the problem leads to the proper Bayesian inverse problem of cross-spectral matrices. These inverse solutions are our formal definition for cross-spectral ESI (cESI), which requires a priori of the source cross-spectrum to counter the severe ill-condition and high-dimensionality of matrices. However, inverse solutions for this problem were NP-hard to tackle or approximated within iterations with bad-conditioned matrices in the standard ESI setup. We introduce cESI with a joint a priori probability upon the source cross-spectrum to avoid these problems. cESI inverse solutions are low-dimensional ones for the set of random vector instances and not random matrices. We achieved cESI inverse solutions through the variational approximations via our Spectral Structured Sparse Bayesian Learning (ssSBL) algorithm https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning. We compared low-density EEG (10-20 system) ssSBL inverse solutions with reference cESIs for two experiments: (a) high-density MEG that were used to simulate EEG and (b) high-density macaque ECoG that were recorded simultaneously with EEG. The ssSBL resulted in two orders of magnitude with less distortion than the state-of-the-art ESI methods. Our cESI toolbox, including the ssSBL method, is available at https://github.com/CCC-members/BC-VARETA_Toolbox.

Enhancing oscillations in intracranial electrophysiological recordings with data-driven spatial filters

In invasive electrophysiological recordings, a variety of neural oscillations can be detected across the cortex, with overlap in space and time. This overlap complicates measurement of neural oscillations using standard referencing schemes, like common average or bipolar referencing. Here, we illustrate the effects of spatial mixing on measuring neural oscillations in invasive electrophysiological recordings and demonstrate the benefits of using data-driven referencing schemes in order to improve measurement of neural oscillations. We discuss referencing as the application of a spatial filter. Spatio-spectral decomposition is used to estimate data-driven spatial filters, a computationally fast method which specifically enhances signal-to-noise ratio for oscillations in a frequency band of interest. We show that application of these data-driven spatial filters has benefits for data exploration, investigation of temporal dynamics and assessment of peak frequencies of neural oscillations. We demonstrate multiple use cases, exploring between-participant variability in presence of oscillations, spatial spread and waveform shape of different rhythms as well as narrowband noise removal with the aid of spatial filters. We find high between-participant variability in the presence of neural oscillations, a large variation in spatial spread of individual rhythms and many non-sinusoidal rhythms across the cortex. Improved measurement of cortical rhythms will yield better conditions for establishing links between cortical activity and behavior, as well as bridging scales between the invasive intracranial measurements and noninvasive macroscale scalp measurements.

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

Electroencephalography/Magnetoencephalography (EEG/MEG) source localization involves the estimation of neural activity inside the brain volume that underlies the EEG/MEG measures observed at the sensor array. In this paper, we consider a Bayesian finite spatial mixture model for source reconstruction and implement Ant Colony System (ACS) optimization coupled with Iterated Conditional Modes (ICM) for computing estimates of the neural source activity. Our approach is evaluated using simulation studies and a real data application in which we implement a nonparametric bootstrap for interval estimation. We demonstrate improved performance of the ACS-ICM algorithm as compared to existing methodology for the same spatiotemporal model.