Anzolin, A. | Search bioRxiv

bioRxiv2023

Measuring Connectivity in Linear Multivariate Processes with Penalized Regression Techniques

The evaluation of time and frequency domain measures of coupling and causality relies on the parametric representation of linear multivariate processes. The study of temporal dependencies among time series is based on the identification of a Vector Autoregressive model. This procedure is pursued through the definition of a regression problem solved by means of Ordinary Least Squares (OLS) estimator. However, its accuracy is strongly influenced by the lack of data points and a stable solution is not always guaranteed. To overcome this issue, it is possible to use penalized regression techniques. The aim of this work is to compare the behavior of OLS with different penalized regression methods used for a connectivity analysis in different experimental conditions. Bias, accuracy in the reconstruction of network structure and computational time were used for this purpose. Different penalized regressions were tested by means of simulated data implementing different ground-truth networks under different amounts of data samples available. Then, the approaches were applied to real electroencephalographic signals (EEG) recorded from a healthy volunteer performing a motor imagery task. Penalized regressions outperform OLS in simulation settings when few data samples are available. The application on real EEG data showed how it is possible to use features extracted from brain networks for discriminating between two tasks even in conditions of data paucity. Penalized regression techniques can be used for brain connectivity estimation and can be exploited for the computation of all the connectivity estimators based on linearity assumption overcoming the limitations imposed by the classical OLS.

bioengineering↗

bioRxiv2018

Effect of head volume conduction on directed connectivity estimated between reconstructed EEG sources

Electrical activity recorded on the scalp using electroencephalography (EEG) results from the mixing of signals originating from different regions of the brain as well as from artefactual sources. In order to investigate the role of distinct brain areas in a given experiment, the signal recorded on the sensors is typically projected back into the brain (source reconstruction) using algorithms that address the so-called EEG \"inverse problem\". Once that the activity of sources located inside of the brain has been reconstructed, it is often desirable to study the statistical dependencies among them, in particular to quantify directional dynamical interactions between brain areas. Unfortunately, even when performing source reconstruction, the superposition of signals that is due to the propagation of activity from sources to sensors cannot be completely undone, resulting in potentially biased estimates of directional functional connectivity. Here we perform a set of simulations involving interacting sources, and quantify source connectivity estimation performance as a function of the location of the sources, their distance to each other, the noise level, the source reconstruction algorithm, and the connectivity estimator. The generated source activity was projected onto the scalp and projected back to the cortical level using two source reconstruction algorithms, Linearly Constrained Minimum Variance (LCMV) beamforming and Exact Low-resolution Tomography (eLORETA). In source space, directed connectivity was estimated using Multi-Variate Granger Causality (MVGC), Time-Reversed Granger Causality (TRGC) and Partial Directed Coherence (PDC), and the estimated connectivity was compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance.

neuroscience↗