EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition.

Mediation analysis assesses whether an exposure directly produces changes in cognitive behavior or is influenced by intermediate "mediators". Electroencephalographic (EEG) spectral measurements have been previously used as effective mediators representing diverse aspects of brain function. However, it has been necessary to collapse EEG measures onto a single scalar using standard mediation methods. In this article, we overcome this limitation and examine EEG frequency-resolved functional connectivity measures as a mediator using the full EEG cross-spectral tensor (CST). Since CST samples do not exist in Euclidean space but in the Riemannian manifold of positive-definite tensors, we transform the problem, allowing for the use of classic multivariate statistics. Toward this end, we map the data from the original manifold space to the Euclidean tangent space, eliminating redundant information to conform to a "compressed CST." The resulting object is a matrix with rows corresponding to frequencies and columns to cross spectra between channels. We have developed a novel matrix mediation approach that leverages a nuclear norm regularization to determine the matrix-valued regression parameters. Furthermore, we introduced a global test for the overall CST mediation and a test to determine specific channels and frequencies driving the mediation. We validated the method through simulations and applied it to our well-studied 50+-year Barbados Nutrition Study dataset by comparing EEGs collected in school-age children (5-11 years) who were malnourished in the first year of life with those of healthy classmate controls. We hypothesized that the CST mediates the effect of malnutrition on cognitive performance. We can now explicitly pinpoint the frequencies (delta, theta, alpha, and beta bands) and regions (frontal, central, and occipital) in which functional connectivity was altered in previously malnourished children, an improvement to prior studies. Understanding the specific networks impacted by a history of postnatal malnutrition could pave the way for developing more targeted and personalized therapeutic interventions. Our methods offer a versatile framework applicable to mediation studies encompassing matrix and Hermitian 3D tensor mediators alongside scalar exposures and outcomes, facilitating comprehensive analyses across diverse research domains.

Automatic Detection of Fiducial Landmarks Toward the Development of an Application for Digitizing the Locations of EEG Electrodes: Occipital Structure Sensor-Based Work.

The reconstruction of electrophysiological sources within the brain is sensitive to the constructed head model, which depends on the positioning accuracy of anatomical landmarks known as fiducials. In this work, we propose an algorithm for the automatic detection of fiducial landmarks of EEG electrodes on the 3D human head model. Our proposal combines a dimensional reduction approach with a perspective projection from 3D to 2D object space; the eye and ear automatic detection in a 2D face image by two cascades of classifiers and geometric transformations to obtain 3D spatial coordinates of the landmarks and to generate the head coordinate system, This is accomplished by considering the characteristics of the scanner information. Capturing the 3D model of the head is done with Occipital Inc. ST01 structure sensor and the implementation of our algorithm was carried out on MATLAB R2018b using the Computer Vision Toolbox and the FieldTrip Toolbox. The experimental results were aimed at recursively exploring the efficacy of the facial feature detectors as a function of the projection angle; they show that robust results are obtained in terms of false acceptance rate. Our proposal is an initial step of an approach for the automatic digitization of electrode locations. The experimental results demonstrate that the proposed method detects anatomical facial landmarks automatically, accurately, and rapidly.