Finding electrophysiological sources of aging-related processes using penalized least squares with Modified Newton-Raphson algorithm

In this work, we evaluate the flexibility of a modified Newton-Raphson (MNR) algorithm for finding electrophysiological sources in both simulated and real data, and then apply it to different penalized models in order to compare the sources of the EEG theta rhythm in two groups of elderly subjects with different levels of declined physical performance. As a first goal, we propose the MNR algorithm for estimating general multiple penalized least squares (MPLS) models and show that it is capable to find solutions that are simultaneously sparse and smooth. This algorithm allowed to address known and novel models such as the Smooth Non-negative Garrote and the Non-negative Smooth LASSO. We test its ability to solve the EEG inverse problem with multiple penalties -using simulated data- in terms of localization error, blurring and visibility, as compared with traditional algorithms. As a second goal, we explore the electrophysiological sources of the theta activity extracted from resting-state EEG recorded in two groups of older adults, which belong to a longitudinal study to assess the relationship between measures of physical performance (gait speed) decline and normal cognition. The groups contained subjects with good and bad physical performance in the two evaluations (6 years apart). In accordance to clinical studies, we found differences in EEG theta sources for the two groups, specifically, subjects with declined physical performance presented decreased temporal sources while increased prefrontal sources that seem to reflect compensating mechanisms to ensure a stable walking