SignificanceSubcortical structures play a critical role in brain functions such as sensory perception, memory, emotion, and consciousness. There are limited options for assessing neuronal dynamics within subcortical structures in humans. Magnetoencephalography and electroencephalography can measure electromagnetic fields generated by subcortical activity. But localizing the sources of these fields is very difficult, because the fields generated by subcortical structures are small and cannot be distinguished from distributed cortical activity. We show that cortical and subcortical fields can be distinguished if the cortical sources are sparse. We then describe an algorithm that uses sparsity in a hierarchical fashion to jointly localize cortical and subcortical sources. Our work offers alternative perspectives and tools for assessing subcortical brain dynamics in humans.

The sleep onset process (SOP) is a dynamic process correlated with a multitude of behavioral and physiological markers. A principled analysis of the SOP can serve as a foundation for answering questions of fundamental importance in basic neuroscience and sleep medicine. Unfortunately, current methods for analyzing the SOP fail to account for the overwhelming evidence that the wake/sleep transition is governed by continuous, dynamic physiological processes. Instead, current practices coarsely discretize sleep both in terms of state, where it is viewed as a binary (wake or sleep) process, and in time, where it is viewed as a single time point derived from subjectively scored stages in 30-second epochs, effectively eliminating SOP dynamics from the analysis. These methods also fail to integrate information from both behavioral and physiological data. It is thus imperative to resolve the mismatch between the physiological evidence and analysis methodologies. In this paper, we develop a statistically and physiologically principled dynamic framework and empirical SOP model, combining simultaneously-recorded physiological measurements with behavioral data from a novel breathing task requiring no arousing external sensory stimuli. We fit the model using data from healthy subjects, and estimate the instantaneous probability that a subject is awake during the SOP. The model successfully tracked physiological and behavioral dynamics for individual nights, and significantly outperformed the instantaneous transition models implicit in clinical definitions of sleep onset. Our framework also provides a principled means for cross-subject data alignment as a function of wake probability, allowing us to characterize and compare SOP dynamics across different populations. This analysis enabled us to quantitatively compare the EEG of subjects showing reduced alpha power with the remaining subjects at identical response probabilities. Thus, by incorporating both physiological and behavioral dynamics into our model framework, the dynamics of our analyses can finally match those observed during the SOP.

Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness.

Our approach provides substantial performance improvements over existing methods using computationally efficient algorithms that will facilitate practical applications in both neuroscience and medicine.