Bridging M/EEG Source Imaging and Independent Component Analysis Frameworks Using Biologically Inspired Sparsity Priors.

Electromagnetic source imaging (ESI) and independent component analysis (ICA) are two popular and apparently dissimilar frameworks for M/EEG analysis. This letter shows that the two frameworks can be linked by choosing biologically inspired source sparsity priors. We demonstrate that ESI carried out by the sparse Bayesian learning (SBL) algorithm yields source configurations composed of a few active regions that are also maximally independent from one another. In addition, we extend the standard SBL approach to source imaging in two important directions. First, we augment the generative model of M/EEG to include artifactual sources. Second, we modify SBL to allow for efficient model inversion with sequential data. We refer to this new algorithm as recursive SBL (RSBL), a source estimation filter with potential for online and offline imaging applications. We use simulated data to verify that RSBL can accurately estimate and demix cortical and artifactual sources under different noise conditions. Finally, we show that on real error-related EEG data, RSBL can yield single-trial source estimates in agreement with the experimental literature. Overall, by demonstrating that ESI can produce maximally independent sources while simultaneously localizing them in cortical space, we bridge the gap between the ESI and ICA frameworks for M/EEG analysis.

The open EEGLAB portal Interface: High-Performance computing with EEGLAB.

EEGLAB signal processing environment is currently the leading open-source software for processing electroencephalographic (EEG) data. The Neuroscience Gateway (NSG, nsgportal.org) is a web and API-based portal allowing users to easily run a variety of neuroscience-related software on high-performance computing (HPC) resources in the U.S. XSEDE network. We have reported recently (Delorme et al., 2019) on the Open EEGLAB Portal expansion of the free NSG services to allow the neuroscience community to build and run MATLAB pipelines using the EEGLAB tool environment. We are now releasing an EEGLAB plug-in, nsgportal, that interfaces EEGLAB with NSG directly from within EEGLAB running on MATLAB on any personal lab computer. The plug-in features a flexible MATLAB graphical user interface (GUI) that allows users to easily submit, interact with, and manage NSG jobs, and to retrieve and examine their results. Command line nsgportal tools supporting these GUI functionalities allow EEGLAB users and plug-in tool developers to build largely automated functions and workflows that include optional NSG job submission and processing. Here we present details on nsgportal implementation and documentation, provide user tutorials on example applications, and show sample test results comparing computation times using HPC versus laptop processing.

What Can Local Transfer Entropy Tell Us about Phase-Amplitude Coupling in Electrophysiological Signals?

Modulation of the amplitude of high-frequency cortical field activity locked to changes in the phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristic. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data. In both cases, we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information estimated phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis. The current work sets the foundations for further use of local transfer entropy for estimating PAC process dynamics, and extends and complements our previous work on using local mutual information to compute PAC (MIPAC).

Unraveling the spatiotemporal brain dynamics during a simulated reach-to-eat task.

The reach-to-eat task involves a sequence of action components including looking, reaching, grasping, and feeding. While cortical representations of individual action components have been mapped in human functional magnetic resonance imaging (fMRI) studies, little is known about the continuous spatiotemporal dynamics among these representations during the reach-to-eat task. In a periodic event-related fMRI experiment, subjects were scanned while they reached toward a food image, grasped the virtual food, and brought it to their mouth within each 16-s cycle. Fourier-based analysis of fMRI time series revealed periodic signals and noise distributed across the brain. Independent component analysis was used to remove periodic or aperiodic motion artifacts. Time-frequency analysis was used to analyze the temporal characteristics of periodic signals in each voxel. Circular statistics was then used to estimate mean phase angles of periodic signals and select voxels based on the distribution of phase angles. By sorting mean phase angles across regions, we were able to show the real-time spatiotemporal brain dynamics as continuous traveling waves over the cortical surface. The activation sequence consisted of approximately the following stages: (1) stimulus related activations in occipital and temporal cortices; (2) movement planning related activations in dorsal premotor and superior parietal cortices; (3) reaching related activations in primary sensorimotor cortex and supplementary motor area; (4) grasping related activations in postcentral gyrus and sulcus; (5) feeding related activations in orofacial areas. These results suggest that phase-encoded design and analysis can be used to unravel sequential activations among brain regions during a simulated reach-to-eat task.

Fast and robust Block-Sparse Bayesian learning for EEG source imaging.

We propose a new Sparse Bayesian Learning (SBL) algorithm that can deliver fast, block-sparse, and robust solutions to the EEG source imaging (ESI) problem in the presence of noisy measurements. Current implementations of the SBL framework are computationally expensive and typically handle fluctuations in the measurement noise using different heuristics that are unsuitable for real-time imaging applications. We address these shortcomings by decoupling the estimation of the sensor noise covariance and the sparsity profile of the sources, thereby yielding an efficient two-stage algorithm. In the first stage, we optimize a simplified non-sparse generative model to get an estimate of the sensor noise covariance and a good initialization of the group-sparsity profile of the sources. Sources obtained at this stage are equivalent to those estimated with the popular inverse method LORETA. In the second stage, we apply a fast SBL algorithm with the noise covariance fixed to the value obtained in the first stage to efficiently shrink to zero groups of sources that are irrelevant for explaining the EEG measurements. In addition, we derive an initialization to the first stage of the algorithm that is optimal in the least squares sense, which prevents delays due to suboptimal initial conditions. We validate our method on both simulated and real EEG data. Simulations show that the method is robust to measurement noise and performs well in real-time, with faster performance than two state of the art SBL solvers. On real error-related negativity EEG data, we obtain source images in agreement with the experimental literature. The method shows promise for real-time neuroimaging and brain-machine interface applications.

Validation of periodic fMRI signals in response to wearable tactile stimulation.

To map cortical representations of the body, we recently developed a wearable technology for automatic tactile stimulation in human functional magnetic resonance imaging (fMRI) experiments. In a two-condition block design experiment, air puffs were delivered to the face and hands periodically. Surface-based regions of interest (S-ROIs) were initially identified by thresholding a linear statistical measure of signal-to-noise ratio of periodic response. Across subjects, S-ROIs were found in the frontal, primary sensorimotor, posterior parietal, insular, temporal, cingulate, and occipital cortices. To validate and differentiate these S-ROIs, we develop a measure of temporal stability of response based on the assumption that a periodic stimulation evokes stable (low-variance) periodic fMRI signals throughout the entire scan. Toward this end, we apply time-frequency analysis to fMRI time series and use circular statistics to characterize the distribution of phase angles for data selection. We then assess the temporal variability of a periodic signal by measuring the path length of its trajectory in the complex plane. Both within and outside the primary sensorimotor cortex, S-ROIs with high temporal variability and deviant phase angles are rejected. A surface-based probabilistic group-average map is constructed for spatial screening of S-ROIs with low to moderate temporal variability in non-sensorimotor regions. Areas commonly activated across subjects are also summarized in the group-average map. In summary, this study demonstrates that analyzing temporal characteristics of the entire fMRI time series is essential for second-level selection and interpretation of S-ROIs initially defined by an overall linear statistical measure.

Mapping Generative Models onto a Network of Digital Spiking Neurons.

Stochastic neural networks such as Restricted Boltzmann Machines (RBMs) have been successfully used in applications ranging from speech recognition to image classification, and are particularly interesting because of their potential for generative tasks. Inference and learning in these algorithms use a Markov Chain Monte Carlo procedure called Gibbs sampling, where a logistic function forms the kernel of this sampler. On the other side of the spectrum, neuromorphic systems have shown great promise for low-power and parallelized cognitive computing, but lack well-suited applications and automation procedures. In this work, we propose a systematic method for bridging the RBM algorithm and digital neuromorphic systems, with a generative pattern completion task as proof of concept. For this, we first propose a method of producing the Gibbs sampler using bio-inspired digital noisy integrate-and-fire neurons. Next, we describe the process of mapping generative RBMs trained offline onto the IBM TrueNorth neurosynaptic processor-a low-power digital neuromorphic VLSI substrate. Mapping these algorithms onto neuromorphic hardware presents unique challenges in network connectivity and weight and bias quantization, which, in turn, require architectural and design strategies for the physical realization. Generative performance is analyzed to validate the neuromorphic requirements and to best select the neuron parameters for the model. Lastly, we describe a design automation procedure which achieves optimal resource usage, accounting for the novel hardware adaptations. This work represents the first implementation of generative RBM inference on a neuromorphic VLSI substrate.

Closed-loop brain-machine-body interfaces for noninvasive rehabilitation of movement disorders.

Traditional approaches for neurological rehabilitation of patients affected with movement disorders, such as Parkinson's disease (PD), dystonia, and essential tremor (ET) consist mainly of oral medication, physical therapy, and botulinum toxin injections. Recently, the more invasive method of deep brain stimulation (DBS) showed significant improvement of the physical symptoms associated with these disorders. In the past several years, the adoption of feedback control theory helped DBS protocols to take into account the progressive and dynamic nature of these neurological movement disorders that had largely been ignored so far. As a result, a more efficient and effective management of PD cardinal symptoms has emerged. In this paper, we review closed-loop systems for rehabilitation of movement disorders, focusing on PD, for which several invasive and noninvasive methods have been developed during the last decade, reducing the complications and side effects associated with traditional rehabilitation approaches and paving the way for tailored individual therapeutics. We then present a novel, transformative, noninvasive closed-loop framework based on force neurofeedback and discuss several future developments of closed-loop systems that might bring us closer to individualized solutions for neurological rehabilitation of movement disorders.

Basis selection for maximally independent EEG sources.

We suggest a solution to the following problem: "Given multichannel linear source mixture data Y, and an overcomplete dictionary, A, of source projections, ai, how can we construct a complete basis, A0, by selecting columns from A such that the sources X = A0(-1)Y are as statistically independent as possible from each other?". While conventional independent component analysis (ICA) methods learn the mixing matrix A0 from scratch given Y, we restrict ourselves to selecting basis vectors from a known overcomplete dictionary. We develop two methods based on modifications of the maximum likelihood equivalent of the Infomax approach and the reconstruction-ICA (RICA) algorithm. We show that on realistic synthetic electroencephalographic (EEG) data our algorithms can find the true sources in the case of a highly coherent dictionary while requiring relatively fewer data points compared to other algorithms. On real EEG data, our algorithms obtain higher mutual information reduction.

Comparison of averaging and regression techniques for estimating Event Related Potentials.

The traditional method of estimating an Event Related Potential (ERP) is to take the average of signal epochs time locked to a set of similar experimental events. This averaging method is useful as long as the experimental procedure can sufficiently isolate the brain or non-brain process of interest. However, if responses from multiple cognitive processes, time locked to multiple classes of closely spaced events, overlap in time with varying inter-event intervals, averaging will most likely fail to identify the individual response time courses. For this situation, we study estimation of responses to all recorded events in an experiment by a single model using standard linear regression (the rERP technique). Applied to data collected during a Rapid Serial Visual Presentation (RSVP) task, our analysis shows: (1) The rERP technique accounts for more variance in the data than averaging when individual event responses are highly overlapping; (2) the variance accounted for by the estimates is concentrated into a fewer ICA components than raw EEG channel signals.

Measure projection analysis: a probabilistic approach to EEG source comparison and multi-subject inference.

A crucial question for the analysis of multi-subject and/or multi-session electroencephalographic (EEG) data is how to combine information across multiple recordings from different subjects and/or sessions, each associated with its own set of source processes and scalp projections. Here we introduce a novel statistical method for characterizing the spatial consistency of EEG dynamics across a set of data records. Measure Projection Analysis (MPA) first finds voxels in a common template brain space at which a given dynamic measure is consistent across nearby source locations, then computes local-mean EEG measure values for this voxel subspace using a statistical model of source localization error and between-subject anatomical variation. Finally, clustering the mean measure voxel values in this locally consistent brain subspace finds brain spatial domains exhibiting distinguishable measure features and provides 3-D maps plus statistical significance estimates for each EEG measure of interest. Applied to sufficient high-quality data, the scalp projections of many maximally independent component (IC) processes contributing to recorded high-density EEG data closely match the projection of a single equivalent dipole located in or near brain cortex. We demonstrate the application of MPA to a multi-subject EEG study decomposed using independent component analysis (ICA), compare the results to k-means IC clustering in EEGLAB (sccn.ucsd.edu/eeglab), and use surrogate data to test MPA robustness. A Measure Projection Toolbox (MPT) plug-in for EEGLAB is available for download (sccn.ucsd.edu/wiki/MPT). Together, MPA and ICA allow use of EEG as a 3-D cortical imaging modality with near-cm scale spatial resolution.

Event-driven contrastive divergence for spiking neuromorphic systems.

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However, the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Visual recognition and inference using dynamic overcomplete sparse learning.

We present a hierarchical architecture and learning algorithm for visual recognition and other visual inference tasks such as imagination, reconstruction of occluded images, and expectation-driven segmentation. Using properties of biological vision for guidance, we posit a stochastic generative world model and from it develop a simplified world model (SWM) based on a tractable variational approximation that is designed to enforce sparse coding. Recent developments in computational methods for learning overcomplete representations (Lewicki & Sejnowski, 2000; Teh, Welling, Osindero, & Hinton, 2003) suggest that overcompleteness can be useful for visual tasks, and we use an overcomplete dictionary learning algorithm (Kreutz-Delgado, et al., 2003) as a preprocessing stage to produce accurate, sparse codings of images. Inference is performed by constructing a dynamic multilayer network with feedforward, feedback, and lateral connections, which is trained to approximate the SWM. Learning is done with a variant of the back-propagation-through-time algorithm, which encourages convergence to desired states within a fixed number of iterations. Vision tasks require large networks, and to make learning efficient, we take advantage of the sparsity of each layer to update only a small subset of elements in a large weight matrix at each iteration. Experiments on a set of rotated objects demonstrate various types of visual inference and show that increasing the degree of overcompleteness improves recognition performance in difficult scenes with occluded objects in clutter.

Frequency characterization of blood glucose dynamics.

Examples of the frequency range of blood glucose dynamics of normal subjects and subjects with diabetes are reported here, based on data from the literature. The frequency band edge was determined from suitable, frequently sampled blood glucose recordings using two methods: frequency domain estimation and signal reconstruction. The respective maximum acceptable sampling intervals, or Nyquist sampling periods (NSP), required to accurately represent blood glucose dynamics were calculated. Preliminary results based on the limited data available in the literature indicate that although blood glucose NSP values are higher in most diabetic subjects, values in some diabetic subjects are indistinguishable from those of normal subjects. High fidelity monitoring sufficient to follow the intrinsic blood glucose dynamics of all diabetic subjects requires a NSP of approximately 10 min, corresponding to a continuous frequency band edge of approximately 1 x 10(-3) Hz. This analysis provides key information for the design of clinical studies that include blood glucose dynamics and for the design of new glucose monitoring systems.

Dictionary learning algorithms for sparse representation.

Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations. Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error).