Dopamine and deep brain stimulation accelerate the neural dynamics of volitional action in Parkinson's disease.

The ability to initiate volitional action is fundamental to human behaviour. Loss of dopaminergic neurons in Parkinson's disease is associated with impaired action initiation, also termed akinesia. Both dopamine and subthalamic deep brain stimulation (DBS) can alleviate akinesia, but the underlying mechanisms are unknown. An important question is whether dopamine and DBS facilitate de novo build-up of neural dynamics for motor execution or accelerate existing cortical movement initiation signals through shared modulatory circuit effects. Answering these questions can provide the foundation for new closed-loop neurotherapies with adaptive DBS, but the objectification of neural processing delays prior to performance of volitional action remains a significant challenge. To overcome this challenge, we studied readiness potentials and trained brain signal decoders on invasive neurophysiology signals in 25 DBS patients (12 female) with Parkinson's disease during performance of self-initiated movements. Combined sensorimotor cortex electrocorticography (ECoG) and subthalamic local field potential (LFP) recordings were performed OFF therapy (N = 22), ON dopaminergic medication (N = 18) and ON subthalamic deep brain stimulation (N = 8). This allowed us to compare their therapeutic effects on neural latencies between the earliest cortical representation of movement intention as decoded by linear discriminant analysis classifiers and onset of muscle activation recorded with electromyography (EMG). In the hypodopaminergic OFF state, we observed long latencies between motor intention and motor execution for readiness potentials and machine learning classifications. Both, dopamine and DBS significantly shortened these latencies, hinting towards a shared therapeutic mechanism for alleviation of akinesia. To investigate this further, we analysed directional cortico-subthalamic oscillatory communication with multivariate granger causality. Strikingly, we found that both therapies independently shifted cortico-subthalamic oscillatory information flow from antikinetic beta (13-35 Hz) to prokinetic theta (4-10 Hz) rhythms, which was correlated with latencies in motor execution. Our study reveals a shared brain network modulation pattern of dopamine and DBS that may underlie the acceleration of neural dynamics for augmentation of movement initiation in Parkinson's disease. Instead of producing or increasing preparatory brain signals, both therapies modulate oscillatory communication. These insights provide a link between the pathophysiology of akinesia and its' therapeutic alleviation with oscillatory network changes in other non-motor and motor domains, e.g. related to hyperkinesia or effort and reward perception. In the future, our study may inspire the development of clinical brain computer interfaces based on brain signal decoders to provide temporally precise support for action initiation in patients with brain disorders.

Identifying good practices for detecting inter-regional linear functional connectivity from EEG.

Aggregating voxel-level statistical dependencies between multivariate time series is an important intermediate step when characterising functional connectivity (FC) between larger brain regions. However, there are numerous ways in which voxel-level data can be aggregated into inter-regional FC, and the advantages of each of these approaches are currently unclear. In this study we generate ground-truth data and compare the performances of various pipelines that estimate directed and undirected linear phase-to-phase FC between regions. We test the ability of several existing and novel FC analysis pipelines to identify the true regions within which connectivity was simulated. We test various inverse modelling algorithms, strategies to aggregate time series within regions, and connectivity metrics. Furthermore, we investigate the influence of the number of interactions, the signal-to-noise ratio, the noise mix, the interaction time delay, and the number of active sources per region on the ability of detecting phase-to-phase FC. Throughout all simulated scenarios, lowest performance is obtained with pipelines involving the absolute value of coherency. Further, the combination of dynamic imaging of coherent sources (DICS) beamforming with directed FC metrics that aggregate information across multiple frequencies leads to unsatisfactory results. Pipelines that show promising results with our simulated pseudo-EEG data involve the following steps: (1) Source projection using the linearly-constrained minimum variance (LCMV) beamformer. (2) Principal component analysis (PCA) using the same fixed number of components within every region. (3) Calculation of the multivariate interaction measure (MIM) for every region pair to assess undirected phase-to-phase FC, or calculation of time-reversed Granger Causality (TRGC) to assess directed phase-to-phase FC. We formulate recommendations based on these results that may increase the validity of future experimental connectivity studies. We further introduce the free ROIconnect plugin for the EEGLAB toolbox that includes the recommended methods and pipelines that are presented here. We show an exemplary application of the best performing pipeline to the analysis of EEG data recorded during motor imagery.

Alterations in rhythmic and non-rhythmic resting-state EEG activity and their link to cognition in older age.

While many structural and biochemical changes in the brain have previously been associated with older age, findings concerning functional properties of neuronal networks, as reflected in their electrophysiological signatures, remain rather controversial. These discrepancies might arise due to several reasons, including diverse factors determining general spectral slowing in the alpha frequency range as well as amplitude mixing between the rhythmic and non-rhythmic parameters. We used a large dataset (N = 1703, mean age 70) to comprehensively investigate age-related alterations in multiple EEG biomarkers taking into account rhythmic and non-rhythmic activity and their individual contributions to cognitive performance. While we found strong evidence for an individual alpha peak frequency (IAF) decline in older age, we did not observe a significant relationship between theta power and age while controlling for IAF. Not only did IAF decline with age, but it was also positively associated with interference resolution in a working memory task primarily in the right and left temporal lobes suggesting its functional role in information sampling. Critically, we did not detect a significant relationship between alpha power and age when controlling for the 1/f spectral slope, while the latter one showed age-related alterations. These findings thus suggest that the entanglement of IAF slowing and power in the theta frequency range, as well as 1/f slope and alpha power measures, might explain inconsistencies reported previously in the literature. Finally, despite the absence of age-related alterations, alpha power was negatively associated with the speed of processing in the right frontal lobe while 1/f slope showed no consistent relationship to cognitive performance. Our results thus demonstrate that multiple electrophysiological features, as well as their interplay, should be considered for the comprehensive assessment of association between age, neuronal activity, and cognitive performance.

A benchmark for prediction of psychiatric multimorbidity from resting EEG data in a large pediatric sample.

Psychiatric disorders are among the most common and debilitating illnesses across the lifespan and begin usually during childhood and adolescence, which emphasizes the importance of studying the developing brain. Most of the previous pediatric neuroimaging studies employed traditional univariate statistics on relatively small samples. Multivariate machine learning approaches have a great potential to overcome the limitations of these approaches. On the other hand, the vast majority of existing multivariate machine learning studies have focused on differentiating between children with an isolated psychiatric disorder and typically developing children. However, this line of research does not reflect the real-life situation as the majority of children with a clinical diagnosis have multiple psychiatric disorders (multimorbidity), and consequently, a clinician has the task to choose between different diagnoses and/or the combination of multiple diagnoses. Thus, the goal of the present benchmark is to predict psychiatric multimorbidity in children and adolescents. For this purpose, we implemented two kinds of machine learning benchmark challenges: The first challenge targets the prediction of the seven most prevalent DSM-V psychiatric diagnoses for the available data set, of which each individual can exhibit multiple ones concurrently (i.e. multi-task multi-label classification). Based on behavioral and cognitive measures, a second challenge focuses on predicting psychiatric symptom severity on a dimensional level (i.e. multiple regression task). For the present benchmark challenges, we will leverage existing and future data from the biobank of the Healthy Brain Network (HBN) initiative, which offers a unique large-sample dataset (N = 2042) that provides a wide array of different psychiatric developmental disorders and true hidden data sets. Due to limited real-world practicability and economic viability of MRI measurements, the present challenge will permit only resting state EEG data and demographic information to derive predictive models. We believe that a community driven effort to derive predictive markers from these data using advanced machine learning algorithms can help to improve the diagnosis of psychiatric developmental disorders.

Empirical Bayesian localization of event-related time-frequency neural activity dynamics.

Accurate reconstruction of the spatio-temporal dynamics of event-related cortical oscillations across human brain regions is an important problem in functional brain imaging and human cognitive neuroscience with magnetoencephalography (MEG) and electroencephalography (EEG). The problem is challenging not only in terms of localization of complex source configurations from sensor measurements with unknown noise and interference but also for reconstruction of transient event-related time-frequency dynamics of cortical oscillations. We recently proposed a robust empirical Bayesian algorithm for simultaneous reconstruction of complex brain source activity and noise covariance, in the context of evoked and resting-state data. In this paper, we expand upon this empirical Bayesian framework for optimal reconstruction of event-related time-frequency dynamics of regional cortical oscillations, referred to as time-frequency Champagne (TFC). This framework enables imaging of five-dimensional (space, time, and frequency) event-related brain activity from M/EEG data, and can be viewed as a time-frequency optimized adaptive Bayesian beamformer. We evaluate TFC in both simulations and several real datasets, with comparisons to benchmark standards - variants of time-frequency optimized adaptive beamformers (TFBF) as well as the sLORETA algorithm. In simulations, we demonstrate several advantages in estimating time-frequency cortical oscillatory dynamics compared to benchmarks. With real MEG data, we demonstrate across many datasets that the proposed approach is robust to highly correlated brain activity and low SNR data, and is able to accurately reconstruct cortical dynamics with data from just a few epochs.

Temporal Signatures of Criticality in Human Cortical Excitability as Probed by Early Somatosensory Responses.

Brain responses vary considerably from moment to moment, even to identical sensory stimuli. This has been attributed to changes in instantaneous neuronal states determining the system's excitability. Yet the spatiotemporal organization of these dynamics remains poorly understood. Here we test whether variability in stimulus-evoked activity can be interpreted within the framework of criticality, which postulates dynamics of neural systems to be tuned toward the phase transition between stability and instability as is reflected in scale-free fluctuations in spontaneous neural activity. Using a novel noninvasive approach in 33 male human participants, we tracked instantaneous cortical excitability by inferring the magnitude of excitatory postsynaptic currents from the N20 component of the somatosensory evoked potential. Fluctuations of cortical excitability demonstrated long-range temporal dependencies decaying according to a power law across trials, a hallmark of systems at critical states. As these dynamics covaried with changes in prestimulus oscillatory activity in the alpha band (8-13 Hz), we establish a mechanistic link between ongoing and evoked activity through cortical excitability and argue that the co-emergence of common temporal power laws may indeed originate from neural networks poised close to a critical state. In contrast, no signatures of criticality were found in subcortical or peripheral nerve activity. Thus, criticality may represent a parsimonious organizing principle of variability in stimulus-related brain processes on a cortical level, possibly reflecting a delicate equilibrium between robustness and flexibility of neural responses to external stimuli.SIGNIFICANCE STATEMENT Variability of neural responses in primary sensory areas is puzzling, as it is detrimental to the exact mapping between stimulus features and neural activity. However, such variability can be beneficial for information processing in neural networks if it is of a specific nature, namely, if dynamics are poised at a so-called critical state characterized by a scale-free spatiotemporal structure. Here, we demonstrate the existence of a link between signatures of criticality in ongoing and evoked activity through cortical excitability, which fills the long-standing gap between two major directions of research on neural variability: the impact of instantaneous brain states on stimulus processing on the one hand and the scale-free organization of spatiotemporal network dynamics of spontaneous activity on the other.

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm.

Robust estimation of the number, location, and activity of multiple correlated brain sources has long been a challenging task in electromagnetic brain imaging from M/EEG data, one that is significantly impacted by interference from spontaneous brain activity, sensor noise, and other sources of artifacts. Recently, we introduced the Champagne algorithm, a novel Bayesian inference algorithm that has shown tremendous success in M/EEG source reconstruction. Inherent to Champagne and most other related Bayesian reconstruction algorithms is the assumption that the noise covariance in sensor data can be estimated from "baseline" or "control" measurements. However, in many scenarios, such baseline data is not available, or is unreliable, and it is unclear how best to estimate the noise covariance. In this technical note, we propose several robust methods to estimate the contributions to sensors from noise arising from outside the brain without the need for additional baseline measurements. The incorporation of these methods for diagonal noise covariance estimation improves the robust reconstruction of complex brain source activity under high levels of noise and interference, while maintaining the performance features of Champagne. Specifically, we show that the resulting algorithm, Champagne with noise learning, is quite robust to initialization and is computationally efficient. In simulations, performance of the proposed noise learning algorithm is consistently superior to Champagne without noise learning. We also demonstrate that, even without the use of any baseline data, Champagne with noise learning is able to reconstruct complex brain activity with just a few trials or even a single trial, demonstrating significant improvements in source reconstruction for electromagnetic brain imaging.

Unification of sparse Bayesian learning algorithms for electromagnetic brain imaging with the majorization minimization framework.

Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms under the majorization-minimization (MM) framework. This unification perspective not only provides a useful theoretical framework for comparing different algorithms in terms of their convergence behavior, but also provides a principled recipe for constructing novel algorithms with specific properties by designing appropriate bounds of the Bayesian marginal likelihood function. Second, building on the MM principle, we propose a novel method called LowSNR-BSI that achieves favorable source reconstruction performance in low signal-to-noise-ratio (SNR) settings. Third, precise knowledge of the noise level is a crucial requirement for accurate source reconstruction. Here we present a novel principled technique to accurately learn the noise variance from the data either jointly within the source reconstruction procedure or using one of two proposed cross-validation strategies. Empirically, we could show that the monotonous convergence behavior predicted from MM theory is confirmed in numerical experiments. Using simulations, we further demonstrate the advantage of LowSNR-BSI over conventional SBL in low-SNR regimes, and the advantage of learned noise levels over estimates derived from baseline data. To demonstrate the usefulness of our novel approach, we show neurophysiologically plausible source reconstructions on averaged auditory evoked potential data.

Machine Learning for Health: Algorithm Auditing & Quality Control.

Developers proposing new machine learning for health (ML4H) tools often pledge to match or even surpass the performance of existing tools, yet the reality is usually more complicated. Reliable deployment of ML4H to the real world is challenging as examples from diabetic retinopathy or Covid-19 screening show. We envision an integrated framework of algorithm auditing and quality control that provides a path towards the effective and reliable application of ML systems in healthcare. In this editorial, we give a summary of ongoing work towards that vision and announce a call for participation to the special issue  Machine Learning for Health: Algorithm Auditing & Quality Control in this journal to advance the practice of ML4H auditing.

Functional connectivity of EEG is subject-specific, associated with phenotype, and different from fMRI.

A variety of psychiatric, behavioral and cognitive phenotypes have been linked to brain ''functional connectivity'' -- the pattern of correlation observed between different brain regions. Most commonly assessed using functional magnetic resonance imaging (fMRI), here, we investigate the connectivity-phenotype associations with functional connectivity measured with electroencephalography (EEG), using phase-coupling. We analyzed data from the publicly available Healthy Brain Network Biobank. This database compiles a growing sample of children and adolescents, currently encompassing 1657 individuals. Among a variety of assessment instruments we focus on ten phenotypic and additional demographic measures that capture most of the variance in this sample. The largest effect sizes are found for age and sex for both fMRI and EEG. We replicate previous findings of an association of Intelligence Quotient (IQ) and Attention Deficit Hyperactivity Disorder (ADHD) with the pattern of fMRI functional connectivity. We also find an association with socioeconomic status, anxiety and the Child Behavior Checklist Score. For EEG we find a significant connectivity-phenotype relationship with IQ. The actual spatial patterns of functional connectivity are quite different between fMRI and source-space EEG. However, within EEG we observe clusters of functional connectivity that are consistent across frequency bands. Additionally we analyzed reproducibility of functional connectivity. We compare connectivity obtained with different tasks, including resting state, a video and a visual flicker task. For both EEG and fMRI the variation between tasks was smaller than the variability observed between subjects. We also found an increase of reliability with increasing frequency of the EEG, and increased sampling duration. We conclude that, while the patterns of functional connectivity are distinct between fMRI and phase-coupling of EEG, they are nonetheless similar in their robustness to the task, and similar in that idiosyncratic patterns of connectivity predict individual phenotypes.

A Simulation Framework for Benchmarking EEG-Based Brain Connectivity Estimation Methodologies.

Due to its high temporal resolution, electroencephalography (EEG) is widely used to study functional and effective brain connectivity. Yet, there is currently a mismatch between the vastness of studies conducted and the degree to which the employed analyses are theoretically understood and empirically validated. We here provide a simulation framework that enables researchers to test their analysis pipelines on realistic pseudo-EEG data. We construct a minimal example of brain interaction, which we propose as a benchmark for assessing a methodology's general eligibility for EEG-based connectivity estimation. We envision that this benchmark be extended in a collaborative effort to validate methods in more complex scenarios. Quantitative metrics are defined to assess a method's performance in terms of source localization, connectivity detection and directionality estimation. All data and code needed for generating pseudo-EEG data, conducting source reconstruction and connectivity estimation using baseline methods from the literature, evaluating performance metrics, as well as plotting results, are made publicly available. While this article covers only EEG modeling, we will also provide a magnetoencephalography version of our framework online.

Quantifying the Effect of Demixing Approaches 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 artifactual 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 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 to 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 beamforming and 'Exact' low-resolution tomography (eLORETA). In source space, directed connectivity was estimated using multi-variate Granger causality and time-reversed Granger causality, and compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance.

Elucidating relations between fMRI, ECoG, and EEG through a common natural stimulus.

Human brain mapping relies heavily on fMRI, ECoG and EEG, which capture different physiological signals. Relationships between these signals have been established in the context of specific tasks or during resting state, often using spatially confined concurrent recordings in animals. But it is not certain whether these correlations generalize to other contexts relevant for human cognitive neuroscience. Here, we address the case of complex naturalistic stimuli and ask two basic questions. First, how reliable are the responses evoked by a naturalistic audio-visual stimulus in each of these imaging methods, and second, how similar are stimulus-related responses across methods? To this end, we investigated a wide range of brain regions and frequency bands. We presented the same movie clip twice to three different cohorts of subjects (NEEG = 45, NfMRI = 11, NECoG = 5) and assessed stimulus-driven correlations across viewings and between imaging methods, thereby ruling out task-irrelevant confounds. All three imaging methods had similar repeat-reliability across viewings when fMRI and EEG data were averaged across subjects, highlighting the potential to achieve large signal-to-noise ratio by leveraging large sample sizes. The fMRI signal correlated positively with high-frequency ECoG power across multiple task-related cortical structures but positively with low-frequency EEG and ECoG power. In contrast to previous studies, these correlations were as strong for low-frequency as for high frequency ECoG. We also observed links between fMRI and infra-slow EEG voltage fluctuations. These results extend previous findings to the case of natural stimulus processing.

Consistency of EEG source localization and connectivity estimates.

As the EEG inverse problem does not have a unique solution, the sources reconstructed from EEG and their connectivity properties depend on forward and inverse modeling parameters such as the choice of an anatomical template and electrical model, prior assumptions on the sources, and further implementational details. In order to use source connectivity analysis as a reliable research tool, there is a need for stability across a wider range of standard estimation routines. Using resting state EEG recordings of N=65 participants acquired within two studies, we present the first comprehensive assessment of the consistency of EEG source localization and functional/effective connectivity metrics across two anatomical templates (ICBM152 and Colin27), three electrical models (BEM, FEM and spherical harmonics expansions), three inverse methods (WMNE, eLORETA and LCMV), and three software implementations (Brainstorm, Fieldtrip and our own toolbox). Source localizations were found to be more stable across reconstruction pipelines than subsequent estimations of functional connectivity, while effective connectivity estimates where the least consistent. All results were relatively unaffected by the choice of the electrical head model, while the choice of the inverse method and source imaging package induced a considerable variability. In particular, a relatively strong difference was found between LCMV beamformer solutions on one hand and eLORETA/WMNE distributed inverse solutions on the other hand. We also observed a gradual decrease of consistency when results are compared between studies, within individual participants, and between individual participants. In order to provide reliable findings in the face of the observed variability, additional simulations involving interacting brain sources are required. Meanwhile, we encourage verification of the obtained results using more than one source imaging procedure.

The New York Head-A precise standardized volume conductor model for EEG source localization and tES targeting.

In source localization of electroencephalograpic (EEG) signals, as well as in targeted transcranial electric current stimulation (tES), a volume conductor model is required to describe the flow of electric currents in the head. Boundary element models (BEM) can be readily computed to represent major tissue compartments, but cannot encode detailed anatomical information within compartments. Finite element models (FEM) can capture more tissue types and intricate anatomical structures, but with the higher precision also comes the need for semi-automated segmentation, and a higher computational cost. In either case, adjusting to the individual human anatomy requires costly magnetic resonance imaging (MRI), and thus head modeling is often based on the anatomy of an 'arbitrary' individual (e.g. Colin27). Additionally, existing reference models for the human head often do not include the cerebro-spinal fluid (CSF), and their field of view excludes portions of the head and neck-two factors that demonstrably affect current-flow patterns. Here we present a highly detailed FEM, which we call ICBM-NY, or "New York Head". It is based on the ICBM152 anatomical template (a non-linear average of the MRI of 152 adult human brains) defined in MNI coordinates, for which we extended the field of view to the neck and performed a detailed segmentation of six tissue types (scalp, skull, CSF, gray matter, white matter, air cavities) at 0.5mm(3) resolution. The model was solved for 231 electrode locations. To evaluate its performance, additional FEMs and BEMs were constructed for four individual subjects. Each of the four individual FEMs (regarded as the 'ground truth') is compared to its BEM counterpart, the ICBM-NY, a BEM of the ICBM anatomy, an 'individualized' BEM of the ICBM anatomy warped to the individual head surface, and FEMs of the other individuals. Performance is measured in terms of EEG source localization and tES targeting errors. Results show that the ICBM-NY outperforms FEMs of mismatched individual anatomies as well as the BEM of the ICBM anatomy according to both criteria. We therefore propose the New York Head as a new standard head model to be used in future EEG and tES studies whenever an individual MRI is not available. We release all model data online at neuralengr.com/nyhead/ to facilitate broad adoption.

Identifying Granger causal relationships between neural power dynamics and variables of interest.

Power modulations of oscillations in electro- and magnetoencephalographic (EEG/MEG) signals have been linked to a wide range of brain functions. To date, most of the evidence is obtained by correlating bandpower fluctuations to specific target variables such as reaction times or task ratings, while the causal links between oscillatory activity and behavior remain less clear. Here, we propose to identify causal relationships by the statistical concept of Granger causality, and we investigate which methods are bests suited to reveal Granger causal links between the power of brain oscillations and experimental variables. As an alternative to testing such causal links on the sensor level, we propose to linearly combine the information contained in each sensor in order to create virtual channels, corresponding to estimates of underlying brain oscillations, the Granger-causal relations of which may be assessed. Such linear combinations of sensor can be given by source separation methods such as, for example, Independent Component Analysis (ICA) or by the recently developed Source Power Correlation (SPoC) method. Here we compare Granger causal analysis on power dynamics obtained from i) sensor directly, ii) spatial filtering methods that do not optimize for Granger causality (ICA and SPoC), and iii) a method that directly optimizes spatial filters to extract sources the power dynamics of which maximally Granger causes a given target variable. We refer to this method as Granger Causal Power Analysis (GrangerCPA). Using both simulated and real EEG recordings, we find that computing Granger causality on channel-wise spectral power suffers from a poor signal-to-noise ratio due to volume conduction, while all three multivariate approaches alleviate this issue. In real EEG recordings from subjects performing self-paced foot movements, all three multivariate methods identify neural oscillations with motor-related patterns at a similar performance level. In an auditory perception task, the application of GrangerCPA reveals significant Granger-causal links between alpha oscillations and reaction times in more subjects compared to conventional methods.

Solving the EEG inverse problem based on space-time-frequency structured sparsity constraints.

We introduce STOUT (spatio-temporal unifying tomography), a novel method for the source analysis of electroencephalograpic (EEG) recordings, which is based on a physiologically-motivated source representation. Our method assumes that only a small number of brain sources are active throughout a measurement, where each of the sources exhibits focal (smooth but localized) characteristics in space, time and frequency. This structure is enforced through an expansion of the source current density into appropriate spatio-temporal basis functions in combination with sparsity constraints. This approach combines the main strengths of two existing methods, namely Sparse Basis Field Expansions (Haufe et al., 2011) and Time-Frequency Mixed-Norm Estimates (Gramfort et al., 2013). By adjusting the ratio between two regularization terms, STOUT is capable of trading temporal for spatial reconstruction accuracy and vice versa, depending on the requirements of specific analyses and the provided data. Due to allowing for non-stationary source activations, STOUT is particularly suited for the localization of event-related potentials (ERP) and other evoked brain activity. We demonstrate its performance on simulated ERP data for varying signal-to-noise ratios and numbers of active sources. Our analysis of the generators of visual and auditory evoked N200 potentials reveals that the most active sources originate in the temporal and occipital lobes, in line with the literature on sensory processing.

Dimensionality reduction for the analysis of brain oscillations.

Neuronal oscillations have been shown to be associated with perceptual, motor and cognitive brain operations. While complex spatio-temporal dynamics are a hallmark of neuronal oscillations, they also represent a formidable challenge for the proper extraction and quantification of oscillatory activity with non-invasive recording techniques such as EEG and MEG. In order to facilitate the study of neuronal oscillations we present a general-purpose pre-processing approach, which can be applied for a wide range of analyses including but not restricted to inverse modeling and multivariate single-trial classification. The idea is to use dimensionality reduction with spatio-spectral decomposition (SSD) instead of the commonly and almost exclusively used principal component analysis (PCA). The key advantage of SSD lies in selecting components explaining oscillations-related variance instead of just any variance as in the case of PCA. For the validation of SSD pre-processing we performed extensive simulations with different inverse modeling algorithms and signal-to-noise ratios. In all these simulations SSD invariably outperformed PCA often by a large margin. Moreover, using a database of multichannel EEG recordings from 80 subjects we show that pre-processing with SSD significantly increases the performance of single-trial classification of imagined movements, compared to the classification with PCA pre-processing or without any dimensionality reduction. Our simulations and analysis of real EEG experiments show that, while not being supervised, the SSD algorithm is capable of extracting components primarily relating to the signal of interest often using as little as 20% of the data variance, instead of > 90% variance as in case of PCA. Given its ease of use, absence of supervision, and capability to efficiently reduce the dimensionality of multivariate EEG/MEG data, we advocate the application of SSD pre-processing for the analysis of spontaneous and induced neuronal oscillations in normal subjects and patients.

The effect of linear mixing in the EEG on Hurst exponent estimation.

Although the long-range temporal correlation (LRTC) of the amplitude fluctuations of neuronal EEG/MEG oscillations is widely acknowledged, the majority of studies to date have been performed in sensor space, disregarding the mixing effects implied by volume conduction and confounding noise. While the effect of mixing on the evaluation of evoked responses and connectivity measures has been extensively studied, there are, to date, no studies reporting on the differences in the values of the estimated Hurst exponents when moving between sensor and source space representations of the multivariate data or on the effect of noise. Such differences, if not duly acknowledged, may lead to erroneous data interpretations. We show in simulations and in theory that measuring Hurst exponents in sensor space may lead to an incomplete picture of the LRTC properties of the underlying data and that noise may significantly bias the estimate of the Hurst exponent of the underlying signal. Moreover, these predictions are confirmed in real data, where we analyze the amplitude dynamics of neuronal oscillations in the resting state from EEG data. By moving either to an independent components representation or to a source representation which maximizes the signal to noise ratio in the alpha frequency range, we observe greater variance, skewness and kurtosis over measured Hurst exponents than in sensor space. We confirm the suitability of conventional source separation methodology by introducing a novel algorithm HeMax which obtains a source maximizing the Hurst exponent in the amplitude dynamics of narrow band oscillations. Our findings imply that the long-range correlative properties of the EEG should be studied in source space, in such a way that the SNR is maximized, or at least with spatial decomposition techniques approximating source activities, rather than in sensor space.

On the interpretation of weight vectors of linear models in multivariate neuroimaging.

The increase in spatiotemporal resolution of neuroimaging devices is accompanied by a trend towards more powerful multivariate analysis methods. Often it is desired to interpret the outcome of these methods with respect to the cognitive processes under study. Here we discuss which methods allow for such interpretations, and provide guidelines for choosing an appropriate analysis for a given experimental goal: For a surgeon who needs to decide where to remove brain tissue it is most important to determine the origin of cognitive functions and associated neural processes. In contrast, when communicating with paralyzed or comatose patients via brain-computer interfaces, it is most important to accurately extract the neural processes specific to a certain mental state. These equally important but complementary objectives require different analysis methods. Determining the origin of neural processes in time or space from the parameters of a data-driven model requires what we call a forward model of the data; such a model explains how the measured data was generated from the neural sources. Examples are general linear models (GLMs). Methods for the extraction of neural information from data can be considered as backward models, as they attempt to reverse the data generating process. Examples are multivariate classifiers. Here we demonstrate that the parameters of forward models are neurophysiologically interpretable in the sense that significant nonzero weights are only observed at channels the activity of which is related to the brain process under study. In contrast, the interpretation of backward model parameters can lead to wrong conclusions regarding the spatial or temporal origin of the neural signals of interest, since significant nonzero weights may also be observed at channels the activity of which is statistically independent of the brain process under study. As a remedy for the linear case, we propose a procedure for transforming backward models into forward models. This procedure enables the neurophysiological interpretation of the parameters of linear backward models. We hope that this work raises awareness for an often encountered problem and provides a theoretical basis for conducting better interpretable multivariate neuroimaging analyses.