Minimum Norm Estimate Research Articles

Comparison of Machine Learning Techniques Based Brain Source Localization Using EEG Signals

The brain is the most complex organ of the human body with millions of connections and activations. The electromagnetic signals are generated inside the brain due to a mental or physical task performed. These signals excite a bunch of neurons within a particular lobe depending upon the nature of the task performed. To localize this activity, certain machine learning (ML) techniques in conjunction with a neuroimaging technique (M/EEG, fMRI, PET) are developed. Different ML techniques are provided in the literature for brain source localization. Among them, the most common are: minimum norm estimation (MNE), low resolution brain electromagnetic tomography (LORETA) and Bayesian framework based multiple sparse priors (MSP). In this research work, EEG is used as a neuroimaging technique. EEG data is synthetically generated at SNR=5dB. Afterwards, ML techniques are applied to estimate the active sources. Each dataset is run for multiple trials (>40). The performance is analyzed using free energy and localization error as performance indicators. Furthermore, MSP is applied with a variant number of patches to observe the impact of patches on source localization. It is observed that with an increased number of patches, the sources are localized with more precision and accuracy as expressed in terms of free energy and localization error, respectively. The patches optimization within the Bayesian Framework produces improved results in terms of free energy and localization error.

A novel approach of decoding EEG four-class motor imagery tasks via scout ESI and CNN

Objective. To develop and implement a novel approach which combines the technique of scout EEG source imaging (ESI) with convolutional neural network (CNN) for the classification of motor imagery (MI) tasks. Approach. The technique of ESI uses a boundary element method (BEM) and weighted minimum norm estimation (WMNE) to solve the EEG forward and inverse problems, respectively. Ten scouts are then created within the motor cortex to select the region of interest (ROI). We extract features from the time series of scouts using a Morlet wavelet approach. Lastly, CNN is employed for classifying MI tasks. Main results. The overall mean accuracy on the Physionet database reaches 94.5% and the individual accuracy of each task reaches 95.3%, 93.3%, 93.6%, 96% for the left fist, right fist, both fists and both feet, correspondingly, validated using ten-fold cross validation. We report an increase of up to 14.4% for overall classification compared with the competitive results from the state-of-the-art MI classification methods. Then, we add four new subjects to verify the validity of the method and the overall mean accuracy is 92.5%. Furthermore, the global classifier was adapted to single subjects improving the overall mean accuracy to 94.54%. Significance. The combination of scout ESI and CNN enhances BCI performance of decoding EEG four-class MI tasks.

A wrapped time-frequency combined selection in the source domain

The selection of time segment and frequency band always play a vital role in the decoding of Motor Imagery Tasks (MI-tasks), especially for the feature extraction of MI-Electroencephalographic (MI-EEG). The excavation of valuable and discriminative feature information needs to be based on the reliable time-frequency analysis, which is the foremost precondition for feature engineering. However, relying on the high temporal resolution of MI-EEG, traditional feature extraction methods can only conduct the time-frequency analysis according to the superficial neurophysiological rhythm of EEG in the sensor domain. And more detailed time-frequency characteristics could hardly be embodied in a few channels of MI-EEG signals, which leads to a coarse selection of time-frequency interval and the resulted lower decoding effect. Therefore, a neurophysiology-based technique is needed for performing more exact time-frequency analysis. Based on the advanced EEG Source Imaging, a Wrapped Time-Frequency combined Selection in the Source Domain, which is denoted as WTFS-SD, is proposed for decoding the MI-tasks by applying Weighted Minimum Norm Estimate and CSP based sub-band feature extraction in this paper. Abundant comparative experiments are conducted on the BCI2000 system dataset with six subjects, and the results show that the proposed methods can select subject-specific optimal frequency band and TOI, which yields the highest average classification rate of 93.14% by 9-fold cross-validation at the same chance level as well as a superior mean kappa coefficient of 0.8627 across all subjects compared to other prevalent methods. This study will enhance the decoding of complex MI-tasks and be helpful for the development of intelligent BCI system.

Transcranial magnetic stimulation-evoked potentials after the stimulation of the right-hemispheric homologue of Broca's area.

The combination of transcranial magnetic stimulation and electroencephalography can be applied to probe effective connectivity. Neurons are excited by magnetic pulses, which produce transcranial magnetic stimulation-evoked potentials that can be monitored with electroencephalography. Effective connectivity refers to causal connections in the brain; it describes how different brain areas communicate with each other. Broca's area is crucial for all phases of speech processing and is located in the frontotemporal region of the cortex. Only a few studies have investigated this region using transcranial magnetic stimulation-electroencephalography because of the large cranial muscles that are located over these areas, resulting in large artifacts covering the transcranial magnetic stimulation-evoked potentials. However, it is shown that this obstacle can be overcome with new artifact-removal tools. We used minimum-norm estimation to locate the sources of the neuronal signals in electroencephalography data after stimulating the right-hemispheric homologue of Broca's area in three right-handed subjects; it was shown that the spreading of brain activity might be different for different individuals and that the brain activity spread fast to the contralateral hemisphere.

Post-hoc Labeling of Arbitrary M/EEG Recordings for Data-Efficient Evaluation of Neural Decoding Methods.

Many cognitive, sensory and motor processes have correlates in oscillatory neural source activity, which is embedded as a subspace in the recorded brain signals. Decoding such processes from noisy magnetoencephalogram/electroencephalogram (M/EEG) signals usually requires data-driven analysis methods. The objective evaluation of such decoding algorithms on experimental raw signals, however, is a challenge: the amount of available M/EEG data typically is limited, labels can be unreliable, and raw signals often are contaminated with artifacts. To overcome some of these problems, simulation frameworks have been introduced which support the development of data-driven decoding algorithms and their benchmarking. For generating artificial brain signals, however, most of the existing frameworks make strong and partially unrealistic assumptions about brain activity. This limits the generalization of results observed in the simulation to real-world scenarios. In the present contribution, we show how to overcome several shortcomings of existing simulation frameworks. We propose a versatile alternative, which allows for an objective evaluation and benchmarking of novel decoding algorithms using real neural signals. It allows to generate comparatively large datasets with labels being deterministically recoverable from the arbitrary M/EEG recordings. A novel idea to generate these labels is central to this framework: we determine a subspace of the true M/EEG recordings and utilize it to derive novel labels. These labels contain realistic information about the oscillatory activity of some underlying neural sources. For two categories of subspace-defining methods, we showcase how such labels can be obtained—either by an exclusively data-driven approach (independent component analysis—ICA), or by a method exploiting additional anatomical constraints (minimum norm estimates—MNE). We term our framework post-hoc labeling of M/EEG recordings. To support the adoption of the framework by practitioners, we have exemplified its use by benchmarking three standard decoding methods—i.e., common spatial patterns (CSP), source power-comodulation (SPoC), and convolutional neural networks (ConvNets)—wrt. Varied dataset sizes, label noise, and label variability. Source code and data are made available to the reader for facilitating the application of our post-hoc labeling framework.

Quantitative Evaluation in Estimating Sources Underlying Brain Oscillations Using Current Source Density Methods and Beamformer Approaches.

Brain oscillations from EEG and MEG shed light on neurophysiological mechanisms of human behavior. However, to extract information on cortical processing, researchers have to rely on source localization methods that can be very broadly classified into current density estimates such as exact low-resolution brain electromagnetic tomography (eLORETA), minimum norm estimates (MNE), and beamformers such as dynamic imaging of coherent sources (DICS) and linearly constrained minimum variance (LCMV). These algorithms produce a distributed map of brain activity underlying sustained and transient responses during neuroimaging studies of behavior. On the other hand, there are very few comparative analyses that evaluates the “ground truth detection” capabilities of these methods. The current article evaluates the reliability in estimation of sources of spectral event generators in the cortex using a two-pronged approach. First, simulated EEG data with point dipoles and distributed dipoles are used to validate the accuracy and sensitivity of each one of these methods of source localization. The abilities of the techniques were tested by comparing the localization error, focal width, false positive (FP) ratios while detecting already known location of neural activity generators under varying signal-to-noise ratios (SNRs). Second, empirical EEG data during auditory steady state responses (ASSRs) in human participants were used to compare the distributed nature of source localization. All methods were successful in recovery of point sources in favorable signal to noise scenarios and could achieve high hit rates if FPs are ignored. Interestingly, focal activation map is generated by LCMV and DICS when compared to eLORETA while control of FPs is much superior in eLORETA. Subsequently drawbacks and strengths of each method are highlighted with a detailed discussion on how to choose a technique based on empirical requirements.

Do the posterior midline cortices belong to the electrophysiological default-mode network?

The default-mode network (DMN) and its principal core hubs in the posterior midline cortices (PMC), i.e., the precuneus and the posterior cingulate cortex, play a critical role in the human brain structural and functional architecture. Because of their centrality, they are affected by a wide spectrum of brain disorders, e.g., Alzheimer's disease. Non-invasive electrophysiological techniques such as magnetoencephalography (MEG) are crucial to the investigation of the neurophysiology of the DMN and its alteration by brain disorders. However, MEG studies relying on band-limited power envelope correlation diverge in their ability to identify the PMC as a part of the DMN in healthy subjects at rest. Since these works were based on different MEG recording systems and different source reconstruction pipelines, we compared DMN functional connectivity estimated with two distinct MEG systems (Elekta, now MEGIN, and CTF) and two widely used reconstruction algorithms (Minimum Norm Estimation and linearly constrained minimum variance Beamformer). Our results identified the reconstruction method as the critical factor influencing PMC functional connectivity, which was significantly dampened by the Beamformer. On this basis, we recommend that future electrophysiological studies on the DMN should rely on Minimum Norm Estimation (or close variants) rather than on the classical Beamformer. Crucially, based on analytic knowledge about these two reconstruction algorithms, we demonstrated with simulations that this empirical observation could be explained by the existence of a spontaneous linear, approximately zero-lag synchronization structure between areas of the DMN or among multiple sources within the PMC. This finding highlights a novel property of the neural dynamics and functional architecture of a core human brain network at rest.

The impact of improved MEG–MRI co-registration on MEG connectivity analysis

Co-registration between structural head images and functional MEG data is needed for anatomically-informed MEG data analysis. Despite the efforts to minimize the co-registration error, conventional landmark- and surface-based strategies for co-registering head and MEG device coordinates achieve an accuracy of typically 5–10 mm. Recent advances in instrumentation and technical solutions, such as the development of hybrid ultra-low-field (ULF) MRI–MEG devices or the use of 3D-printed individualized foam head-casts, promise unprecedented co-registration accuracy, i.e., 2 mm or better. In the present study, we assess through simulations the impact of such an improved co-registration on MEG connectivity analysis.We generated synthetic MEG recordings for pairs of connected cortical sources with variable locations. We then assessed the capability to reconstruct source-level connectivity from these recordings for 0–15-mm co-registration error, three levels of head modeling detail (one-, three- and four-compartment models), two source estimation techniques (linearly constrained minimum-variance beamforming and minimum-norm estimation MNE) and five separate connectivity metrics (imaginary coherency, phase-locking value, amplitude-envelope correlation, phase-slope index and frequency-domain Granger causality).We found that beamforming can better take advantage of an accurate co-registration than MNE. Specifically, when the co-registration error was smaller than 3 mm, the relative error in connectivity estimates was down to one-third of that observed with typical co-registration errors. MNE provided stable results for a wide range of co-registration errors, while the performance of beamforming rapidly degraded as the co-registration error increased. Furthermore, we found that even moderate co-registration errors (>6 mm, on average) essentially decrease the difference of four- and three- or one-compartment models. Hence, a precise co-registration is important if one wants to take full advantage of highly accurate head models for connectivity analysis.We conclude that an improved co-registration will be beneficial for reliable connectivity analysis and effective use of highly accurate head models in future MEG connectivity studies.

Dynamic Functional Network Connectivity in Schizophrenia with Magnetoencephalography and Functional Magnetic Resonance Imaging: Do Different Timescales Tell a Different Story?

The importance of how brain networks function together to create brain states has become increasingly recognized. Therefore, an investigation of eyes-open resting-state dynamic functional network connectivity (dFNC) of healthy controls (HC) versus that of schizophrenia patients (SP) via both functional magnetic resonance imaging (fMRI) and a novel magnetoencephalography (MEG) pipeline was completed. The fMRI analysis used a spatial independent component analysis (ICA) to determine the networks on which the dFNC was based. The MEG analysis utilized a source space activity estimate (minimum norm estimate [MNE]/dynamic statistical parametric mapping [dSPM]) whose result was the input to a spatial ICA, on which the networks of the MEG dFNC were based. We found that dFNC measures reveal significant differences between HC and SP, which depended on the imaging modality. Consistent with previous findings, a dFNC analysis predicated on fMRI data revealed HC and SP remain in different overall brain states (defined by a k-means clustering of network correlations) for significantly different periods of time, with SP spending less time in a highly connected state. The MEG dFNC, in contrast, revealed group differences in more global statistics: SP changed between meta-states (k-means cluster states that are allowed to overlap in time) significantly more often and to states that were more different, relative to HC. MEG dFNC also revealed a highly connected state where a significant difference was observed in interindividual variability, with greater variability among SP. Overall, our results show that fMRI and MEG reveal between-group functional connectivity differences in distinct ways, highlighting the utility of using each of the modalities individually, or potentially a combination of modalities, to better inform our understanding of disorders such as schizophrenia.

MEG Source Imaging and Group Analysis Using VBMEG.

Variational Bayesian Multimodal EncephaloGraphy (VBMEG) is a MATLAB toolbox that estimates distributed source currents from magnetoencephalography (MEG)/electroencephalography (EEG) data by integrating functional MRI (fMRI) (https://vbmeg.atr.jp/). VBMEG also estimates whole-brain connectome dynamics using anatomical connectivity derived from a diffusion MRI (dMRI). In this paper, we introduce the VBMEG toolbox and demonstrate its usefulness. By collaborating with VBMEG's tutorial page (https://vbmeg.atr.jp/docs/v2/static/vbmeg2_tutorial_neuromag.html), we show its full pipeline using an open dataset recorded by Wakeman and Henson (2015). We import the MEG data and preprocess them to estimate the source currents. From the estimated source currents, we perform a group analysis and examine the differences of current amplitudes between conditions by controlling the false discovery rate (FDR), which yields results consistent with previous studies. We highlight VBMEG's characteristics by comparing these results with those obtained by other source imaging methods: weighted minimum norm estimate (wMNE), dynamic statistical parametric mapping (dSPM), and linearly constrained minimum variance (LCMV) beamformer. We also estimate source currents from the EEG data and the whole-brain connectome dynamics from the MEG data and dMRI. The observed results indicate the reliability, characteristics, and usefulness of VBMEG.

Decoding of motor imagery EEG based on brain source estimation

The decoding of Motor Imagery EEG (MI-EEG) is the most crucial part of biosignal processing in the Brain-computer Interface (BCI) system. The traditional recognition mode is always devoted to extracting and classifying the spatiotemporal feature information of MI-EEG in the sensor domain, but these brain dynamic characteristics, which are derived from the cerebral cortical neurons, are reflected more immediately and obviously with high spatial resolution in the source domain. With the development of neuroscience, the state-of-the-art EEG Source Imaging (ESI) technology converts the scalp signals into brain source space and excavates the way for source decoding of MI-EEG. Minimum Norm Estimate (MNE) is a classical and original EEG inverse transformation. Due to the lack of depth weighting of dipoles, it may be more suitable for the estimation of superficial dipoles and will be slightly insufficient for further source classification. In addition, the selection of a Region of Interest (ROI) is usually an essential step in the source decoding of MI-EEG by Independent Component Analysis (ICA), and the most relevant independent component of original EEG signals is transformed into the equivalent current dipoles to obtain the ROI by ESI. Although the excellent results of this method can be obtained for unilateral limb motor imaging EEG signals, which shows more distinct phenomena of event-related desynchronization (ERD), the decoding accuracy may be restricted for more complex multi-limb motor imagery tasks, whose ERD is no longer evident. Therefore, in this paper, we propose a novel brain source estimation to decode MI-EEG by applying Overlapping Averaging (OA) in the temporal domain and Weighted Minimum Norm Estimate (WMNE), which overcomes the limitations of general ROI-based decoding methods and introduces weighting factors to complement the estimation of deep dipoles. Its advantages will be evaluated on a public dataset with five subjects by comparing it with MNE, WMNE, sLORETA, OA-MNE and ICA-WMNE. The proposed method reaches a higher average decoding accuracy of 81.32% compared to other methods by 10-fold cross-validation at the same chance level. This study will increase the universality of the source decoding and facilitate the development of a BCI system in the source domain.

Do the posterior midline cortices belong to the electrophysiological default-mode network?

The default-mode network (DMN) and its principal core hubs in the posterior midline cortices (PMC), i.e., the precuneus and the posterior cingulate cortex, play a critical role in the human brain structural and functional architecture. Because of their centrality, they are affected by a wide spectrum of brain disorders, e.g., Alzheimer's disease. Non-invasive electrophysiological techniques such as magnetoencephalography (MEG) are crucial to the investigation of the neurophysiology of the DMN and its alteration by brain disorders. However, MEG studies relying on band-limited power envelope correlation diverge in their ability to identify the PMC as a part of the DMN in healthy subjects at rest. Since these works were based on different MEG recording systems and different source reconstruction pipelines, we compared DMN functional connectivity estimated with two distinct MEG systems (Elekta, now MEGIN, and CTF) and two widely used reconstruction algorithms (Minimum Norm Estimation and linearly constrained minimum variance Beamformer). Our results identified the reconstruction method as the critical factor influencing PMC functional connectivity, which was significantly dampened by the Beamformer. On this basis, we recommend that future electrophysiological studies on the DMN should rely on Minimum Norm Estimation (or close variants) rather than on the classical Beamformer. Crucially, based on analytic knowledge about these two reconstruction algorithms, we demonstrated with simulations that this empirical observation could be explained by the existence of a spontaneous linear, approximately zero-lag synchronization structure between areas of the DMN or among multiple sources within the PMC. This finding highlights a novel property of the neural dynamics and functional architecture of a core human brain network at rest.

Electrophysiological correlates of cognitive symptoms in multiple sclerosis through neuromagnetic resting-state functional connectivity

Electrophysiological correlates of cognitive symptoms in multiple sclerosis through neuromagnetic resting-state functional connectivity

Retrieval of semantic knowledge in language pre-surgical mapping. A MEG study.

Retrieval of semantic knowledge in language pre-surgical mapping. A MEG study.

Implementation of 16-Channel AMR Sensor Array for Quantitative Mapping of Two-Dimension Current Distribution

Implementation of 16-Channel AMR Sensor Array for Quantitative Mapping of Two-Dimension Current Distribution

Individual Activation Patterns After the Stimulation of Different Motor Areas: A Transcranial Magnetic Stimulation-Electroencephalography Study.

The combination of transcranial magnetic stimulation (TMS) and electroencephalography (EEG) enables one to study effective connectivity and activation order in neuronal networks. To characterize effective connectivity originating from the primary motor cortex (M1), dorsal premotor area (PMd), and supplementary motor area (SMA). Three right-handed volunteers (two men, aged 25-30 years) participated in a navigated TMS-EEG experiment. M1, PMd, and SMA over the nondominant hemisphere were stimulated with 150 TMS pulses. Minimum-norm estimates were derived from the EEG data to estimate the spatial spreading of TMS-elicited neuronal activation on an individual level. The activation order of the cortical areas varied depending on the stimulated area. There were similarities and differences in the spatial distribution of the TMS-evoked potentials between subjects. Similarities in cortical activation patterns were seen at short poststimulus latencies and the differences at long latencies. This pilot study suggests that cortical activation patterns and the activation order of motor areas differ interindividually and depend on the stimulated motor area. It further indicates that TMS-activated effective connections or underlying structural connections vary between subjects. The spatial patterns of TMS-evoked potentials differ between subjects especially at long latencies, when probably more complex neuronal networks are active.

Elastic Net Regularization in Lorentz force evaluation

Lorentz force evaluation is a nondestructive evaluation method applied for the characterization of sub-surface defects in specimen consisting of layers of conducting material. The movement of a specimen under investigation relative to a permanent magnet leads to Lorentz forces that are perturbed in the presence of a defect. A minimum norm estimation (MNE) with Elastic Net Regularization (ENR) is compared to MNE with Tikhonov-Phillips-Regularization (TPR) regarding the ability to determine defect properties from force perturbation signals. A cylindrically shaped defect with diameter of 5 mm and height of 2 mm is examined at depths of 2, 4 and 8 mm. Simulated data obtained by the finite element method and measured data are considered. ENR and TPR estimated the defect depth correctly for simulation and measurement data at depths of 2 and 4 mm, while at 8 mm, only ENR estimated the depth correctly. The defect sizes were slightly overestimated for both ENR and TPR. TPR produced additional spurious solutions at the boundary of the reconstruction grid. We conclude that ENR is more suitable than TPR for MNE in Lorentz force evaluation.

Recent trends and advances in solving the inverse problem for EEG source localization

ABSTRACTThis paper addresses the recent advancements and trends in the field of electroencephalography (EEG) using inverse problem solutions. Using the EEG data of the brain to gather the information regarding the neuronal current source distribution has been a persisting challenge. Since the EEG inverse problem is ill-posed in nature; therefore, it does not offer a unique result. A trivial and precise solution yields a detailed insight regarding the electrical activity as well as the damaged tissue in the brain. Ordinarily, this problem is solved using the regularization techniques, such as minimum norm estimates, mixed-norm estimate, low-resolution electrical tomography, artificial neural networks, and their modified variants. In this paper, the latest algorithmic developments in solving the EEG inverse problem are reviewed. The optimization rendered by these techniques in accurately solving the neural source localization problem is also discussed. The comparative performance analysis of the recent techniques has been presented. Furthermore, a number of future enhancements have also been proposed to further improve the performance of these state-of-the-art techniques.

Requirements for Coregistration Accuracy in On-Scalp MEG

Recent advances in magnetic sensing has made on-scalp magnetoencephalography (MEG) possible. In particular, optically-pumped magnetometers (OPMs) have reached sensitivity levels that enable their use in MEG. In contrast to the SQUID sensors used in current MEG systems, OPMs do not require cryogenic cooling and can thus be placed within millimetres from the head, enabling the construction of sensor arrays that conform to the shape of an individual’s head. To properly estimate the location of neural sources within the brain, one must accurately know the position and orientation of sensors in relation to the head. With the adaptable on-scalp MEG sensor arrays, this coregistration becomes more challenging than in current SQUID-based MEG systems that use rigid sensor arrays. Here, we used simulations to quantify how accurately one needs to know the position and orientation of sensors in an on-scalp MEG system. The effects that different types of localisation errors have on forward modelling and source estimates obtained by minimum-norm estimation, dipole fitting, and beamforming are detailed. We found that sensor position errors generally have a larger effect than orientation errors and that these errors affect the localisation accuracy of superficial sources the most. To obtain similar or higher accuracy than with current SQUID-based MEG systems, RMS sensor position and orientation errors should be < 4,hbox {mm} and < 10^circ, respectively.

Improving the Nulling Beamformer Using Subspace Suppression.

Magnetoencephalography (MEG) captures the magnetic fields generated by neuronal current sources with sensors outside the head. In MEG analysis these current sources are estimated from the measured data to identify the locations and time courses of neural activity. Since there is no unique solution to this so-called inverse problem, multiple source estimation techniques have been developed. The nulling beamformer (NB), a modified form of the linearly constrained minimum variance (LCMV) beamformer, is specifically used in the process of inferring interregional interactions and is designed to eliminate shared signal contributions, or cross-talk, between regions of interest (ROIs) that would otherwise interfere with the connectivity analyses. The nulling beamformer applies the truncated singular value decomposition (TSVD) to remove small signal contributions from a ROI to the sensor signals. However, ROIs with strong crosstalk will have high separating power in the weaker components, which may be removed by the TSVD operation. To address this issue we propose a new method, the nulling beamformer with subspace suppression (NBSS). This method, controlled by a tuning parameter, reweights the singular values of the gain matrix mapping from source to sensor space such that components with high overlap are reduced. By doing so, we are able to measure signals between nearby source locations with limited cross-talk interference, allowing for reliable cortical connectivity analysis between them. In two simulations, we demonstrated that NBSS reduces cross-talk while retaining ROIs' signal power, and has higher separating power than both the minimum norm estimate (MNE) and the nulling beamformer without subspace suppression. We also showed that NBSS successfully localized the auditory M100 event-related field in primary auditory cortex, measured from a subject undergoing an auditory localizer task, and suppressed cross-talk in a nearby region in the superior temporal sulcus.