Estimating Scalp MEG from Whole-Head MEG Measurements

Studies based on whole-head MEG recordings are providing more and more impressive results. In such recordings, the MEG sensors are several centimeters away from the scalp and the positions of the MEG sensors with respect to the head differ from subject to subject, and from session to session for the same subject. In this paper, a method is presented and tested to estimate the scalp MEG distributions from whole-head MEG measurements. The goal is to remove the discrepancy of MEG measurements caused by the various sensor positions with respect to the head, as well as to reduce the smearing effect caused by the distance of the MEG sensors from the scalp. The MEG measurement was first projected to a hypothetical dipole layer within the head volume conductor model using the inverse solution. The scalp MEG estimation was then obtained from the resultant dipole layer by the forward solution. The results from simulation studies, phantom experiments, and the auditory evoked field analysis demonstrated that, with reasonable signal to noise ratios, this method is a feasible way to achieve our goals.     

A Time-Varying Connectivity Analysis from Distributed EEG Sources: A Simulation Study

Time-varying connectivity analysis based on sources reconstructed using inverse modeling of electroencephalographic (EEG) data is important to understand the dynamic behaviour of the brain. We simulated cortical data from a visual spatial attention network with a time-varying connectivity structure, and then simulated the propagation to the scalp to obtain EEG data. Distributed EEG source modeling using sLORETA was applied. We compared different dipole (representing a source) selection strategies based on their time series in a region of interest. Next, we estimated multivariate autoregressive (MVAR) parameters using classical Kalman filter and general linear Kalman filter approaches followed by the calculation of partial directed coherence (PDC). MVAR parameters and PDC values for the selected sources were compared with the ground-truth. We found that the best strategy to extract the time series of a region of interest was to select a dipole with time series showing the highest correlation with the average time series in the region of interest. Dipole selection based on power or based on the largest singular value offer comparable alternatives. Among the different Kalman filter approaches, the use of a general linear Kalman filter was preferred to estimate PDC based connectivity except when only a small number of trials are available. In the latter case, the classical Kalman filter can be an alternative.     

Spatiotemporal noise covariance estimation from limited empirical magnetoencephalographic data

The performance of parametric magnetoencephalography (MEG) and electroencephalography (EEG) source localization approaches can be degraded by the use of poor background noise covariance estimates. In general, estimation of the noise covariance for spatiotemporal analysis is difficult mainly due to the limited noise information available. Furthermore, its estimation requires a large amount of storage and a one-time but very large (and sometimes intractable) calculation or its inverse. To overcome these difficulties, noise covariance models consisting of one pair or a sum of multi-pairs of Kronecker products of spatial covariance and temporal covariance have been proposed. However, these approaches cannot be applied when the noise information is very limited, i.e., the amount of noise information is less than the degrees of freedom of the noise covariance models. A common example of this is when only averaged noise data are available for a limited prestimulus region (typically at most a few hundred milliseconds duration). For such cases, a diagonal spatiotemporal noise covariance model consisting of sensor variances with no spatial or temporal correlation has been the common choice for spatiotemporal analysis. In this work, we propose a different noise covariance model which consists of diagonal spatial noise covariance and Toeplitz temporal noise covariance. It can easily be estimated from limited noise information, and no time-consuming optimization and data-processing are required. Thus, it can be used as an alternative choice when one-pair or multi-pair noise covariance models cannot be estimated due to lack of noise information. To verify its capability we used Bayesian inference dipole analysis and a number of simulated and empirical datasets. We compared this covariance model with other existing covariance models such as conventional diagonal covariance, one-pair and multi-pair noise covariance models, when noise information is sufficient to estimate them. We found that our proposed noise covariance model yields better localization performance than a diagonal noise covariance, while it performs slightly worse than one-pair or multi-pair noise covariance models - although these require much more noise information. Finally, we present some localization results on median nerve stimulus empirical MEG data for our proposed noise covariance model.     

Determining the Number of Independent Sources of the EEG: A Simulation Study on Information Criteria

The separation of signal and noise is an important problem in the analysis of EEG and MEG data. Furthermore, many source localisation strategies need the number of independent signal components as input parameter (e.g., dipole fit, multiple signal classification). Information criteria offer a relatively objective way to separate the space spanned by the principal components of the data covariance matrix into a signal and a noise part. Eighteen such criteria were extensively tested by simulations. They differ with respect to the statistical model of the data, the assumptions on the noise, and the correction term. In the simulations, different dipole sources were used to generate EEG, which was then distorted by Gaussian correlated or uncorrelated noise. The noise level, the accuracy of the noise covariance matrix used by the criteria, the numbers of channels and time samples, and the stochastic or deterministic nature of the source waveforms were varied. The performance of the criteria was very variable. For each criterion, limits for the noise level and the relative inaccuracy of the noise covariance matrix could be established. Taking more channels or time steps did increase the criteria's ability to tolerate noise, but at the same time, made them more vulnerable to inaccuracies in the (estimated) noise covariance matrices. Out of the eighteen criteria investigated, we recommend two criteria that are best suited for the cases of (1) high noise and accurate covariances and (2) low noise and less accurate covariances.     

Spatial filters based on independent component analysis for magnetic noise reduction in the magnetocardiogram

A spatial filter design method to reduce magnetic noise in the magnetocardiogram (MCG) is introduced. Based on the facts that external magnetic noise appearing on multichannel MCG sensors is independent of the cardiac signals and that there is strong spatial correlation among the channels, the independent component analysis (ICA) method was applied to extract the noise components from the measured MCG signals. After extraction of the noise components in a given time period using ICA, a spatial filter was made to reduce the noise components in subsequently acquired MCG signals. In experimental studies of nine healthy volunteers, the spatial filters improved the signal-to-noise ratio of the MCG signals by about 500% on average. This spatial filtering method can be used for measurements of MCG signals in a magnetically noisy environment.     

Noise-free magnetoencephalography recordings of brain function

Perhaps the greatest impediment to acquiring high-quality magnetoencephalography (MEG) recordings is the ubiquitous ambient magnetic field noise. We have designed and built a whole-head MEG system using a helmet-like superconducting imaging surface (SIS) surrounding the array of superconducting quantum interference device (SQUID) magnetometers used to measure the MEG signal. We previously demonstrated that the SIS passively shields the SQUID array from ambient magnetic field noise, independent of frequency, by 25-60 dB depending on sensor location. SQUID 'reference sensors' located on the outside of the SIS helmet measure ambient magnetic fields in very close proximity to the MEG magnetometers while being nearly perfectly shielded from all sources in the brain. The fact that the reference sensors measure no brain signal yet are located in close proximity to the MEG sensors enables very accurate estimation and subtraction of the ambient field noise contribution to the MEG sensors using an adaptive algorithm. We have demonstrated total ambient noise reduction factors in excess of 10(6) (> 120 dB). The residual noise for most MEG SQUID channels is at or near the intrinsic SQUID noise floor, typically 2-3 fT Hz-1/2. We are recording MEG signals with greater signal-to-noise than equivalent EEG measurements.     

A method for combining MEG and EEG to determine the sources

A three-step method is presented which combines an MEG and EEG map over the head to solve the inverse problem (to determine the sources). This method uses the feature that the MEG does not see a radial source, but only a tangential source, while the EEG sees both. A first test is also made of the method, using computer simulation, and the results presented. The purpose of the test is to see if the method is valid with noisy MEG and EEG data, and when some modelling errors are present; a single dipole source was used in a spherical head. It was found that the method works well when the RMS noise at each map location is 5% of the maximum MEG and EEG (readily attained in practice), but breaks down when the noise is 10% (quite noisy data). The modelling errors involved grid size, head radius and distance to the MEG coil, and were studied only through the first step of the method; with errors in a reasonable range, this limited test again worked well.     

Development of a generative model of magnetoencephalography noise that enables brain signal extraction from single-epoch data

We presented a method of rejecting sensor-specific and environmental noise during magnetoencephalography (MEG) measurement that enables the extraction of brain signals from single-epoch data. The method assumes a parametric generative model of MEG data. The model’s optimal parameters were determined from single-epoch data, and noise reduction was performed by the decomposition of data within the optimal model. We confirmed our method’s validity through multiple experiments. Moreover, we compared our method’s performance with that of several previous noise-reduction methods. Finally, we confirmed that the proposed method followed by spatial filtering reduced noise more efficiently.     

Direct reconstruction algorithm of current dipoles for vector magnetoencephalography and electroencephalography

This paper presents a novel algorithm to reconstruct parameters of a sufficient number of current dipoles that describe data (equivalent current dipoles, ECDs, hereafter) from radial/vector magnetoencephalography (MEG) with and without electroencephalography (EEG). We assume a three-compartment head model and arbitrary surfaces on which the MEG sensors and EEG electrodes are placed. Via the multipole expansion of the magnetic field, we obtain algebraic equations relating the dipole parameters to the vector MEG/EEG data. By solving them directly, without providing initial parameter guesses and computing forward solutions iteratively, the dipole positions and moments projected onto the xy-plane (equatorial plane) are reconstructed from a single time shot of the data. In addition, when the head layers and the sensor surfaces are spherically symmetric, we show that the required data reduce to radial MEG only. This clarifies the advantage of vector MEG/EEG measurements and algorithms for a generally-shaped head and sensor surfaces. In the numerical simulations, the centroids of the patch sources are well localized using vector/radial MEG measured on the upper hemisphere. By assuming the model order to be larger than the actual dipole number, the resultant spurious dipole is shown to have a much smaller strength magnetic moment (about 0.05 times smaller when the SNR = 16 dB), so that the number of ECDs is reasonably estimated. We consider that our direct method with greatly reduced computational cost can also be used to provide a good initial guess for conventional dipolar/multipolar fitting algorithms.     

Anatomically constrained dipole adjustment (ANACONDA) for accurate MEG/EEG focal source localizations

This paper proposes an alternative approach to enhance localization accuracy of MEG and EEG focal sources. The proposed approach assumes anatomically constrained spatio-temporal dipoles, initial positions of which are estimated from local peak positions of distributed sources obtained from a pre-execution of distributed source reconstruction. The positions of the dipoles are then adjusted on the cortical surface using a novel updating scheme named cortical surface scanning. The proposed approach has many advantages over the conventional ones: (1) as the cortical surface scanning algorithm uses spatio-temporal dipoles, it is robust with respect to noise; (2) it requires no a priori information on the numbers and initial locations of the activations; (3) as the locations of dipoles are restricted only on a tessellated cortical surface, it is physiologically more plausible than the conventional ECD model. To verify the proposed approach, it was applied to several realistic MEG/EEG simulations and practical experiments. From the several case studies, it is concluded that the anatomically constrained dipole adjustment (ANACONDA) approach will be a very promising technique to enhance accuracy of focal source localization which is essential in many clinical and neurological applications of MEG and EEG.     

Real-time kalman filter applied to biomechanical data for state estimation and numerical differentiation

This study focused on the application of real-time Kalman filters to biomechanical data and, in particular, the simulation environment used to compare the performance of modified and standard two-state Kalman filters when estimating displacement and velocity from noisy displacement data. The modification proposed in this paper was the numerical tachometer, augmented by a median smoother. The numerical tachometer integrated the derivative estimates from finite differences of noisy sampled data into the Kalman filter structure; the median smoother acted before differentiation, to protect from grossly erroneous measurements. The numerical tachometer allowed better fits to the simulated data than can be achieved without it: the root mean square errors decreased by 10% in the displacement domain and by 54% in the velocity domain, for sampling frequencies and signal contamination levels that were typical in human movement sciences. The sensitivity to errors in the modelling of the signal and noise characteristics was less than in the standard filter implementation. The use of the median smoother improved the robustness of the filtering algorithm against additive white Gaussian measurement noise and allowed the cancellation of isolated noise spikes.     

Removing Cardiac Artefacts in Magnetoencephalography with Resampled Moving Average Subtraction

Magnetoencephalography (MEG) signals are commonly contaminated by cardiac artefacts (CAs). Principle component analysis and independent component analysis have been widely used for removing CAs, but they typically require a complex procedure for the identification of CA-related components. We propose a simple and efficient method, resampled moving average subtraction (RMAS), to remove CAs from MEG data. Based on an electrocardiogram (ECG) channel, a template for each cardiac cycle was estimated by a weighted average of epochs of MEG data over consecutive cardiac cycles, combined with a resampling technique for accurate alignment of the time waveforms. The template was subtracted from the corresponding epoch of the MEG data. The resampling reduced distortions due to asynchrony between the cardiac cycle and the MEG sampling times. The RMAS method successfully suppressed CAs while preserving both event-related responses and high-frequency (>45 Hz) components in the MEG data.     

Precision of dipole localization in a spherical volume conductor: A comparison of referential EEG,magnetoencephalography and scalp current density methods

Summary In this study, we determined the influence of dipole orientation, dipole location, and number of recording sites on the precision of dipole localization in a spherical volume conductor. We compared localization from referential EEG (R-EEG), scalp current density EEG (SCD-EEG) and magnetoencephalography (MEG). Dipole orientation had a small influence on the precision of dipole localization for R-EEG and SCD-EEG. Dipole location relative to the recording sites, dipole depth, and number of recording channels strongly influenced the precision of dipole localization. Assuming equal signal to noise conditions for each recording method, MEG and SCD-EEG had a similar precision for dipole localization of a single tangential dipole source and both methods were more precise than R-EEG. However, SCD-EEG was inferior to MEG for distinguishing a single tangential current source from a pair of deeper radial current sources. In summary, these results suggest that the MEG will be most useful for localization of multiple simultaneous dipole sources.     

Linear Inverse Solutions: Simulations from a Realistic Head Model in MEG

Summary: Distributed linear solutions are widely used in source localization to solve the ill-posed EEG/MEG inverse problem. In the classical approach based on dipole sources, these methods estimate the current densities at a great number of brain sites, typically at the nodes of a 3-D grid which discretizes the chosen solution space. The estimated current density distributions are displayed as brain electromagnetic tomography (BET) images. We have tested well known minimum norm solutions (MN, WMN, LORETA) and other linear inverse solutions [WROP, sLORETA, interference uniform, gain uniform, weight vector normalized (WVN), and a new solution named SLF (Standardized Lead Field)], using a MEG configuration (BTi Magnes 2500 WH with 148 axial magnetometers) and a realistic head model using BEM (Boundary Element Method). The solutions were compared in a noise-free condition and in the presence of noise using the classical dipole localization errors (DLE) together with a new figure of merit that we called max gain uniformity, which measures the capability of an inverse linear solution to show spots of activity with similar amplitudes on the brain electromagnetic tomographies when multiple dipole sources with similar moments are simultaneously active. Whereas some solutions (sLORETA, interference uniform and SLF) were capable of zero dipole localization errors in the noise-free case, none of them reached 100% of correct dipole localizations in the presence of a high level of Gaussian noise. The SLF solution, which has the advantage to be independent from any regularization parameter, presented the best results with the lowest max gain uniformities, with almost 100% of correct dipole localizatious with 10% of noise and more than 90% of correct localizations with 30% of noise added to the data. Nevertheless, no solution was able to combine at the same time a correct localization of single sources and the capability to visualize multiple sources with comparable amplitudes on the brain electromagnetic tomographies.     

时空模型结合模拟退火进行脑磁源的定位

脑磁源的定位问题是脑磁图（magnetoencephalography,MEG)研究的一个基本问题，其中多偶极子定位是脑磁逆问题研究当中的难点。本文通过研究脑磁图的时空模型STSM（spatio-temoral source modeling)，提出将时空模型与模拟退火相结合进行多偶极子的定位，以克服其他优化方法易落入局部极小的不足，时空模型中偶极子参数经分解可分为线性部分和非线形部分，只对非线性部分进行模拟退火优化大大降低了优化空间的维数。通过与MUSIC（MUltiple SIgnal Classification)方法的比较，发现将时空模型与模拟退火相结合可以相对降低对源信号独立性的要求。     

Localization of human somatosensory cortex using spatially filtered magnetoencephalography

A spatial filter algorithm based on minimum-variance beamforming (synthetic aperture magnetometry (SAM)) was applied to single trial neuromagnetic recordings in order to localize primary somatosensory cortex. Magnetoencephalography (MEG) responses to electrical stimulation of the right and left median nerve were recorded using a whole-head MEG system and localized using both SAM spatial filtering and dipole analysis. Spatial filtering was applied to single trial neuromagnetic recordings to produce 3-dimensional difference images of source power between active (0–50 ms) and control states (−50–0 ms) in the range of 15–300 Hz. Average difference between N20m dipole location and location of maximal increase in power in the SAM images was 3.7 mm (1.5 mm SD) and localized to primary somatosensory cortex. Time-frequency analysis of spatially filtered output for the peak SAM locations showed a brief (10 ms) increase in the 60–100 Hz band coincident with the N20m response and a longer duration (approx. 80 ms) increase in power in the 10–40 Hz band following N20m onset. These results indicate that beamformer based spatial filter methods such as SAM can be used to localize temporally discrete cortical activity produced by median nerve stimulation.     

Detecting Functional Connectivity in fMRI Using PCA and Regression Analysis

A fMRI connectivity analysis approach combining principal component analysis (PCA) and regression analysis is proposed to detect functional connectivity between the brain regions. By first using PCA to identify clusters within the vectors of fMRI time series, more energy and information features in the signal can be maintained than using averaged values from brain regions of interest. Then, regression analysis can be applied to the extracted principal components in order to further investigate functional connectivity. Finally, t-test is applied and the patterns with t-values lager than a threshold are considered as functional connectivity mappings. The validity and reliability of the presented method were demonstrated with both simulated data and human fMRI data obtained during behavioral task and resting state. Compared to the conventional functional connectivity methods such as average signal based correlation analysis, independent component analysis (ICA) and PCA, the proposed method achieves competitive performance with greater accuracy and true positive rate (TPR). Furthermore, the ‘default mode’ and motor network results of resting-state fMRI data indicate that using PCA may improve upon application of existing regression analysis methods in study of human brain functional connectivity.     

Dipole Localization of Human Induced Focal Afterdischarge Seizure in Simultaneous Magnetoencephalography and Electrocorticography

Localizations were compared for the same human seizure between simultaneously measured MEG and iEEG, which were both co-registered to MRI. The whole-cortex neuromagnetometer localized a dipole in a sphere phantom, co-registered to the MEG sensor array, with an error of 1.4 mm. A focal afterdischarge seizure was induced in a patient with partial epilepsy, by stimulation at a subdural electrocorticography (ECoG) electrode with a known location, which was co-registered to the MRI and to the MEG sensor array. The simultaneous MEG and ECoG during the 30-second seizure was measured and analyzed using the single, moving dipole model, which is the localization model used clinically. The dipole localizations from simultaneous whole cortex 68-channel MEG and 64-channel ECoG were then compared for the repetitive spiking at six different times during the seizure. There were two main regions of MEG and ECoG activity. The locations of these regions were confirmed by determining the location clusters of 8,000 dipoles on ECoG at consecutive time points during the seizure. The mean distances between the stimulated electrode location versus the dipole location of the MEG and versus the dipole location of the ECoG were each about one (1) centimeter. The mean distance between the dipole locations of the MEG versus the dipole locations of the ECoG was about 2 cm. These errors were compared to errors of MEG and ECoG reported previously for phantoms and for somatosensory evoked responses (SER) in patients. Comparing the findings from the present study to those from prior studies, there appeared to be the expected stepwise increase in mean localization error progressing from the phantom, to the SER, to the seizure.     

By our bootstraps: Comparing methods for measuring auditory 40 Hz steady‐state neural activity

Although the 40 Hz auditory steady‐state response (ASSR) is of clinical interest, the construct validity of EEG and MEG measures of 40 Hz ASSR cortical microcircuits is unclear. This study evaluated several MEG and EEG metrics by leveraging findings of (a) an association between the 40 Hz ASSR and age in the left but not right hemisphere, and (b) right‐ > left‐hemisphere differences in the strength of the 40 Hz ASSR. The contention is that, if an analysis method does not demonstrate a left 40 Hz ASSR and age relationship or hemisphere differences, then the obtained measures likely have low validity. Fifty‐three adults were presented 500 Hz stimuli modulated at 40 Hz while MEG and EEG were collected. ASSR activity was examined as a function of phase similarity (intertrial coherence) and percent change from baseline (total power). A variety of head models (spherical and realistic) and a variety of dipole source modeling strategies (dipole source localization and dipoles fixed to Heschl's gyri) were compared. Several sensor analysis strategies were also tested. EEG sensor measures failed to detect left 40 Hz ASSR and age associations or hemisphere differences. A comparison of MEG and EEG head‐source models showed similarity in the 40 Hz ASSR measures and in estimating age and left 40 Hz ASSR associations, indicating good construct validity across models. Given a goal of measuring the 40 Hz ASSR cortical microcircuits, a source‐modeling approach was shown to be superior in measuring this construct versus methods that rely on EEG sensor measures.     

Source analysis of median nerve and finger stimulated somatosensory evoked potentials: Multichannel simultaneous recording of electric and magnetic fields combined with 3d-MR tomography

Summary At the current state of technology, multichannel simultaneous recording of combined electric potentials and magnetic fields should constitute the most powerful tool for separation and localization of focal brain activity. We performed an explorative study of multichannel simultaneous electric SEPs and magnetically recorded SEFs. MEG only sees tangentially oriented sources, while EEG signals include the entire activity of the brain. These characteristics were found to be very useful in separating multiple sources with overlap of activity in time. The electrically recorded SEPs were adequately modelled by three equivalent dipoles located: (1) in the region of the brainstem, modelling the P14 peak at the scalp, (2) a tangentially oriented dipole, modelling the N20-P20 and N30-P30 peaks, and part of the P45, and (3) a radially oriented dipole, modelling the P22 peak and part of the P45, both located in the region of the somatosensory cortex. Magnetically recorded SEFs were adequately modelled by a single equivalent dipole, modelling the N20-P20 and N30-P30 peaks, located close to the posterior bank of the central sulcus, in area 3b (mean deviation: 3 mm). The tangential sources in the electrical data were located 6 mm on average from the area 3b. MEG and EEG was able to locate the sources of finger stimulated SEFs in accordance with the somatotopic arrangement along the central fissure. A combined analysis demonstrated that MEG can provide constraints to the orientation and location of sources and helps to stabilize the inverse solution in a multiple-source model of the EEG.