Semi-analytic three-shell forward calculation for magnetoencephalography.

In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.

Automatic quality control of the numerical accuracy of EEG lead fields.

Precise individualized EEG source localization is predicated on having accurate subject-specific Lead Fields (LFs) obtained from their Magnetic Resonance Images (MRI). LF calculation is a complex process involving several error-prone steps that start with obtaining a realistic head model from the MRI and finalizing with computationally expensive solvers such as the Boundary Element Method (BEM) or Finite Element Method (FEM). Current Big-Data applications require the calculation of batches of hundreds or thousands of LFs. LF. Quality Control is conventionally checked subjectively by experts, a procedure not feasible in practice for larger batches. To facilitate this step, we introduce the Lead Field Automatic-Quality Control Index (LF-AQI) that flags LF with potential errors. We base our LF-AQI on the assumption that LFs obtained from simpler head models, i.e., the homogeneous head model LF (HHM-LF) or spherical head model LF (SHM-LF), deviate only moderately from a "good" realistic test LF. Since these simpler LFs are easier to compute and check for errors, they may serve as "reference LF" to detect anomalous realistic test LF. We investigated this assumption by comparing correlation-based channel ρmin(ref,test)and source τmin(ref,test) similarity indices (SI) between "gold standards," i.e., very accurate FEM and BEM LFs, and the proposed references (HHM-LF and SHM-LF). Surprisingly we found that the most uncomplicated possible reference, HHM-LF had high SI values with the gold standards-leading us to explore further use of the channel ρmin(HHM-LF,test)and source τmin(HHM-LF,test)SI as a basis for our LF-AQI. Indeed, these SI successfully detected five simulated scenarios of LFs artifacts. This result encouraged us to evaluate the SI on a large dataset and thus define our LF-AQI. We thus computed the SI of 1251 LFs obtained from the Child Mind Institute (CMI) MRI dataset. When ρmin(HHM-LF,test)and source τmin(HHM-LF,test) were plotted for all test subjects on a 2D space, most were tightly clustered around the median of a high similarity centroid (HSC), except for a smaller proportion of outliers. We define the LF-AQI for a given LF as the log Euclidean distance between its SI and the HSC median. To automatically detect outliers, the threshold is at the 90th percentile of the CMI LF-AQIs (-0.9755). LF-AQI greater than this threshold flag individual LF to be checked. The robustness of this LF-AQI screening was checked by repeated out-of-sample validation. Strikingly, minor corrections in re-processing the flagged cases eliminated their status as outliers. Furthermore, the "doubtful" labels assigned by LF-AQI were validated by neuroscience students using a Likert scale questionnaire designed to manually check the LF's quality. Item Response Theory (IRT) analysis was applied to the questionnaire results to compute an optimized model and a latent variable θ for that model. A linear mixed model (LMM) between the θ and LF-AQI resulted in an effect with a Cohen's d value of 1.3 and a p-value <0.001, thus validating the correspondence of LF-AQI with the visual quality control. We provide an open-source pipeline to implement both LF calculation and its quality control to allow further evaluation of our index.

Is sensor space analysis good enough? Spatial patterns as a tool for assessing spatial mixing of EEG/MEG rhythms.

Analyzing non-invasive recordings of electroencephalography (EEG) and magnetoencephalography (MEG) directly in sensor space, using the signal from individual sensors, is a convenient and standard way of working with this type of data. However, volume conduction introduces considerable challenges for sensor space analysis. While the general idea of signal mixing due to volume conduction in EEG/MEG is recognized, the implications have not yet been clearly exemplified. Here, we illustrate how different types of activity overlap on the level of individual sensors. We show spatial mixing in the context of alpha rhythms, which are known to have generators in different areas of the brain. Using simulations with a realistic 3D head model and lead field and data analysis of a large resting-state EEG dataset, we show that electrode signals can be differentially affected by spatial mixing by computing a sensor complexity measure. While prominent occipital alpha rhythms result in less heterogeneous spatial mixing on posterior electrodes, central electrodes show a diversity of rhythms present. This makes the individual contributions, such as the sensorimotor mu-rhythm and temporal alpha rhythms, hard to disentangle from the dominant occipital alpha. Additionally, we show how strong occipital rhythms can contribute the majority of activity to frontal channels, potentially compromising analyses that are solely conducted in sensor space. We also outline specific consequences of signal mixing for frequently used assessment of power, power ratios and connectivity profiles in basic research and for neurofeedback application. With this work, we hope to illustrate the effects of volume conduction in a concrete way, such that the provided practical illustrations may be of use to EEG researchers to in order to evaluate whether sensor space is an appropriate choice for their topic of investigation.

Measuring MEG closer to the brain: Performance of on-scalp sensor arrays.

Optically-pumped magnetometers (OPMs) have recently reached sensitivity levels required for magnetoencephalography (MEG). OPMs do not need cryogenics and can thus be placed within millimetres from the scalp into an array that adapts to the individual head size and shape, thereby reducing the distance from cortical sources to the sensors. Here, we quantified the improvement in recording MEG with hypothetical on-scalp OPM arrays compared to a 306-channel state-of-the-art SQUID array (102 magnetometers and 204 planar gradiometers). We simulated OPM arrays that measured either normal (nOPM; 102 sensors), tangential (tOPM; 204 sensors), or all components (aOPM; 306 sensors) of the magnetic field. We built forward models based on magnetic resonance images of 10 adult heads; we employed a three-compartment boundary element model and distributed current dipoles evenly across the cortical mantle. Compared to the SQUID magnetometers, nOPM and tOPM yielded 7.5 and 5.3 times higher signal power, while the correlations between the field patterns of source dipoles were reduced by factors of 2.8 and 3.6, respectively. Values of the field-pattern correlations were similar across nOPM, tOPM and SQUID gradiometers. Volume currents reduced the signals of primary currents on average by 10%, 72% and 15% in nOPM, tOPM and SQUID magnetometers, respectively. The information capacities of the OPM arrays were clearly higher than that of the SQUID array. The dipole-localization accuracies of the arrays were similar while the minimum-norm-based point-spread functions were on average 2.4 and 2.5 times more spread for the SQUID array compared to nOPM and tOPM arrays, respectively.

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.

Forward problem of electrocardiography based on cardiac source vector orientations.

To localize the unusual cardiac activities non-invasively, one has to build a prior forward model that relates the heart, torso, and detectors. This model has to be constructed to mathematically relate the geometrical and functional activities of the heart. Several methods are available to model the prior sources in the forward problem, which results in the lead field matrix generation. In the conventional technique, the lead field assumed the fixed prior sources, and the source vector orientations were presumed to be parallel to the detector plane with the unit strength in all directions. However, the anomalies cannot always be expected to occur in the same location and orientation, leading to misinterpretation and misdiagnosis. To overcome this, the work proposes a new forward model constructed using the VCG signals of the same subject. Furthermore, three transformation methods were used to extract VCG in constructing the time-varying lead fields to steer to the orientation of the source rather than just reconstructing its activities in the inverse problem. In addition, the unit VCG loop of the acute ischemia patient was extracted to observe the changes compared to the normal subject. The abnormality condition was achieved by delaying the depolarization time by 15ms. The results involving the unit vectors of VCG demonstrated the anisotropic nature of cardiac source orientations, providing information about the heart's electrical activity.

Ear-EEG Forward Models: Improved Head-Models for Ear-EEG.

Computational models for mapping electrical sources in the brain to potentials on the scalp have been widely explored. However, current models do not describe the external ear anatomy well, and is therefore not suitable for ear-EEG recordings. Here we present an extension to existing computational models, by incorporating an improved description of the external ear anatomy based on 3D scanned impressions of the ears. The result is a method to compute an ear-EEG forward model, which enables mapping of sources in the brain to potentials in the ear. To validate the method, individualized ear-EEG forward models were computed for four subjects, and ear-EEG and scalp EEG were recorded concurrently from the subjects in a study comprising both auditory and visual stimuli. The EEG recordings were analyzed with independent component analysis (ICA) and using the individualized ear-EEG forward models, single dipole fitting was performed for each independent component (IC). A subset of ICs were selected, based on how well they were modeled by a single dipole in the brain volume. The correlation between the topographic IC map and the topographic map predicted by the forward model, was computed for each IC. Generally, the correlation was high in the ear closest to the dipole location, showing that the ear-EEG forward models provided a good model to predict ear potentials. In addition, we demonstrated that the developed forward models can be used to explore the sensitivity to brain sources for different ear-EEG electrode configurations. We consider the proposed method to be an important step forward in the characterization and utilization of ear-EEG.

Variability of magnetoencephalographic sensor sensitivity measures as a function of age, brain volume and cortical area.

OBJECTIVE: To assess the feasibility and appropriateness of magnetoencephalography (MEG) for both adult and pediatric studies, as well as for the developmental comparison of these factors across a wide range of ages. METHODS: For 45 subjects with ages from 1 to 24years (infants, toddlers, school-age children and young adults), lead fields (LFs) of MEG sensors are computed using anatomically realistic boundary element models (BEMs) and individually-reconstructed cortical surfaces. Novel metrics are introduced to quantify MEG sensor focality. RESULTS: The variability of MEG focality is graphed as a function of brain volume and cortical area. Statistically significant differences in total cerebral volume, cortical area, MEG global sensitivity and LF focality are found between age groups. CONCLUSIONS: Because MEG focality and sensitivity differ substantially across the age groups studied, the cortical LF maps explored here can provide important insights for the examination and interpretation of MEG signals from early childhood to young adulthood. SIGNIFICANCE: This is the first study to (1) investigate the relationship between MEG cortical LFs and brain volume as well as cortical area across development, and (2) compare LFs between subjects with different head sizes using detailed cortical reconstructions.