Invariance in current dipole moment density across brain structures and species: physiological constraint for neuroimaging

An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling

Objective.In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.Approach.We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a 'silver-standard' solution found by subsequent 4:1 global refinement of the adaptively-refined model.Main results.Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.Significance.This error has especially important implications for TES dosing prediction-where the stimulation strength plays a central role-and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

Limiting parameter range for cortical-spherical mapping improves activated domain estimation for attention modulated auditory response

BACKGROUND

Attention is one of the factors involved in selecting input information for the brain. We applied a method for estimating domains with clear boundaries using magnetoencephalography (the domain estimation method) for auditory-evoked responses (N100m) to evaluate the effects of attention in milliseconds. However, because the surface around the auditory cortex is folded in a complicated manner, it is unknown whether the activity in the auditory cortex can be estimated.

NEW METHOD

The parameter range to express current sources was set to include the auditory cortex. Their search region was expressed as a direct product of the parameter ranges used in the adaptive diagonal curves.

RESULTS

Without a limitation of the range, activity was estimated in regions other than the auditory cortex in all cases. However, with the limitation of the range, the activity was estimated in the primary or higher auditory cortex. Further analysis of the limitation of the range showed that the domains activated during attention included the regions activated during no attention for the participants whose amplitudes of N100m were higher during attention.

COMPARISON WITH EXISTING METHOD

We proposed a method for effectively limiting the search region to evaluate the extent of the activated domain in regions with complex folded structures.

CONCLUSION

To evaluate the extent of activated domains in regions with complex folded structures, it is necessary to limit the parameter search range. The area of the activated domains in the auditory cortex may increase by attention on the millisecond timescale.

Simulation study on high spatio-temporal resolution acousto-electrophysiological neuroimaging

Objective.Acousto-electrophysiological neuroimaging (AENI) is a technique hypothesized to record electrophysiological activity of the brain with millimeter spatial and sub-millisecond temporal resolution. This improvement is obtained by tagging areas with focused ultrasound (fUS). Due to mechanical vibration with respect to the measuring electrodes, the electrical activity of the marked region will be modulated onto the ultrasonic frequency. The region's electrical activity can subsequently be retrieved via demodulation of the measured signal. In this study, the feasibility of this hypothesized technique is tested.Approach.This is done by calculating the forward electroencephalography response under quasi-static assumptions. The head is simplified as a set of concentric spheres. Two sizes are evaluated representing human and mouse brains. Moreover, feasibility is assessed for wet and dry transcranial, and for cortically placed electrodes. The activity sources are modeled by dipoles, with their current intensity profile drawn from a power-law power spectral density.Results.It is shown that mechanical vibration modulates the endogenous activity onto the ultrasonic frequency. The signal strength depends non-linearly on the alignment between dipole orientation, vibration direction and recording point. The strongest signal is measured when these three dependencies are perfectly aligned. The signal strengths are in the pV-range for a dipole moment of 5 nAm and ultrasonic pressures within Food and Drug Administration (FDA)-limits. The endogenous activity can then be accurately reconstructed via demodulation. Two interference types are investigated: vibrational and static. Depending on the vibrational interference, it is shown that millimeter resolution signal detection is possible also for deep brain regions. Subsequently, successful demodulation depends on the static interference, that at MHz-range has to be sub-picovolt.Significance.Our results show that mechanical vibration is a possible underlying mechanism of acousto-electrophyisological neuroimaging. This paper is a first step towards improved understanding of the conditions under which AENI is feasible.

On the clinical utility of on-scalp MEG: A modeling study of epileptic activity source estimation

OBJECTIVE

Epilepsy surgery requires localization of the seizure onset zone (SOZ). Today this can only be achieved by intracranial electroencephalography (iEEG). The iEEG electrode placement is guided by findings from non-invasive modalities that cannot themselves detect SOZ-generated initial seizure activity. On scalp magnetoencephalography (osMEG), with sensors placed on the scalp, demonstrates higher sensitivity than conventional MEG (convMEG) and could potentially detect early seizure activity. Here, we modeled EEG, convMEG and osMEG to compare the modalities' ability to localize SOZ activity and to detect epileptic spikes.

METHODS

We modeled seizure propagation within ten epileptic networks located in the mesial and lateral temporal lobe; basal, dorsal, central and frontopolar frontal lobe; parietal and occipital lobe as well as insula and cingulum. The networks included brain regions often involved in focal epilepsy. 128-channel osMEG, convMEG, EEG and combined osMEG + EEG and convMEG + EEG were modeled, and the SOZ source estimation accuracy was quantified and compared using Student's t-test.

RESULTS

OsMEG was significantly (p-value <0.01) better than both convMEG and EEG at detecting the earliest SOZ-generated seizure activity and epileptic spikes, and better at localizing seizure activity from all epileptic networks (p < 0.01).

CONCLUSIONS

Our modeling results clearly show that osMEG has an unsurpassed potential to detect both epileptic spikes and seizure activity from all simulated anatomical sites.

SIGNIFICANCE

No clinically available non-invasive technique can detect SOZ activity from all brain regions. Our study indicates that osMEG has the potential to become an important clinical tool, improving both non-invasive SOZ localization and iEEG electrode placement accuracy.

Optimization of patient-specific stereo-EEG recording sensitivity

Stereo-EEG is a minimally invasive technique used to localize the origin of epileptic activity (the epileptogenic zone) in patients with drug-resistant epilepsy. However, current stereo-EEG trajectory planning methods are agnostic to the spatial recording sensitivity of implanted electrodes. In this study, we used image-based patient-specific computational models to design optimized stereo-EEG electrode configurations. Patient-specific optimized electrode configurations exhibited substantially higher recording sensitivity than clinically implanted configurations, and this may lead to a more accurate delineation of the epileptogenic zone. The optimized configurations also achieved equally good or better recording sensitivity with fewer electrodes compared with clinically implanted configurations, and this may reduce the risk for complications, including intracranial haemorrhage. This approach improves localization of the epileptogenic zone by transforming the clinical use of stereo-EEG from a discrete ad hoc sampling to an intelligent mapping of the regions of interest.

An Adaptive H-Refinement Method for the Boundary Element Fast Multipole Method for Quasi-static Electromagnetic Modeling

Objective

In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.

Approach

We propose, describe, and systematically investigate an AMR method using the Boundary Element Method with Fast Multipole Acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy.The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a "silver-standard" solution found by subsequent 4:1 global refinement of the adaptively-refined model.

Main Results

Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.

Significance

This error has especially important implications for TES dosing prediction - where the stimulation strength plays a central role - and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

Relative Contributions of Different Neural Sources to the EEG

Dogma dictates that the EEG signal is generated by postsynaptic currents (PSCs) because there are an enormous number of synapses in the brain, and PSCs have relatively long durations. However, PSCs are not the only potential source of electric fields in the brain. Action potentials, afterpolarizations, and presynaptic activity can also generate electric fields. Experimentally it is exceedingly difficult to delineate the contributions of different sources because they are casually linked. However, using computational modeling, we can interrogate the relative contributions of different neural elements to the EEG. We used a library of neuron models with morphologically realistic axonal arbors to quantify the relative contributions of PSCs, action potentials, and presynaptic activity to the EEG signal. Consistent with prior assertions, PSCs were the largest contributor to the EEG, but action potentials and afterpolarizations can also make appreciable contributions. For a population of neurons generating simultaneous PSCs and action potentials, we found that the action potentials accounted for up to 20% of the source strength while PSCs accounted for the other 80% and presynaptic activity negligibly contributed. Additionally, L5 PCs generated the largest PSC and action potential signals indicating that they the dominant EEG signal generator. Further, action potentials and afterpolarizations were sufficient to generate physiological oscillations, indicating that they are valid source contributors to the EEG. The EEG emerges from a combination of multiple different source, and, while PSCs are the largest contributor, other sources are non-negligible and should be included in modeling, analysis and interpretation of the EEG.

Sensing local field potentials with a directional and scalable depth electrode array

Objective. A variety of electrophysiology tools are available to the neurosurgeon for diagnosis, functional therapy, and neural prosthetics. However, no tool can currently address these three critical needs: (a) access to all cortical regions in a minimally invasive manner; (b) recordings with microscale, mesoscale, and macroscale resolutions simultaneously; and (c) access to spatially distant multiple brain regions that constitute distributed cognitive networks.Approach.We modeled, designed, and demonstrated a novel device for recording local field potentials (LFPs) with the form factor of a stereo-electroencephalographic electrode and combined with radially distributed microelectrodes.Main results. Electro-quasistatic models demonstrate that the lead body amplifies and shields LFP sources based on direction, enablingdirectional sensitivity andscalability, referred to as thedirectional andscalable (DISC) array.In vivo,DISC demonstrated significantly improved signal-to-noise ratio, directional sensitivity, and decoding accuracy from rat barrel cortex recordings during whisker stimulation. Critical for future translation, DISC demonstrated a higher signal to noise ratio (SNR) than virtual ring electrodes and a noise floor approaching that of large ring electrodes in an unshielded environment after common average referencing. DISC also revealed independent, stereoscopic current source density measures whose direction was verified after histology.Significance. Directional sensitivity of LFPs may significantly improve brain-computer interfaces and many diagnostic procedures, including epilepsy foci detection and deep brain targeting.

Towards a mesoscale physical modeling framework for stereotactic-EEG recordings

Objective.Stereotactic-electroencephalography (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMMs). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements.Approach.We provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept.Main results.CSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of NMMs is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer).Significance.Our results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.

Ideal current dipoles are appropriate source representations for simulating neurons for intracranial recordings

OBJECTIVE

To determine whether dipoles are an appropriate simplified representation of neural sources for stereo-EEG (sEEG).

METHODS

We compared the distributions of voltages generated by a dipole, biophysically realistic cortical neuron models, and extended regions of cortex to determine how well a dipole represented neural sources at different spatial scales and at electrode to neuron distances relevant for sEEG. We also quantified errors introduced by the dipole approximation of neural sources in sEEG source localization using standardized low-resolution electrotomography (sLORETA).

RESULTS

For pyramidal neurons, the coefficient of correlation between voltages generated by a dipole and neuron model were > 0.9 for distances > 1 mm. For small regions of cortex (∼0.1 cm2), the error in voltages between a dipole and region was < 100 µV for all distances. However, larger regions of active cortex (>5 cm2) yielded > 50 µV errors within 1.5 cm of an electrode when compared to single dipoles. Finally, source localization errors were < 5 mm when using dipoles to represent realistic neural sources.

CONCLUSIONS

Single dipoles are an appropriate source model to represent both single neurons and small regions of active cortex, while multiple dipoles are required to represent large regions of cortex.

SIGNIFICANCE

Dipoles are computationally tractable and valid source models for sEEG.

L1-norm vs. L2-norm fitting in optimizing focal multi-channel tES stimulation: linear and semidefinite programming vs. weighted least squares

BACKGROUND AND OBJECTIVE

This study focuses on Multi-Channel Transcranial Electrical Stimulation, a non-invasive brain method for stimulating neuronal activity under the influence of low-intensity currents. We introduce a mathematical formulation for finding a current pattern that optimizes an L1-norm fit between a given focal target distribution and volumetric current density inside the brain. L1-norm is well-known to favor well-localized or sparse distributions compared to L2-norm (least-squares) fitted estimates.

METHODS

We present a linear programming approach that performs L1-norm fitting and penalization of the current pattern (L1L1) to control the number of non-zero currents. The optimizer filters a large set of candidate solutions using a two-stage metaheuristic search from a pre-filtered set of candidates.

RESULTS

The numerical simulation results obtained with both 8- and 20-channel electrode montages suggest that our hypothesis on the benefits of L1-norm data fitting is valid. Compared to an L1-norm regularized L2-norm fitting (L1L2) via semidefinite programming and weighted Tikhonov least-squares method (TLS), the L1L1 results were overall preferable for maximizing the focused current density at the target position, and the ratio between focused and nuisance current magnitudes.

CONCLUSIONS

We propose the metaheuristic L1L1 optimization approach as a potential technique to obtain a well-localized stimulus with a controllable magnitude at a given target position. L1L1 finds a current pattern with a steep contrast between the anodal and cathodal electrodes while suppressing the nuisance currents in the brain, hence, providing a potential alternative to modulate the effects of the stimulation, e.g., the sensation experienced by the subject.

Practical Fundamentals of Clinical MEG Interpretation in Epilepsy

Magnetoencephalography (MEG) is a neurophysiologic test that offers a functional localization of epileptic sources in patients considered for epilepsy surgery. The understanding of clinical MEG concepts, and the interpretation of these clinical studies, are very involving processes that demand both clinical and procedural expertise. One of the major obstacles in acquiring necessary proficiency is the scarcity of fundamental clinical literature. To fill this knowledge gap, this review aims to explain the basic practical concepts of clinical MEG relevant to epilepsy with an emphasis on single equivalent dipole (sECD), which is one the most clinically validated and ubiquitously used source localization method, and illustrate and explain the regional topology and source dynamics relevant for clinical interpretation of MEG-EEG.

Statistical power: Implications for planning MEG studies

Statistical power is key for robust, replicable science. Here, we systematically explored how numbers of trials and subjects affect statistical power in MEG sensor-level data. More specifically, we simulated "experiments" using the MEG resting-state dataset of the Human Connectome Project (HCP). We divided the data in two conditions, injected a dipolar source at a known anatomical location in the "signal condition", but not in the "noise condition", and detected significant differences at sensor level with classical paired t-tests across subjects, using amplitude, squared amplitude, and global field power (GFP) measures. Group-level detectability of these simulated effects varied drastically with anatomical origin. We thus examined in detail which spatial properties of the sources affected detectability, looking specifically at the distance from closest sensor and orientation of the source, and at the variability of these parameters across subjects. In line with previous single-subject studies, we found that the most detectable effects originate from source locations that are closest to the sensors and oriented tangentially with respect to the head surface. In addition, cross-subject variability in orientation also affected group-level detectability, boosting detection in regions where this variability was small and hindering detection in regions where it was large. Incidentally, we observed a considerable covariation of source position, orientation, and their cross-subject variability in individual brain anatomical space, making it difficult to assess the impact of each of these variables independently of one another. We thus also performed simulations where we controlled spatial properties independently of individual anatomy. These additional simulations confirmed the strong impact of distance and orientation and further showed that orientation variability across subjects affects detectability, whereas position variability does not. Importantly, our study indicates that strict unequivocal recommendations as to the ideal number of trials and subjects for any experiment cannot be realistically provided for neurophysiological studies and should be adapted according to the brain regions under study.

Magnetoencephalography Signal Processing, Forward Modeling, Magnetoencephalography Inverse Source Imaging, and Coherence Analysis

Magnetoencephalography (MEG) is a noninvasive functional imaging technique for the brain. MEG directly measures the magnetic signal due to neuronal activation in gray matter with high spatial localization accuracy. The first part of this article covers the overall concepts of MEG and the forward and inverse modeling techniques. It is followed by examples of analyzing evoked and resting-state MEG signals using a high-resolution MEG source imaging technique. Next, different techniques for connectivity and network analysis are reviewed with examples showing connectivity estimates from resting-state and epileptic activity.

Boundary Element Fast Multipole Method for Enhanced Modeling of Neurophysiological Recordings

OBJECTIVE

A new numerical modeling approach is proposed which provides forward-problem solutions for both noninvasive recordings (EEG/MEG) and higher-resolution intracranial recordings (iEEG).

METHODS

The algorithm is our recently developed boundary element fast multipole method or BEM-FMM. It is based on the integration of the boundary element formulation in terms of surface charge density and the fast multipole method originating from its inventors. The algorithm still possesses the major advantage of the conventional BEM - high speed - but is simultaneously capable of processing a very large number of surface-based unknowns. As a result, an unprecedented spatial resolution could be achieved, which enables multiscale modeling.

RESULTS

For non-invasive EEG/MEG, we are able to accurately solve the forward problem with approximately 1 mm anatomical resolution in the cortex within 1-2 min given several thousand cortical dipoles. Targeting high-resolution iEEG, we are able to compute, for the first time, an integrated electromagnetic response for an ensemble (2,450) of tightly packed realistic pyramidal neocortical neurons in a full-head model with 0.6 mm anatomical cortical resolution. The neuronal arbor is comprised of 5.9 M elementary 1.2 μm long dipoles. On a standard server, the computations require about 5 min.

CONCLUSION

Our results indicate that the BEM-FMM approach may be well suited to support numerical multiscale modeling pertinent to modern high-resolution and submillimeter iEEG.

SIGNIFICANCE

Based on the speed and ease of implementation, this new algorithm represents a method that will greatly facilitate simulations at multi-scale across a variety of applications.

Spatial fidelity of MEG/EEG source estimates: A general evaluation approach

Low spatial resolution is often cited as the most critical limitation of magneto- and electroencephalography (MEG and EEG), but a unifying framework for quantifying the spatial fidelity of M/EEG source estimates has yet to be established; previous studies have focused on linear estimation methods under ideal scenarios without noise. Here we present an approach that quantifies the spatial fidelity of M/EEG estimates from simulated patch activations over the entire neocortex superposed on measured resting-state data. This approach grants more generalizability in the evaluation process that allows for, e.g., comparing linear and non-linear estimates in the whole brain for different signal-to-noise ratios (SNR), number of active sources and activation waveforms. Using this framework, we evaluated the MNE, dSPM, sLORETA, eLORETA, and MxNE methods and found that the spatial fidelity varies significantly with SNR, following a largely sigmoidal curve whose shape varies depending on which aspect of spatial fidelity that is being quantified and the source estimation method. We believe that these methods and results will be useful when interpreting M/EEG source estimates as well as in methods development.

Parametrizing the Conditionally Gaussian Prior Model for Source Localization with Reference to the P20/N20 Component of Median Nerve SEP/SEF

In this article, we focused on developing the conditionally Gaussian hierarchical Bayesian model (CG-HBM), which forms a superclass of several inversion methods for source localization of brain activity using somatosensory evoked potential (SEP) and field (SEF) measurements. The goal of this proof-of-concept study was to improve the applicability of the CG-HBM as a superclass by proposing a robust approach for the parametrization of focal source scenarios. We aimed at a parametrization that is invariant with respect to altering the noise level and the source space size. The posterior difference between the gamma and inverse gamma hyperprior was minimized by optimizing the shape parameter, while a suitable range for the scale parameter can be obtained via the prior-over-measurement signal-to-noise ratio, which we introduce as a new concept in this study. In the source localization experiments, the primary generator of the P20/N20 component was detected in the Brodmann area 3b using the CG-HBM approach and a parameter range derived from the existing knowledge of the Tikhonov-regularized minimum norm estimate, i.e., the classical Gaussian prior model. Moreover, it seems that the detection of deep thalamic activity simultaneously with the P20/N20 component with the gamma hyperprior can be enhanced while using a close-to-optimal shape parameter value.

Realistic modeling of mesoscopic ephaptic coupling in the human brain

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.

Noninvasive electromagnetic source imaging of spatiotemporally distributed epileptogenic brain sources

Brain networks are spatiotemporal phenomena that dynamically vary over time. Functional imaging approaches strive to noninvasively estimate these underlying processes. Here, we propose a novel source imaging approach that uses high-density EEG recordings to map brain networks. This approach objectively addresses the long-standing limitations of conventional source imaging techniques, namely, difficulty in objectively estimating the spatial extent, as well as the temporal evolution of underlying brain sources. We validate our approach by directly comparing source imaging results with the intracranial EEG (iEEG) findings and surgical resection outcomes in a cohort of 36 patients with focal epilepsy. To this end, we analyzed a total of 1,027 spikes and 86 seizures. We demonstrate the capability of our approach in imaging both the location and spatial extent of brain networks from noninvasive electrophysiological measurements, specifically for ictal and interictal brain networks. Our approach is a powerful tool for noninvasively investigating large-scale dynamic brain networks.

Noninvasive electromagnetic measurements are utilized effectively to estimate large scale dynamic brain networks. Sohrabpour et al. propose a novel electrophysiological source imaging approach to estimate the location and size of epileptogenic tissues in patients with epilepsy.

Detectability of cerebellar activity with magnetoencephalography and electroencephalography

Electrophysiological signals from the cerebellum have traditionally been viewed as inaccessible to magnetoencephalography (MEG) and electroencephalography (EEG). Here, we challenge this position by investigating the ability of MEG and EEG to detect cerebellar activity using a model that employs a high‐resolution tessellation of the cerebellar cortex. The tessellation was constructed from repetitive high‐field (9.4T) structural magnetic resonance imaging (MRI) of an ex vivo human cerebellum. A boundary‐element forward model was then used to simulate the M/EEG signals resulting from neural activity in the cerebellar cortex. Despite significant signal cancelation due to the highly convoluted cerebellar cortex, we found that the cerebellar signal was on average only 30–60% weaker than the cortical signal. We also made detailed M/EEG sensitivity maps and found that MEG and EEG have highly complementary sensitivity distributions over the cerebellar cortex. Based on previous fMRI studies combined with our M/EEG sensitivity maps, we discuss experimental paradigms that are likely to offer high M/EEG sensitivity to cerebellar activity. Taken together, these results show that cerebellar activity should be clearly detectable by current M/EEG systems with an appropriate experimental setup.

Permutation Statistics for Connectivity Analysis between Regions of Interest in EEG and MEG Data

Connectivity estimates based on electroencephalography (EEG) and magnetoencephalography (MEG) are unique in their ability to provide neurophysiologically meaningful spectral and temporal information non-invasively. This multi-dimensional aspect of the MEG/EEG based connectivity increases the challenges of the analysis and interpretation of the data. Many MEG/EEG studies address this complexity by using a hypothesis-driven approach, which focuses on particular regions of interest (ROI). However, if an effect is distributed unevenly over a large ROI and variable across subjects, it may not be detectable using conventional methods. Here, we propose a novel approach, which enhances the statistical power for weak and spatially discontinuous effects. This results in the ability to identify statistically significant connectivity patterns with spectral, temporal, and spatial specificity while correcting for multiple comparisons using nonparametric permutation methods. We call this new approach the Permutation Statistics for Connectivity Analysis between ROI (PeSCAR). We demonstrate the processing steps with simulated and real human data. The open-source Matlab code implementing PeSCAR are provided online.

Simulating human sleep spindle MEG and EEG from ion channel and circuit level dynamics

BACKGROUND

Although they form a unitary phenomenon, the relationship between extracranial M/EEG and transmembrane ion flows is understood only as a general principle rather than as a well-articulated and quantified causal chain.

METHOD

We present an integrated multiscale model, consisting of a neural simulation of thalamus and cortex during stage N2 sleep and a biophysical model projecting cortical current densities to M/EEG fields. Sleep spindles were generated through the interactions of local and distant network connections and intrinsic currents within thalamocortical circuits. 32,652 cortical neurons were mapped onto the cortical surface reconstructed from subjects' MRI, interconnected based on geodesic distances, and scaled-up to current dipole densities based on laminar recordings in humans. MRIs were used to generate a quasi-static electromagnetic model enabling simulated cortical activity to be projected to the M/EEG sensors.

RESULTS

The simulated M/EEG spindles were similar in amplitude and topography to empirical examples in the same subjects. Simulated spindles with more core-dominant activity were more MEG weighted.

COMPARISON WITH EXISTING METHODS

Previous models lacked either spindle-generating thalamic neural dynamics or whole head biophysical modeling; the framework presented here is the first to simultaneously capture these disparate scales.

CONCLUSIONS

This multiscale model provides a platform for the principled quantitative integration of existing information relevant to the generation of sleep spindles, and allows the implications of future findings to be explored. It provides a proof of principle for a methodological framework allowing large-scale integrative brain oscillations to be understood in terms of their underlying channels and synapses.

Non-invasive laminar inference with MEG: Comparison of methods and source inversion algorithms

Magnetoencephalography (MEG) is a direct measure of neuronal current flow; its anatomical resolution is therefore not constrained by physiology but rather by data quality and the models used to explain these data. Recent simulation work has shown that it is possible to distinguish between signals arising in the deep and superficial cortical laminae given accurate knowledge of these surfaces with respect to the MEG sensors. This previous work has focused around a single inversion scheme (multiple sparse priors) and a single global parametric fit metric (free energy). In this paper we use several different source inversion algorithms and both local and global, as well as parametric and non-parametric fit metrics in order to demonstrate the robustness of the discrimination between layers. We find that only algorithms with some sparsity constraint can successfully be used to make laminar discrimination. Importantly, local t-statistics, global cross-validation and free energy all provide robust and mutually corroborating metrics of fit. We show that discrimination accuracy is affected by patch size estimates, cortical surface features, and lead field strength, which suggests several possible future improvements to this technique. This study demonstrates the possibility of determining the laminar origin of MEG sensor activity, and thus directly testing theories of human cognition that involve laminar- and frequency-specific mechanisms. This possibility can now be achieved using recent developments in high precision MEG, most notably the use of subject-specific head-casts, which allow for significant increases in data quality and therefore anatomically precise MEG recordings.

Section

Analysis methods.

Classifications

Source localization: inverse problem; Source localization: other.

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Laminar inferences can be made with MEG using both local and global fit metrics.

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Source inversion algorithms with sparsity constraints performed best.

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Classification is affected by patch size estimates, anatomy, and lead field strength.

Evaluation of realistic layouts for next generation on-scalp MEG: spatial information density maps

While commercial magnetoencephalography (MEG) systems are the functional neuroimaging state-of-the-art in terms of spatio-temporal resolution, MEG sensors have not changed significantly since the 1990s. Interest in newer sensors that operate at less extreme temperatures, e.g., high critical temperature (high-T c) SQUIDs, optically-pumped magnetometers, etc., is growing because they enable significant reductions in head-to-sensor standoff (on-scalp MEG). Various metrics quantify the advantages of on-scalp MEG, but a single straightforward one is lacking. Previous works have furthermore been limited to arbitrary and/or unrealistic sensor layouts. We introduce spatial information density (SID) maps for quantitative and qualitative evaluations of sensor arrays. SID-maps present the spatial distribution of information a sensor array extracts from a source space while accounting for relevant source and sensor parameters. We use it in a systematic comparison of three practical on-scalp MEG sensor array layouts (based on high-T c SQUIDs) and the standard Elekta Neuromag TRIUX magnetometer array. Results strengthen the case for on-scalp and specifically high-T c SQUID-based MEG while providing a path for the practical design of future MEG systems. SID-maps are furthermore general to arbitrary magnetic sensor technologies and source spaces and can thus be used for design and evaluation of sensor arrays for magnetocardiography, magnetic particle imaging, etc.

Using generative models to make probabilistic statements about hippocampal engagement in MEG

Magnetoencephalography (MEG) enables non-invasive real time characterization of brain activity. However, convincing demonstrations of signal contributions from deeper sources such as the hippocampus remain controversial and are made difficult by its depth, structural complexity and proximity to neocortex. Here, we demonstrate a method for quantifying hippocampal engagement probabilistically using simulated hippocampal activity and realistic anatomical and electromagnetic source modelling. We construct two generative models, one which supports neuronal current flow on the cortical surface, and one which supports neuronal current flow on both the cortical and hippocampal surface. Using Bayesian model comparison, we then infer which of the two models provides a more likely explanation of the dataset at hand. We also carry out a set of control experiments to rule out bias, including simulating medial temporal lobe sources to assess the risk of falsely positive results, and adding different types of displacements to the hippocampal portion of the mesh to test for anatomical specificity of the results. In addition, we test the robustness of this inference by adding co-registration error and sensor level noise. We find that the model comparison framework is sensitive to hippocampal activity when co-registration error is <3 mm and the sensor-level signal-to-noise ratio (SNR) is >-20 dB. These levels of co-registration error and SNR can now be achieved empirically using recently developed subject-specific head-casts.

Local recording of biological magnetic fields using Giant Magneto Resistance-based micro-probes

The electrical activity of brain, heart and skeletal muscles generates magnetic fields but these are recordable only macroscopically, such as in magnetoencephalography, which is used to map neuronal activity at the brain scale. At the local scale, magnetic fields recordings are still pending because of the lack of tools that can come in contact with living tissues. Here we present bio-compatible sensors based on Giant Magneto-Resistance (GMR) spin electronics. We show on a mouse muscle in vitro, using electrophysiology and computational modeling, that this technology permits simultaneous local recordings of the magnetic fields from action potentials. The sensitivity of this type of sensor is almost size independent, allowing the miniaturization and shaping required for in vivo/vitro magnetophysiology. GMR-based technology can constitute the magnetic counterpart of microelectrodes in electrophysiology, and might represent a new fundamental tool to investigate the local sources of neuronal magnetic activity.

Direct neural current imaging in an intact cerebellum with magnetic resonance imaging

The ability to detect neuronal currents with high spatiotemporal resolution using magnetic resonance imaging (MRI) is important for studying human brain function in both health and disease. While significant progress has been made, we still lack evidence showing that it is possible to measure an MR signal time-locked to neuronal currents with a temporal waveform matching concurrently recorded local field potentials (LFPs). Also lacking is evidence that such MR data can be used to image current distribution in active tissue. Since these two results are lacking even in vitro, we obtained these data in an intact isolated whole cerebellum of turtle during slow neuronal activity mediated by metabotropic glutamate receptors using a gradient-echo EPI sequence (TR=100ms) at 4.7T. Our results show that it is possible (1) to reliably detect an MR phase shift time course matching that of the concurrently measured LFP evoked by stimulation of a cerebellar peduncle, (2) to detect the signal in single voxels of 0.1mm(3), (3) to determine the spatial phase map matching the magnetic field distribution predicted by the LFP map, (4) to estimate the distribution of neuronal current in the active tissue from a group-average phase map, and (5) to provide a quantitatively accurate theoretical account of the measured phase shifts. The peak values of the detected MR phase shifts were 0.27-0.37°, corresponding to local magnetic field changes of 0.67-0.93nT (for TE=26ms). Our work provides an empirical basis for future extensions to in vivo imaging of neuronal currents.

Incorporating priors for EEG source imaging and connectivity analysis

Electroencephalography source imaging (ESI) is a useful technique to localize the generators from a given scalp electric measurement and to investigate the temporal dynamics of the large-scale neural circuits. By introducing reasonable priors from other modalities, ESI reveals the most probable sources and communication structures at every moment in time. Here, we review the available priors from such techniques as magnetic resonance imaging (MRI), functional MRI (fMRI), and positron emission tomography (PET). The modality's specific contribution is analyzed from the perspective of source reconstruction. For spatial priors, EEG-correlated fMRI, temporally coherent networks (TCNs) and resting-state fMRI are systematically introduced in the ESI. Moreover, the fiber tracking (diffusion tensor imaging, DTI) and neuro-stimulation techniques (transcranial magnetic stimulation, TMS) are also introduced as the potential priors, which can help to draw inferences about the neuroelectric connectivity in the source space. We conclude that combining EEG source imaging with other complementary modalities is a promising approach toward the study of brain networks in cognitive and clinical neurosciences.