Four-channel optically pumped magnetometer for a magnetoencephalography sensor array.

We present a novel four-channel optically pumped magnetometer (OPM) for magnetoencephalography that utilizes a two-color pump/probe scheme on a single optical axis. We characterize its performance across 18 built sensor modules. The new sensor implements several improvements over our previously developed sensor including lower vapor-cell operating temperature, improved probe-light detection optics, and reduced optical power requirements. The sensor also has new electromagnetic field coils on the sensor head which are designed using stream-function-based current optimization. We detail the coil design methodology and present experimental characterization of the coil performance. The magnetic sensitivity of the sensor is on average 12.3 fT/rt-Hz across the 18 modules while the average gradiometrically inferred sensitivity is about 6.0 fT/rt-Hz. The sensor 3-dB bandwidth is 100 Hz on average. The on-sensor coil performance is in good agreement with the simulations.

Single-trial classification of evoked responses to auditory tones using OPM- and SQUID-MEG.

Objective.Optically pumped magnetometers (OPMs) are emerging as a near-room-temperature alternative to superconducting quantum interference devices (SQUIDs) for magnetoencephalography (MEG). In contrast to SQUIDs, OPMs can be placed in a close proximity to subject's scalp potentially increasing the signal-to-noise ratio and spatial resolution of MEG. However, experimental demonstrations of these suggested benefits are still scarce. Here, to compare a 24-channel OPM-MEG system to a commercial whole-head SQUID system in a data-driven way, we quantified their performance in classifying single-trial evoked responses.Approach.We measured evoked responses to three auditory tones in six participants using both OPM- and SQUID-MEG systems. We performed pairwise temporal classification of the single-trial responses with linear discriminant analysis as well as multiclass classification with both EEGNet convolutional neural network and xDAWN decoding.Main results.OPMs provided higher classification accuracies than SQUIDs having a similar coverage of the left hemisphere of the participant. However, the SQUID sensors covering the whole helmet had classification scores larger than those of OPMs for two of the tone pairs, demonstrating the benefits of a whole-head measurement.Significance.The results demonstrate that the current OPM-MEG system provides high-quality data about the brain with room for improvement for high bandwidth non-invasive brain-computer interfacing.

The effect of spatial sampling on the resolution of the magnetostatic inverse problem.

In magnetoencephalography, linear minimum norm inverse methods are commonly employed when a solution with minimal a priori assumptions is desirable. These methods typically produce spatially extended inverse solutions, even when the generating source is focal. Various reasons have been proposed for this effect, including intrisic properties of the minimum norm solution, effects of regularization, noise, and limitations of the sensor array. In this work, we express the lead field in terms of the magnetostatic multipole expansion and develop the minimum-norm inverse in the multipole domain. We demonstrate the close relationship between numerical regularization and explicit suppression of spatial frequencies of the magnetic field. We show that the spatial sampling capabilities of the sensor array and regularization together determine the resolution of the inverse solution. For the purposes of stabilizing the inverse estimate, we propose the multipole transformation of the lead field as an alternative or complementary means to purely numerical regularization.

A minimum assumption approach to MEG sensor array design.

Objective.Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements.Approach.We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array ofmperfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise.Main results.We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity.Significance.Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.

Effects of head modeling errors on the spatial frequency representation of MEG.

Objectives.We aim to investigate the effects of head model inaccuracies on signal and source reconstruction accuracies for various sensor array distances to the head. This allows for the assessment of the importance of head modeling for next-generation magnetoencephalography (MEG) sensors, optically-pumped magnetometers (OPM).Approach.A 1-shell boundary element method (BEM) spherical head model with 642 vertices of radius 9 cm and conductivity of 0.33 S m-1was defined. The vertices were then randomly perturbed radially up to 2%, 4%, 6%, 8% and 10% of the radius. For each head perturbation case, the forward signal was calculated for dipolar sources located at 2 cm, 4 cm, 6 cm and 8 cm from the origin (center of the sphere), and for a 324 sensor array located at 10 cm to 15 cm from the origin. Equivalent current dipole (ECD) source localization was performed for each of these forward signals. The signal for each perturbed spherical head case was then analyzed in the spatial frequency domain, and the signal and ECD errors were quantified relative to the unperturbed case.Main results.In the noiseless and high signal-to-noise ratio (SNR) case of approximately ≥6 dB, inaccuracies in our spherical BEM head conductor models lead to increased signal and ECD inaccuracies when sensor arrays are placed closer to the head. This is true especially in the case of deep and superficial sources. In the noisy case however, the higher SNR for closer sensor arrays allows for an improved ECD fit and outweighs the effects of head geometry inaccuracies.Significance.OPMs may be placed directly on the head, as opposed to the more commonly used superconducting quantum interference device sensors which must be placed a few centimeters away from the head. OPMs thus allow for signals of higher spatial resolution to be captured, resulting in potentially more accurate source localizations. Our results suggest that an increased emphasis on accurate head modeling for OPMs may be necessary to fully realize its improved source localization potential.

A Four-channel Optically Pumped Magnetometer for a Magnetoencephalography Sensor Array.

We present a novel four-channel OPM sensor for magnetoencephalography that utilizes a two-color pump/probe scheme on a single optical axis. We characterize its performance across 18 built sensor modules. The new sensor implements several improvements over our previously developed sensor including lower vapor-cell operating temperature, improved probe-light detection optics, and reduced optical power requirements. The sensor also has new electromagnetic field coils on the sensor head which are designed using stream-function-based current optimization. We detail the coil design methodology and present experimental characterization of the coil performance. The magnetic sensitivity of the sensor is on average 12.3 fT/rt-Hz across the 18 modules while the average gradiometrically inferred sensitivity is about 6.0 fT/rt-Hz. The sensor 3-dB bandwidth is 100 Hz on average. The on-sensor coil performance is in good agreement with the simulations.

Calibration and Localization of Optically Pumped Magnetometers Using Electromagnetic Coils.

In this paper, we propose a method to estimate the position, orientation, and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer, and model these discreetly sampled fields using vector spherical harmonics (VSH) functions. We then localize and calibrate an OPM by minimizing the sum of squared errors between the model signals and the OPM responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the OPM sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. The currents that should be applied to the coils for approximating these low-order field components can be determined based on the VSH models. Computationally simple initial estimates of the OPM sensor parameters follow. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2°, and 0.8%, respectively. Lastly, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average dipole position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG.

Cross-Axis projection error in optically pumped magnetometers and its implication for magnetoencephalography systems.

Optically pumped magnetometers (OPMs) developed for magnetoencephalography (MEG) typically operate in the spin-exchange-relaxation-free (SERF) regime and measure a magnetic field component perpendicular to the propagation axis of the optical-pumping photons. The most common type of OPM for MEG employs alkali atoms, e.g. 87Rb, as the sensing element and one or more lasers for preparation and interrogation of the magnetically sensitive states of the alkali atoms ensemble. The sensitivity of the OPM can be greatly enhanced by operating it in the SERF regime, where the alkali atoms' spin exchange rate is much faster than the Larmor precession frequency. The SERF regime accommodates remnant static magnetic fields up to ±5 nT. However, in the presented work, through simulation and experiment, we demonstrate that multi-axis magnetic signals in the presence of small remnant static magnetic fields, not violating the SERF criteria, can introduce significant error terms in OPM's output signal. We call these deterministic errors cross-axis projection errors (CAPE), where magnetic field components of the MEG signal perpendicular to the nominal sensing axis contribute to the OPM signal giving rise to substantial amplitude and phase errors. Furthermore, through simulation, we have discovered that CAPE can degrade localization and calibration accuracy of OPM-based magnetoencephalography (OPM-MEG) systems.

Spatial sampling of MEG and EEG based on generalized spatial-frequency analysis and optimal design.

In this paper, we analyze spatial sampling of electro- (EEG) and magnetoencephalography (MEG), where the electric or magnetic field is typically sampled on a curved surface such as the scalp. By simulating fields originating from a representative adult-male head, we study the spatial-frequency content in EEG as well as in on- and off-scalp MEG. This analysis suggests that on-scalp MEG, off-scalp MEG and EEG can benefit from up to 280, 90 and 110 spatial samples, respectively. In addition, we suggest a new approach to obtain sensor locations that are optimal with respect to prior assumptions. The approach also allows to control, e.g., the uniformity of the sensor locations. Based on our simulations, we argue that for a low number of spatial samples, model-informed non-uniform sampling can be beneficial. For a large number of samples, uniform sampling grids yield nearly the same total information as the model-informed grids.

Potential of on-scalp MEG: Robust detection of human visual gamma-band responses.

Electrophysiological signals recorded intracranially show rich frequency content spanning from near-DC to hundreds of hertz. Noninvasive electromagnetic signals measured with electroencephalography (EEG) or magnetoencephalography (MEG) typically contain less signal power in high frequencies than invasive recordings. Particularly, noninvasive detection of gamma-band activity (>30 Hz) is challenging since coherently active source areas are small at such frequencies and the available imaging methods have limited spatial resolution. Compared to EEG and conventional SQUID-based MEG, on-scalp MEG should provide substantially improved spatial resolution, making it an attractive method for detecting gamma-band activity. Using an on-scalp array comprised of eight optically pumped magnetometers (OPMs) and a conventional whole-head SQUID array, we measured responses to a dynamic visual stimulus known to elicit strong gamma-band responses. OPMs had substantially higher signal power than SQUIDs, and had a slightly larger relative gamma-power increase over the baseline. With only eight OPMs, we could obtain gamma-activity source estimates comparable to those of SQUIDs at the group level. Our results show the feasibility of OPMs to measure gamma-band activity. To further facilitate the noninvasive detection of gamma-band activity, the on-scalp OPM arrays should be optimized with respect to sensor noise, the number of sensors and intersensor spacing.

Optical Co-registration of MRI and On-scalp MEG.

To estimate the neural generators of magnetoencephalographic (MEG) signals, MEG data have to be co-registered with an anatomical image, typically an MR image. Optically-pumped magnetometers (OPMs) enable the construction of on-scalp MEG systems providing higher sensitivity and spatial resolution than conventional SQUID-based MEG systems. We present a co-registration method that can be applied to on-scalp MEG systems, regardless of the number of sensors. We apply a structured-light scanner to create a surface mesh of the subject's head and the sensor array, which we fit to the MR image. We quantified the reproducibility of the mesh and localised current dipoles with a phantom. Additionally, we measured somatosensory evoked fields (SEFs) to median nerve stimulation and compared the dipole positions between on-scalp and SQUID-based systems. The scanner reproduced the head surface with <1 mm error. Phantom dipoles were localised with 2.1 mm mean error. SEF dipoles corresponding to the P35m response for OPMs were well localised to the somatosensory cortex, while SQUID dipoles for two subjects were erroneously localised to the motor cortex. The developed co-registration method is inexpensive, fast and can easily be applied to on-scalp MEG. It is more convenient than traditional co-registration methods while also being more accurate.

On-scalp MEG system utilizing an actively shielded array of optically-pumped magnetometers.

The spatial resolution of magnetoencephalography (MEG) can be increased from that of conventional SQUID-based systems by employing on-scalp sensor arrays of e.g. optically-pumped magnetometers (OPMs). However, OPMs reach sufficient sensitivity for neuromagnetic measurements only when operated in a very low absolute magnetic field of few nanoteslas or less, usually not reached in a typical magnetically shielded room constructed for SQUID-based MEG. Moreover, field drifts affect the calibration of OPMs. Static and dynamic suppression of interfering fields is thus necessary for good-quality neuromagnetic measurements with OPMs. Here, we describe an on-scalp MEG system that utilizes OPMs and external compensation coils that provide static and dynamic shielding against ambient fields. In a conventional two-layer magnetically shielded room, our coil system reduced the maximum remanent DC-field component within an 8-channel OPM array from 70 to less than 1 nT, enabling the sensors to operate in the sensitive spin exchange relaxation-free regime. When compensating field drifts below 4 Hz, a low-frequency shielding factor of 22 dB was achieved, which reduced the peak-to-peak drift from 1.3 to 0.4 nT and thereby the standard deviation of the sensor calibration from 1.7% to 0.5%. Without band-limiting the field that was compensated, a low-frequency shielding factor of 43 dB was achieved. We validated the system by measuring brain responses to electric stimulation of the median nerve. With dynamic shielding and digital interference suppression methods, single-trial somatosensory evoked responses could be detected. Our results advance the deployment of OPM-based on-scalp MEG in lighter magnetic shields.

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 [Formula: see text] and [Formula: see text], respectively.

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.