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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.

Optically-pumped magnetometers (OPM) -- next-generation magnetoencephalography (MEG) sensors -- may be placed directly on the head, unlike the more commonly used superconducting quantum interference device (SQUID) sensors, which must be placed a few centimeters away. This allows for signals of higher spatial resolution to be captured, resulting in potentially more accurate source localization. In this paper, we show that in the noiseless and high signal-to-noise ratio (SNR) case of approximately $\geq 6$ dB, inaccuracies in boundary element method (BEM) head conductor models (or equivalently, inaccurate volume current models) lead to increased signal and equivalent current dipole (ECD) source localization inaccuracies when sensor arrays are placed closer to the head. This is true especially in the case of deep and superficial sources where volume current contributions are high. 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. This calls for an increase in emphasis in head modeling to reduce inverse modeling errors, especially as the field of MEG strives for closer sensor arrays and cleaner signals. An analytical form to obtain the magnetic field errors for small perturbations in the BEM head geometry is also provided.

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 a sensor by minimizing the sum of squared errors between the model signals and the sensor responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. By determining the coil currents based on the VSH models, the coil fields can approximate these low-order field components, yielding computationally simple initial estimates of the sensor parameters. 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{\deg} and 0.8%, respectively. Last, 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 position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG., Comment: 21 pages, 6 figures

A non-invasive functional-brain-imaging system based on optically-pumped-magnetometers (OPM) is presented. The OPM-based magnetoencephalography (MEG) system features 20 OPM channels conforming to the subject's scalp. Due to proximity (12 mm) of the OPM channels to the brain, it is anticipated that this MEG system offers an enhanced spatial resolution as it can capture finer spatial features compared to traditional MEG systems employing superconducting quantum interference device (SQUID). We have conducted two MEG experiments on three subjects: somatosensory evoked magnetic field (SEF) and auditory evoked magnetic field (AEF) using our OPM-based MEG system and a commercial SQUID-based MEG system. We have cross validated the robustness of our system by calculating the distance between the location of the equivalent current dipole (ECD) yielded by our OPM-based MEG system and the ECD location calculated by the commercial SQUID-based MEG system. We achieved sub-centimeter accuracy for both SEF and AEF responses in all three subjects.

We describe a multichannel magnetoencephalography (MEG) system that uses optically pumped magnetometers (OPMs) to sense the magnetic fields of the human brain. The system consists of an array of 20 OPM channels conforming to the human subject's head, a person-sized magnetic shield containing the array and the human subject, a laser system to drive the OPM array, and various control and data acquisitions systems. We conducted two MEG experiments: auditory evoked magnetic field (AEF) and somatosensory evoked magnetic field (SEF), on three healthy male subjects, using both our OPM array and a 306-channel Elekta-Neuromag superconducting quantum interference device (SQUID) MEG system. The described OPM array measures the tangential components of the magnetic field as opposed to the radial component measured by all SQUID-based MEG systems. Herein we compare the results of the OPM- and SQUID-based MEG systems on the auditory and somatosensory data recorded in the same individuals on both systems.