Adaptive multipole models of optically pumped magnetometer data

Multipole expansions have been used extensively in the Magnetoencephalography (MEG) literature for mitigating environmental interference and modelling brain signal. However, their application to Optically Pumped Magnetometer (OPM) data is challenging due to the wide variety of existing OPM sensor and array designs. We therefore explore how such multipole models can be adapted to provide stable models of brain signal and interference across OPM systems. Firstly, we demonstrate how prolate spheroidal (rather than spherical) harmonics can provide a compact representation of brain signal when sampling on the scalp surface with as few as 100 channels. We then introduce a type of orthogonal projection incorporating this basis set. The Adaptive Multipole Models (AMM), which provides robust interference rejection across systems, even in the presence of spatially structured nonlinearity errors (shielding factor is the reciprocal of the maximum fractional nonlinearity error). Furthermore, this projection is always stable, as it is an orthogonal projection, and will only ever decrease the white noise in the data. However, for array designs that are suboptimal for spatially separating brain signal and interference, this method can remove brain signal components. We contrast these properties with the more typically used multipole expansion, Signal Space Separation (SSS), which never reduces brain signal amplitude but is less robust to the effect of sensor nonlinearity errors on interference rejection and can increase noise in the data if the system is sub-optimally designed (as it is an oblique projection). We conclude with an empirical example utilizing AMM to maximize signal to noise ratio (SNR) for the stimulus locked neuronal response to a flickering visual checkerboard in a 128-channel OPM system and demonstrate up to 40 dB software shielding in real data.