Tierney Tim M, Seedat Zelekha, St Pier Kelly, Mellor Stephanie, Barnes Gareth R
Department of Imaging Neuroscience, UCL Queen Square Institute of Neurology, University College London, London, UK.
Diagnostic Suite, Young Epilepsy, St Piers Lane, Surrey, UK.
Hum Brain Mapp. 2024 Mar;45(4):e26596. doi: 10.1002/hbm.26596.
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.
多极展开已在脑磁图（MEG）文献中广泛用于减轻环境干扰和对脑信号进行建模。然而，由于现有的光泵磁力仪（OPM）传感器和阵列设计种类繁多，将其应用于OPM数据具有挑战性。因此，我们探讨如何调整这种多极模型，以提供跨OPM系统的稳定脑信号和干扰模型。首先，我们展示了在头皮表面使用少至100个通道进行采样时，长椭球（而非球形）谐波如何能够紧凑地表示脑信号。然后，我们引入了一种包含此基集的正交投影。自适应多极模型（AMM），即使在存在空间结构非线性误差（屏蔽因子是最大分数非线性误差的倒数）的情况下，也能在系统间提供强大的干扰抑制。此外，这种投影始终是稳定的，因为它是正交投影，并且只会降低数据中的白噪声。然而，对于在空间上分离脑信号和干扰方面次优的阵列设计，此方法可能会去除脑信号成分。我们将这些特性与更常用的多极展开——信号空间分离（SSS）进行对比，SSS从不降低脑信号幅度，但对传感器非线性误差对干扰抑制的影响不太稳健，并且如果系统设计次优（因为它是斜投影），可能会增加数据中的噪声。我们以一个实证示例作为结论，该示例利用AMM在128通道OPM系统中最大化对闪烁视觉棋盘的刺激锁定神经元反应的信噪比（SNR），并在实际数据中展示高达40 dB的软件屏蔽。
