The problem of reconstructing brain activity from electric potential measurements performed on the surface of a human head is not an easy task: not just because the solution of the related inverse problem is fundamentally ill-posed (not unique), but because the methods utilized in constructing a synthetic forward solution themselves contain many inaccuracies. One of these is the fact that the usual method of modelling primary currents in the human head via dipoles brings about at least 2 modelling errors: one from the singularity introduced by the dipole, and one from placing such dipoles near conductivity discontinuities in the active brain layer boundaries. In this article we observe how the removal of possible source locations from the surfaces of active brain layers affects the localisation accuracy of two inverse methods, sLORETA and Dipole Scan, at different signal-to-noise ratios (SNR), when the H(div) source model is used. We also describe the finite element forward solver used to construct the synthetic EEG data, that was fed to the inverse methods as input, in addition to the meshes that were used as the domains of the forward and inverse solvers. Our results suggest that there is a slight general improvement in the localisation results, especially at lower noise levels. The applied inverse algorithm and brain compartment under observation also affect the accuracy.

翻译：从人体头皮表面电位测量数据重建脑电活动并非易事：这不仅是因为相关逆问题的解本质上具有病态性（非唯一性），更因为用于构建合成正演解的方法本身存在诸多不精确性。其中一个关键因素是由于常规采用偶极子模型模拟人脑初级电流会产生至少两类建模误差：偶极子引入的奇异性误差，以及将此类偶极子置于活性脑组织层边界电导率不连续处产生的误差。本文研究了在采用H(div)源模型时，从活性脑组织表面移除潜在源位置对两种逆方法（sLORETA和偶极子扫描）在不同信噪比下的定位精度的影响。同时我们详细描述了用于构建合成脑电图数据的有限元正演求解器（该数据作为逆方法的输入）以及作为正演和逆求解器计算域的网格结构。研究结果表明：源空间剥皮处理对定位结果具有轻微的整体改善效果，尤其在较低噪声水平下更为显著；同时逆算法类型及所观测的脑组织分区也会影响定位精度。