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：从人类头部表面电位测量中重建大脑活动的问题并非易事：这不仅仅是因为相关逆问题的解本质上是不适定的（非唯一），还因为构建合成正向解所使用的方法本身包含诸多不准确性。其中之一是，通过偶极子对大脑中初级电流进行建模的常规方法会引入至少两种建模误差：一种来自偶极子引入的奇异性，另一种来自将这些偶极子放置在有源脑层边界处的电导率不连续附近。本文研究了当使用H(div)源模型时，从有源脑层表面移除可能的源位置如何影响两种逆方法（sLORETA和偶极子扫描）在不同信噪比下的定位精度。我们还描述了用于构建合成脑电图数据的有限元正向求解器（该数据作为逆方法的输入），以及用作正向和逆向求解器域的网格。我们的结果表明，定位结果有轻微的整体改善，尤其是在较低噪声水平下。所应用的逆算法和所观察的脑区室也会影响精度。