Abstract We propose an approach and the numerical algorithm for mapping the electroencephalographic (EEG) data from the scalp to the cortex. The algorithm is based on the solution of ill-posed Cauchy problem for the Laplace’s equation using tetrahedral finite elements. The FEM-based scheme allows to calculate the volumetric distribution of a potential over the head volume. We demonstrate the usage of the the algorithm for accurate estimation of the depth of electric sources in the head. The algorithm sufficiently increases the spatial resolution of the EEG technique making it comparable with intracranial techniques.

中文翻译：

---

基于 FEM 的头皮到皮层脑电图数据映射通过柯西问题的解决方案

摘要 我们提出了一种将脑电图 (EEG) 数据从头皮映射到皮层的方法和数值算法。该算法基于使用四面体有限元求解拉普拉斯方程的不适定柯西问题。基于 FEM 的方案允许计算头部体积上电位的体积分布。我们演示了该算法用于准确估计头部电源深度的用法。该算法充分提高了 EEG 技术的空间分辨率，使其与颅内技术相媲美。