IEEE Trans Biomed Eng. 2020 May;67(5):1232-1242. doi: 10.1109/TBME.2019.2933836. Epub 2019 Aug 8.
To demonstrate the role of surface charge and power dissipation in the analysis of EEG measurements.
The forward EEG problem is formulated in terms of surface charge density. Using bounds based on power dissipation, the integral equations for forward solutions are shown to satisfy bounds on their eigenvalue structure.
We show that two physical variables, dissipated power and the accumulated charge at interfaces, can be used in formulating the forward problem. We derive the boundary integral equations satisfied by the charge and show their connection to the integral equations for the potential that are known from other approaches. We show how the dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in EEG boundary element methods. Using the eigenvalue structure, we propose a new method for the solution of the forward problem, where the integral kernels are regularized by the exclusion of eigenvectors associated to a finite range of eigenvalues. We demonstrate the method on a head model with realistic shape.
The eigenvalue analysis of the EEG forward problem is given a clear interpretation in terms of power dissipation and surface charge density.
The use of these variables enhances our understanding of the structure of EEG, makes connection with other techniques and contributes to the development of new analysis algorithms.
展示表面电荷和功率耗散在 EEG 测量分析中的作用。
以表面电荷密度的形式来表述正向 EEG 问题。利用基于功率耗散的界，正向解的积分方程被证明满足其特征值结构的界。
我们表明，两个物理变量，耗散功率和界面处的累积电荷，可以用于正向问题的构建。我们推导出满足电荷的边界积分方程，并展示它们与其他方法中已知的电位积分方程之间的联系。我们展示了耗散功率如何确定出现在 EEG 边界元方法中的积分算子的特征值范围的界。利用特征值结构，我们提出了一种正向问题的新求解方法，其中通过排除与有限特征值范围相关的特征向量来正则化积分核。我们在具有真实形状的头模型上演示了该方法。
EEG 正向问题的特征值分析可以根据功率耗散和表面电荷密度进行清晰的解释。
这些变量的使用增强了我们对 EEG 结构的理解，与其他技术建立了联系，并有助于开发新的分析算法。
