Petrov Yury
Northeastern University, 125 NI, 360 Huntington Avenue, Boston, Massachusetts 02115, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011917. doi: 10.1103/PhysRevE.86.011917. Epub 2012 Jul 18.
This study reports on a solution to Poisson's equation describing an electric potential and field generated by a dipolar current source positioned inside a set of concentric spherical shells characterized by a homogeneous anisotropic conductivity inside each shell. Formulas giving a unique continuation of potentials and fields between the shells are derived. The formulas are applied to a spherical model of the human head to show that (i) real human skulls comprising isotropic compact and cancellous bone layers can be closely approximated by a single shell with radial-tangential conductivity anisotropy ~1:2 and radial conductivity equal to 1/30 of the brain/scalp conductivity; (ii) errors due to the spherical approximation of the head shape are of the same magnitude as errors due to poorly known electrical properties of the modeled head tissues; (iii) commonly used electroencephalography (EEG) average reference contributes 15% of the signal (on the average) and, therefore, makes EEG measurements significantly nonlocal; and (iv) the surface Laplacian of EEG measurements closely approximates electric currents at the skull-scalp interface, providing a parameter-free (up to a constant factor) deblurring and dereferencing of EEG data. These results can be useful for localization of sources underlying electric activity of the brain.
本研究报告了一种泊松方程的求解方法，该方程描述了位于一组同心球壳内部的偶极电流源所产生的电势和电场，每个球壳内部具有均匀各向异性电导率。推导了给出球壳间电势和电场唯一延拓的公式。这些公式应用于人体头部的球形模型，以表明：（i）由各向同性致密骨层和松质骨层组成的真实人类头骨可以通过具有径向 - 切向电导率各向异性约为1:2且径向电导率等于脑/头皮电导率1/30的单个球壳来紧密近似；（ii）由于头部形状的球形近似所导致的误差与由于所建模的头部组织电特性知之甚少所导致的误差大小相同；（iii）常用的脑电图（EEG）平均参考贡献了15%的信号（平均而言），因此使EEG测量具有显著的非局部性；（iv）EEG测量的表面拉普拉斯算子紧密近似头骨 - 头皮界面处的电流，为EEG数据提供了无参数（除一个常数因子外）的去模糊和去参考。这些结果对于大脑电活动潜在源的定位可能是有用的。
