EEG for Current With Two-Dimensional Support.
EEG for Current With Two-Dimensional Support.
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脑电图用于电流，并获得二维支持。
DOI：
10.1109/tbme.2017.2785342
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Leahy RM
中科院分区：
文献类型：
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作者：
Dassios G;Fokas AS;Hashemzadeh P;Leahy RM
由头皮脑电计算神经元电流密度的逆问题是高度不适定的。在某种程度上，这是由于电流源和头皮电位之间的映射的非唯一性。我们开发了一个明确的公式，头皮EEG的源限制到皮层表面的电流分量，影响EEG信号。从准静态形式的麦克斯韦方程出发，我们推导出一个只涉及电流“可见”部分的公式（即，影响EEG测量的电流的部分），以及取决于三维域Ωc、Ωf以及ΩB和Ωs的拓扑和电导率的某些辅助函数，其对大脑、脑脊液、骨头和头皮。我们推导出一般嵌套拓扑的头皮势的表达式，以及球面和椭球面的特殊情况。我们证实，在电流位于厚度为2δ的大脑球壳中的情况下，所得到的头皮电位与δ = 10− 8 m时通过三维公式得到的电位一致。电流的“可见”部分可以被明确地表征，并且由其垂直于表面的分量和产生电流的剩余切向分量的特定函数的组合组成。由此产生的能力，以限制源空间大大降低了在逆解的模糊程度，提供了更稳定的逆解的潜力，因为辅助功能，定义的映射可以有效地使用标准的数值方法计算。
The inverse problem of computing the neuronal current density from scalp EEG is highly ill-posed. In part, this is due to the nonuniqueness of the mapping between current sources and scalp potentials. We develop an explicit formula for the scalp EEG for sources constrained to the cortical surface in terms only of the components of the current that affect the EEG signal. Starting from the quasistatic form of Maxwell’s equations, we develop a formula that involves only the “visible” part of the current (i.e. the part of the current that affects the EEG measurements), as well as certain auxiliary functions which depend on the topology and conductivity of the three dimensional domains Ωc, Ωf, and Ωb and Ωs, that model the spaces occupied by the cerebrum, cerebrospinal fluid, bone and scalp respectively. we derive expressions for the scalp potential for a general nested topology, as well as for the special case of spherical and ellipsoidal surfaces. We verify that the resulting scalp potential, in the case that the current resides in a spherical shell in the cerebrum of thickness 2δ, agrees with the potential obtained via the three-dimensional, formulation, for δ = 10−8m. the “visible” part of the current can be explicitly characterized and consists of a combination of its component normal to the surface and of a certain function generating the remaining tangential components of the current. The resulting ability to restrict the source space greatly reduces the degree of ambiguity in the inverse solutions, offering the potential for more stable inverse solutions, since the auxiliary functions that define the mapping can be computed efficiently using standard numerical methods.