The point spread function of the human head and its implications for transcranial current stimulation
The point spread function of the human head and its implications for transcranial current stimulation
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DOI：
10.1088/0031-9155/57/20/6459
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发表时间：
2012-10-21
影响因子：
3.5
通讯作者：
Parra, Lucas C.
中科院分区：
文献类型：
--
作者：
Dmochowski, Jacek P.;Bikson, Marom;Parra, Lucas C.
合理开发经颅电流刺激（TCS）需要解决“正向问题”：计算头皮电流的应用所产生的头部电场分布。前向模型的推导代表了脑刺激研究中的主要努力，模型复杂度从球壳到基于磁共振成像的个性化头部模型。尽管有这样的努力，一个容易获得的基准头部模型是非常需要的个性化建模是不希望的（观察一般人口趋势，而不是个体差异）或不可行的。在这里，我们推导出一个封闭形式的线性系统，其中所施加的电流的感应电势。它示出，在球谐（傅立叶）域中，一个简单的标量乘法与头皮上的电流密度在大脑中的电位。等效地，头部中的电流密度遵循头皮电流分布和头部的点扩散函数之间的球面卷积，我们推导出。因此，如果知道头皮电流的球谐表示（即，要采用的电极位置和电流强度），则可以容易地计算头部内任何点处的所得电场。相反，也可以很容易地确定在大脑中产生任意电场所需的头皮电流分布（tCS中的“向后问题”）。我们展示了简单和实用的模型与一系列的特征曲线，扫过各种刺激参数：电极尺寸，刺激深度，头部尺寸和阳极-阴极分离。最后，理论上最佳的蒙太奇为目标的一个无穷小的点在大脑中示出。
Rational development of transcranial current stimulation (tCS) requires solving the 'forward problem': the computation of the electric field distribution in the head resulting from the application of scalp currents. Derivation of forward models has represented a major effort in brain stimulation research, with model complexity ranging from spherical shells to individualized head models based on magnetic resonance imagery. Despite such effort, an easily accessible benchmark head model is greatly needed when individualized modeling is either undesired (to observe general population trends as opposed to individual differences) or unfeasible. Here, we derive a closed-form linear system which relates the applied current to the induced electric potential. It is shown that in the spherical harmonic (Fourier) domain, a simple scalar multiplication relates the current density on the scalp to the electric potential in the brain. Equivalently, the current density in the head follows as the spherical convolution between the scalp current distribution and the point spread function of the head, which we derive. Thus, if one knows the spherical harmonic representation of the scalp current (i.e. the electrode locations and current intensity to be employed), one can easily compute the resulting electric field at any point inside the head. Conversely, one may also readily determine the scalp current distribution required to generate an arbitrary electric field in the brain (the 'backward problem' in tCS). We demonstrate the simplicity and utility of the model with a series of characteristic curves which sweep across a variety of stimulation parameters: electrode size, depth of stimulation, head size and anode-cathode separation. Finally, theoretically optimal montages for targeting an infinitesimal point in the brain are shown.