Electrical and Computer Engineering, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, United States of America.
J Neural Eng. 2021 May 4;18(4). doi: 10.1088/1741-2552/abebc3.
When currents are injected into the scalp, e.g. during transcranial current stimulation, the resulting currents generated in the brain are substantially affected by the changes in conductivity and geometry of intermediate tissue. In this work, we introduce the concept of 'skull-transparent' currents, for which the changing conductivity does not significantly alter the field while propagating through the head.We establish transfer functions relating scalp currents to head potentials in accepted simplified models of the head, and find approximations for which skull-transparency holds. The current fields resulting from specified current patterns are calculated in multiple head models, including MRI heads and compared with homogeneous heads to characterize the transparency. Experimental validation is performed by measuring the current field in head phantoms.The main theoretical result is derived from observing that at high spatial frequencies, in the transfer function relating currents injected into the scalp to potential generated inside the head, the conductivity terms form a multiplicative factor and do not otherwise influence the transfer function. This observation is utilized to design injected current waveforms that maintain nearly identical focusing patterns independently of the changes in skull conductivity and thickness for a wide range of conductivity and thickness values in an idealized spherical head model as well as in a realistic MRI-based head model. Experimental measurements of the current field in an agar-based head phantom confirm the transparency of these patterns.Our results suggest the possibility that well-chosen patterns of current injection result in precise focusing inside the brain even withoutknowledge of exact conductivities of intermediate layers.
当电流注入头皮时，例如在经颅电流刺激期间，大脑中产生的电流会受到中间组织电导率和几何形状变化的极大影响。在这项工作中，我们引入了“颅骨透明”电流的概念，对于这种电流，在通过头部传播时，电导率的变化不会显著改变电场。我们建立了头皮电流与头部电位之间的传递函数，这些传递函数适用于头部简化模型，并找到了保持颅骨透明性的近似值。在多个头部模型中计算了指定电流模式产生的电流场，包括 MRI 头部，并与均匀头部进行比较，以表征透明度。通过在头部体模中测量电流场来进行实验验证。主要的理论结果源于观察到，在高空间频率下，在将头皮注入电流与头部内部产生的电位相关联的传递函数中，电导率项形成一个乘法因子，而不会以其他方式影响传递函数。这一观察结果被用于设计注入电流波形，这些波形在理想球形头部模型以及基于 MRI 的实际头部模型中，在广泛的电导率和厚度范围内，保持几乎相同的聚焦模式，而与颅骨电导率和厚度的变化无关。在基于琼脂的头部体模中测量电流场的实验证实了这些模式的透明性。我们的结果表明，即使不知道中间层的确切电导率，选择合适的电流注入模式也有可能实现大脑内部的精确聚焦。
