This paper deals with the boundary element (BE) approach to modelling of transcranial electric stimulation as an alternative to the widely used finite element method (FEM). The advantages of the BE approach are listed in the paper and demonstrated on a computational example. The formulation is based on the quasi-static approximation of currents and voltages induced in living tissues while the head is represented by a three layered model consisting of skin, skull and brain tissues. Another contribution is the fact that the uncertainty present in the tissue conductivity values is taken into account by modelling them as uniformly distributed random variables. The stochastic collocation method (SCM) is applied for propagation of the uncertainty to the output electric scalar potential. Accordingly, stochastic moments are computed and sensitivity analysis is carried out using the ANalysis Of VAriance approach (ANOVA). The results given in the paper show the efficiency of the BE-SCM combination. Inspecting the results obtained from the proposed BE-SCM approach it is clear that the confidence intervals are appreciably larger in the interior tissues. The impact of the skull's conductivity is shown to be negligible for most of the observation points while the skin and brain conductivities have a significant impact on the output value.

本文探讨了经颅电刺激建模的边界元（BE）方法，以替代广泛使用的有限元方法（FEM）。本文列出了BE方法的优点，并在一个计算示例中进行了演示。该公式基于活组织中感应的电流和电压的准静态近似值，而头部则由包含皮肤，头骨和脑组织的三层模型表示。另一个贡献是，通过将它们电导率建模为均匀分布的随机变量，可以将存在于组织电导率值中的不确定性考虑在内。随机配置方法（SCM）用于将不确定性传播到输出电标量电势。因此，计算随机矩，并使用变异分析法（ANOVA）进行灵敏度分析。本文给出的结果表明了BE-SCM组合的效率。检查从提出的BE-SCM方法获得的结果，很明显，内部组织的置信区间明显更大。头骨电导率的影响对于大多数观察点而言可以忽略不计，而皮肤和大脑的电导率对输出值有很大影响。