Stochastic-deterministic boundary element modelling of transcranial electric stimulation using a three layer head model

Abstract

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.