Accuracy of the Finite Element Method in Deep Brain Stimulation modelling

Deep Brain Stimulation (DBS) is a widely established treatment for Parkinson´s Disease where electrical pulsatile stimulation is delivered to a target area in the brain by means of an implanted electrode. To understand better how the stimuli propagate through the brain of the patient, mathematical models of various levels of sophistication have been developed using Finite Element Methods (FEM). However, the accuracy of these models, aiming mostly at stimuli tuning in and individualization of DBS systems, is still unclear. One complication is posed by the interface between the encapsulation tissue surrounding the electrode lead and the bulk brain tissue. It is usually modelled as a discontinuity in the electric conductivity, which translates into a discontinuity of the first derivative of the electric potential. The goal of this study is to analyze the accuracy of the solution yielded by the FEM tool using different interface models between the two media, comparing it to the one predicted in the literature. The obtained results suggest that, although a discontinuous conductivity will not introduce any extra numerical inaccuracies, exchanging the interface with a discontinuous conductivity for a smooth transition might yield more accurate model solutions.