Modeling and behavior of the simulation of electric propagation during deep brain stimulation

Deep brain stimulation (DBS) is an effective treatment for Parkinson's disease. In the literature, there are a wide variety of mathematical and computational models to describe electric propagation during DBS; however unfortunately, there is no clarity about the reasons that justify the use of a specific model. In this work, we present a detailed mathematical formulation of the DBS electric propagation that supports the use of a model based on the Laplace Equation. Moreover, we performed DBS simulations for several geometrical models of the brain in order to determine whether geometry size, shape and ground location influence electric stimulation prediction by using the Finite Element Method (FEM). Theoretical and experimental analysis show, firstly, that under the correct assumptions, the Laplace equation is a suitable alternative to describe the electric propagation, and secondly, that geometrical structure, size and grounding of the head volume affect the magnitude of the electric potential, particularly for monopolar stimulation. Results show that, for monopolar stimulation, basic and more realistic models can differ more than 2900%.