Electric propagation modeling of Deep Brain Stimulation (DBS) using the finite element method (FEM)

Deep Brain Stimulation (DBS) is a clinical treatment for Parkinson disease and has demonstrated the effective control of some of the symptoms related with Parkinson. DBS consist in the implantation of a neurostimulator into a region of the brain such as the subthalamic nucleus, the internal globus pallidus, etc. The electrodes are configured with a desired electric pulse in order to achieve the neural activation of the objective regions. Parameters of the stimulation pulse are experimentally adjusted for the neurologist during several sessions. In recent years, some efforts has been realized in order to facilitate the selection of the optimal parameters for DBS therapy without the experimental process, using head models that includes the electrical properties and geometry of the different brain structures in which the electric propagation is desired. The large variety of electromagnetic phenomena can all be described by the Maxwell's equations, which are also the basis for deep brain stimulation modelling. In particular, the Laplace equation is well suited for computing the electric propagation due DBS. For solving the Laplace equation in complex geometries is used the finite element method (FEM), which allows to compute of a numerical solution of differential equations applied over several domains by the creation of a structured mesh. The state of art works presented in the context of DBS modelling such as [1] [2] commonly uses a commercial software for FEM calculation. Since there is no way to measure the potentials directly from the brain during DBS, propagation models of the brain must be builded to determine the electric propagation. Nowadays, several GNU libraries for FEM computing are available. This work addresed the use of FEnICS library for C++ and phyton for solving the electric propagation in 2D and 3D geometrical models. With this in mind, we are interested in estimating the voltage propagation, around the DBS lead, in a particular area of the brain. Results show that the GNU libraries are well suited for FEM-DBS modelling in contrast to the obtained results using commercial software found in the literature.