A latent force model for describing electric propagation in deep brain stimulation: A simulation study

Deep brain stimulation (DBS) is a neurosurgical method used to treat symptoms of movement disorders by implanting electrodes in deep brain areas. Often, the DBS modeling approaches found in the literature assume a quasi-static approximation, and discard any dynamic behavior. Nevertheless, in a real DBS system the stimulus corresponds to a wave that changes as a function of time. It is clear that DBS demands an approach that takes into account the time-varying behavior of the input stimulus. In this work, we present a novel latent force model for describing the dynamic electric propagation occurred during DBS. The performance of the proposed model was studied by simulations under different conditions. The results show that our approach is able to take into account the time variations of the source and the produced field. Moreover, by restricting our model it is possible to obtain solutions for electrostatic formulations, here experimental results were compared with the finite element method. Additionally, our approach allows a solution to the inverse problem, which is a valuable clinical application allowing the appropriate tuning of the DBS device by the expert physician.