Comparison of Model Order Reduction Methods for a Linear Finite Element Model of an Electrically Stimulated Neuron

Computer simulations of the reaction of neurons to electric stimulation can help to improve the understanding of the mechanisms behind deep brain stimulation. This is necessary to develop better treatments for patients who suffer from Parkinson’s disease, epilepsy, or other disorders. Since detailed and accurate computer simulations of neurons are computationally expensive, different methods are available to reduce this complexity. In this paper, we aim to reduce the computational complexity of a linear finite-element model of a neuron, which is placed atop a planar electrode, by applying three different model order reduction methods. Precisely, we use Krylov subspace-based model order reduction, proper orthogonal decomposition, and operator inference to obtain reduced models of different orders. Furthermore, we compare the quality of the obtained reduced-order models with the full-size finite-element model. Additionally, we compare the computational (CPU) time to construct the different reduced-order models.