Multiscale Finite Element Model of the Electrically Active Neural Tissue

The paper presents a mathematical approach to modeling of continuous, spatial and active neural tissue. It combines a nonlinear discrete cell membrane model with spatial bidomain model into one multiscale problem. The bidomain allows us to simulate the action potential (AP) propagation in the selected human brain neural tissues. The evoked potentials are stimulated by applying artificial stimulation current in the nonlinear cell model which is equivalent to direct injection of current by the internal electrode. Such approach can be used to model electrical stimulation of the neural tissue during the surgical operations or stimulation by surgically implanted devices. The model can be extended to deal with external electric or magnetic stimulus. The main focus of the paper is put on numerical adaptation of the bidomain commonly used for modeling human heart activity to new area of interest: human neural system. The authors present two formulations of the bidomain model. The first uses a pair of intra and extracellular potentials, and the second uses a pair of extracellular potential and membrane voltage. Both formulations are compared with respect to results and numerical efficiency.