Quantifying the effects of material property frequency dispersion in volume conductor models of deep brain stimulation

The aim of this study was to examine and quantify the effect of frequency dispersion in the electrical conductivity and relative permittivity of the isotropic brain tissue on the electric potential distribution due to deep brain stimulation. A finite element model was used to determine the transfer function between the stimulus and the voltage estimated at the location of a neuron in the surrounding tissue. Isotropic brain tissue was represented using resistive, capacitive and dispersive formulations. Constant current and constant voltage stimuli were examined, using direct, capacitive and double-layer electrode coupling. Non-dispersive capacitive solutions were found to exhibit higher root mean square errors relative to fully dispersive solutions than purely resistive solutions under constant current and constant voltage stimulation. It is concluded that to fully capture the capacitive effects the frequency dependent electrical conductivity and relative permittivity should be explicitly incorporated into capacitive bulk tissue models.