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The objective of this study was to investigate the role of frequency-dependent material properties on the voltage response and neural activation in a volume conductor model for deep brain stimulation (DBS). A finite element model of the brain was developed comprising tissue heterogeneity of gray matter, white matter, and cerebrospinal fluid, which was derived from magnetic resonance images of the SRI24 multi-channel brain atlas. A model of the Medtronic DBS 3387 lead surrounded by an encapsulation layer was positioned in the subthalamic nucleus (STN). The frequency-dependent properties of brain tissue and their single-frequency approximations were modelled as voltageand current-controlled equivalent circuits. The frequency of best approximation, for which the pulse deviation between the single-frequency and frequency-dependent voltage response were minimal, was computed in a frequency range between 130 Hz and 1:3 MHz. Single-frequency approximations of the DBS pulses and the resulting volume of tissue activated (VTA) were found to be in good agreement with the pulses and VTAs obtained from the frequency-dependent solution. Single-frequency approximations were computed by combining finite element method with equivalent circuits. This method allows a fast computation of the time-dependent voltage response in the proximity of the stimulated target by requiring only one finite element computation.

Single Frequency Approximation of Volume Conductor Models for Deep Brain Stimulation using Equivalent Circuits