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

### Christian Schmidt, Ursula van Rienen

#### Abstract

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 voltage- and 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.

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#### Paper Citation

#### in Harvard Style

Schmidt C. and van Rienen U. (2013). **Single Frequency Approximation of Volume Conductor Models for Deep Brain Stimulation using Equivalent Circuits** . In *Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2013)* ISBN 978-989-8565-36-5, pages 38-47. DOI: 10.5220/0004223700380047

#### in Bibtex Style

@conference{biosignals13,

author={Christian Schmidt and Ursula van Rienen},

title={Single Frequency Approximation of Volume Conductor Models for Deep Brain Stimulation using Equivalent Circuits},

booktitle={Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2013)},

year={2013},

pages={38-47},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004223700380047},

isbn={978-989-8565-36-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2013)

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

SN - 978-989-8565-36-5

AU - Schmidt C.

AU - van Rienen U.

PY - 2013

SP - 38

EP - 47

DO - 10.5220/0004223700380047