Quasistatic approximation in neuromodulation

Boshuo Wang, Angel V. Peterchev, Gabriel Gaugain, Risto J. Ilmoniemi, Warren M. Grill, Marom Bikson, Denys Nikolayev*

*Corresponding author for this work

Research output: Contribution to journalReview Articlepeer-review

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Abstract

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace’s equation) are solved for the spatial distribution of the field, which is separated from the field’s temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Original languageEnglish
Article number041002
Pages (from-to)1-24
Number of pages24
JournalJOURNAL OF NEURAL ENGINEERING
Volume21
Issue number4
DOIs
Publication statusPublished - 1 Aug 2024
MoE publication typeA2 Review article, Literature review, Systematic review

Keywords

  • conductivity
  • electric field
  • multi-stage modeling
  • neural stimulation
  • neuromodulation
  • quasistatic approximation

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