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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 language | English |
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Article number | 041002 |
Pages (from-to) | 1-24 |
Number of pages | 24 |
Journal | JOURNAL OF NEURAL ENGINEERING |
Volume | 21 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Aug 2024 |
MoE publication type | A2 Review article, Literature review, Systematic review |
Keywords
- conductivity
- electric field
- multi-stage modeling
- neural stimulation
- neuromodulation
- quasistatic approximation
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ConnectToBrain: Connecting to the Networks of the Human Brain
Ilmoniemi, R. (Principal investigator), Aydogan, D. B. (Project Member), Sinisalo, H. (Project Member), Li, L. (Project Member), Mäkinen, A. (Project Member), Pankka, H. (Project Member), Souza, V. (Project Member), Makkonen, M. (Project Member), Nieminen, A. (Project Member), Nissilä, I. (Project Member), Laine, M. (Project Member), Parvin, S. (Project Member), Rissanen, I. (Project Member), Kicic, D. (Project Member), Lioumis, P. (Project Member), Koistinen, L. (Project Member), Kahilakoski, O.-P. (Project Member), Raij, T. (Project Member), Soto de la Cruz, A. (Project Member), Tommila, T. (Project Member), Ylöstalo, T. (Project Member), Ukharova, E. (Project Member), Metsomaa, J. (Project Member), Vaalto, S. (Project Member), Granö, I. (Project Member), Koponen, M. (Project Member), Roine, T. (Project Member), Ahola, O. (Project Member) & Lujala, A. (Project Member)
01/08/2019 → 31/08/2026
Project: EU: ERC grants