Quasistatic approximation in neuromodulation

Quasistatic approximation in neuromodulation

January 2024 | Boshuo Wang, Angel V. Peterchev, Gabriel Gaugain, Risto J. Ilmoniemi, Warren M. Grill, Marom Bikson, and Denys Nikolayev
The paper "Quasistatic approximation in neuromodulation" by Boshuo Wang et al. defines and explains the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation in neuromodulation. 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: no wave propagation or self-induction in tissue, linear tissue properties, purely resistive tissue, and non-dispersive tissue. These assumptions allow for the assignment of a fixed conductivity to each tissue and the solution of simplified equations (e.g., Laplace’s equation) for the spatial distribution of the electric field (E-field), which is separated from the temporal waveform. The authors explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. They 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. The paper also provides recommendations for communicating the use of QSA in modeling studies to promote transparency and reproducibility.The paper "Quasistatic approximation in neuromodulation" by Boshuo Wang et al. defines and explains the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation in neuromodulation. 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: no wave propagation or self-induction in tissue, linear tissue properties, purely resistive tissue, and non-dispersive tissue. These assumptions allow for the assignment of a fixed conductivity to each tissue and the solution of simplified equations (e.g., Laplace’s equation) for the spatial distribution of the electric field (E-field), which is separated from the temporal waveform. The authors explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. They 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. The paper also provides recommendations for communicating the use of QSA in modeling studies to promote transparency and reproducibility.
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[slides and audio] Quasistatic approximation in neuromodulation