January 2024 | Boshuo Wang, Angel V. Peterchev, Gabriel Gaugain, Risto J. Ilmoniemi, Warren M. Grill, Marom Bikson, and Denys Nikolayev
The quasistatic approximation (QSA) is a simplification used in neuromodulation modeling to calculate electric and magnetic fields in tissues. It is based on four assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. These assumptions allow the use of simplified equations, such as Laplace's equation, to model the spatial distribution of fields, separating them from their temporal waveform. QSA is widely used in neuromodulation, including electrical and magnetic stimulation techniques like transcranial electrical stimulation (tES), transcranial magnetic stimulation (TMS), and spinal cord stimulation (SCS). While QSA is typically applied to low-frequency signals (below 100 kHz), it is not suitable for high-frequency or light-based stimulation. The paper discusses the application of QSA in various neuromodulation contexts, including the separation of spatial and temporal components of fields, the use of QSA in multi-stage modeling pipelines, and the implications of relaxing assumptions. It also addresses the frequency dependence of tissue electrical parameters and the validity of QSA in different applications. The paper concludes with recommendations for transparent and reproducible use of QSA in neuromodulation modeling.The quasistatic approximation (QSA) is a simplification used in neuromodulation modeling to calculate electric and magnetic fields in tissues. It is based on four assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. These assumptions allow the use of simplified equations, such as Laplace's equation, to model the spatial distribution of fields, separating them from their temporal waveform. QSA is widely used in neuromodulation, including electrical and magnetic stimulation techniques like transcranial electrical stimulation (tES), transcranial magnetic stimulation (TMS), and spinal cord stimulation (SCS). While QSA is typically applied to low-frequency signals (below 100 kHz), it is not suitable for high-frequency or light-based stimulation. The paper discusses the application of QSA in various neuromodulation contexts, including the separation of spatial and temporal components of fields, the use of QSA in multi-stage modeling pipelines, and the implications of relaxing assumptions. It also addresses the frequency dependence of tissue electrical parameters and the validity of QSA in different applications. The paper concludes with recommendations for transparent and reproducible use of QSA in neuromodulation modeling.