A complete-electrode-model-based forward approach for transcranial temporal interference stimulation with linearization: A numerical simulation study

Abstract

Background and Objective: Transcranial temporal interference stimulation (tTIS) is a promising non-invasive brain stimulation technique in which interference between electrical current fields extends the possibilities of electrical brain stimulation. This study aims to establish and evaluate the complete electrode model (CEM), a set of boundary conditions incorporating electrode impedance and contact patch, as a forward simulation technique for tTIS and investigate linearized CEM as a surrogate. Methods: The electric potential distribution in the head was simulated using the finite element method (FEM) combined with the CEM. A frequency-dependent lead field formulation and its linearization with respect to electrode impedance were implemented to reflect the capacitive properties of electrode interfaces. The simulations were conducted in a realistic multi-compartment head model, where the accuracy of the surrogate was evaluated against the full nonlinear model across two different changes in contact impedance from the initial Rc=270Ω to Rc∈{1270,5270}Ω. Results: The CEM-based forward simulation successfully reproduced the volumetric stimulating fields induced by tTIS. The linearized CEM model closely matched the full nonlinear model within a predefined peak signal-to-noise ratio (PSNR) threshold for relative error. Both models exhibited the highest sensitivity near the focal region of tTIS. Conclusion: The results demonstrate that linearization with respect to frequency can yield a computationally efficient approximation of the lead field, retaining sufficient accuracy within a practical PSNR threshold. The surrogate captures key sensitivity characteristics of the full model, particularly near the focal region, highlighting its potential for tasks where frequent updates of stimulation parameters are required.