Uncertainty analysis of tissue conductivities in temporal interference stimulation based on polynomial chaos expansion

Temporal interference (TI) stimulation offers a non-invasive approach to stimulate deep regions in the brain, utilizing two pairs of electrodes generating high-frequency electrical waveforms with a slight difference in frequency. When these waveforms interfere spatially and temporally within the brain, they generate a focus region with an amplitude-modulated waveform, that couples into neurons. To optimize and understand the clinical applications of TI, the finite element method (FEM) is used to simulate the resultant electric fields from TI stimulation. However, a notable challenge in predicting TI electric field using simulations is the accurate representation of various tissue conductivities. The existing literature shows vast variations in these values, stemming from different measurement techniques, experimental setups, and individual differences among subjects. While methods like the Monte Carlo analysis provide uncertainty analyses, they necessitate multiple FEM simulations, leading to high computational costs. Our study explores a more efficient alternative approach known as non-intrusive polynomial chaos expansion to achieve the same. This method constructs a polynomial surrogate model, mapping the relationship between tissue conductivities and the TI electric field, cutting down the number of needed simulations. Once this surrogate model is in place, it can rapidly assess uncertainties related to tissue conductivities. To assess the applicability of the method, we apply our approach to a multimodal imaging-based highly detailed anatomical computer brain model to investigate how tissue conductivity uncertainties impact the uncertainty of the resultant TI electric field across three distinct stimulation targets.