Uncertainty analysis of brain tissue conductivities in Temporal Interference (TI) stimulation

Temporal interference (TI) stimulation is a novel non-invasive brain stimulation technique that enables focal, steerable and deep brain stimulation. During TI stimulation, two high-frequency (kHz) electrical sinusoidal waveforms are applied, with a slightly different frequency between each electrode pair, that interfere inside the brain, resulting in a superimposed waveform that is amplitude modulated at the target frequency (several to tens of Hz). To understand and improve experimental and clinical results, numerical techniques such as the finite element method (FEM) are commonly used to simulate the electric fields generated by TI stimulation. However, accurately representing the various tissue conductivities in these models poses a challenge due to significant variations found in the literature. These variations can be attributed to differences in measurement techniques, experimental protocols, and individual differences among subjects and with subject age, making it difficult to predict the electric field of TI stimulation accurately. In conventional practice, performing systematic uncertainty analyses, such as using Monte Carlo methods, requires conducting numerous FEM simulations to estimate the complex multi-dimensional relationship between the field and the conductivities. Unfortunately, this approach often leads to extensive computational expenses. In this study, we are exploring an alternative approach known as non-intrusive polynomial chaos expansion. This method constructs a polynomial surrogate model that captures the functional relationship between tissue conductivities and the TI electric field, requiring fewer simulations compared to conventional approaches. Once the surrogate model is obtained, uncertainties associated with the conductivities can be propagated through it very fast. This model is then used to reveal how variations in these parameters impact the uncertainty in the resultant TI electric field. Additionally, the surrogate model allows for the computation of sensitivity measures derived from the polynomial coefficients. These measures then can be used to identify the most influential conductivities in the model.