Computational models of temporal interference stimulation (TIS) commonly report a single electric-field estimate for a given anatomy and electrode montage. The authors sought to quantify how non-deterministic tetrahedral mesh generation—which does not produce a unique discretisation for a fixed tissue-label image—introduces numerical variability in TIS simulations. The study measured variability across independent mesh realisations and compared that with variability from repeated downstream simulation execution on a single, fixed mesh.
Ten head models were evaluated. For each head model two anatomical targets were specified: the left hippocampus and the right primary motor cortex (M1). For every model and each target the investigators generated 40 independent tetrahedral meshes (independent mesh realisations) and performed one complete TIS simulation on each mesh realisation.
Separately, for each participant the mesh whose parcel-level field estimate was closest to the cohort median was selected. Using that single, fixed mesh per participant, downstream operations (the solver and post-processing pipeline) were repeated 40 times to evaluate run-to-run variability when the geometry is held constant.
Across both procedures the dataset comprised 1,600 TIS simulations in total (40 remesh runs × 10 models for independent-mesh experiments, plus the repeated fixed-mesh executions). The workflow isolating remesh stochasticity versus solver/post-processing variability was designed to determine which step in the pipeline drives observed variability.
The primary outcome was defined as the spatial median of the TIS envelope field within a spherical target region located at the anatomical target (left hippocampus or right M1). Variability was quantified within participants using coefficients of variation across the repeated runs. Cohort ordering effects were assessed using Kendall’s tau to compare rank consistency across single-run realisations. A bootstrap analysis was used to evaluate the effect of averaging multiple independent remesh runs on suppressing stochastic noise.
Across independently remeshed runs the authors observed percent-level variability in the primary outcome. Within-participant coefficients of variation for the spatial median of the TIS envelope field ranged from 1.81% to 3.65% for the hippocampus and from 1.62% to 2.79% for M1. These figures quantify the distribution of the envelope-field median across 40 independent mesh realisations per participant and target.
When downstream operations were repeated 40 times on a selected fixed mesh per participant, run-to-run standard deviation decreased by more than 99%. This dramatic reduction demonstrates that nearly all observed workflow variability is attributable to the stochastic process of mesh generation rather than solver instability, numerical rounding, or post-processing procedures. In other words, with geometry held constant the TIS pipeline produced highly repeatable field estimates.
Using single-run mesh realisations preserved overall cohort ordering: the median Kendall’s tau was 0.867 for hippocampus and 0.911 for M1, indicating strong but not perfect agreement in participant rank ordering across single-run realisations. Despite preservation of global ordering, single-run remeshes frequently inverted the rank order of participant pairs whose predicted fields were similar, revealing that pairwise comparisons near threshold or with small differences are susceptible to stochastic mesh-induced rank flips.
A bootstrap analysis performed by the authors indicated that averaging across multiple independent remesh runs substantially reduced stochastic noise. Specifically, averaging five to ten independent remesh simulations was sufficient to effectively suppress the variability introduced by non-deterministic mesh realisations according to the authors’ analysis.
These results quantify single-workflow repeatability rather than absolute error relative to any ground truth. The study demonstrates that non-deterministic tetrahedral mesh generation produces percent-level variability in TIS envelope-field estimates and that this stochastic variation is the dominant source of run-to-run variability in the tested pipeline. Repeated solver execution on a fixed mesh yields negligible additional variability.
Consequently, when experimental conclusions depend on subtle field differences between participants or on fixed neuromodulation thresholds, stochastic mesh variation should be controlled or mitigated. The authors’ bootstrap results support a practical mitigation strategy: average multiple independent remesh runs (five to ten) to suppress stochastic noise from mesh realisations.
Note: This work reports single-workflow repeatability based on the described simulations. Details beyond what appears in the source (for example, per-subject numerical tables, exact bootstrap sampling parameters, or implementation specifics) were not reported in the source.