Spatiotemporal dynamics of TMS-Evoked responses: A dual damped sine model analysis of cortical site and stimulation condition effects

Transcranial magnetic stimulation combined with EEG (TMS-EEG) provides a non-invasive window into cortical excitability and connectivity. However, interpreting TMS-evoked potentials (TEPs) remains challenging due to pervasive artifacts and the limited physiological interpretability of descriptive analytical approaches. We introduce the Dual Damped Sine (DDS) model, a parametric framework that decomposes TEPs into physiologically meaningful parameters: amplitudes (A 1 , A 2 ), frequencies (f 1 , f 2 ), and damping constants (γ 1 , γ 2 ). We applied DDS to the publicly available OpenNeuro dataset ds001849 to assess its ability to capture site- and condition-specific cortical responses. DDS achieved excellent model fits (median R 2 ≈ 0.95; RMSE ≤ 10 -6 ) and revealed significant site- and condition-specific differences in the early TEP window (15-80 ms). Active TMS produced larger amplitudes and stronger damping, particularly at DLPFC, with frequencies constrained to physiological bands. These findings are consistent with previous evidence that early TEP components reflect site-specific cortical activation (Siebner et al., 2019; Freedberg et al., 2020). Comparison with existing methods :While traditional similarity metrics quantify global waveform differences, DDS provides mechanistic interpretation of TEP dynamics through its parametric decomposition. The model captures how cortical responses evolve in time, offering insights into excitatory-inhibitory dynamics. DDS represents a novel analytical approach that not only confirms established findings about early TEP specificity but also provides physiologically interpretable parameters describing cortical response dynamics. This parametric framework advances TMS-EEG methodology by bridging the gap between waveform analysis and neurophysiological interpretation.