A power law predicts held-out SEEG N1 amplitude better than an exponential law in 8 patients

Pre-registered test of the shape of the decrease of cortico-cortical evoked potential (CCEP) N1 amplitude with distance. Data: 2,316 expert-checked other-shaft N1s from 8 patients in OpenNeuro ds005448 v1.0.0. For each patient we fit ln|A| = a − d/λ (exponential) and ln|A| = a − k ln d (power law), then compared held-out squared error with 5-fold cross-validation grouped by stimulation pair. The power law gave a lower error in 7 of 8 patients (mean difference +0.052, bootstrap 95% CI +0.014 to +0.109, exact sign-flip p = 0.016; median relative decrease 7%). With same-shaft rows added, 8/8 patients favored the power law (p = 0.008). In the 10–60 mm window, the difference was not significant (6/8, p = 0.14), so most of the effect comes from the near and far ends. A model with both terms did not improve on the better single model. The shape of N1 probability did not separate the two laws (p = 0.88). The fitted exponent k was 0.35–1.16 (median 0.65); the exponential length was 19–84 mm, so one fixed length scale did not transfer across patients. Distance explained a small part of amplitude variance (held-out R² at most 0.38). Limits: one center, MNI straight-line distance, only detected N1s (small far responses can be missing), and recording reference and current not modeled.

stereo-EEG · cortico-cortical evoked potentials · N1 amplitude · distance decay · power law · exponential model · cross-validation · epilepsy