What question did this study set out to answer?

To estimate cortical field observables in children with ADHD using EEG and evaluate their potential as discriminators.

May 17, 2026Open Access

EEG-Based Estimation of Cortical Field Observables in Pediatric ADHD: Coherence Length ξ and Effective Control Parameter λₑff as Robust Cross-Modal Discriminators, with a Methodological Note on C1 Estimation

Key Points

To estimate cortical field observables in children with ADHD using EEG and evaluate their potential as discriminators.
Analyzed a publicly available 19-channel EEG dataset from 61 ADHD and 60 neurotypical controls ages 7-12.
Estimated coherence length ξ, effective control parameter λ_eff, and global integration C1 using Ginzburg-Landau framework.
Conducted sensitivity analysis comparing raw and bandpass-filtered signals (1–40 Hz) for all observables.
Coherence length ξ: ADHD 0.074s vs Control 0.105s, d=1.220, p_FDR<0.001; largest effect size.
Effective control parameter λ_eff: ADHD -473 vs Control -229, d=1.108, p_FDR<0.001.
C1 was significant in raw signals (d=0.764, p_FDR=0.0004) but not in filtered signals.

Abstract

This paper applies the Cortical Informational Field Theory (CIFT) Ginzburg-Landau framework to a publicly available 19-channel EEG dataset (IEEE DataPort; Mohammadi et al. ; 61 ADHD + 60 neurotypical controls; ages 7–12 years; DSM-IV confirmed; 128 Hz) to estimate three cortical field observables: C1 = |⟨Φ⟩| (global integration), temporal coherence length ξ, and effective control parameter λₑff = −D₀/ξ². Key findings (FDR-corrected, Benjamini-Hochberg): - ξ: ADHD 0. 074 ± 0. 022s vs Control 0. 105 ± 0. 028s · d=1. 220 · pFDR<0. 001 ★ — largest effect size - λₑff: ADHD −473 ± 515 vs Control −229 ± 191 · d=1. 108 · pFDR<0. 001 ★ - C2 (Shannon entropy): emerges as significant after bandpass filtering (d=0. 388 · pFDR=0. 049 ★) - C1: significant in raw signals (d=0. 764 · pFDR=0. 0004) but NOT robust to bandpass filtering (d=0. 172 · p=0. 352 ns) — indicating that raw-signal C1 reflects low-frequency amplitude artifacts rather than genuine global field integration. Valid C1 estimation requires source-level EEG reconstruction or MEG. A systematic sensitivity analysis compares raw vs bandpass-filtered (1–40 Hz) signals for all observables. ξ and λₑff survive filtering with large effect sizes; C1 does not.

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