Organised and Dissipated Neural Energy: A Two-Dimensional Marker of Phenomenal State from Resting EEG

Abstract

Abstract A fundamental question for consciousness science is what changes in the brain when phenomenal experience arises or restructures. Current EEG metrics of consciousness fall into two classes: empirically calibrated clinical indices (Bispectral Index, Odd Ratio Product) and theoretically motivated complexity measures (Lempel-Ziv complexity, Perturbational Complexity Index). Both classes share a critical limitation: they are one-dimensional, tracking only the level of consciousness, not its internal structure. We introduce a two-dimensional framework built on a single theoretically grounded metric: η (spatial efficiency), defined as the ratio of organised oscillatory power to total oscillatory power across five frequency bands. η = ||Ψ|| / ||A||, where Ψ is the Effective Power Vector (amplitude weighted by spatial pattern stability Sγ) and A is the total amplitude vector. η is amplitude-independent by construction and is motivated simultaneously by the Free Energy Principle (Friston 2010), Global Workspace Theory (Dehaene & Changeux 2011), and predictive processing accounts (Seth & Bayne 2022): each predicts that conscious states require the active maintenance of organised spatial patterns of neural activity. A complementary metric, angle(Ψ,Δ), quantifies the structural tension between organised and dissipated energy vectors, providing a second dimension sensitive to within-state phenomenal structure. We validate η and angle(Ψ,Δ) across four independent EEG datasets. In the Bajwa propofol sedation dataset (N=20), η achieves AUC=0.970 (d=2.24, p<0.001), substantially outperforming the Odd Ratio Product (AUC=0.855, d=1.54) and Lempel-Ziv Complexity (AUC=0.742), which increases paradoxically under sedation. η is independent of the aperiodic (1/f) EEG component (r=0.219, p=0.353), confirming it measures spatial organisation rather than spectral tilt. In the Chennu graded sedation dataset (N=20), η and angle(Ψ,Δ) both track sedation depth monotonically (r=−0.408, p=0.0002 and r=+0.387, p=0.0004 respectively), with η achieving AUC=1.000 for baseline versus moderate sedation while LZC fails (AUC=0.612, p=0.231). In a polysomnographic sleep dataset (N=7), η follows the phenomenological gradient Wake > REM > N2 > N3, correctly placing REM above N3 (d=+1.78, p=0.016). Critically, angle(Ψ,Δ) reveals a structural paradox absent from any existing metric: N2 sleep shows the maximum angle (66.9°±3.7°), significantly exceeding both Wake (52.3°, d=2.04, p=0.016) and N3 (51.0°, d=1.81, p=0.016), reflecting spindle-driven decoupling of frequency bands at minimum η. In a reversal learning dataset (N=22), η falls transiently at the moment of rule reversal (d=−2.58, p<0.001) while angle(Ψ,Δ) rises (d=0.69, p=0.009), demonstrating sensitivity to within-conscious phenomenal reorganisation inaccessible to level-based metrics. We argue that spatial efficiency constitutes a new class of EEG consciousness metric: theoretically grounded, two-dimensional, and sensitive to both phenomenal level and phenomenal structure. Keywords: consciousness; EEG; spatial organisation; sleep; propofol sedation; global workspace theory; free energy principle; Odd Ratio Product; spatial efficiency