Quantifying Consciousness

The visual at the top of this page is the thesis, animated. A sandpile of EEG-like cells fires and cascades — neuronal avalanches in miniature. Each cascade contributes to running estimates of two quantities on the bottom: σ (the branching ratio, a system’s distance from criticality) and LZC (Lempel-Ziv complexity, how compressible the activity stream is). The moving dot is where the system currently sits in that 2D phase space. The four faint clouds are the four patient groups the thesis studied — Vegetative State, Minimally Conscious State, Emerging-MCS, and healthy Controls. Click anywhere on the top half to perturb the system and push it toward criticality.

Context

Ben Gurion University, Department of Brain and Cognitive Sciences, September 2018. Done in Dr. Oren Shriki’s Computational Psychiatry Lab, with clinical co-supervision by Prof. Gal Ifergane (Soroka University Medical Center). The lab’s broader program uses computational tools — criticality, network dynamics, statistical models — to characterize neurological and psychiatric states; this work is one strand of that.

The clinical motivation: misdiagnosis rates for Disorders of Consciousness sit around 40% with bedside behavioral exams. Patients are routinely classified as Vegetative when they retain awareness, or vice versa. The aspirational long-term outcome is a bedside EEG-based level-of-consciousness measure, computed in minutes, that complements (or corrects) the behavioral assessment.

The contribution

The headline isn’t replicating prior work that Lempel-Ziv complexity discriminates conscious from non-conscious EEG — others had shown that. The contribution is the framing:

σ (a system’s distance from criticality) is itself a proxy for integration and differentiation in Integrated Information Theory terms — and consciousness lives in a specific corner of the 2D LZC × σ phase space.

The argument is a syllogism: IIT says I&D ↔ consciousness; the criticality literature says consciousness ↔ σ ≈ 1; therefore σ is the operational quantity that already carries both IIT axes. The thesis develops this and shows that the 2D phase space cleanly separates healthy controls from all DOC groups — controls live near σ ≈ 1 with high LZC, while DOC groups cluster subcritical (σ < 1) with low LZC.

What was done

• A custom EEG recording paradigm (MATLAB Simulink model + GUI) for the data-acquisition side at the lab.
• A preprocessing pipeline including a custom heartbeat-artifact detector that rejects cardiac-related ICA components — a known confound that prior work had not removed.
• Lempel-Ziv Complexity computed per channel after Hilbert transform and rate-binarization, then averaged across channels.
• Neuronal avalanche analysis — power-law fits over avalanche size distributions, parameter sweeps over threshold (3.0–4.5 STD) and time-bin size, extracting α (size exponent), τ (duration exponent), σ (branching ratio), and a cutoff scale.
• Both metrics computed on 183 subjects × 4 tasks = 732 datasets, across Vegetative (n=77), Minimally Conscious (n=70), Emerging-MCS (n=24), and healthy controls (n=12).

The code forms one pipeline in three parts — preprocessing, complexity, and criticality analysis.

Key findings

• LZC discriminates monotonically along the consciousness spectrum (F = 48.99, p < 10⁻²⁵). All pairwise contrasts significant after Bonferroni correction, except VS–MCS.
• All DOC groups are significantly subcritical (σ < 1). Healthy controls sit near σ ≈ 1.05 — right on the knife edge of criticality, where the criticality literature predicts consciousness lives.
• The σ–LZC relationship is non-linear (Pearson R = 0.09, n.s.) — which the thesis reads as consistent with, though not itself evidence for, a phase-transition picture of consciousness as an emergent critical phenomenon.

The original thesis

The full document — methodology in detail, results across the parameter sweeps, all 21 figures, philosophical framing, future-work prescriptions for a bedside device — is embedded below.

Key figures inside the thesis

Browse to these in the embed above:

• Figure 8 — LZC scores per group. The monotonic progression from VS → CTR.
• Figure 10 — [σ, α] phase diagram across groups. The criticality map.
• Figure 17 — Avalanche size distribution P(s) per group, on log-log axes. Controls follow the −3/2 power-law line further before the cutoff; DOC groups cut off much earlier.
• Figure 20 — LZC × σ averages. The conceptual climax — the 2D phase space that grounds the visualization at the top of this page.
• Figure 21 — Theoretical conjecture: integration & differentiation. The inverted-U you can see faintly traced in the phase space above.