Perturbational complexity index

Citation: Casali, A. G., Gosseries, O., Rosanova, M., Boly, M., Sarasso, S., Casali, K. R., Casarotto, S., Bruno, M.-A., Laureys, S., Tononi, G., and Massimini, M. A theoretically based index of consciousness independent of sensory processing and behavior. Science Translational Medicine 5(198), 198ra105. Published 14 August 2013; accepted 10 June 2013. DOI: 10.1126/scitranslmed.3006294.

Reading status and exact scope

Main article fully read; scientific supplement still inaccessible. This paper is not counted as a completed full-package reading. This summary preserves the work already done while leaving the supplementary reading obligation explicit.

Read on 29 September 2026 from the publisher-formatted PDF deposited in the authors' institutional ORBi repository, which labels it a publisher postprint. The PDF contains 12 physical pages: two publisher front-matter pages plus the complete ten-page research article. All 815 lines of extracted text were read, including the editor's summary, article, Methods, equations, captions, all references, declarations and acknowledgments. All five main figures were visually inspected from rendered physical pages 4–7. There are no main-article tables. References were read as bibliography; their underlying papers were not opened or used as independently read evidence.

The missing supplement is the 15-page 5-198ra105_sm.pdf, listed by the article as Materials and Methods, Figures S1–S5, Tables S1–S2 and references 54–61. The current and legacy publisher downloads and ordinary downloadSupplement endpoint returned HTTP 403. Parallel author/institutional and public-archive searches have not supplied the file. Supplementary source modeling, significance testing, Lempel–Ziv implementation details, sensitivity comparisons and full patient/stimulation tables are therefore not independently verified here. Main-text descriptions of those topics are distinguished from verified supplementary results. The source/provenance record retains retrieval history and will be updated if the supplement becomes accessible.

Archive: papers/consciousness_connectomics/casali2013_pci.pdf, .txt and .provenance.json. The PDF is the published article, not a preprint; the cover records a publisher download on 16 August 2013. Its final page confirms DOI, dates and citation. No raw data or analysis code was rerun.

Question and empirical strategy

Can a direct perturbation of cortex reveal whether the brain supports widespread, differentiated interactions, even when a person cannot perform a sensory, motor or cognitive task? The intended clinical problem is that inability to communicate may reflect impaired input/output pathways rather than absent experience.

The study introduces the perturbational complexity index (PCI). It is an empirical complexity measure inspired by the proposed joint importance of integration and differentiation. It is not a synaptic connectome, direct calculation of IIT's intrinsic integrated information, or identification of a person's experienced content. The article itself contrasts practical PCI with theoretical measures then limited to small simulated systems or restrictive assumptions.

The authors explicitly call the study hypothesis-generating, with open-label designs. They establish reference distributions in healthy people and compare them with measurements in separate patients with stable clinical diagnoses. This is stronger than one correlation within a single state, but different from a prospectively frozen, blinded diagnostic trial in an unselected population.

How PCI is constructed

1. Apply TMS directly to cortex using MRI-guided positioning and record the evoked response with 60-channel TMS-compatible EEG. Repeated pulses yield an averaged response; the index concerns the early response within approximately 300 milliseconds.

2. Estimate cortical current sources. Figure 1 specifies a weighted minimum-norm inverse solution and three-sphere BERG forward model. Apply nonparametric bootstrap statistics at source level to distinguish evoked activity from baseline variability.

3. Encode significant activation as a binary matrix, SS(x,t): one for a significant source at a time point, zero otherwise. Figure 1 sorts sources by their total poststimulus activity. Exact thresholding and sequence-processing details remain in the missing supplement.

4. Calculate Lempel–Ziv complexity, approximating how many distinct patterns are needed to represent the binary sequence. Normalize by sequence length and binary source entropy:

   PCI = c_L × log₂(L) / [L × H(L)],

   where H(L) = −p₁ log₂(p₁) − (1−p₁) log₂(1−p₁) and p₁ is the proportion of significant entries.

This normalization aims to reduce dependence on the total amount of activation and emphasize nonredundant patterns. The paper states that maximally complex responses approach PCI = 1 asymptotically; this is not a demonstrated universal finite-sample bound under every acquisition pipeline.

The motivating contrast is illustrated in one subject: awake stimulation produced a distributed sequence with PCI 0.51; the same-intensity NREM stimulation produced a local response with PCI 0.23; stronger NREM stimulation produced a much larger but stereotyped response with PCI 0.21. Thus response strength and spatial spread alone do not account for the displayed complexity contrast. Calling this a joint measure of integration and differentiation is an operational interpretation, not proof that it equals every formal definition of causal integration.

Participants, recordings and labels

The article reports 208 sessions in 52 people: 32 healthy participants and 20 brain-injured patients. Of these data, 57 measurements in 24 people came from previous studies; 151 measurements in 28 people were newly recorded. Repeated stimulation sites/sessions are not independent additional people.

Healthy reference comparisons comprised 152 sessions: 110 awake measurements and 42 NREM/anesthesia measurements. Eight healthy control participants supplied 72 retained waking sessions while stimulation site, intensity and eyes-open/closed conditions varied. Other cohorts included six sleep participants and six participants for each anesthetic: midazolam, xenon and propofol. Six intermediate-propofol recordings and two additional sleep-stage recordings explain the eight sessions beyond the 152 reference plus 48 patient sessions. Figure 4 identifies the REM/sleep-transition illustration as subject 9; the protocol prose's phrase “one additional subject” is not treated as justification to change the authors' overall count.

The sleep protocol used consolidated NREM stage 3, with some stronger-intensity stimulation. For anesthesia, the protocols targeted Modified Observer's Assessment of Alertness and Sedation (MOAAS) level 1, unresponsiveness to mild prodding/shaking; intermediate propofol targeted levels 2–3. These are behavioral state definitions, not direct access to subjective experience. A single REM observation was accompanied by a dream report after awakening.

Patients underwent four CRS-R assessments over one week. Six VS/UWS patients showed only reflexive behavior in all evaluations. Six MCS patients met criteria in at least three evaluations, including the recording day. Six patients had emerged from MCS and recovered functional communication despite severe impairments; two locked-in patients communicated through eye movements. TMS targeted bilateral frontal/parietal sites where accessible; visibly damaged cortical tissue was avoided. The full patient etiologies and demographic table remain unread in the inaccessible supplement.

Results and what the apparent threshold means

Healthy waking values were higher than every NREM/anesthesia value. Linear mixed models accounted for unbalanced repeated measurements and subject-level effects; pairwise contrasts used Bonferroni adjustment. Stimulation site/intensity had no significant effect within the tested retained data and were removed from reduced models. Nonsignificant effects here do not establish invariance to every site, intensity, montage or brain lesion.

The reference endpoints 0.31 and 0.44 are respectively the largest observed unconscious-condition value and smallest observed alert-waking value. They are empirical sample boundaries, not theory-derived constants. The main article does not present a blinded, preregistered ROC threshold selected in training and evaluated in a held-out diagnostic cohort, nor prospective clinical sensitivity/specificity estimates with uncertainty. Consequently, “perfect separation in these recordings” should not become “a universally accurate 0.31 consciousness detector.”

The 20 patients are different people from the healthy reference cohort, providing a useful clinical comparison. Yet this remains the same open-label, hypothesis-generating study with patients selected for stable diagnoses. The main article does not establish that the complete algorithm and all exclusions were frozen before inspecting patient outcomes. It expressly requests larger independent samples and testing of behaviorally unresponsive but conscious individuals. That limitation is especially relevant to the narrow gap between the maximum reference value 0.31 and minimum MCS value 0.32.

Patient groups overlapped numerically: MCS and emerged-MCS ranges overlap extensively. PCI therefore did not uniquely classify all diagnostic categories. A graded relationship with responsiveness or impairment also does not establish a linear scale of the amount or richness of subjective experience.

In six propofol participants, intermediate sedation values lay between deep anesthesia and waking values. The one sleep-stage illustration had PCI 0.39 at sleep onset and 0.46 in REM with later dream report. This offers an informative dissociation from ordinary external responsiveness, but one REM case and two locked-in patients cannot establish broad accuracy across disconnected consciousness. Ketamine, larger dreaming cohorts and command-following despite a VS diagnosis were proposed as future tests, not results of this experiment.

Causal interpretation and measurement limits

TMS is an intervention; PCI is a measured response feature. Direct stimulation probes how activity propagates after a controlled perturbation. It supplies evidence about effective interactions that spontaneous correlation alone cannot supply. It does not selectively manipulate PCI while holding other neural factors fixed, demonstrate that raising PCI causes experience, or establish complexity as necessary and sufficient for consciousness. Source reconstruction and binarization remain model-dependent transformations of scalp measurements.

“Independent of sensory processing and behavior” describes what the measurement procedure requires from the participant. Its validation still uses waking behavior, anesthetic responsiveness, clinical CRS-R diagnoses and a later dream report. It is therefore report-free at acquisition, not free of behavioral/report assumptions in the evidence linking its value to experience. Stable clinical diagnoses also do not provide an infallible ground truth about inaccessible private experience.

The authors acknowledge that reliable PCI requires a significant evoked cortical response and that stimulation over injured tissue can be inaccurate. Low-SNR or muscle-contaminated waking recordings were excluded; complete rejection rules and the supplementary SNR/entropy analysis remain unavailable. An absent or poor evoked response should not be silently interpreted as a validated measurement of absent consciousness. The main Methods reduce confounding by avoiding visible lesions, but that also narrows applicability to arbitrary damaged sites.

The proposed relevance of approximately 100-ms divergence to recurrent cortical interactions is an interpretation consistent with the timing, not direct identification of particular recurrent synaptic loops. Likewise, the claim that perturbational complexity suppresses noise/common-driver problems is a design rationale, not proof of immunity to all residual stimulation artifacts or modeling errors. These limits do not erase the observed across-condition separation; they determine what it establishes.

Implications for connectomics and emulation

This paper adds a concrete testable dimension beyond a wiring inventory: how a system responds over time to a localized intervention. Matching anatomy, resting covariance or verbal behavior alone would not imply matching this perturbational response.

For a connectome-based simulation, an analogous experiment could examine propagation, temporal diversity, response strength and the consequences of changing model parameters. That would be a model-validation test. The numerical human PCI boundaries cannot simply be transferred to simulated state variables: stimulation scale, observation model, spatial sampling, noise, source reconstruction, binarization and temporal resolution would all need justification and calibration. A simulation can generate complicated compressible or incompressible trajectories without this study having shown that it experiences anything.

PCI is not Φ. Evidence that its empirical values align with these human states does not uniquely confirm IIT, exclude other accounts of distributed recurrent processing, establish substrate independence, or show that a copied connectome preserves a person's identity. No copying or continuity experiment was performed.

Remaining reading obligation: retrieve and read the complete scientific supplement, including all five supplementary figures and two tables, then reassess implementation details, exclusions, participant information and threshold interpretation. Until then, retain this as a scoped main-article summary rather than a completed paper record.

Supplement retry (added 2026-09-29, main session)

A bounded retry found no new route:

• Europe PMC lists the article as not deposited and without supplementary files.
• The publisher link now returns a Cloudflare challenge, which was not circumvented.
• The six Wayback captures of the supplement URL are all 302 redirects, with no PDF.

Routes and statuses are in papers/consciousness_connectomics/casali2013_pci_supplement_retry_2026-09-29.access_log.json. The supplement remains unread and this paper remains an incomplete reading. It can be closed only with a copy obtained through legitimate access, such as an institutional subscription or the authors.