Network dynamics scale with levels of awareness

Small world topologies are thought to provide a valuable insight into human brain organisation and consciousness. However, functional magnetic resonance imaging studies in consciousness have not yielded consistent results. Given the importance of dynamics for both consciousness and cognition, here we investigate how the diversity of brain dynamics pertaining to small world topology (quantified by sample entropy; dSW-E) scales with decreasing levels of awareness (i.e., sedation and disorders of consciousness). Paying particular attention to result reproducibility, we show that dSW-E is a consistent predictor of levels of awareness even when controlling for the underlying functional connectivity dynamics. We find that dSW-E of subcortical and cortical areas are predictive, with the former showing higher and more robust effect sizes across analyses. Consequently, we propose that the dynamic reorganisation of the functional information architecture, in particular of the subcortex, is a characteristic that emerges with awareness and has explanatory power beyond that of the complexity of dynamic functional connectivity.

of SW when calculated dynamically, proved more informative and showed the same intuitive patterns 193 of decreasing complexity in lower levels of awareness (Fig 2, S2). 194 It is important to assess whether these graph theory entropy metrics truly reflect the temporal 195 complexity of the functional architecture (i.e., topology), or can be explained more parsimoniously by This control analysis included both dFC-E and dSW-E as co-variate predictors in the same ordinal 213 logistic regression and found the latter remained significant. This suggests that the temporal 214 complexity of the functional SW architecture predicts increasing levels of awareness above and 215 beyond what can be explained by the complexity ("compressibility") of dynamic functional 216 connectivity. This may be taken as a strong indication that the dynamic information produced 217 (measured via sample entropy (Richman & Moorman, 2000)  Given that dynamic entropy of both SW measures (φ & σ) consistently predicts levels of awareness at 245 the whole-brain level, we sought to explore whether the dSW-E of major cito-architectonically distinct 246 subdivisions of the brain (i.e., Cortex, subcortex and cerebellum) are relevant to consciousness and differentially explain the above whole-brain effects found in both high and low granularity 248 Remarkably, the effect sizes for the subcortex were greater than those of the cortex. The LON-DOC 260 datasets showed convergent results with the exception of the high granularity cortical parcellation 261 (400 nodes; p=0.08, S6). Furthermore, when we added dFC-E as a covariate to dSW-E, both the cortex 262 and subcortex remained significant, whilst the cerebellum dSW-E was borderline significant (p=0.055; 263 S7). When controlling for dFC-E, the Subcortex dSW-E again had higher regression coefficients (coef=-264 1.83) than the cortex (coef=-1.25) in both datasets, although the cortex violated regression 265 assumptions in the CAM-DOC analysis (S7). 266 To confirm whether the subcortex dSW-E was more predictive of levels of awareness than the cortex, 267 we inserted dSW-E of the three subsystems within the same model and calculated the odds ratio for 268 each. We found that an increase of 1 of the subcortical dSW-E increased the chance of being in the 269 Given that subcortical dSW-E has more predictive power than the cortex, we sought to investigate 309 whether this striking effect ( awareness; but importantly, we additionally show that SW architecture dynamics have consistent 348 explanatory power above and beyond the variations in functional connectivity. This suggests that 349 awareness has characteristic dynamic global information architectures (topologies) that cannot be 350 reduced to simple FC. In other words, the dynamic re-configuration of the global functional 351 architecture ("the interrelation of parts"), rather than the absolute synchronisation of brain regions, 352 may be particularly important to consciousness. These findings, therefore, speak to theories that posit 353 a global workspace (of information (Baars, 2005)), or the irreducibility of the whole to its parts (Tononi 354 et al., 2016). In fact, we show that the dynamics of architectures that favour both integration and 355 segregation between different information modules, consistently scale with increasing levels of 356 awareness. It is therefore possible that such architectures may contribute to an integrated dynamic 357 global workspace of information across time. 358 A key result of this study may supply some interpretations in regards to what may be particularly 359 important for consciousness emergence. This is the difference between cortical and subcortical 360 effects. Despite the cortex was a significant predictor on its own, we found that the complexity of 361 dynamic subcortical topology is more consistent and powerful in predicting levels of awareness than 362 the cortex. This suggests that the complexity of topological functional dynamics in the subcortex is 363 particularly sensitive to different levels of awareness. In fact, the subcortical system is thought to 364 provide fundamental (affective, interoceptive and sensory) inputs for cortical processing, and is 365 Given the potential existence of many different types (or dimensions) of consciousness, that the 414 dynamic complexity of several graph theory properties may display predictive power, and that these 415 measures display high within condition standard deviations (Fig 2 & 3); we tentatively suggest that 416 these results may primarily relate to the epi-phenomenology of consciousness. In other words, the 417 dynamic complexity of functional topology necessarily arises with consciousness, but it may not be a 418 sufficient condition for the emergence of awareness. 419 As for the strengths and weakness of this study; the temporal resolution of the data-collection 420 technique and the sliding window approach constitute a limitation of this study, as it only can measure 421 coarse timescales of brain activity. Furthermore, DOC data is inherently noisy and is characterised by 422 high degrees of variability and misdiagnosis. We selected this subset of participants out of a bigger 423 dataset to ensure the data had acceptable quality. The ordering of conditions into decreasing levels 424 of awareness may be controversial, in that it reduces subjective qualitative states to a two-425 dimensional quantity, despite being clinically (Giacino et  The additional use of an independent dataset to validate results, and the use of different parcellations 432 (with different brain region definitions but similar numbers, and with similar definitions but different 433 granularities, S1) serve to augment assurance in these results (Hallquist & Hillary, 2018). 434 We conclude, with a reasonable amount of confidence, that the complexity of dynamic topology (in 435 other words: the re-organisation of functional information architecture) does increase with the 436 emerging of awareness. We tentatively suggest that dynamics of information processing architecture 437 indirectly reflects changes in cognitive content/mental state which is an intuitive characteristic of the 438 vernacular "stream of consciousness". The predictive power of the subcortex's dynamic topology is 439 higher and more consistent compared to that of the cortex or the cerebellum, suggesting that the 440 dynamic re-organisation of this system may be particularly important in typical awareness. 441 442

Cambridge anaesthesia dataset (CAM) 444
Participants -CAM dataset 445 446 Ethical approval was obtained from the Cambridgeshire 2 Regional Ethics committee (Adapa et al., 447 2014). 25 participants were recruited, however due to incomplete data in the cortex and procedure 448 failure a subset of 18 were taken for further analyses. All participants were healthy and were native 449 English speakers (50% males). Mean age was 33.3 (19-52). Two senior anaesthetists were present 450 during scanning. Electrocardiography and pulse oximetry were continuously performed whilst 451 measures of blood pressure, heart rate and oxygen saturation were recorded regularly. 452

Anaesthetic Protocol -Cam Dataset 453
Propofol sedation was administered intravenously via "target controlled infusion" with a Plasma 454 Concentration mode. An Alaris PK infusion pump (Carefusion, Basingstoke, UK) was used which was 455 controlled via the Marsh pharmacokinetic model. The anaesthesiologist can thus decide on a desired 456 plasma 2 "target" and the system will regulate the infusion rates using patient characteristics as 457 covariates. Three target plasma levels were used -no drug (awake control), 0.6 µg/ml (low sedation), 458 1.2 µg/ml (moderate sedation). In this study only the moderate sedation is used. Data for this latter 459 condition was taken 20 minutes after cessation of sedation. Blood samples were taken at the end of 460 each titration period, before plasma target was altered. The level of sedation was probed verbally 461 immediately before and after each of the scanning runs. participants were included in this study (Naci et al., 2018). 483

Anaesthetic Procedure -LON dataset 484
The procedure was supervised by two anaesthesiologists and one anaesthetic nurse in the scanning 485 room. Participants also performed an auditory target-detection task and a memory verbal recall to 486 assess level of awareness independently from the anaesthesiologists. Additionally, an infrared camera 487 was used to further assess level of wakefulness. 488 Propofol was administered intravenously using a Baxter AS50 (Singapore); stepwise increments were 489 applied via a computer-controlled infusion pump until all three assessors agreed that Ramsay level 5 490 was reached (i.e. no responsiveness to visual or verbal incitements). If necessary, further manual 491 adjustments were made to reach target concentrations of propofol which were predicted and maintained stable by a pharmacokinetic simulation software (TIVA trainer). This software also 493 measured blood concentration levels following the Marsh 3-compartment model. The initial propofol 494 concentration target was 0.6 μg/ml, and step-wise increments of 0.3 μg/ml were applied after which 495 Ramsay score was assessed. This procedure was repeated until participants stopped answering to 496 verbally and where rousable only by physical stimulation at which point data collection would begin. 497 Oxygen titration was put in place to ensure SpO2 above 96%. The mean estimated effect site propofol 498 concentration was 2.48 (1.82-3.14) μg/ml and propofol concentration whilst the mean plasma for MCS). These were selected out of a bigger dataset due to their relatively intact neuroanatomy. 514 These patients were treated and scanned at the Wolfson Brain Imaging Center, Addenbrookes hospital 515 (Cambridge, UK). Written Informed consent was obtained from an individual that had legal responsibility on making decisions on the patient's behalf. These participants were split into 517 vegetative state and minimally conscious groups (n = 12 for UWS and 11 for MCS) in accordance to 518 the diagnosis given by the attending physician at Addenbrookes hospital. Mean CRS-r score was 8.3 519 (standard deviation 2.03), For the UWSS group 7, (SD 1.41) and 9.75 (Sd 1.54) For the MCS group. 520 Mean age for the UWS group was (40.16) SD 13.63; and for the MCS group (39,18, S.D 18.13). In the 521 UWS group the aetiology was described as TBI for 3 patients, one hypoxia, one edema and the 522 remaining participants having the pathology caused by anoxia. In the MCS group nine of the patients 523 had a Traumatic brain injury, one a cerebral bleed and one anoxia. In the MCS group 7 were male; 524 whilst in the UWS group 8 were male. This dataset received ethical approval from the National 525

Magnetic Resonance Imaging Protocol -DOC dataset 527
A varying number of functional tasks, anatomical and diffusion MRI images were taken for the DOC 528 participants. Only the Resting-state data was used for this study. This was acquired for 10 minutes 529 (300 volumes, TR=2s) using a siemens TRIO 3T scanner. The functional images were acquired using an 530 echo planar sequence. Parameters include: 3x3x3.75mmm resolution, TR/TE = 2000ms/30ms, 78 531 degrees FA. Anatomical images T1-weighted images were acquired using a repetition time of 2300ms, 532 TE=2.47ms, 150 slices with a cubic resolution of 1 mm. 533

534
All functional images were preprocessed in the same way using an in-house matlab script that used 535 SPM12 functions (https://www.fil.ion.ucl.ac.uk/spm/software/spm12). After removing the first 5 536 scans to reach scanner equilibrium, slice-timing correction was performed (reference slice=no. 17). 537 Volumes were realigned to the mean functional image. This process produced re-alignment 538 parameters which were included in the time series extraction covariates. Finally, using the mean 539 functional image, spatial normalization to an EPI-template was conducted using the function "old 540 norm" in SPM as this yielded consistently good results. Participant-specific cerebral spinal fluid and white matter maps, used for the time series extraction (See below), were also created using an in-542 house Matlab (2016a) script based on SPM functions. Visual inspection of normalization to standard 543 space was carried for all datasets. Particular attention was given to the DOC dataset because of the 544 effect that lesions may have on spatial transformations. Due to insufficient coverage of the cerebellum 545 in a UWS patient, these data were excluded from analyses involving the cerebellum. The ART quality-assurance/motion-artifact rejection toolbox 552 (https://www.nitrc.org/projects/artifact_detect) was also used to further clean the timeseries data. 553 Linear de-trending and a 0.008 to 0.09 Hz band-pass filter was applied to eliminate low-frequency 554 scanner drifts and high-frequency noise. The time-series were extracted controlling for the nuisance 555 To further guard from the problem of the FC-driven GTA difference problems, a particularly stringent 580 proportional threshold was used to define graphs. 5 thresholds going from 5% to 25% in 5% increases 581 were used to test a wide-range of connection densities (Godwin et al., 2015;Monti et al., 2013). The 582 graph theory values for each of these thresholds were then averaged to form the independent 583 variables in inferential analyses. Only positive correlations were considered as is typical for network 584 neuroscience due to the dubious interpretation and the preprocessing contingencies associated with 585 negative weights (Dixon et al., 2017;Huang et al., 2020;Rubinov & Sporns, 2010). 586 These weighted-thresholded matrices were analysed using in-house matlab scripts which utilised 587 functions from the brain connectivity toolbox (Rubinov & Sporns, 2010). In accordance to previous 588 advice (Hallquist & Hillary, 2018), given how GTA results may be driven by specific parcellations (Hallquist & Hillary, 2018;Papo et al., 2016;Yao et al., 2015), the reproducibility of GTA results was 590 tested through the use of several network definitions (see S1). 591 For the creation of time-varying (dynamic) connectivity matrices, a sliding-window approach was 592 used. In accordance to previous studies (Luppi et  The modularity algorithm (Rubinov & Sporns, 2010) works by detecting the (computationally) optimal 658 community structure by dividing the network into groups of nodes with maximised within group 659 connections and minimised between group connection. Here we used the weighted version of 660 modularity (Rubinov & Sporns, 2010). derived from approximate entropy, which in turn is based upon Kolomogorov complexity 684 (Kolmogorov, 1965;Mitchell, 2011). The underlying notion being that a complex system cannot be 685 easily described, whilst a simple system can be quickly and briefly summarized. 686 Sample entropy takes two timeseries segments of different lengths and compares how well each of 687 these segments explains the rest of the timeseries (via the default Chebyshev distance measure). 688 Sample entropy is a ratio between how well the smaller segment explains the data compared to the 689 larger segment, and thus higher values indicating decreased self-similarity and increased complexity. The sequence lengths or timeseries lengths (max=2, min=1) were taken from a study which has looked 695 at sample entropy of graph theory properties in functional MRI (Pedersen, Omidvarnia, Walz, Zalesky, 696 & Jackson, 2017). Also taken from this study is the tolerance for accepting matches of similarity which 697 was set to 0.2 times the standard deviation. The algorithm used in this paper was used in a previous 698 study with the original creators of the Sample entropy algorithm (Richman & Moorman, 2000). 699 700 Inferential Analyses: Ordinal Logistic Regression