Distributed harmonic patterns of structure-function dependence orchestrate human consciousness

A central question in neuroscience is how consciousness arises from the dynamic interplay of brain structure and function. Departing from the predominant location- centric view in neuroimaging, here we provide an alternative perspective on the neural signatures of human consciousness: one that is intrinsically centered on how the distributed network architecture of the human structural connectome shapes functional activation across scales. We decompose cortical dynamics of resting-state functional MRI into fundamental distributed patterns of structure- function association: the harmonic modes of the human structural connectome. We contrast wakefulness with a wide spectrum of states of consciousness, spanning chronic disorders of consciousness but also pharmacological perturbations of consciousness induced with the anaesthetic propofol and the psychoactive drugs ketamine and LSD. Decomposing this wide spectrum of states of consciousness in terms of “connectome harmonics” reveals a generalisable structure-function signature of loss of consciousness, whether due to anaesthesia or brain injury. A mirror-reverse of this harmonic signature characterises the altered state induced by LSD or ketamine, reflecting psychedelic-induced decoupling of brain function from structure. The topology and neuroanatomy of the human connectome are crucial for shaping the repertoire of connectome harmonics into a fine-tuned indicator of consciousness, correlating with physiological and subjective scores across datasets and capable of discriminating between behaviourally indistinguishable sub-categories of brain-injured patients, tracking the presence of covert consciousness. Overall, connectome harmonic decomposition identifies meaningful relationships between neurobiology, brain function, and conscious experience.


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Understanding the neural underpinnings of human consciousness is a major 70 challenge of contemporary neuroscience (Koch et al., 2016). Converging evidence 71 suggests that consciousness is supported by a dynamic repertoire of brain activity    Luppi et al., 2021d). Rather than focusing on the direct quantification of structure-function correspondence in empirical data, these approaches aim to simulate brain activity from structural connectivity. dependence in the signal, so connectome harmonics quantify how brain activity is 122 constrained by the underlying structural network on which it unfolds.    Figure 1C,D). Therefore, CHD is fundamentally 215 different from, and complementary to, traditional approaches to functional MRI 216 data analysis. This is because CHD does not view functional brain activity as 217 composed of signals from discrete spatial locations, but rather as composed of 218 contributions from distinct spatial frequencies: each connectome harmonic is a 219 whole-brain pattern with a characteristic spatial scale (granularity)from an entire 220 hemisphere to just a few millimetres. consider how brain activity across states of consciousness is shaped by the brain's 231 distributed network of structural connections, reflecting the contribution of global 232 patterns at different spatial scales -each arising from the network topology of the 233 human connectome. We emphasise that neither approach is inherently superior, 234 but rather they each provide a unique perspective on brain function: one localised, 235 the other distributed. The traditional spatially-resolved approach and our 236 frequency-resolved approach are two synergistic sides of the same coin. (temporal dependence versus spatial dependence on the connectome network 247 structure). Indeed, this means that even the most suitable neuroimaging modalities 248 for each analysis are different: CHD relies on fMRI data with high spatial resolution, 249 but which have a restricted content of temporal frequencies (the BOLD signals 250 used here were all band-pass filtered in the low-frequency range as part of 251 standard denoising procedures), whereas Fourier investigations of consciousness 252 require high temporal resolution and are therefore typically performed on electro-253 or magneto-encephalography data. Please note that throughout this article, unless 254 otherwise specified, our use of the word "frequency" refers to the frequency of 255 connectome harmonics (spatial granularity, from fine-grained to coarse-grained).

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High-resolution structural connectome 258 Whereas alternative approaches to harmonic mode decomposition rely exclusively 259 on white-matter connectivity between macroscopic brain regions defined by sub-260 dividing the brain into discrete parcels (Abdelnour et  The structural connectome of each subject was then represented as a binary 298 adjacency matrix A, treating each cortical surface vertex as a node: for each pair i 299 and j of the n = 18,715 cortical surface grey matter nodes, Aij was set to 1 if there 300 was a white matter tract connecting them, as estimated from the deterministic 301 tractography step described above (in order to account for long-range 302 connections); or if they were adjacent in the gray matter cortical surface 303 representation, thereby accounting for the presence of local (1-6mm) connections 304 within the grey matter (the importance of accounting for short-range grey-matter 305 connections in addition to long-range white matter tracts was demonstrated in a 306 recent study (Naze et al., 2021)). If neither long-range nor short-range connections 307 between i and j existed, Aij was set to 0. This procedure resulted in a symmetric 308 (undirected) binary matrix (Atasoy et al., 2016).

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The individual adjacency matrices were then averaged across the 10 HCP subjects 311 to obtain a group-average matrix ̅ , encoding a representative structural 312 conenctome We then define the degree matrix D of the graph as: .

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(1)  Consequently, total brain energy at time t is given by  symmetrised to preserve this important property. We then proceeded with the 478 normal CHD analysis workflow as described above. Sixteen healthy volunteer subjects were recruited for scanning. The acquisition 495 procedures are described in detail in a previous study . In 496 addition to the original 16 volunteers, data were acquired for nine additional 497 participants using the same procedures, bringing the total number of participants 498 in this dataset to 25 (11 males, 14 females; mean age 34.7 years, SD = 9.0 years).

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Ethical approval for these studies was obtained from the Cambridgeshire 2  Minimally Conscious State (N = 12) due to brain injury were included in this study 589 (Table 1).  The first task involved motor imagery ("tennis task"): each patient was asked to 600 imagine being on a tennis court swinging their arm to hit the ball back and forth 601 with an imagined opponent. The second was a task of spatial imagery ("navigation

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Patients who exhibited significantly greater brain activation in the appropriate 617 regions (supplementary motor area (SMA) for the tennis task, and 618 parahippocampal place area (PPA) for the navigation task, respectively) during 619 either of the volitional mental imagery tasks than rest (i.e., those who exhibited 620 evidence of being able to respond to the task) were deemed to be covertly 621 conscious (N = 8); for brevity, we refer to these positive responders as "fMRI+".

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Conversely, we refer to patients who did not respond to either task (negative 623 responders), and who therefore did not exhibit detectable evidence of covert 624 consciousness (N = 14), as "fMRI-". (Table 1).  2015). All participants underwent a screening interview in which they were 648 asked whether they had previously been diagnosed or treated for any mental 649 health problems and whether they had ever taken any psychotropic medications.

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Participants reporting a personal history of any mental health problems or a history 651 of any treatment were excluded from the study. All participants were right-handed,    783 We preprocessed the functional imaging data using a standard pipeline,

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With an increasing connectome harmonic number k, we obtain more complex and fine-grained

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The overall binned energy spectrum across subjects and time points is constructed by discretising    Connectome harmonic decomposition of fMRI data from N=20 volunteers revealed 1000 a significant increase in total brain energy during infusion with a sub-anaesthetic 1001 dose of ketamine, compared with placebo (Table S1 and Figure S3J). Sub-  (Table S2).  Table S3). In 1077 particular, whenever a statistically significant difference was observed in terms of 1078 the propofol projection, a significant difference in the same direction was also 1079 detected in terms of the DOC projection, and corresponding differences in the 1080 opposite direction were observed for the ketamine and LSD projections ( Figure 5).

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Therefore, these results support the notion that two opposite energy patterns 1082 across the connectome harmonic spectrum characterise loss of consciousness 1083 and the psychedelic state, respectively. Note that nothing mandates that these 1084 should be the only two patterns observed; indeed, when considering our test-retest 1085 data, the MVS does not resemble either of the two main patterns that we observed 1086 for alterations of consciousness ( Figure S2).

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Furthermore, we demonstrate that the generalisability of connectome harmonic 1148 signatures also extends to the psychedelic state (note that from here on we use 1149 the term "psychedelic" to refer to the phenomenology that is shared by classic  Figure 6C). In other words, the 1157 more a subject's energy pattern becomes similar to the connectome harmonic 1158 signature of the psychedelic state (as extracted from the ketamine dataset), the 1159 more intense that subject will rate the subjective experience induced by LSD.   Our results support each of these predictions (Figure 7 and Table S4). Ketamine  Figure S8 and Table S4). with linear mixed effects modelling, by treating condition as a fixed effect (indicated on the Y axis along with 95% CI) and subjects as random effects. Timepoints were also included as random 1227 effects, nested within subjects. *** p < 0.001; ** p < 0.01; . p < 0.10.

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Conversely, neither mild sedation nor recovery (during which volunteers were   Here, we set out to address a key challenge of contemporary neuroscience: Recall that formally, the progression from low-to high-frequency connectome 1308 harmonics reflects increasing decoupling of functional brain activity from the   previous studies quantified the diversity of brain signals by focusing on the 1355 temporal dimension ("Does the brain visit few or many states in a given period of 1356 time?"). In contrast, here we quantified diversity in terms of the repertoire of 1357 connectome harmonic frequencies that contribute to brain activity ("Do we need a 1358 wide or restricted repertoire of connectome harmonics to build the brain activity we 1359 observed?"). Therefore, our harmonic-based measure of diversity and the entropy 1360 of temporal signals provide complementary rather than redundant perspectives.   (Figure 6), suggesting that connectome harmonics may provide a bridge 1414 between brain structure, function, and phenomenology (subjective experience).

Role of the high-resolution representative human connectome for
1417 decomposing consciousness 1418 It is essential to realize that the general principle of harmonic mode decomposition 1419 does not require the harmonic modes to be derived from the same subject who is 1420 providing the functional data. In fact, the harmonic modes do not even need to 1421 have a biological origin at all. At one extreme, researchers have successfully 1422 employed harmonics derived from a sphere to investigate how brain activity 1423 depends on the most general geometric properties of the brain and skull (Gabay 1424 and Robinson, 2017; Mukta et al., 2017). At the other extreme, investigators whose 1425 focus is subject-specific insight, rather than generalization across datasets, could 1426 perform CHD using each individual's own connectome.

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Our choice of using the harmonic modes of a high-resolution representative human 1429 connectome (replicated using data from 985 HCP subjects) enabled us to strike a 1430 balance between these two extremes, combining neurobiological insight with 1431 generalizability. On one hand, given our goal of obtaining connectome harmonic 1432 signatures of each state of consciousness that can be meaningfully compared 1433 across subjects and across datasets, it was imperative for us to use the same set 1434 of basis functions (i.e., harmonic modes of the same representative connectome) 1435 to decompose different datasets. In this respect, CHD based on a representative 1436 connectome is not conceptually different from the traditional spatially-resolved 1437 view of brain activity, which to be able to refer to the same localized region across 1438 individuals, requires spatial normalization to a standard template (e.g., MNI-152), 1439 and use of a standard parcellation, both obtained from aggregating neuroimaging 1440 data across healthy individuals (Eickhoff et al., 2018).    1476 It is noteworthy that although we stratified our DOC patients based on their 1477 performance on mental imagery tasks in the scanner, our connectome harmonic 1478 analysis was entirely based on resting-state (i.e., task-free) fMRI data, which 1479 imposes no cognitive demands on patients, unlike task-based paradigms (Naci et