Reduced emergent character of neural dynamics in patients with a disrupted connectome

High-level brain functions are widely believed to emerge from the orchestrated activity of multiple neural systems. However, lacking a formal definition and practical quantification of emergence for experimental data, neuroscientists have been unable to empirically test this long-standing conjecture. Here we investigate this fundamental question by leveraging a recently proposed framework known as “Integrated Information Decomposition,” which establishes a principled information-theoretic approach to operationalise and quantify emergence in dynamical systems — including the human brain. By analysing functional MRI data, our results show that the emergent and hierarchical character of neural dynamics is significantly diminished in chronically unresponsive patients suffering from severe brain injury. At a functional level, we demonstrate that emergence capacity is positively correlated with the extent of hierarchical organisation in brain activity. Furthermore, by combining computational approaches from network control theory and whole-brain biophysical modelling, we show that the reduced capacity for emergent and hierarchical dynamics in severely brain-injured patients can be mechanistically explained by disruptions in the patients’ structural connectome. Overall, our results suggest that chronic unresponsiveness resulting from severe brain injury may be due to structural impairment of the fundamental neural infrastructures required for brain dynamics to support emergence.

3 organisation of a structural network shapes its ability to influence the functional dynamics that 78 take place over it.

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A unique opportunity to investigate how emergence is related to both functional and structural 80 characteristics of the human brain comes from studying patients with chronic disorders of 81 consciousness (DOCs) as a result of severe brain injury. Chronic DOCs involve permanent 82 neuroanatomical damage, including disruption of the brain's structural connectivity and 83 dynamics 24- 35 . In addition to providing a powerful avenue to relate brain organisation and 84 (dys)function, this approach also addresses a pressing need to understand how the structural 85 and functional brain reorganisation induced by DOC patients' injuries prevent them from 86 recovering 36,37 . Therefore, in the present work we combine functional and diffusion MRI data 87 to study brain function and structure in a cohort of 21 DOC patients and 18 healthy controls.

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We leverage ΦID and network control theory to investigate the relationship between 89 emergence in brain dynamics, on one hand, and healthy and pathological aspects of the 90 brain's structural and functional architecture, on the other.

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Our main hypothesis was that emergent and hierarchical character of brain activity should be 92 diminished in the brains of severely brain-injured unresponsive patients. Further, we 93 hypothesised that the capability of these patients' anatomical connectomes to control brain 94 activity should be compromised as a result of their injury. Crucially, these hypotheses are 95 tightly interconnected: emergence and hierarchy are two distinct but complementary ways of 96 viewing the same dynamics, and a controllability shapes the repertoire of dynamics that the 97 structural connectome can entertain. Therefore, as our final hypothesis we expect that causal 98 emergence, functional hierarchy and structural controllability should be related to each other.

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To obtain mechanistic insights beyond pure correlation, we address this last hypothesis using 100 whole-brain computational models, which simulate neurobiologically realistic brain dynamics 101 based on different empirical connectomes 15,37-43 . The model-generated dynamics can then 102 be directly interrogated in terms of causal emergence via ΦID, through the same process as 103 the empirical brain dynamics. This approach enables us to seek a mechanistic interpretation 104 of our results. Through these convergent, multimodal investigations we shed light on how 105 healthy and pathological brain structure influences brain dynamics.

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Here, we adopted the recently developed mathematical framework of Integrated Information 108 Decomposition (ΦID) to quantify causal emergence in the dynamics of the human blood-4 oxygen-level dependent (BOLD) signal from fMRI data of N=18 healthy controls and N=21 110 DOC patients, further subdivided into N=10 patients diagnosed with unresponsiveness 111 wakefulness syndrome (UWS, also known as the vegetative state), and N=11 patients in a 112 minimally conscious state (MCS), who can occasionally exhibit behavioural signs consistent 113 with transitory responsiveness. Through this powerful new approach to quantify emergence, 114 we sought to investigate the fundamental connection between emergence and human 115 consciousness, and how they both relate to relevant aspects of brain function (spatiotemporal 116 hierarchy) and structure (network controllability).

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Diminished emergence in the brain dynamics of DOC patients 118 To empirically investigate the hypothesis that the macroscale capacity for emergence is 119 diminished in chronically unresponsive brain-injured patients, we adopted the account of 120 causal emergence recently formalised by ΦID (Methods). A macroscale feature Vt is said to 121 be causally emergent if it has "unique" predictive power over the future evolution of the system 122 Xtin the sense of providing information about the dynamics of the system that cannot be 123 found in any of the parts of the system when considered separately. Thus, supervenience is 124 a relationship between the macroscale (for example, the shape of a flock of birds) and the 125 microscale (the individual birds) at a particular point in time, whereas emergence pertains to 126 the joint dynamics of the macro-and the microscale 1 . Crucially, ΦID allows one to measure 127 the maximal amount of unique predictive power that any emergent feature could have with 128 respect to the microscale, which upper-bounds the ability of the system to host emergent 129 featureshence termed "emergence capacity" (see Methods).

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Here, we employed ΦID to measure the capability for causal emergence of the coevolving 131 activity of pairs of brain regions, based on their fMRI BOLD signals at rest (see Methods for 132 details of how ΦID's information-theoretic quantities are computed). In other words, we 133 quantify the capacity of pairs of regions to give rise to emergent behaviour together. By 134 averaging the resulting estimates of emergence capacity across all pairs, we obtained an 135 estimate of the global emergence capacity across the brain for each subject.

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An analysis of variance revealed a significant effect of disorder severity (control, MCS or UWS) 137 on the mean values of emergence capacity (F(2,37) = 26.08, p < 0.001), with subsequent post-138 hoc tests (corrected for multiple comparisons using the Benjamini-Hochberg procedure to 139 control the false discovery rate 44 ) indicating that healthy controls had significantly higher 140 capacity for causal emergence than both MCS and UWS patients across brain regions -as 141 well as a trend towards significance for the difference between patient groups (p = 0.072) (see 142 Figure 1 and Table S1). Thus, supporting our first hypothesis, we identified that lower causal 143 emergence is observed in chronically unresponsive patients after severe brain injury.

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Information Decomposition as the average emergence capacity between each pair of discretised regional fMRI 150 BOLD signals (Methods and Figure S1). The framework rests on the following definitions. Given a system 151 composed of multiple elements that co-evolve over time, we say that a macroscale feature is supervenient on 152 the state of the system at time t, denoted by , if is fully determined by (beyond the addition of noise), if 153 anything about that can be predicted from the system's previous state, −1 can also be predicted from the 154 system's current state, (A). Then, a supervenient feature is said to be causally emergent if it has "unique" 155 predictive power over the future evolution of in the sense of providing information about the dynamics of the 156 system that cannot be found in any of the parts of the system when considered separately. (C) Violin plots of each 6 ( Figure S2A), and using a different information-theoretic formalism (Methods and Figure S2B)

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we proceeded to test whether DOCs also induce a reduction in the spatio-temporal hierarchy 175 of brain function.

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Operationally, intrinsic-driven ignition (IDI) is obtained by identifying "driver events" of 177 unusually high activity in spontaneous BOLD signals of each region and measuring the 178 concomitant activity occurring in the rest of the brain. Importantly, regions generally vary in 179 the extent of the ignition they typically elicit, and the spatial variability of the mean IDI across 180 regions defines the brain's spatio-temporal hierarchy. In other words, when driver events in 181 some regions are able to recruit a large fraction of the brain while events in others not at all, 182 brain dynamics can be characterised as being highly hierarchical 14,45 .

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Results supported our hypothesis of diminished spatio-temporal hierarchy in the functional 184 brain activity of DOC patients: an ANOVA revealed a significant effect of diagnosis on the 185 spatiotemporal hierarchy of ignition (F(2,37) = 11.28, p < 0.001), with follow-up t-tests 186 indicating that UWS patients exhibited reduced hierarchical organisation compared with both 187 MCS patients and healthy controls ( Figure 2B and

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To ensure the robustness of our results, we repeated our analyses pertaining to both 205 emergence capacity and spatio-temporal hierarchy after controlling for mean framewise 206 displacement as a covariate of no interest ( Figure S3) and using a different parcellation size 207 (129 ROIs; Figure S4).

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Reduced network controllability of the DOC connectome 209 Our results so far have shown that the brain activity of chronically unresponsive brain-injured 210 patients compared to healthy controls is characterised by decreased causal emergence, and,

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possibly closely related to this, a diminished spatio-temporal hierarchy of brain dynamics.

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Crucially, however, brain dynamics are fundamentally shaped by the underlying structural 213 connectome on which they unfold 18-22 -and indeed DOC patients often exhibit disrupted 214 structural connectivity due to their injury, as well as subsequent complications and atrophy.

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To study how reductions in emergence and spatio-temporal hierarchy are related to brain 216 8 structure we leverage principles of network control theory, which has recently become a 217 prominent approach to investigate the relationship between the brain's network structure and 218 its ability to support different kinds of functional dynamics 23,47-55 .

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Given a system of active elements (e.g., brain regions) interconnected by a network of 220 structural connections (here, from the human connectome project), the organisation of the 221 network's connections can be studied via control theory to determine how to intervene on the 222 system to achieve a desired configuration of activity of its elements ( Figure 3A,B). Specifically,

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if energy is injected into the system via a particular node or set of nodes, it will spread to the 224 rest of the system according to the network's connectivity, so that the activity of individual 225 elements will be differently affected. As a consequence, a specific desired pattern of activity 226 may be best achieved by intervening on some nodes rather than others. Nodes requiring    Figure 3D). Post-hoc pairwise t-tests (FDR-controlled) to explore 251 the significant effect from the ANOVA indicated significantly higher modal controllability across 252 brain regions for healthy controls than either MCS or UWS patients (Table S4). Analogous 253 results were also obtained when using a different parcellation size (129 ROIs; Figure S5). 10 can be injected locally into the system, and it will spread to the rest of the system based on its network organisation.

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Average controllability quantifies the network's support for moving the system from an initial configuration of activity

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(green) to easy-to-reach configurations (blue), whereas modal controllability quantifies the network's support for 272 moving the system to difficult-to-reach configurations of activity (yellow

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Causal evidence for structure-function relationships from whole-brain

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We fitted three whole-brain DMF models, each using a connectome obtained from combining

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Our results reveal that the capacity for causal emergence across the brain is significantly 360 reduced following severe brain injury leading to chronic unresponsiveness. Subsequently, we 361 investigated functional and structural correlates of emergence in the human brain.

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Finally, it is worth acknowledging that our results did not always identify statistically significant 428 differences between healthy controls and MCS patients, or between MCS and UWS patients.

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We believe that this is likely due in part to our limited sample sizes and statistical stringency,    automatic motor reactions (e.g., scratching, pulling the bed sheet), visual fixation and pursuit, 478 or localisation to noxious stimulation. Since this study focused on whole-brain properties, 479 coverage of most of the brain was required, and we followed the same criteria as in our 480 previous studies 25,26,71 : before analysis took place, patients were systematically excluded if 481 an expert neuroanatomist blinded to diagnosis judged that they displayed excessive focal brain damage (over one third of one hemisphere), or if brain damage led to suboptimal 483 segmentation and normalisation, or due to excessive head motion in the MRI scanner 484 (exceeding 3mm translation or 3 degrees rotation). One additional patient was excluded due 485 to incomplete acquisition. A total of 21 adults (13 males; 17-70 years; mean time post injury: 486 13 months) meeting diagnostic criteria for unresponsive wakefulness syndrome/vegetative 487 state (UWS; N = 10) or minimally conscious state (MCS; N = 11) due to brain injury were 488 included in this study (Table 1).

Acquisition of Diffusion-Weighted Imaging Data 502
As we previously reported 25,71 , the DOC patients' data were acquired over the course of

FMRI Data Acquisition 521
Resting-state fMRI was acquired for 5:20 minutes (160 volumes, TR=2000ms) using a 522 Siemens Trio 3T scanner (Erlangen, Germany). The acquisition parameters were the same 523 as those for the DOC patients: Functional images (32 slices) were acquired using an echo 524 planar sequence, with the following parameters: 3 x 3 x 3.75mm resolution, TR = 2000ms, TE 525 = 30ms, 78 degrees FA. High-resolution T1-weighted anatomical images were also acquired, 526 using an MPRAGE sequence with the following parameters: TR = 2300ms, TE = 2.47ms, 150 527 slices, resolution 1 x 1 x 1mm. Data from two subjects were excluded due to incomplete 528 acquisition, leaving N=18 healthy controls for the functional analysis.

Acquisition of Diffusion-Weighted Imaging Data 531
The diffusion-weighted acquisition scheme was the same 63-directions scheme used for the 532 DOC patients, as described above and in previous work (Luppi et

DWI Preprocessing and Tractography 575
The diffusion data were preprocessed with MRtrix3 tools, following the same pipeline as in our

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After preprocessing, the DTI data were reconstructed using the model-free q-space 585 diffeomorphic reconstruction algorithm (QSDR) implemented in DSI Studio (www.dsi-586 studio.labsolver.org) 95 , following our previous work 25,71,96 . Use of QSDR is desirable when 587 investigating group differences 95,97,98 because this algorithm preserves the continuity of fiber 588 geometry for subsequent tracking 95 , since it reconstructs the distribution of the density of 589 diffusing water in standard space. This approach has therefore been adopted in previous 590 connectomics studies focusing on healthy individuals 23 but also brain-injured patients 99

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One can now consider the amount of information flowing from the system's past to its future, 619 known as time-delayed mutual information (TDMI) and given by ( − 1 , − 2 ; 1 , 2 ) 5 .

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Following the insights of Williams and Beer 101 , the information that two source variables X

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The latter can be thought of as "the macroscale having causal influence on the macroscale, 644 above and beyond the microscale effects" 1 . Here we focus on the system's "emergence 645 capacity", the combination of both downward causation and causal decoupling.

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In practice, our method for computing the emergence capacity involves obtaining the full 647 integrated information decomposition of the system, which is achieved by setting up a linear

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In accordance with our previous work 6,104 and previous studies using information-661 theoretic measures in the context of functional MRI data, for these analyses we used a 662 state-of-the-art toolbox 105 to deconvolve the hemodynamic response function from our 663 regional BOLD signal timeseries.

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Spatiotemporal Hierarchy from Intrinsic-driven Ignition 666 "Intrinsic-driven ignition" 14 quantifies the extent to which spontaneously occurring ("intrinsic") 667 local events elicit whole-brain activation ("ignition"). For this analysis, first the BOLD signal is

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which has been previously used as a model of both BOLD signals and neural activity 23,108 .

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Here, x is a vector describing the state of each brain region at a given point in time (e.g. in

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terms of neural activation as given by the BOLD signal magnitude -though note that the 718 network control framework is agnostic about the nature of the system's activity), and A is the 719 adjacency matrix representing the structural connectome (to ensure Schur stability, the 720 adjacency matrix is divided by its largest singular value + 1 23,99

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Network control analysis enables us to investigate the ability of each brain region to influence 726 the brain's dynamics in different ways. Technically, the "controllability" of a dynamical system 727 (such as the human brain) refers to the extent to which the state of the dynamical system in

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Based on this controllability framework, we focus on two complementary control strategies for 736 determining how the system can be moved towards different states (i.e., regional activation 737 patterns): "average" and "modal" controllability 23 .

Average controllability 740
If the states that are accessible to the system are conceptualised as constituting an energy 741 landscape, then average controllability describes how easily the system can transition 742 between nearby states on this landscape. Average controllability of a network then equals to 743 the average input energy needed at a set of control nodes, averaged over all possible target 744 states. It is well-established that average input energy is proportional to Trace( −1 ). However, 745 since the trace of the inverse Gramian is often uncomputable due to ill-conditioning, we follow

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From this definition, a region will have high modal controllability if it is able to control all the 760 dynamic modes of the system, which implies that they are well-suited to drive the system 761 towards difficult-to-reach configurations in the energy landscape 23 .

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For both average and modal controllability, whole-brain values can be obtained by taking the 763 mean of all regional controllability values, as per prior work 52 . Whole-brain computational modelling 767 Macroscale whole-brain computational models represent regional activity in terms of two key 768 ingredients: (i) a biophysical model of each region's local dynamics; and (ii) inter-regional 769 anatomical connectivity. Thus, such in silico models provide a well-suited tool to investigate 770 how the structural connectivity of the brain shapes the corresponding macroscale neural

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The structural connectivity (SC) for the DMF model used here was obtained by following the 781 procedure described by Wang et al. 43 to derive a consensus structural connectivity matrix. A

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The DMF model has one free parameter, known as "global coupling" and denoted by G, which 787 accounts for differences in transmission between brain regions, considering the effects of 788 neurotransmission but also synaptic plasticity mechanisms. Thus, separately for each group, 789 we used a model informed by that group's consensus connectome to generate 40 simulations 790 for each value of G between 0.1 and 2.5, using increments of 0.1. Finally, we set the G 791 parameter to the value just before the one at which the simulated firing of each model became 792 unstable, reflecting a near-critical regime.

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Subsequently, for each group, 40 further simulations were obtained from the corresponding 794 DMF model with the optimal G parameter. A Balloon-Windkessel hemodynamic model 109 was 795 then used to turn simulated regional neuronal activity into simulated regional BOLD signal.

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Finally, simulated regional BOLD signal was bandpass filtered in the same range as the 797 empirical data (0.008-0.09 Hz, or 0.04-0.07 Hz for the intrinsic ignition analysis).

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As an alternative way of finding the most suitable value of G for the simulation of each 799 condition, we adopted the approach previously described 67,68,70,71 which aims to obtain the 800 best match between empirical and simulated functional connectivity dynamics. First, we 801 quantified empirical functional connectivity dynamics (FCD) in terms of Pearson correlation 802 between regional BOLD timeseries, computed within a sliding window of 30 TRs with