An engine for systematic discovery of cause-effect relationships between brain structure and function

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Luppi , View ORCID Profile Filip Milisav , View ORCID Profile Laura E. Suarez , View ORCID Profile Golia Shafiei , View ORCID Profile Jakub Vohryzek , View ORCID Profile Yonatan Sanz Perl , Hana Ali , View ORCID Profile Fernando E. Rosas , View ORCID Profile Pedro A. M. Mediano , View ORCID Profile Bratislav Misic , View ORCID Profile Gustavo Deco , View ORCID Profile Morten Kringelbach doi: https://doi.org/10.1101/2025.04.05.647237 Andrea I. Luppi 1 Centre for Eudaimonia and Human Flourishing, Department of Psychiatry, University of Oxford , Oxford, UK 2 St John’s College Cambridge , Cambridge, UK 3 Montréal Neurological Institute, McGill University , Montréal, QC, Canada Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Andrea I. Luppi For correspondence: luppi272{at}gmail.com andrea.luppi{at}psych.ox.ac.uk Filip Milisav 3 Montréal Neurological Institute, McGill University , Montréal, QC, Canada Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Filip Milisav Laura E. Suarez 3 Montréal Neurological Institute, McGill University , Montréal, QC, Canada Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Laura E. Suarez Golia Shafiei 4 Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania , Philadelphia, PA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Golia Shafiei Jakub Vohryzek 5 Centre for Brain and Cognition, Pompeu Fabra University , Barcelona, Spain Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jakub Vohryzek Yonatan Sanz Perl 5 Centre for Brain and Cognition, Pompeu Fabra University , Barcelona, Spain 6 Universidad de San Andrés , Buenos Aires, Argentina 7 National Scientific and Technical Research Council (CONICET ), Buenos Aires, Argentina Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Yonatan Sanz Perl Hana Ali 1 Centre for Eudaimonia and Human Flourishing, Department of Psychiatry, University of Oxford , Oxford, UK Find this author on Google Scholar Find this author on PubMed Search for this author on this site Fernando E. Rosas 1 Centre for Eudaimonia and Human Flourishing, Department of Psychiatry, University of Oxford , Oxford, UK 8 Department of Informatics, University of Sussex , Brighton, UK Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Fernando E. Rosas Pedro A. M. Mediano 9 Department of Computing, Imperial College London , London, UK Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Pedro A. M. Mediano Bratislav Misic 3 Montréal Neurological Institute, McGill University , Montréal, QC, Canada Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Bratislav Misic Gustavo Deco 5 Centre for Brain and Cognition, Pompeu Fabra University , Barcelona, Spain 10 ICREA, Catalan Institution for Research and Advanced Studies , Barcelona, Spain Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Gustavo Deco Morten Kringelbach 1 Centre for Eudaimonia and Human Flourishing, Department of Psychiatry, University of Oxford , Oxford, UK 11 Centre for Music in the Brain, Aarhus University , Aarhus, Denmark Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Morten Kringelbach Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract Characterising how perturbations of brain architecture influence brain function is essential to understand the origins of brain dysfunction, and devise potential avenues of treatment. Here we introduce a computational engine for systematic causal discovery of the functional consequences of altering network architecture and local biophysics in the brain. We integrate multimodal anatomical and functional neuroimaging to implement over 2, 000 in-silico brains, and provide mechanistic insight into the functional consequences of local lesions, global wiring, and empirically-derived maps of regional cytoarchitecture and chemoarchitecture. We comprehensively assess how each manipulation of brain macrostructure reshapes spatial and temporal signal coordination, information dynamics, and functional hierarchy—as well as spontaneous co-activation of meta-analytic cognitive circuits, and > 6, 000 dimensions of local neural dynamics. Our computational model systematically identifies which features of brain architecture have overlapping or antagonistic causal influence over each dimension of brain function, and how functional properties are traded off against each other across disorders and neuromodulation. We find that regions’ functional vulnerability to lesions in silico recapitulates their vulnerability to neurodevelopmental and psychiatric in vivo , along a core-periphery organisation. We provide convergent evidence that the brain’s wiring diagram is finely tuned to favour the hierarchical integration of information. Notably, our model successfully recapitulates known empirical results that have not been modelled before, including desynchronisation and flattening of the brain’s functional hierarchy induced by psychedelic 5 HT 2 A agonists. To catalyse future discoveries, we make this resource freely available to the neuroscience community through an interactive website ( https://systematic-causal-mapping.up.railway.app/ ), where users can interrogate our systematic database of simulated cause-effect relationships. Altogether, we provide a powerful computational engine to predict the functional consequences of experimental or clinical interventions, and drive neuroscientific hypothesis-generation. INTRODUCTION A central goal of neuroscience is to obtain a mechanistic understanding of how coordinated brain activity emerges from the architecture of the human brain. Characterising how interventions on brain structure will influence brain function is also imperative for clinical and translational neuroscience, to identify successful avenues of treatment. However, a major obstacle to this endeavour is the brain’s heterogeneity and causal degeneracy. At the microscale, individual brain regions exhibit distinctive profiles of cyto-and chemo-architecture, [ 1 – 12 ], shaping the biophysical and computational properties of local circuitry [ 13 – 23 ]. At the macroscale, specialised brain regions interact over a complex network of anatomical connections: the structural connectome [ 13 , 16 , 24 – 27 ]. Additionally, causal relations between brain structure and function are many-to-many. The same structural scaffold supports a diversity of functional configurations, as brain regions form and dissolve coalitions to execute different cognitive operations [ 13 , 16 , 24 , 28 – 34 ]. Conversely, non-overlapping focal lesions can produce overlapping functional symptoms [ 35 – 38 ]. Thus, there are both convergent and divergent relationships between brain structure and function [ 39 – 41 ]. Overcoming the challenge of causal degeneracy requires developing a systematic mapping between changes in brain macrostructure (regional biophysics, inter-regional wiring) and their consequences on brain function. However, avenues for experimental intervention on brain architecture are severely limited in vivo — especially for global properties such as the network topology of the connectome. In humans we are restricted to pharmacology, or naturally occurring variation in brain structure due to lesions and surgery, development, or neurocognitive disorders. Some manipulations remain even beyond the greater experimental accessibility of animal models. Computational models of brain activity are ideally suited for mechanistic investigation of the links between brain architecture and function. They provide complete access for both manipulation and recording beyond what is biologically possible—including rewiring the entire connectivity of the brain into any desired configuration [ 42 – 53 ]. However, individual studies rarely use the same model and focus on hand-picked structural and functional properties of interest. This lack of methodological standardisation limits the field’s capacity to compare, generalise, and synthesise results from the modelling literature as a whole. To overcome these challenges, here we execute a comprehensive structure-to-function causal mapping in silico , characterising how brain regions act, interact, and relate to each other along multiple dimensions. To ensure a standardised baseline for comparison, we use the same implementation throughout: a dynamic mean-field model (DMF) of excitatory and inhibitory populations, representing cortical regions and coupled according to the wiring diagram of the human connectome reconstructed from in vivo tractography ( Fig. 1a ) [ 63 , 64 ]. Being amenable to separate manipulations of regional excitation, inhibition, and wiring, the DMF model provides an ideal balance of biophysical realism and computational tractability. This computational tractability enables us to systematically manipulate network connectivity and local biophysics across over 2, 000 ‘in silico brains’, and then map the effects of each intervention onto the most comprehensive battery of functional readouts to date ( Fig. 1a ). Specifically, we consider nearly 100 distinct manipulations of brain structure, which include: Download figure Open in new tab Figure 1. Systematic causal mapping of structural perturbations to their functional consequences with computational brain models ( a ) The biophysical mean-field model comprises local excitatory and inhibitory neural masses, representing brain regions, coupled according to the empirical wiring of the human brain reconstructed from diffusion tractography. ( b ) The model’s local and global properties are systematically perturbed: (1) by rewiring or scaling the global connectivity; (2) by lesioning the local connectivity of each region; (3) by tuning each region’s recurrent excitation according to empirical maps of disorder-related cortical atrophy; (4) by modulating regional excitation-inhibition balance according to PET-derived maps of neurotransmitter receptor density. Each perturbation is systematically mapped onto informational, hierarchical, spatial, and temporal aspects of global functional organisation, as well as thousands of individual dynamical features, and the expression of meta-analytic brain patterns recapitulating fundamental cognitive operations. ( c ) Example of information measures: redundancy, synergy, information storage, and information transfer [ 54 ] ( d ) Example measures of hierarchical organisation: the range of the principal gradient of functional connectivity (FC) is used as proxy for the unimodal-transmodal functional processing hierarchy [ 55 ]; and the FC can be divided into a hierarchy of nested modules [ 56 ] ( e ) Example measures of spatial signal coordination: network modularity, and network small-world organisation due to the presence of shortcuts between local clusters. ( f ) Example temporal measures: temporal (ir)reversibility of the signal [ 57 ], and metastability (here quantified as the temporal variance of the global synchrony) [ 58 , 59 ]. ( g ) Representative examples from our comprehensive sampling of univariate dynamical features. Features are obtained from the highly comparative time-series analysis toolbox ( hctsa ) covering the broad literature on time-series analysis in neuroscience increasing or decreasing the global effective coupling between all regions; rewiring the global network topology into specific configurations; lesioning the local connectivity of each cortical region; implementing changes in cortical cytoarchitecture from cortical thickness reflecting 11 neurological, psychiatric, and neurodevelopmental diagnostic categories across over 17 000 patients [ 65 – 67 ] implementing ‘virtual pharmacology’ by tuning regional excitation and inhibition according to 15 maps of neurotransmitter receptor density, obtained from in vivo positron emission tomography (PET) scans in > 1 200 participants [ 2 ] On the functional side, we map each macrostructural manipulation onto four key dimensions of global brain functional organisation: Information dynamics (integrated information; synergy; redundancy; transfer entropy; and active information storage) [ 54 , 68 ] ( Fig. 1b ) Temporal signal coordination (synchrony, metastability, intrinsic timescale, and temporal irreversibility) [ 57 – 59 , 69 – 71 ] ( Fig. 1c ); Spatial signal coordination (prevalence of anticorrelations; modularity and small-world propensity of the functional connectome) [ 72 – 74 ] ( Fig. 1d ) Functional hierarchical organisation (local-global propagation of intrinsic “ignition” events; principal gradient of functional connectivity; and nested modular organisation) [ 55 , 56 , 75 ]( Fig. 1e ). We further complement these global read-outs by: [start=5]Assessing thousands of univariate time-series features of brain dynamics [ 60 , 61 ] ( Fig. 1f ); Quantifying the brain’s spontaneous self-organisation into macroscale functional circuits associated with fundamental cognitive operations, defined using the NeuroSynth meta-analytic engine [ 62 , 76 ] ( Fig. 1g ). This systematic structure-to-function mapping establishes a resource for computational ‘reverse inference’. Researchers will be able to consult our comprehensive look-up table of over 500 000 combinations of structural interventions and functional read-outs, to identify which causal manipulations would be more or less consistent with an empirically observed effect, over-coming the need to develop ad-hoc models for each new empirical observation. This resource is freely available to the neuroscience community through our interactive website ( https://systematic-causal-mapping.up.railway.app/ ). At the same time, this work provides a computational engine to predict the functional consequences of experimental or clinical interventions, and drive hypothesis-generation. Altogether, we integrate multimodal neuroimaging data (functional MRI, diffusion tractography, cortical morphometry, PET) to systematically discover which aspects of brain structure have overlapping or antagonistic causal influence over each dimension of brain function, and how functional properties are traded off against each other. RESULTS Overview: Computational modelling to integrate multimodal brain structure and function We use biophysical modelling to provide mechanistic insight into the functional consequences of manipulating the brain’s local and global wiring, cytoarchitecture, and chemoarchitecture, across an extensive battery of readouts: regional activity, inter-regional interactions, and the emergence of cognitively relevant circuits. Network-based brain models generate biologically plausible simulations of brain activity by combining two key ingredients: (i) a mathematical representation of the local biophysics of each brain region; and (ii) a wiring diagram of the anatomical connectivity between regions [ 44 , 50 , 64 ]. Models can vary widely in terms of complexity and biological realism. Specifically, here we simulate BOLD signals for 68 anatomically-defined regions of the Desikan-Killiany cortical atlas [ 77 ], using a dynamic mean-field (DMF) model of excitatory and inhibitory populations [ 18 , 63 , 64 ]. A cortical model ensures that the same model can be used to integrate and compare all our datasets, some of which are only available for the cortex. Regions are then coupled according to the empirical structural connectivity between regions of the human brain, obtained as a consensus connectome from 100 individuals of the Human Connectome Project [ 78 ], reconstructed from in vivo diffusion MRI tractography ( Methods ). The DMF model has a free parameter, known as ‘global coupling’ and denoted by G , which scales all weights in the structural connectivity to account for the effectiveness of signal transmission between brain regions. To tune the model, we identify the value of G where the model produces the most realistic brain dynamics. In the literature, there are many criteria for identifying the best-fitting value of the global effective coupling; for example, maximising metastability or the similarity between empirical and simulated FC [ 23 , 75 , 79 – 83 ]. To avoid the issue of circular analysis, here we explicitly choose not to use as fitting criterion any of the functional read-outs defined above, whose use we reserve for model assessment. Instead, we follow a well established procedure [ 18 , 64 , 84 – 86 ], minimising the Kolmogorov-Smirnov distance between the model’s functional connectivity dynamics (FCD; the correlation between instantaneous functional connectivity measured at different points in time) and the group-wise FCD obtained from fMRI BOLD signals of 100 individuals from the Human Connectome Project (see Methods for details). This approach captures both spatial and temporal features of the data, better differentiating between optimal and suboptimal values of G than alternative fitting methods [ 18 ]. Since the model with G = 1.6 produces dynamics that most faithfully recapitulate the empirical spatiotemporal dynamics of human BOLD signals (Fig. S1), all our analyses are performed starting from a model tuned with G = 1.6. Functional consequences of regional biophysics Role of neurotransmitter systems: ‘Virtual pharmacology’ from gradients of receptor expression A prominent advantage of the dynamic mean-field model is that it can be enriched with regionally heterogeneous excitatory and inhibitory dynamics. What are the functional consequences of heterogeneous modulations of local biophysics? This question bears clear clinical relevance for our mechanistic understanding of pharmacological interventions. Pharmacology is a cornerstone of modern clinical practice, being routinely and widely used to treat psychiatric and other mental health conditions. Many pharmacological agents reshape cognition and behaviour by engaging the brain’s rich array of neurotransmitter receptors, reshaping local biophysics [ 87 – 89 ]. It is therefore of great value to understand the functional consequences of engaging different neurotransmitter systems. However, even when a drug’s molecular targets are relatively specific and well-characterised, it can be challenging to translate from microscale effects of engaging a specific receptor in vitro , to the drug’s macroscale effects on the human brain in vivo . One of the many reasons is that receptor expression is not uniform across the brain, but rather each region is characterised by a unique profile of receptor expression [ 1 – 3 ]. Computational modelling can contribute to bridging this gap between in vitro and in vivo . For example, biophysical whole-brain models with heterogeneous dynamics based on the empirical distribution of specific receptors across the cortex can recapitulate the effects of serotonergic, dopaminergic, nicotinic, or GABA-ergic agents on macroscale brain activity [ 18 , 19 , 80 , 81 , 90 – 93 ]. Here, we adopt the same approach for our ‘virtual pharmacology’. We systematically characterise how diverse aspects of brain function are reshaped by engaging each of 15 excitatory and inhibitory neurotransmitter receptors across 8 neurotransmitter systems, quantified from in vivo PET across over 1200 human volunteers [ 2 ] ( Fig. 2a ). Following the approach of [ 18 ], the effect of engaging an excitatory receptor ( mGluR 5 , NMDA, α 4 β 2 , 5 HT 2 A , 5 HT 4 , 5 HT 6 D 1 , M 1 ) is modelled by increasing the excitatory gain parameter of each region, according to that region’s receptor density (normalised between 0 and 1). Likewise, the effect of engaging an inhibitory receptor ( GABA A , D 2 , MOR, CB 1 , H 3 , 5 HT 1 A , 5 HT 1 B ) is modelled by increasing the inhibitory gain parameter of each region, according to that region’s receptor density (normalised between 0 and 1) - as per [ 91 ]. Note that no additional parameter tuning is performed, but rather we directly use the normalised values for each map. Download figure Open in new tab Figure 2. Functional consequences of engaging neurotransmitter systems | (a) The effect of engaging each excitatory (resp., inhibitory) neurotransmitter receptor are modelled by varying the excitatory (resp., inhibitory) gain of each region, in proportion to its normalised receptor density measured from in vivo PET [ 2 ]. The regional distribution of each receptor is shown on the cortical surface. (b) Virtual pharmacology recapitulates known empirical results, including desynchronisation and flattening of the brain’s functional hierarchy induced by 5 HT 2 A agonists. Three distinct groups of neurotransmitter receptors can be discerned from their functional consequences. Heatmap shows how modulating regional excitatory or inhibitory gain according to empirical receptor density reshapes the functional organisation of the brain, in terms of effect size (Hedge’s g ) against the un-perturbed model. Our computational assessment indicates that nearly every measure of brain functional organisation can be either increased or decreased through virtual pharma-cology, depending on which neurotransmitter receptor is engaged—with three broad groups of receptors being evident, consisting of the excitatory receptors, and two groups of inhibitory receptors ( Fig. 2b ). However, functional measures differ in terms of their overall susceptibility to virtual pharmacology. Some exhibit comparatively weak responses throughout (e.g., metastability, intrinsic timescale), or comparatively strong responses throughout (e.g., anticorrelations, hierarchical integration). In contrast, other aspects of brain functional organisation appear relatively unaffected by all but a select few receptors, such as temporal irreversibility being selectively responsive to GABA A , 5-HT 1A , 5-HT 1B , CB 1 and MU receptors ( Fig. 2b ). Overall, the fact that each of the functional properties considered here can be manipulated bi-directionally, lends credence to the possibility of using in silico pharmacology to devise treatments for re-balancing brain function. Crucially, many of our in silico predictions are successfully validated against the empirical consequences of pharmacological interventions in vivo . Reductions of synchrony and hierarchical integration, and contraction of the functional hierarchy, have been reported for several anaesthetics including GABA-ergic agents [ 94 – 96 ]. These results are consistent with our model’s predictions from engaging GABA A receptors. We note that anaesthesia also tends to reduce anticorrelations [ 74 ], whereas our model predicts an increase. However, the same prediction of increased anticorrelations under heterogeneous GABA receptor engagement was also made by the model of [ 92 ], in line with our own results. Our model further predicts that global synchrony of fMRI signals should be substantially reduced by agonism of the 5 HT 2 A receptor—and indeed, a recent large-scale study of the serotonin 2A receptor agonist psilocybin reported that psilocybin desynchronises the human brain [ 97 ]. 5 HT 2 A receptor agonsist DMT, LSD, and psilocy-bin also ‘flatten’ the functional hierarchy of the human brain [ 98 , 99 ]: this is again consistent with our model’s results. Role of intrinsic excitability: ‘Virtual patients’ from gradients of cortical thickness abnormality Although pharmacology can temporarily modulate regional biophysics, another another clinically relevant application of our model is to assess the functional consequences of cytoarchitectonic heterogeneity. There is growing evidence that many neurodevelopmental, neurodegenerative, and psychiatric disorders are not restricted to single regions, but rather affect the entire cortex, often with complex combinations of atrophy and enlargement [ 65 – 67 , 100 ]. To model realistic perturbations of local biophysical properties, we turn to the ENIGMA consortium’s large-scale database of changes in cortical thickness associated with 11 neurological, neurodevelopmental, and neuropsychiatric diagnostic categories [ 65 – 67 , 100 ] ( Fig. 3a ). Our approach is inspired by recent work that employed atrophy maps from Alzheimer’s disease and frontotemporal dementia to modulate local parameters in a whole-brain model [ 101 ]. For each diagnostic category, we generate ‘virtual patients’ by modulating the regional level of intrinsic excitability in the model according to the regional pattern of increases or decreases in cortical thickness associated with that condition ( Fig. 3 ). Namely, when atrophy of cortical thickness is observed, we model it as reduced excitation; and when an increase in thickness is observed, we increase excitation in the corresponding region. While we acknowledge that this is inevitably a simplification, it is based on the rationale that most neurons are excitatory, and therefore increases or decreases in grey matter would also primarily involve excitatory neurons. Indeed, a similar approach has been adopted before to model the effects of cortical thickness abnormalities in silico [ 102 ]. Download figure Open in new tab Figure 3. Functional consequences of changes in intrinsic excitability from cortical thickness abnormality | (a) The effects of cortical thickness abnormality are modelled by varying the intrinsic excitation level of each region, in proportion to the extent of its cortical thickness alteration from healthy controls (Cohen’s d , as provided by the ENIGMA Toolbox [ 65 ]): atrophied regions have less excitation, and regions of increased thickness have greater excitation. The empirical changes in cortical thickness associated with each diagnostic category are shown on the cortical surface. (b) Synchrony and the prevalence of anticorrelations are especially susceptible to changes in intrinsic excitation. Heatmap shows how modulating regional excitation according to each empirical pattern of cortical thickness abnormality reshapes the functional organisation of the brain, in terms of effect size (Hedge’s g ) against the un-perturbed model. adhd = attention deficit/hyperactivity disorder; asd = autistic spectrum disorder; ocd = obsessive- compulsive disorder; ige = idiopathic generalised epilepsy; right tle = right temporal lobe epilepsy; left tle = left temporal lobe epilepsy. We find that different aspects of brain functional organisation are differentially affected by cortex-wide changes in regional intrinsic excitation. Some measures (e.g., modularity, prevalence of anticorrelations) tend to increase throughout, whereas others (e.g., synchrony, hierarchical integration) are reduced by most perturbations ( Fig. 3b ). However, even when the direction of change is relatively consistent, the magnitude can vary widely depending on the specific diagnostic category that is used for the perturbation. Overall, both the direction and magnitude of change are dependent on the specific combination of functional measure and regional pattern ( Fig. 3b ). Some of the model’s computational predictions have already found empirical validation. Numerous reports indicate that schizophrenia and bipolar disorder are characterised by reductions of fMRI global synchrony and functional connectivity [ 103 – 107 ]—consistent with our model’s indication of reduced synchrony and redundancy (which is closely linked with FC). Our model also predicts that the cortical thickness changes associated with epilepsy should induce reduced fMRI synchrony and increased modularity. Surprisingly, this is in fact consistent with empirical evidence: although epilepsy is famously associated with EEG hyper-synchrony during seizures, fMRI studies instead indicate decreased FC as a common finding in patients at rest [ 108 , 109 ]. More broadly, the similar functional consequences resulting from diverse patterns of cortical thickness abnormality is consistent with the growing recognition that most diagnostic categories have intricate co-morbidities [ 110 – 112 ]. Functional role of inter-regional connectivity Global manipulations Having considered one of the two main ingredients of whole-brain models—regional biophysics —we now turn to the other: inter-regional connections between regions. Given the prominent role of the global effective coupling ( G ) in determining model goodness-of-fit in the literature (for example, by finding the value of G that maximises some property such as synchrony or metastability [ 79 , 83 , 85 ]), we take the opportunity provided by our model to systematically evaluate the impact of global coupling on the broader set of functional properties of the brain. We simulate BOLD signals using models with G values ranging from 0.1 to 3.0, in increments of 0.1, which scales the strength of inter-regional connections in the model’s structural connectome to determine the effective connectivity between regions. At each value of G , we compute our entire battery of functional properties, to examine how they change as a function of inter-regional effective coupling; greater value of effective coupling indicates stronger signal transmission between regions. We find that functional properties exhibit a diverse range of behaviours in response to changes in the global effective coupling. Whereas some measures monotonically increase or decrease with greater coupling (e.g., anticorrelations, functional hierarchy) others are relatively insensitive to changes in the effective coupling between regions, except at the very highest values (e.g., information storage, intrinsic timescale). Finally, several functional measures (including hierarchical integration and all information-theoretic ones) exhibit non-linear relationships with the effective coupling between regions, characterised by prominent peaks or valleys around G = 2.2: higher than the optimal working point of G = 1.6 where the KS divergence between empirical and simulated FCD is minimised (Fig. S2). On one hand, the observation that many functional properties including metastability and integrated information peak around the same level of effective coupling, is consistent with previous modelling literature [ 113 ]. On the other hand, by considering a much broader repertoire of functional measures we can finally see that the bigger picture is more complex. The global level of effective coupling has drastically variable effects across different aspects of functional brain organisation. Indeed, many measures appear to exhibit their most extreme value away from the point where our model best fits the empirical data. Crucially, this observation is relevant beyond the specific dataset or criterion that we used for fitting, or the specific point of best-fit identified here: since different measures peak at different coupling levels, it follows that no single value of global effective coupling can simultaneously maximise all functional properties, regardless of how ‘best fit’ is defined. Rather, complex trade-offs exist between different functional properties. The indication that the brain does not simultaneously maximise all its functional properties is not only an important neurobiological insight. It also bears consequences for computational modelling. It is common practice in the literature to fit models by maximising a single functional feature (such as synchrony or metastability [ 79 , 83 , 85 ]). However, our results highlight the need to look at the bigger picture, and take into account the brain’s broader repertoire of functional properties. As an alternative approach to interrogate the functional role of global network organisation, we can also keep the global effective coupling fixed at the optimal working point, and instead rewire how regions are connected. This kind of global rewiring into a desired topology is not currently possible in living organisms, where we are limited to assessing naturally-occurring variation across individuals or across species. In contrast, by selectively disrupting or preserving any chosen features of the network, computational models provide a unique avenue to understand how specific aspects of global network organisation influence brain dynamics - highlighting the power and flexibility of this approach. We rewire the connectome according to seven network rewiring schemes [ 114 ]: binary network (preserving topology but setting all weights to the same value), lattice network with preserved weight distribution, modular network with preserved weight distribution, and four types of increasingly constrained random networks: fully random (but preserving the distribution of edge weights) [ 115 ], weight-and degree-preserving [ 116 ], strength-preserving (i.e., preserving both a region’s number of connections and their combined weight) [ 117 ], and geometry-preserving (i.e., preserving degree and also connection length, to respect the spatial embedding of the empirical connectome) [ 118 ] (Fig. S3a). Notably, we find that biophysical models based on the empirical human connectome exhibit the highest values of integrated information and redundancy, as well as most measures of hierarchical organisation (Fig. S3b). We also find that increasingly drastic interventions on the brain’s network structure incur a corresponding deterioration of the brain’s functional properties (Fig. S3c). It is noteworthy that the largest repercussions arise from binarisation, which preserves topology but erases the heterogeneity of weight distribution. The result is a prominent reduction in measures of synchrony and hierarchy, with increased prevalence of anticorrelations (Fig. S3b). However, the presence of heterogeneous edge weights alone is not enough to preserve the functional properties of the empirical human connectome: although this property is preserved by all other rewiring schemes than binarisation, profound functional differences still exist among them (Fig. S3c). Rather, it is also important to take into account how edge weights are distributed across nodes: functional differences with the empirical human connectome are minimised for the strength-preserving rewiring, which maintains each region’s weighted degree (sum of its edge weights; Fig. S3c). Overall, our in silico rewiring of the human connectome reveals the importance of edge weights, and how they are aggregated across regions. Local structural lesions Having addressed the dynamical consequences of local biophysics and global network organisation, we next consider a middle-ground between the two, by probing the role of local structural connectivity on a region-by-region basis. Whereas the global manipulations considered above are only possible in silico , perturbations of a region’s connectivity can be viewed as simulating the effects of a focal lesion. Concretely, we implement local perturbations as follows: for each region of the Desikan-Killiany atlas (combined across both hemispheres), we implement a “virtual lesion” by setting all its connections to 1 / 10 of their original strength. We then use the bio-physical model to generate new regional BOLD signals based on the lesioned connectome, for N = 30 repetitions. From these simulated BOLD signals, we compute our entire battery of functional measures, and obtain an effect size (Hedge’s g , whose interpretation is analogous to Cohen’s d ) from comparing them against the same measures obtained from the original (un-perturbed) connectome. Therefore, our results reflect the brain-wide effects of local lesions. To visualise the results, we plot them on the cortical surface such that each region’s colour reflects the statistical effect size (magnitude and direction) of the change in brain-wide measure, resulting from virtually lesioning that region 4a). Our results indicate that most measures of brain function tend to be either consistently increased or consistently decreased by local structural lesions, with lesion location influencing the magnitude of change, but not its direction. For example, most lesions induce increases in network modularity, and reductions in synchrony—as might be expected since the underlying structural connectome is becoming less connected. However, we also observe exceptions where both notable increases and decreases can be seen (e.g., intrinsic timescale, synergy, active information storage; Fig. 4a ). Download figure Open in new tab Figure 4. Functional consequences of local structural lesions | ( a ) Most measures of brain function (e.g., synchrony) tend to be either consistently increased or consistently decreased by local structural lesions. Each brain map shows, for each cortical region, the effect size (Hedge’s g ) from comparing whole-brain values obtained from N = 30 simulations with the empirical (un-perturbed) connectome, and N = 30 simulations from the locally lesioned connectome. Location on the brain map corresponds to the lesioned region (note that the same region is lesioned simultaneously in both hemispheres). Positive values (red) indicate lesioned > empirical, and negative values (blue) indicate lesioned < empirical. ( b ) The principal component of dynamical susceptibility to local perturbations delineates a core-periphery axis of cortical organisation. Brain scores are shown on the cortical surface on the left, and the contribution of each functional property to the principal component is shown on the right. ( c ) NeuroSynth decoding reveals that the principal axis of susceptibility to local lesions differentiates regions pertaining to externally-oriented versus internally-oriented modes of cognition. Bars indicate spatial correlation; statistical significance is assessed against spatial autocorrelation-preserving null models [ 119 ]; only significant terms that survive FDR correction across 123 total NeuroSynth terms are shown To summarise the role of each cortical region in re-shaping global functional properties of the brain, we apply principal component analysis (PCA) on the regions-by-measures matrix. Principal components provide a low-dimensional representation that best explains the association between regions and functional measures. Regions with similar consequences on our battery of functional measures will exhibit similar PC scores. We find that a single principal component accounts for most of the variance (92%) in functional susceptibility to local structural lesions. This principal component of local susceptibility (‘susceptibility PC1’ for short) delineates a core-periphery axis of cortical organisation, being an-chored in ventromedial cortices at one extreme, and lateral-dorsal cortices at the other extreme ( Fig. 4b ). The ventromedial end is primarily associated with measures of hierarchical organisation and temporal signal co-ordination, whereas measures of spatial coordination are associated with the dorsolateral end ( Fig. 4b ). To characterise the cognitive relevance of this spatial pattern, we perform a term-based meta-analysis using 123 meta-analytic brain maps from the neuroimaging literature, available in the online database NeuroSynth [ 62 ]. A large number of NeuroSynth cortical patterns are significantly spatially correlated with the principal axis of functional susceptibility to local structural lesions, even after correcting for multiple comparisons and the effect of spatial autocorrelation [ 114 , 119 ] ( Fig. 4c ). In particular, many of the terms significantly associated with the dorsolateral end pertain to goal-directed behaviour (‘action’, ‘skill’, ‘planning’, ‘expertise’, ‘goal’, among others). In contrast, terms associated with the ventromedial end pertain to emotion (‘arousal’, ‘fear’, ‘anxiety’, ‘valence’, ‘emotion’) and mental health (‘stress’, ‘psychosis’, ‘addiction’). Thus, we may characterise the principal axis of susceptibility to local lesions as differentiating regions pertaining to externally-oriented versus internally-oriented modes of cognition. Since the models differ only in terms of which region’s connections are lesioned, any differences must be attributed to network properties. This ability to isolate the causal roles of different features is a key advantage of computational modelling. Therefore, we next seek to determine which aspects of the network organisation of the empirical (un-lesioned) structural connectome account for the regional pattern of functional susceptibility to lesions (summarised by the susceptibility PC1). Specifically, we consider several key aspects of regional network organisation: the weighted degree (sum of a node’s connection weights); local efficiency (a measure of how well interconnected a node’s neighbours are); participation coefficient (diversity of modules that a node connects to); and average and modal controllability, which account for connectivity across paths of varying length to estimate a node’s ability to steer network dynamics to-wards easy-to-reach (average controllability) or hard-to-reach (modal controllability) activation states [ 120 ]. To disentangle the respective contributions of these various structural properties, we use dominance analysis [ 121 ], which compares all possible combinations of predictors to identify their relative contribution to the total variance explained. Our results indicate that the principal component of susceptibility to local lesions is best predicted by how well-connected each region is (both directly, in terms of nodes’ weighted degree, and indirectly, as quantified by average and modal controllability metrics), but with little regard for whether its neighbours are themselves connected, or whether they belong to diverse modules (Fig. S4b). It stands to reason that the best predictor of a region’s impact on functional measures is its weighted degree: regions with higher weighted degree will be those whose connections suffer the most drastic change in connectivity, in absolute terms. Demonstrating the empirical validity of this prediction, our virtual lesion results suggest that most structural lesions will reduce functional and ignition-based measures of hierarchy in the brain - consistent with reports in patients with severe brain injuries [ 122 ]. We also contextualise the susceptibility PC1 with respect to other large-scale patterns of cortical anatomy and function. Anatomically we consider intracortical myelination (quantified from in vivo T1w:T2w MRI ratio; [ 9 ]); the principal component of gene expression from the Allen Human Brain Atlas database (AHBA PC1 [ 10 ]); the principal component of receptor density from in vivo PET (receptor PC1; [ 2 ]). Functionally we consider the principal component of meta-analytic activation from the NeuroSynth database (NeuroSynth PC1 [ 62 , 123 ]); and the principal gradient of functional connectivity [ 55 ]. Remarkably, we find that the principal component of susceptibility to local lesions is best recapitulated by the principal component of NeuroSynth meta-analytic activation, which alone accounts for more variance (>50%) than all other predictions combined (Fig. S4c). Finally, we consider how regions resemble each other in terms of their functional susceptibility to structural lesions, by correlating each pair of regions across measures. This produces a matrix of co-susceptibility to structural lesions (Fig. S4d). Across regions, we find that regions’ co-susceptibility to structural lesions in our model, is significantly associated with regions’ co-susceptibility to abnormalities in cortical thickness across 11 neurological, neurodevelopmental, and neuropsychiatric diagnostic categories from the ENIGMA consortium, reflecting cortical morphometry data from over 17 000 patients [ 65 , 67 ] (Fig. S4d). In other words, regions that induce similar functional changes when their connectivity is lesioned in silico , tend to be similarly susceptible to empirical cortical abnormality—suggesting that our model-based functional phenotyping may be capturing some fundamental underlying aspects of brain organisation. Reshaping univariate dynamical features of brain activity Up to this point, we considered functional consequences in terms of cortex-wide functional organisation. Next, we evaluate the effects of each perturbation across a battery of 21 dynamical features of individual BOLD time-series [ 124 ]. These features were chosen to be representative of the broader literature on dynamical systems, encompassing > 6 000 time-series properties such as linear and nonlinear autocorrelation, periodicity, forecasting, and statistical distribution of the data-points [ 60 , 61 ]—which we also compute and make available to the reader through our interactive website: https://systematic-causal-mapping.up.railway.app/ ( Fig. 5a ; see Fig. S7 for investigation of the relationship between local dynamics and global functional connectivity). Download figure Open in new tab Figure 5. Effects of model perturbations on dynamical features of neural time-series | (a) Examples of dynamical features of univariate time-series include temporal autocorrelation, entropy, and statistics of the data distribution. (b) Dynamical features become most extreme as global effective coupling increases. Percent change in each univariate dynamical feature is shown as a function of the global effective coupling parameter G , compared against the value observed for the best-fitting model ( G =1.6). (c) Dynamical features are especially sensitive to the distribution of weights, being most perturbed by binarisation rather than any kind of weight-preserving rewiring. Heatmap shows the effect of global network rewiring across a battery of 21 univariate dynamical features (each averaged across all brain regions), in terms of effect size (Hedge’s g ). (d) Heatmap shows the effect (Hedge’s g ) across a battery of 21 univariate dynamical features, upon lesioning the structural connectivity of each cortical region. (e) A localised-versus-distributed principal component summarises the effects of local structural lesions on univariate dynamics, accounting for 35% of the variance. (f) Reshaping intrinsic regional excitation according to cortical thickness abnormality can either increase or decrease each feature, but not both. Heatmap shows the effect (Hedge’s g ) on our 21 dynamical features, upon heterogeneously increasing or decreasing intrinsic excitation of each region, according to empirical patterns of cortical thickness abnormality. (g) Nearly every univariate dynamical feature can be both increased and decreased by virtual pharmacology, depending on which empirical receptor maps are used to modulate excitatory or inhibitory gain. Heatmap shows the effect (Hedge’s g ) across our battery of 21 dynamical features [ 124 ], upon simulating engagement of each neurotransmitter receptor. adhd = We find that dynamical features vary in their sensitivity to changes of the global effective coupling ( Fig. 5b ). As with global functional organisation, the value of the effective coupling parameter G where most univariate dynamical features exhibit maxima or minima is higher than the optimal value of G = 1.6 where the fit between simulated and empirical FCD is maximised ( Fig. 5b ). However, many global functional features tend to peak around G = 2.2, whereas most univariate dynamical features exhibit the most pronounced changes beyond this point, at the very highest values of global coupling. Thus, we find that univariate and global aspects of brain function are differentially sensitive to the level of global effective coupling between regions ( Fig. 5b ). Pertaining to global network organisation, we find that for most univariate features, the most extreme values (highest or lowest) are produced by biophysical models based on the empirical human connectome, such that different rewirings will only decrease (resp., increase) the univariate feature ( Fig. 5c ). This is consistent with what we observed for global features, as is the fact that dynamical features are especially sensitive to the distribution of weights, being most perturbed by binarisation rather than any kind of rewiring that preserves the weight distribution ( Fig. 5c ). In contrast, we find that many univariate dynamical features can exhibit both increases and decreases as a result of local structural lesions, depending on lesion location ( Fig. 5d ). This pattern represents a departure both from what is observed with global rewiring, and from what is observed for global features, for which more lesions tend to induce either increases or decreases, but not both. As a result, the principal component of univariate dynamical susceptibility to local lesions is different from the principal component of global functional susceptibility ( Fig. 5e ). Instead of a broad ventromedial-versus-dorsolateral division, we observe a localised-versus-distributed spatial pattern. Namely, one extreme is localised to the precuneus and the neighbouring visual and somatosensory medial cortices, driven by features such as periodicity and forecasting error. The other extreme is instead more distributed, exhibiting three separate peaks in lateral prefrontal, angular gyrus, and inferior temporal cortices. This end of the principal component is primarily driven by linear and nonlinear autocorrelation and intrinsic timescale ( Fig. 5e ). When we consider the effects of virtual disease, implemented as regionally heterogeneous perturbations of local biophysics based on empirical cortical thickness abnormality, the results on univariate time-series features once again resemble those observed for global functional organisation. Namely, reshaping intrinsic regional excitation according to cortical thickness abnormality can either increase or decrease each feature, but not both, instead primarily differing in the magnitude of induced change ( Fig. 5f ). In contrast, nearly every univariate dynamical feature can be both increased and decreased by virtual pharmacology, depending on which empirical receptor maps are used to modulate excitatory or inhibitory gain ( Fig. 5g ). Here we focused on the results of univariate features after aggregating them across the entire brain. However, there are undoubtedly rich patterns of structure-function relationships to be found, by looking at the spatial distribution of individual features across the cortex. Therefore, we release the results of our simulations as a resource for the scientific community: users can freely explore all results through our interactive website at https://systematic-causal-mapping.up.railway.app/ . Emergence of functional circuits as an alternative window onto brain function Finally, up to this point we considered brain function in terms of how brain regions act and interact (i.e., the sense in which the field typically refers to ‘structure-function relationships’ [ 13 , 24 , 26 ]. However, a complementary way to model brain function was adopted by Luppi et al. [ 102 ], who used network control theory to induce patterns of regional brain activity corresponding to different cognitive operations, derived from meta-analytic aggregation. Indeed, it is well established in cognitive and systems neuroscience that different brain regions form functional circuits that support different cognitive operations. Even at rest, regions exhibit preferential fMRI co-activation with other regions belonging to the same cognitive circuit [ 125 – 128 ]. Inspired by Luppi et al. [ 102 ], here we use the automated meta-analytic engine NeuroSynth to extract brain patterns reflecting the association between each cortical region, and a set of fundamental cognitive operations: attention, cognitive control, emotion, vision (fixation), language, memory, and movement (shown in Fig. 6a ). We then use our model to ask how each perturbation affects the ability of regions belonging to the same cognitive circuit to co-activate together. Practically, we do so by quantifying at each point in time, the magnitude of the spatial correlation between spontaneous activity and each meta-analytic pattern [ 76 ]. Download figure Open in new tab Figure 6. Effects of model perturbations on the emergence of cognitive functional circuits | (a) NeuroSynth meta-analytic patterns for representative cognitive operations (values are z-scored; note that NeuroSynth does not distinguish activations from de-activations). (b) Weaker coupling impairs regions’ ability to self-organise into cognitively meaningful circuits. Percent change in the match between simulated brain activity and meta-analytic brain patterns, as a function of the global effective coupling parameter G , compared against the value observed for the best-fitting model ( G =1.6). (c) The human structural connectome is the most appropriate network architecture for supporting co-activations for every single cognitive operation. Heatmap shows the effect of global network rewiring on the match between simulated brain activity and meta-analytic brain patterns, in terms of effect size (Hedge’s g ). (d) Lesioning regions that are strongly involved with a given cognitive operation produces a strong negative impact on the brain’s ability to express the corresponding cognitive pattern. Each brain map shows, for each cortical region, the effect of lesioning that region on the match between simulated brain activity and meta-analytic brain patterns, in terms of increased or decreased correlation compared against the baseline model. (e) Emotion-related co-activations are consistently the most affected by disease-related changes in cortical abnormality. Heatmap shows the effect (Hedge’s g ) on the match between simulated brain activity and meta-analytic brain patterns, upon heterogeneously increasing or decreasing intrinsic excitation of each region, according to empirical patterns of cortical thickness abnormality. (f) Most cognitive brain patterns can be modulated bi-directionally by appropriate engagement of different neurotransmiter systems. Heatmap shows the effect (Hedge’s g ) on the match between simulated brain activity and meta-analytic brain patterns, upon simulating engagement of each neurotransmitter receptor. adhd = attention deficit/hyperactivity disorder; asd = autistic spectrum disorder; ocd = obsessive-compulsive disorder; ige = idiopathic generalised epilepsy; right tle = right temporal lobe epilepsy; left tle = left temporal lobe epilepsy. We find that regional co-activations become least brain-like for values of effective coupling close to zero, as indicated by reduced prevalence of each meta-analytic map in the simulated BOLD signals ( Fig. 6b ). This is an important sanity check: if the effective coupling is too low, regions are effectively isolated and unable to influence each other. They cannot self-organise into cognitively meaningful patterns. We also see that at higher values of effective coupling some cognitive patterns would be expressed more strongly than in the balanced model—but this improvement would be incurred at the expense of others ( Fig. 6b ). Another reassuring observation about the validity of our model is that lesioning regions that are strongly involved with a given cognitive operation produces a strong negative impact on the brain’s ability to express the corresponding cognitive pattern ( Fig. 6d ). This result matches the expectation that regions’ ability to co-activate together depends on the anatomical connectivity between them. We also find that the human structural connectome is the most appropriate network architecture for supporting co-activations for every single cognitive operation ( Fig. 6c ). Even relatively conservative rewiring schemes that preserve the weighted degree and geometric embedding lead to notable reductions in the expression of cognitive patterns in spontaneous brain activity ( Fig. 6c ). Most cognitive patterns are also impaired following perturbations intended to simulate different disorders—with the notable exception of ADHD ( Fig. 6e ). In particular, we find that emotion-related co-activations are consistently the most affected, not just for depression but across all diagnostic categories ( Fig. 6e ). The emotion pattern is also particularly affected by our in vitro pharmacology. More broadly, we see that engaging most receptors will suppress the expression of every cognitive pattern. However, three receptors exert the opposite effect, boosting the expression of most cognitive patterns (except for movement): histamine H 3 , dopamine D 2 and serotonin 1A ( Fig. 6f ). As a result, the expression of 6 out of 7 cognitive brain patterns can be modulated bi-directionally by appropriate engagement of different neurotransmiter systems—fully in line with our results pertaining to global functional organisation and local dynamics ( Fig. 6f ). Intriguingly, we also find that some cognitive patterns are paradoxically boosted upon lesioning specific regions. This phenomenon tends to occur for regions that are negatively associated with the patterns in question. Such a paradoxical boost may be due to the lesioned region belonging to a competing functional circuit: consistent with the existence of anti-coordinated patterns of activity in the human brain across both task and rest [ 129 , 130 ]. Convergent functional consequences of local and global macrostructural interventions Since the functional consequences of perturbations are evaluated in terms of the same set of functional measures, we can correlate these measures against each other (with perturbations as data-points), to ask whether there are systematic associations between different aspects of brain function, as revealed by similar changes in response to perturbations. For each of the four perturbation types (local lesions, global network rewiring, neuromodulation, and cortical thickness abnormality) we find a similar division of functional properties into two broadly opposite clusters (SI Fig. S5a-d). The first, larger cluster includes most measures of hierarchy and temporal signal coordination (except intrinsic timescale) as well as redundancy and integrated information. The other, smaller cluster broadly pertains to segregation/differentiation (including modularity, anticorrelations, but also synergy, AIS and intrinsic timescale) (Fig. S5). The same two clusters are found in response to each of the four perturbations, as indicated by statistically significant correlations between each pair of correlation matrices S6). Altogether, by comparing how measures of brain function respond similarly or differently to a variety of causal manipulations, we find that they converge onto two broadly opposite categories, reflecting integration and segregation/differentiation. DISCUSSION Understanding the mechanistic origins of brain function in the connectivity and physiology of the brain is a central endeavour for cognitive, systems, and computational neuroscience. Capitalising on the unparalleled experimental accessibility of computational models, here we systematically evaluated in silico the functional consequences of causally manipulating the brain’s network wiring and regional cyto- and chemo-architecture. Our computational structure-to-function mapping characterised the effects of each intervention against a comprehensive battery of functional measures encompassing information dynamics, spatial and temporal signal coordination, and hierarchical organisation—as well as spontaneous co-activation of distinct cognitive circuits, and thousands of univariate time-series features from the broader literature on dynamical systems[ 60 , 61 ]. To catalyse additional discoveries, we make all results openly available for the neuroscience community through our interactive website ( https://systematic-causal-mapping.up.railway.app/ )—encompassing over 6 000 local and global functional read-outs, for each of 97 distinct causal interventions. Revealing the functional role of connectome architecture Our modelling approach provides insights about the functional roles of distinct architectural features in the human structural connectome, by enabling systematic manipulations of the brain’s wiring diagram that would be simply unfeasible in vivo . We found that every form of global network rewiring impaired the brain’s ability to self-organise into cognitively relevant patterns, indicating that the empirical human connectome may be the most suitable wiring diagram for supporting cognition. Across both local and global manipulations, we also provide convergent evidence that the brain’s anatomical wiring diagram is finely tuned to favour the integration of information and hierarchical organisation, in support of diverse cognitive functions. The empirical human connectome was the most conducive network architecture for these fundamental properties, with virtually all local lesions inducing reductions in hierarchy and integration, and increasingly disruptive rewiring of global network topology inducing increasingly large deviations. These results are consistent with those of Fukushima and Sporns [ 52 ], who found that connectome topology and geometry both contribute to realistic integration-segregation dynamics in a Kuramoto model, but without fully accounting for them—in line with our own results. More specifically, our global and local rewiring provide convergent evidence for prominent roles of both heterogeneous structural weights and their regional distribution. Across both univariate time-series features and global functional organisation, the most extreme differences were observed for the binary network, highlighting the crucial role of a heterogeneous weight distribution. Once heterogeneous weights are present, their distributed across regions (i.e. nodes’ weighted degree) becomes key, as indicated by the similarity of the strength-preserving rewiring to the empirical connectome in terms of functional outcomes (outperforming the various perturbations that preserve the number of connections, but without preserving their combined weight). This result is also in line with our observation that following localised structural lesions, weighted degree is the dominant predictor of the resulting influence on global functional organisation. Many previous modelling studies have investigated the effects of lesions, rewiring, and regional heterogeneity on brain function [ 53 , 91 , 131 –134]. In particular, the importance of weighted degree for predicting the functional effects of local interventions is highly consistent with reports from a diverse range of models and perturbations. These include local lesions in Kuramoto and neural mass models [ 135 – 137 ] as well as local stimulation in Kuramoto [ 138 ] or Wilson-Cowan models [ 139 ]. Notably, Vasa and colleagues [ 131 ] evaluated synchrony and metastability after local lesions in a Kuramoto model of coupled oscillators. On balance, both global metastability and global synchrony were decreased by lesions— as in our own model. However, lesioning some midline cortical regions could produce small increases in metastability: precisely what we also observed. This consistency of observations is reassuring especially since they were obtained using different models, hinting at broader generalisability of the present results. In addition to this computational convergence across modelling strategies and functional read-outs, the consistent observation that brain function is especially vulnerable to perturbations of high-centrality nodes is relevant for our understanding of disease [ 136 ]. Specifically, connectome hubs (the most highly connected nodes) are disproportionally implicated across a variety of brain disorders [ 140 – 142 ]. Among possible reasons, a high number of connections implies greater metabolic demand to sustain firing, making high-strength nodes more vulnerable to hypoxic injury [ 140 , 143 ]. Altogether, when considering the distribution and placement of structural connections, our results indicate that the human connectome is the most suitable wiring scheme to promote information integration, hierarchical organisation, and the emergence of cognitively-relevant coalitions. Trade-offs in the functional organisation of the human brain In addition to network wiring, interactions between regions also depend on the global level of coupling across the entire network, and on the local biophysical properties of each individual region. Crucially, our systematic assessment reveals that most measures including measures of hierarchy, integrated information and cognitive co-activations are not maximised at the value of global effective coupling where we observe the best fit between simulated and empirical brain activity. Note that although we quantified model fit using the FCD criterion (which is not one of the measures that we assessed, thereby avoiding issues of circular analysis), the observation that measures are not all maximised together is independent of which fitting criterion is chosen. This is because, regardless of which value of G is identified as the best fit for the real human brain, there is no value of G for which all functional features are maximised. Likewise, we found that virtually any chosen measure of brain function can be individually increased or decreased by means of in silico pharmacology—but not all together. For any functional measure that is increased by pharma-cology or changing the effective coupling, there is at least one other whose expression is reduced. This observation does not contradict the optimality of connectome wiring discussed above, since changes in network wiring were performed while the global effective coupling and regional excitation and inhibition were kept fixed. However, the question arises: Why does the human brain not maximise all functional properties to-gether? A possible reason why the model’s optimal fitting point to the empirical data ( G = 1.6) is not where most functional measures peak ( G = 2.2), may be because other aspects of functional organisation are instead minimised around G = 2.2, giving rise to trade-offs between competing properties that cannot be satisfied to-gether. Indeed, we observed two main clusters of functional properties that behave in opposite ways in response to most causal manipulations. These clusters may be broadly described as pertaining to integration and segregation/differentiation, respectively. Many of the properties in both clusters are widely held to be beneficial for computation and cognition, such as information integration and hierarchical organisation, but also small-world architecture and information storage [ 54 , 56 , 72 , 75 , 144 –146]. However, our model shows that such properties tend to behave in opposite fashion across most manipulations, such that when some are optimal others display their least favourable value. Furthermore, this antagonistic behaviour becomes increasingly prominent at higher levels of effective coupling, where the most extreme values are observed in each direction: the closer the model comes to optimising some properties, the further it will be from optimising others. The best-fitting point of the model may represent a solution to this complex trade-off between competing desiderata. Indeed, this interpretation is in line with the model of Deco and colleagues [ 146 ], who found that the best fitting to empirical fMRI signals occurs at an intermediate value of the global coupling, where neither measures of integration nor segregation are maximised, but rather the two are balanced against each other. This balancing act may afford the brain the flexibility to shift between different configurations depending on environmental demands—for example thanks to endogenous engagement of different neurotransmitter systems, as suggested by our own simulations with receptor maps. Core-periphery organisation of brain function Notably, the principal component of regions’ functional susceptibility to local structural lesions divides the cortex into two clear extremes. On one hand, a set of regions situated at the brain’s core (medially and ventrally), associated with internally-oriented cognitive processes (emotion, arousal, valence, memory). On the other hand, a set of regions situated at the anatomical periphery (dorsal and lateral) that pertain to more externally-oriented modes of cognition, such as attention and working memory, vision, motion, and action. Broadly, one may think of the core regions as determining what goals to pursue, and the peripheral regions as determining how to pursue them. Indeed, a similar core-periphery organisation was also found by Gollo et al [ 133 ], who related these regions with interoception and exteroception, respectively. In turn, this core-periphery distinction maps onto the two broad categories of global functional measures. Lesions to the core, value-related regions map onto measures of integration. Lesions to the peripheral regions related to perception and action map onto measures of segregation/differentiation. We also found that the principal component of local functional susceptibility is best predicted by the principal component of NeuroSynth co-activation, far outstripping predictors derived from anatomy or even resting-state FC. In other words, regions that are involved in the same cognitive processes in vivo , as indicated by meta-analytic co-activation, also exhibit similar responses to perturbations in our in silico model. Similarly, regions’ co-susceptibility to structural lesions recapitulates their co-susceptibility to cortical thickness abnormalities associated with a variety of diagnostic categories from the ENIGMA consortium—further supported by correlations with NeuroSynth maps pertaining to mental health terms (stress, fear, anxiety, psychosis, addiction). Therefore, our computational structure-to-function mapping recapitulates both regions’ vulnerability to brain disease, and their joint involvement across different cognitive operations—even though neither of these properties was explicitly introduced into our model of local lesions. By revealing regions’ joint involvement in cognitive circuits and functional brain properties, our model is inspired by ‘lesion network mapping’ [ 35 , 38 ]. NeuroSynth identifies functional circuits by finding statistical associations between cognitive constructs and cortical locations across neuroimaging studies [ 62 , 125 , 128 ]. In contrast, lesion network mapping identifies circuits of regions that produce common neurological symptoms when lesioned— even when the lesion locations themselves do not overlap. Our present approach provides a way to map from lesions to their predicted functional consequences. Brain function from dynamics to cognition The main meaning of ‘brain function’ that we adopted in the present study reflects how brain regions act, interact, and relate to each other along multiple dimensions. To also approach ‘brain function’ from a different angle, we identified functional circuits that co-activate together to support fundamental cognitive operations— from attention to emotion and movement—as indicated by meta-analytic co-activation across thousands of neuroimaging studies [ 62 ]. We found that the brain’s ability to self-organise into functional cognitive circuits is highly sensitive to the wiring of the human structural connectome. We also found that lesioning pivotal members of a functional circuit will destabilise the entire circuit, diminishing its prevalence in spontaneous brain activity. This pattern of results from our in silico model is clearly consistent with empirical observations in vivo from neuropsychology, with its long tradition of deciphering the functional roles of different cortical regions by examining the cognitive deficits of patients with focal lesions [ 38 , 147 – 155 ]. Overall, the results of our ‘virtual neuropsychology’ indicate that the emergence of cognitive circuits in brain activity is strongly dependent on the anatomical connectivity between regions. We also found that the expression of cognitive circuits in brain activity is compromised for nearly every in silico model of diagnostic categories. In particular, the meta-analytic pattern reflecting emotional processing is the most affected across disorders: possibly reflecting a shared dimension of symptomatology among many diagnostic categories. It is therefore noteworthy that the opposite result can be obtained by engaging D 2 , H 3 , and 5 HT 1 A receptors, which promote the emergence of specific cognitive patterns in spontaneous brain activity. The dopamine D 2 receptor is the main target of many antipsychotic drugs [ 156 – 159 ]. Likewise, the serotonin 1A receptor is targeted by some atypical antipsychotics, and several medications with antidepressant and anxi-olytic effects [ 159 – 163 ]. Based on these computational predictions, future work may investigate whether psy-chiatric disorders reduce the prevalence of specific cognitive patterns in patients’ spontaneous brain activity—and whether the same patterns are restored by medication acting on D 2 or 5 HT 1 A receptors. Future work will be able to expand on the present results along several directions. Models can vary greatly in their level of neurobiological detail and associated trade-off between interpretability and complexity, ranging from phenomenological Ising and Kuramoto models, to detailed Hodgkin-Huxley models. Indeed, ‘all models are wrong; the practical question is how wrong do they have to be to not be useful” (George Box, 1919-2013). Potential future extensions that do not require distinguishing excitatory and inhibitory dynamics may adopt the Hopf model to better capture oscillations. Our goal of a systematic many-to-many mapping from perturbations to function(s) imposed further computational burdens due to combinatorial explosion, requiring the use of a relatively coarse-grained model with only 68 cortical regions [ 77 ]. Use of a cortical model further ensured that the same model can integrate all our datasets, some of which are only available for the cortex. Future work could extend our results with subcortical regions; or by lesioning multiple regions at once rather than one at a time [ 164 – 167 ]; or implementing alternative network wiring schemes inspired by development or evolution [ 79 , 168 ]; or simulating different doses of ‘virtual pharmacology’. Directionality of structural connections could also be included in future developments [ 169 – 171 ]. Our model is based on a group-consensus connectome; an important development in the field will be the use of personalised models based on individual subjects’ own neuroimaging data, particularly for patients. On the functional side, alternative functional read-outs may include using the model as an artificial neural network to perform actual tasks [ 172 – 175 ]. Although we have shown our model’s convergence both with empirical observations and with alternative models, every model is inevitably a simplification of the underlying biology: the price for the experimental accessibility and mechanistic insight afforded by computational modelling. Outlook Overall, we identified two antagonistic modes of brain function pertaining to functional integration and segregation, which are supported by ventromedial versus dorsolateral regions, and coincide with internally-oriented and externally-oriented modes of cognition. Because of this antagonistic organisation, no single intervention can increase all functional properties at once, inducing complex trade-offs. Indeed, our modelling results suggest that the wiring of the human connectome may be especially suitable to support the kinds of dynamics that promote hierarchical ignition and integration of information, while balancing other functional desiderata. Supporting this notion, most disease-related alterations of cortical thickness and alternative wiring schemes induce functional deviations from this working point. However, our in silico pharmacology suggests that further bi-directional tuning of each individual property may be possible by acting on the interplay of regional excitation and inhibition through drugs targeting specific neurotransmitters. A fundamental use of computational models is to provide a mechanistic explanation for empirically observed phenomena. Since our results encompass a wide range of both structural interventions and functional read-outs, they can be used for computational ‘reverse inference’, to estimate which causal manipulations would be more or less consistent with an observed functional alteration. For example, inferring whether an individual’s level of effective coupling or regional excitation or inhibition may be higher or lower than average, based on how their profile of functional measures deviates from a normative sample. Indeed, we found that regions’ functional vulnerability to lesions in silico recapitulates their in vivo vulnerability to cortical thickness abnormalities. More broadly, our systematic structure-to-function mapping provides a powerful engine for computational causal discovery. Our model provides unambiguous predictions about the functional consequences that we should expect from a broad range of drugs acting on different neurotransmitter systems. These extensive predictions can be tested in vivo through targeted pharmaco-logical manipulations, potentially guiding the selection of appropriate pharmacological treatments. Predictions about local lesions can also be assessed in non-human animals, for example using chemo- or optogenetic activation and deactivation of specific regions, in combination with functional MRI recording [ 176 – 178 ]. Looking forward, our model could also find use as an in silico screening tool for pre-operative planning (e.g. for patients with brain tumor), to predict the functional impact of resecting tissue from different regions. METHODS Human Connectome Project data We used resting-state functional MRI data from the 100 unrelated subjects (54 females and 46 males, mean age = 29.1 ± 3.7 years) of the HCP 900 subjects data release [ 179 ]. All HCP scanning protocols were approved by the local Institutional Review Board at Washington University in St. Louis. The diffusion-weighted imaging (DWI) acquisition protocol is covered in detail else-where [ 180 ]. Data were acquired using the following parameters. Structural MRI: 3D MPRAGE T1-weighted, TR = 2, 400 ms, TE = 2.14 ms, TI = 1, 000 ms, flip angle = 8 ° , FOV = 224 × 224, voxel size = 0.7 mm isotropic. Two sessions of 15-min resting-state fMRI: gradient-echo EPI, TR = 720 ms, TE = 33.1 ms, flip angle = 52 ° , FOV = 208 ×180, voxel size = 2 mm isotropic. Here, we used functional data from only the first scanning session, in LR direction. We also used diffusion MRI (dMRI) data from the same 100 unrelated participants. The diffusion MRI scan was conducted on a Siemens 3T Skyra scanner using a 2D spin-echo single-shot multiband EPI sequence with a multi-band factor of 3 and monopolar gradient pulse. The spatial resolution was 1.25 mm isotropic. TR=5500 ms, TE=89.50ms. The b-values were 1000, 2000, and 3000 s/mm 2 . The total number of diffusion sampling directions was 90, 90, and 90 for each of the shells in addition to 6 b0 images. We used the version of the data made available in DSI Studio-compatible format at http://brain.labsolver.org/diffusion-mri-templates/hcp-842-hcp-1021 [ 181 ]. Functional MRI preprocessing and denoising HCP-minimally preprocessed data [ 180 ] were used for all acquisitions. The minimal preprocessing pipeline includes bias field correction, functional realignment, motion correction, and spatial normalisation to Montreal Neurological Institute (MNI-152) standard space with 2mm isotropic resampling resolution [ 180 ]. Denoising was performed using the CONN toolbox [ ? ]. The anatomical CompCor (aCompCor) method removes physiological fluctuations by extracting principal components from regions unlikely to be modulated by neural activity; these components are then included as nuisance regressors [ 182 ]. Following this approach, five principal components were extracted from white matter and cerebrospinal fluid signals (using individual tissue masks obtained from the T1-weighted structural MRI images) [ 183 ]; and regressed out from the functional data together with six individual-specific realignment parameters (three translations and three rotations) as well as their first-order temporal derivatives; followed by scrubbing of outliers identified by ART, using Ordinary Least Squares regression [ 183 ]. The de-noised BOLD signal timeseries were linearly detrended and band-pass filtered to eliminate both low-frequency drift effects and high-frequency noise, thus retaining frequencies between 0.008 and 0.09 Hz. Finally, denoised time-series were parcellated into 68 cortical regions from the Desikan-Killiany anatomical atlas [ 184 ]. Human structural connectome from Human Connectome Project We adopted previously reported procedures to reconstruct the human connectome from DWI data. The minimally-preprocessed DWI HCP data [ 180 ] were corrected for eddy current and susceptibility artifact. DWI data were then reconstructed using q-space diffeomorphic reconstruction (QSDR [ 185 ]), as implemented in DSI Studio ( www.dsi-studio.labsolver.org ). QSDR calculates the orientational distribution of the density of diffusing water in a standard space, to conserve the diffusible spins and preserve the continuity of fiber geometry for fiber tracking. QSDR first reconstructs diffusion-weighted images in native space and computes the quantitative anisotropy (QA) in each voxel. These QA values are used to warp the brain to a template QA volume in Montreal Neurological Institute (MNI) space using a nonlinear registration algorithm implemented in the statistical parametric mapping (SPM) software. A diffusion sampling length ratio of 2.5 was used, and the output resolution was 1 mm. A modified FACT algorithm [ 186 ] was then used to perform deterministic fiber tracking on the reconstructed data, with the following parameters [ 187 ]: angular cutoff of 55°, step size of 1.0 mm, minimum length of 10 mm, maximum length of 400 mm, spin density function smoothing of 0.0, and a QA threshold determined by DWI signal in the cerebrospinal fluid. Each of the streamlines generated was automatically screened for its termination location. A white matter mask was created by applying DSI Studio’s default anisotropy threshold (0.6 Otsu’s threshold) to the spin distribution function’s anisotropy values. The mask was used to eliminate streamlines with premature termination in the white matter region. Deterministic fiber tracking was performed until 1, 000, 000 streamlines were reconstructed for each individual. For each individual, their structural connectome was reconstructed by drawing an edge between each pair of regions i and j from the Desikan-Killiany cortical atlas [ 184 ] if there were white matter tracts connecting the corresponding brain regions end-to-end; edge weights were quantified as the number of streamlines connecting each pair of regions, normalised by ROI distance and size. A group-consensus matrix A across participants was then obtained using the distance-dependent procedure of Betzel and colleagues, to mitigate concerns about inconsistencies in reconstruction of individual participants’ structural connectomes [ 188 ]. This approach seeks to preserve both the edge density and the prevalence and length distribution of inter- and intra-hemispheric edge length distribution of individual participants’ connectomes, and it is designed to produce a representative connectome [ 188 , 189 ]. This procedure produces a binary consensus network indicating which edges to preserve. The final edge density was 27%. The weight of each non-zero edge is then computed as the mean of the corresponding non-zero edges across participants. Whole-brain computational model Macroscale whole-brain computational models represent regional activity in terms of two key ingredients: (i) a biophysical model of each region’s local dynamics; and (ii) inter-regional anatomical connectivity. Thus, such in silico models provide a well-suited tool to investigate how the structural connectivity of the brain shapes the corresponding macroscale neural dynamics [ 18 , 43 , 44 , 63 ]. In particular, the Dynamic Mean Field (DMF) model employed here simulates each region (defined via a species-specific brain parcellation scheme) as a macroscopic neural field comprising mutually coupled excitatory and inhibitory populations, providing a neuro-biologically plausible account of regional neuronal firing rate. Specifically, the model simulates local biophysical dynamics of excitatory (NMDA) and inhibitory (GABA) neuronal populations, interacting over long-range neuroanatomical connections. Here, we used a consensus human connectome reconstructed from in vivo diffusion MRI tractography. The following differential equations therefore govern the model’s behaviour: Following previous work [ 18 , 63 , 64 , 91 ], all parameters were set as in Wong and Wang [] [ 79 ]. for each excitatory (E) and inhibitory (I) neural mass, the quantities , and represent its total input current (nA), firing rate (Hz), and synaptic gating variable, respectively. The function F (·) is the transfer function (or F–I curve), representing the non-linear relationship between the input current and the output firing rate of a neural population. Finally, is the local feed-back inhibitory control of region n , which is optimized to keep its average firing rate at approximately 3 Hz, and ν n is uncorrelated Gaussian noise injected to region n . The model’s fixed parameters are reported in 1. Due to its multi-platform compatibility, low memory usage, and high speed, we used the recently developed and publicly available FastDMF library [ 64 ]. The code used to run all the simulations in this study was written in optimised C++ using the high-performance library Eigen . The C++ core of the code, together with Python and Octave/Matlab interfaces is publicly available as FastDMF and maintained at http://www.gitlab.com/concog/fastdmf [ 64 ]. Model fitting and global effective coupling Following [ 18 , 64 ], all but one of the DMF model parameters are set as per [ 190 ], leaving only one free parameter, known as ‘global coupling’ and denoted by G , which controls the overall effectiveness of signal transmission between brain regions (conductivity of the white matter fibers is assumed to be constant across the brain). We first tune G to match the high-quality Human Connectome Project functional MRI dataset [ 179 ]. We set the model to have the same TR as the HCP fMRI data (0.72s), with data filtered in the same frequency band (0.008-0.09 Hz). Then we use a Bayesian optimiser to identify the G value that maximises the fit between model and empirical HCP fMRI data [ 64 ]. Goodness of fit was quantified as the similarity between the data’s and the model’s functional connectivity dynamics (FCD), computed as follows. First, we obtained Pearson correlation matrices between regional fMRI signal time-series, computed within a sliding window of 30 TRs with increments of 3 TRs [ 18 , 91 ]. Subsequently, the resulting matrices of functional connectivity at times t i and t j were themselves correlated, for each pair of timepoints t i and t j , thereby obtaining an FCD matrix of time-versus-time correlations. Thus, each entry in the FCD matrix represents the similarity between functional connectivity patterns at different points in time. The best-fitting value of the G parameter is identified as the one that minimises the Kolmogorov-Smirnov distance between the histograms of empirical (group-wise) and simulated FCD values (obtained from the upper triangular FCD matrix) [ 18 , 91 ]. Use of the FCD is well established as fitting target for the DMF model [ 18 , 64 , 91 ], and we note that this measure is not one of the measures that we investigate in the present study, thereby avoiding the issue of circularity. Local lesions Local perturbations were implemented at the level of each region. For each region in turn (considering both left and right hemispheres together), a locally perturbed connectome was obtained by setting all of that region’s connections to 0.1× its original value, thereby preserving the topology of the connectome and its binary degree (and ensuring that it does not become disconnected), while diminishing the region’s ability to exchange signals with the rest of the brain. For each perturbation, 30 instances of the model were run, with random initial conditions. Global rewiring schemes for the connectome Global perturbations were implemented as rewirings of the connectome. The total number of edges in the network was always preserved, and so was the distribution of edge weights (except for the binary connectome described below). Additional constraints and specifics of each type of rewiring are provided below. For each global perturbation, 30 instances of the model were run, with random initial conditions. Binarisation The first perturbation that we consider is binarisation, whereby all edges’ weights are set to unity, without otherwise altering the network. Random rewiring The network’s edges were randomly rewired. The resulting network has the same edge density and distribution of edge weights, but does not preserve the degree sequence. Modular network To rewire the connectome into a random hierarchical modular network, we began by generating a binary random network with a specified number of densely connected modules (here, 4) linked together by evenly distributed remaining random connections, having the same number of nodes and the same edge density as the original structural connectome. Because this method creates a directed network, the matrix was symmetrized by selecting the upper triangle of the resultant matrix and using these connections to create an undirected, symmetric binary network. Weights were then assigned at random to the non-zero edges by drawing them without replacement from the distribution of empirical edge weights, while preserving network symmetry. Rewiring into a lattice The network was rewired to have a lattice topology, while preserving the degree sequence and the distribution of edge weights [ 117 ]. Degree-preserving random rewiring The well-known Maslov-Sneppen degree-preserving rewired network swaps edges so as to randomise the topology while preserving the exact binary degree of each node (degree sequence), and the overall distribution of edge weights [ 116 ]. Geometry-preserving rewiring In addition to preserving exactly the same degree sequence and exactly the same edge weight distribution as the original network, the cost-preserving model also approximately preserves the original network’s edge length distribution (based on Euclidean distance between regions), and the weight-length relationship [ 118 ]. Degree- and strength-preserving rewiring The last null model employed simulated annealing to preserve the original network’s strength sequence (sum of edge weights incident to each node). Simulated annealing is a stochastic search algorithm that approximates the global minimum of a given function [ 191 ] using the Metropolis technique [ 192 ], controlled by the temperature parameter T . A high temperature regime allows the exploration of costly system configurations, whereas fine-tuned adjustments with smaller effects on the system cost are provided at lower temperatures. Initially, the simulated annealing algorithm is set at a high temperature, preventing the process from getting stuck in local minima. Throughout the procedure, the system is slowly cooled down while descending along the optimization landscape, yielding increasingly limited uphill rearrangements. Here, we minimize the cost function E defined as the sum of squares between the strength sequence vectors of the original and the randomized networks. To optimize this function, weights were randomly permuted among edges. Reconfigurations were only accepted if they lowered the cost of the system or met the probabilistic Metropolis acceptance criterion: r < exp (− ( E ′ − E ) /T ), where r ∼ U (0, 1). The annealing schedule consisted of 100 stages of 10000 permutations with an initial temperature of 1000, halved at each stage. Virtual patients with cortical thickness abnormality maps from the ENIGMA database Spatial maps of case-versus-control cortical thickness were obtained by including all the neurological, neurodevelopmental, and psychiatric diagnostic categories available from the ENIGMA (Enhancing Neuroimaging Genetics through Meta-Analysis) consortium [ 66 , 67 ] and the Enigma toolbox ( https://github.com/MICA-MNI/ENIGMA ) [ 65 ] and recent related publications ( https://github.com/netneurolab/hansen_crossdisorder_vulnerability ) [ 100 ], except for obesity and schizotypy. This resulted in a total of 11 maps, pertaining to 22q11.2 deletion syndrome [ 193 ], attention-deficit/hyperactivity disorder [ 194 ], autism spectrum disorder [ 195 ], idiopathic generalized epilepsy [ 196 ], right temporal lobe epilepsy [ 196 ], left temporal lobe epilepsy [ 196 ], depression [ 197 ], obsessive-compulsive disorder [ 198 ], schizophrenia [ 199 ], bipolar disorder [ 200 ], and Parkinson’s disease [ 201 ]. The ENIGMA consortium is a data-sharing initiative that relies on standardized image acquisition and processing pipelines, such that cortical thickness maps are comparable [ 67 ]. Altogether, over 17 000 patients were scanned across the eleven diagnostic categories, against almost 22 000 controls. The values for each map are effect sizes (Cohen’s d ) of cortical thickness in patient populations versus healthy controls. Imaging and processing protocols can be found at http://enigma.ini.usc.edu/protocols/ . The largest increase in cortical thickness across all diagnostic categories is 0.87 (expressed in terms of Cohen’s d ), whereas the largest decrease is 0.59. For each diagnostic category, we modulate the regional level of intrinsic excitability in the model according to the regional pattern of increases or decreases in cortical thickness associated with that condition, following the rationale of [ 102 ]. Namely, when atrophy of cortical thickness is observed, we model it as reduced intrinsic excitation; and when an increase in thickness is observed, we increase the intrinsic excitation in the corresponding region. Concretely, for each of the 11 ENIGMA maps we modulate the excitatory scaling factor W E of each region, which in the baseline DMF is uniformly set to W E = 1 for all regions, by adding to it the corresponding region’s value of cortical thickness change (a positive number for thickness increase, and a negative number for thinning). For each map, this results in a DMF model with regionally heterogeneous intrinsic excitation. Virtual pharmacology with receptor maps from Positron Emission Tomography Receptor densities were estimated using PET tracer studies for a total of 15 receptors, across 8 neurotrans-mitter systems, recently made available by Hansen and colleagues at https://github.com/netneurolab/hansen_receptors [ 2 ]. These include dopamine (D 1 [ 202 ], D 2 [ 203 – 206 ], serotonin (5-HT 1A [ 207 ], 5-HT 1 B [ 207 – 212 ], 5-HT 2A [ 213 ], 5-HT 4 [ 213 ], 5-HT 6 [ 214 , 215 ], acetylcholine ( α 4 β 2 [ 216 , 217 ], M 1 [ 218 ], glutamate (mGluR 5 [ 219 , 220 ] NMDA [ 221 , 222 ], GABA (GABA A [ 223 ])), histamine (H 3 [ 224 ]), cannabinoid (CB 1 [ 225 – 228 ]) and opioid (MOR [ 229 ]). Volumetric PET images were registered to the MNI-ICBM 152 nonlinear 2009 (version c, asymmetric) template, averaged across participants within each study, then parcellated and receptors with more than one mean image of the same tracer (5-HT 1 B, D 2 ) were combined using a weighted average [ 2 ]. Finally, each map was normalised between 0 and 1. Following the approach of [ 18 ], the effect of engaging an excitatory receptor is modelled by increasing the excitatory gain parameter of each region, according to that region’s receptor density (normalised between 0 and 1). Likewise, the effect of engaging an inhibitory receptor is modelled by increasing the inhibitory gain parameter of each region, according to that region’s receptor density (normalised between 0 and 1)—as per [ 91 ]. Importantly, these previous studies had the goal of investigating whether tuning regional excitatory or inhibitory gain according to specific receptor maps would increase the goodness-of-fit to specific empirical data (obtained under the effects of LSD and anaesthesia, respectively) over and above the fit to placebo/baseline data [ 18 , 91 ]. Therefore, they explicitly optimised an additional global gain-scaling parameter, whose value was allowed to change for each map until the fit to the drug data was maximised for that map. Here, our goal is different. We are not trying to use the receptor maps to maximise the fit to some specific external dataset; rather, we are interested in evaluating the maps’ differential effects on brain function. By using the receptor maps as inputs to the same model, with everything else kept fixed, we can unambiguously conclude that any resulting functional difference is attributable to the map’s identity. Therefore, we do not include a separate global gain scaling parameter to be optimised for each map. Rather, the original excitatory (resp., inhibitory) gain parameter of each region, which is uniformly set to 1 in the baseline model, is then increased by that region’s normalised receptor density value (which ranges between 0 and 1). Future work may expand on this approach by evaluating different scaling values for each receptor map, thereby simulating different doses of ‘virtual pharmacology’. Information dynamics The framework of integrated information decomposition (ΦID) decomposes information flow into interpretable, disjoint parts, providing a taxonomy of “modes” of information dynamics in multivariate dynamical systems. In this section we provide a brief description of (ΦID). Integrated Information Decomposition (ΦID [ 68 ]) is a generalisation of Partial Information Decomposition (PID; [ 230 ]), a technique to decompose the information that multiple source variable have about a single target variable. ΦID generalises PID by extending the formalism to systems with multiple sources and multiple targets. This makes ΦID particularly well-suited for the study of multivariate stochastic processes, where the state of each process at time t can be seen as the sources of information and the states at t ′ > t as targets. In such scenarios, ΦID describes how information is carried by the variables in the system over time. For the case of two sources of information X, Y and one target Z , PID divides their information into four “information atoms:” redundancy (Red), synergy (Syn), and unique of the first and second sources ( Un X and Un Y ). The ΦID of two timeseries (…, X t , X t +1 , …) and (…, Y t , Y t +1 , …) between timepoints t and t ′ considers two sources of information X t , Y t and two targets X t ′ , Y t ′ , and their information is divided into 16 atoms that comprise all possible ways in which the 4 atoms of traditional PID can evolve in time. For example, ΦID’s atom is the information transferred from X t to Y t ′ — i.e. information that was uniquely present in X at time t , and is present only in Y at time t ′ . Similarly, is a case of information erasure : it was present in both X and Y (i.e., redundant) at time t , and is present only Y (and hence not anymore in X ) at time t ′ . As another example, is information that is persistently redundant: it was present redundantly in both X and Y at time t , and stays redundant at time t ′ . Similarly, was carried synergistically by X and Y at time t , and is persistently synergistic at time t ′ . More details about ΦID can be found in Ref. [ 68 ]. Given a time series dataset from a bivariate stochastic process, it is possible to compute all atoms in its ΦID decomposition given a suitable form of the joint probability density function p ( X t , Y t , X t ′ , Y t ′ ). In this work, we take the simple yet empirically useful assumption that this probability density is a multivariate Gaussian distribution (which is an accurate description of functional brain activity data [ 231 ]). Under these assumptions, the mutual information between two random variables U and V can be computed from their joint covariance matrix as where Σ U (resp. Σ V ) is the covariance matrix of U (resp. V ), and Σ UV is the joint covariance matrix of U and V . With this expression, we can compute the mutual information between any pair of (sets of) variables in the data. As an example, the time-delayed mutual information of the joint stochastic process is given by Equipped with this expression for mutual information, we can now tackle the problem of computing the atoms of PID and ΦID. Under reasonable assumptions [ 232 ], the PID of Gaussian variables reduces to the so-called Minimum Mutual Information (MMI) approach, under which redundancy is calculated as for any target variable Z . Similarly, in the case of ΦID, this redundancy measure can be extended to yield the double-redundancy atom, Finally, after calculating with Eq. (10) , PID redundancy with Eq. (9) , and mutual information with Eq. (7) for all relevant system subsets, the other 15 information atoms can be calculated as the solution of a simple linear system of equations, as described in Ref. [ 68 ]. Overlapping segments of the functional time series with one time step (TR) delay were used to define the past and future states. We calculated ΦID for every pair of the original functional time series using time-delayed mutual information (mutual information between the past and future states) under the Gaussian assumption for continuous variables, and the MMI definition of redundancy. An open-source implementation can be found at https://github.com/ Imperial-MIND-lab/integrated-info-decomp. All information-theoretic measures that we include here can be obtained from Information Decomposition. Specifically, we consider the persistent redundancy () and the persistent synergy (), as well as the additional information-dynamic phenomena of Integrated Information, Transfer Entropy, and Active Information Storage, described below. Integrated Information Integrated Information quantifies the co-existence of integration and differentiation in a system. An initial formulation for dynamical systems was introduced by Tononi and Balduzzi [ 233 ] and adapted for use in empirical data by [ 234 ], corresponding to: This formulation is intended to reflect the extent to which the information contained within the whole system ( I ( t ; t +1 )) exceeds the information contained within the sum of the parts and . In other words, it indicates whether ‘the whole is greater than the sum’. However, this initial formulation has well-known shortcomings, including the fact that it can take on negative values. Through the framework of Integrated Information Decomposition we can decompose the constituent elements of Integrated Information and show that it is composed of different information atoms: it contains all the synergistic information in the system, the unique information transferred from X to Y and vice versa, and, importantly, a negative redundancy contribution [ 68 ]. This explains why Φ can be negative, which will occur in redundancy-dominated systems. This subtraction of the double-redundancy occurs because redundancy is (by definition) present in each of the parts of the system, Therefore, when computing the ’sum of the parts’ to subtract from the whole in order to obtain Integrated Information as “whole minus sum of the parts”, the redundant information is double-counted and subtracted twice. Thus, the original formulation of Balduzzi and Tononi is actually not the difference between whole and sum of the parts, but the balance between Integrated Information and redundancy. The proper whole-minus-sum measure of Integrated Information can be obtained by ‘adding back’ the redundancy: [ 68 ]. This is the measure of Integrated Information that we use here. Note that several variants of Φ have been proposed over the years, including the original formulation of Balduzzi and Tononi [ 233 ], other formulations based on causal perturbation [ 235 ] (see [ 236 , 237 ] for comprehensive reviews). Active information storage Active Information Storage (AIS) [ 238 , 239 ], quantifies how much information from a variable’s past remains available in its future (meaning that it has been stored in the variable’s past); formally, it is defined as the mutual information between the present of one variable, , and its own future, (equivalently, the time-delayed mutual information of an individual part of the system). AIS can be obtained from information decomposition in terms of redundancy and unique information, but now taking into account both past and future: Information transfer Information-theoretic measures of transfer were introduced by Schreiber [ 240 ], Massey et al. [ 241 ]. In particular, Schreiber’s Transfer Entropy is one of the most widely used measures of information transfer: considering X as source and Y as target, TE ( X, Y ) quantifies the information about Y’s future that is provided by X’s past, over and above what is already provided by Y’s own past. Hence, TE corresponds to: By explicitly excluding any information in the future of Y that was already present in Y’s own past, TE ensures that information storage in Y is not mistaken as having been transferred [ 238 , 242 ]. Note that this is the same rationale underpinning the Wiener-Granger causality measure of statistical causal discovery [ 243 , 244 ]. Indeed, TE and Granger Causality are identical in linear systems [ 245 ]. TE can also be obtained in terms of information decomposition, and this is what we did here, as follows: Temporal signal coordination Synchrony and Metastability Metastability was quantified using a widely-used proxy signature, the standard deviation of the Kuramoto Order Parameter across time (referred to as std ( KOP ) for brevity) [ 58 , 59 , 85 ]. In turn, the Kuramoto Order Parameter is defined by the following equation: where ψ k ( t ) is the instantaneous phase of each bandpass-filtered BOLD signal at node k (note that the symbol ϕ is often used in equations for the KOP instead of ψ , but here we avoid using ϕ to avoid confusion with the measure of Integrated Information [ 246 ]). Following Shanahan [ 59 ]: we computed the instantaneous phase ψ k ( t ) of each bandpass-filtered signal k using the Hilbert transform. The Hilbert transform yields the associated analytical signals. The analytic signal represents a narrowband signal, s ( t ), in the time domain as a rotating vector with an instantaneous phase, ψ ( t ), and an instantaneous amplitude, A ( t ). Thus, s ( t ) = A ( t ) cos( ψ ( t )). The phase and the amplitude are given by the argument and the modulus, respectively, of the complex signal z ( t ), given by z ( t ) = s ( t ) + iH [ s ( t )], where i is the imaginary unit and H [ s ( t )] is the Hilbert transform of s ( t ). At each point in time, the Kuramoto order parameter measures the global level of synchronization across these oscillating signals. Under complete independence, the phases are uniformly distributed and thus KOP is nearly zero, whereas KOP = 1 if all phases are equal (full synchronization). The variability (standard deviation) of the KOP over time is commonly used as a signature of metastability, first proposed by Shanahan [ 59 ]. If std ( KOP ) is high, it indicates that the system alternates between high and low synchronisation, thereby combining tendencies for integration (high synchrony) and segregation (low synchrony). For each individual (and simulation), we obtain the std ( KOP ) signature of metastability, as well as the maximum observed value of global synchrony. Intrinsic timescale We estimated the intrinsic timescale of each brain region by computing the autocorrelation function of each brain region. Following [ 70 , 247 ], we used least-square fitting to fit a nonlinear exponential decay function to the empirically estimated autocorrelation function. The exponential decay function was fitted as a function of the time lag k Δ between time bins, where k = | i − j |, and obeyed the equation: where A corresponds to a scaling factor, B reflects the offset for contribution of timescales longer than the ob-servation window, and they obey parameter bounds: The intrinsic timescale (i.e., rate of decay) is then given by τ . Temporal irreversibility We estimate pairwise interactions between brain regions by computing time-shifted correlations between both the forward and reversed fMRI BOLD time series of any two regions. This method effectively quantifies the asymmetry in interactions between region pairs, thereby indicating how one region influences another. This approach is inspired by thermodynamics, where the breaking of detailed balance is associated with non-reversibility, often referred to as the ‘arrow of time’ [ 57 ]. Irreversibility is captured as the difference between the time-shifted correlations of forward and reverse time series. To illustrate, consider the detection of irreversibility between two time series, x ( t ) and y ( t ). The temporal dependency between x ( t ) and y ( t ) is measured using time-shifted correlations. For forward evolution, the time-shifted correlation is given by: Similarly, we create a reversed version of x ( t ) (or y ( t )), denoted x r ( t ) (or y r ( t )), by inverting the time sequence. The time-shifted correlation for the reversed evolution is then: The pairwise level of irreversibility, representing the degree of temporal asymmetry or the arrow of time, is quantified as the absolute difference between the forward and reversed time-shifted correlations at a given shift Δ t = T (here, for consistency across species we set T = 1 TR): To compute the whole-brain level of irreversibility, we define forward and reversal matrices of time-shifted correlations for the forward version x n and the reversed backward version of a multidimensional time series, where the subscript n represents different brain regions. These matrices capture the functional causal dependencies between the variables in the forward and artificially generated reversed time series, respectively. The forward and reversed matrices are expressed as: These matrices, representing the functional temporal dependencies, are based on the mutual information derived from the respective time-shifted correlations. FS diff, np is a matrix containing the squared differences of the elements between the forward and reversed matrices: where each element reflects the irreversibility level for that region pair. The mean of this matrix provides a value of whole-brain irreversibility [ 57 ]. Spatial signal coordination Prevalence of anticorrelations We measured the prevalence of anticorrelations as the proportion of negative edges, out of the total number of edges in the functional connectivity matrix. Modularity We constructed a network from the functional connectivity, with nodes being regions and edges being the functional connectivity between them (excluding negative ones). We then applied Newman’s algorithm, which quantifies modularity as the degree to which the network can be subdivided into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges [ 248 ]. Small-World Propensity A small-world network combines the presence of tightly interconnected clusters (characterising lattice networks, and theorised to support specialised processing) with a short characteristic path length (a key feature of random network, facilitating integration between different clusters) [ 144 , 249 ]. Thus, small-worldness represents a mark of optimal balance between global and local processing. We adopted the measure of small-world propensity recently developed by Muldoon et al. [ 72 ], which provides a theoretically principled way to quantify and compare the extent that different networks exhibit small-world structure while accounting for network density. The small-world propensity, SMP , is designed to quantify the extent that a network displays small-world organisation by taking into account the deviation of the network’s empirically observed clustering coefficient, C obs , and characteristic path length, L obs , from equivalent lattice ( C latt , L latt ) and random ( C rand , L rand ) networks: where Thus, Δ C and Δ L quantify the fractional deviation of the empirically observed clustering coefficient and characteristic path length from the corresponding null models according to the definition of a small-world network: namely, a lattice network for the clustering coefficient, and a random network for the characteristic path length [ 72 ]. Following Muldoon et al. [ 72 ], we further bound both measures of fractional deviation Δ C or Δ L between 0 and 1 (to account for the possibility of empirical networks exceeding the corresponding null models), by setting negative values of Δ C or Δ L to 0, and values that exceed unity to be exactly 1. In turn, this ensures that the resulting values of small-world propensity will also be bounded between 0 and 1. Small-world propensity is then interpreted as follows: both a large Δ C or Δ L would indicate a large deviation of the network’s properties from the corresponding properties that define small-world organisation. Thus, large Δ C or Δ L would lead to the measure of small-world propensity becoming closer to zero. Conversely, if a network exhibits both the high clustering coefficient of a lattice and the low path length of a random network (thereby satisfying both requirements of the small-world network definition), then it will have low Δ C and low Δ L , and the small-world propensity as a whole will be closer to 1. Hence, higher small-world propensity intuitively indicates better adherence to the requirements of a small-world network Muldoon et al. [ 72 ]. Hierarchical organisation Spatiotemporal Hierarchy from Intrinsic-driven Ignition ‘Intrinsic-driven ignition’ quantifies the extent to which spontaneously occurring (‘intrinsic’) local events elicit whole-brain activation (‘ignition’) [ 75 , 122 ]. To compute intrinsic-driven ignition, the timeseries are transformed into z-scores, and subsequently thresholded to obtain a binary sequence based on the combined mean and standard deviation of the regional transformed signal, such that σ ( t ) = 1 if z ( t ) > 1 and is crossing the threshold from below, indicating that a local event has been triggered; otherwise, σ ( t ) = 0. Note that the threshold of 1 standard deviation for triggering an event is chosen for consistency with previous work, but it has been demonstrated that the results of this procedure are robust to the specific threshold chosen [ 250 ]. Subsequently, for each brain region, when that region triggers a local event ( σ ( t ) = 1), the resulting global ignition is computed within a time-window of 4 TRs, in line with previous work. An NxN binary matrix M is then constructed, indicating whether in the period of time under consideration two regions i and j both triggered an event ( M ij = 1). Intrinsic-driven ignition (IDI) is given by the size of the largest connected component of this binary matrix M , quantifying the breadth of the global ignition generated by the driver region at time t . To obtain a measure of spatio-temporal hierarchy of local-global integration, each region’s IDI values are averaged over time, and the variability (standard deviation) across regions is then computed. Consequently, higher standard deviation reflects more heterogeneity across brain regions with respect to their capability to induce ignition, which suggests in turn a more elaborate hierarchical organisation between them [ 75 , 122 ]. Hierarchical Integration A distinct but complementary perspective on hierarchical brain function is in terms of nested organisation. Such a perspective can be obtained from studying the brain’s eigenmodes, and how the latter support the balance between integration and segregation across scales [ 56 , 95 ]. Being a symmetric matrix, the functional connectivity can be decomposed as FC = U Λ U T , where U is an orthogonal matrix whose columns are eigenvectors (eigenmodes) of FC, and Λ is a diagonal matrix whose entries are the eigenvalues of FC. Each eigenmode of functional connectivity identifies a distinct pattern of regions that are jointly activated (same sign) or alternate (opposite sign). Therefore, hierarchical modules can be identified based on the concordance or discordance of signs between regions across eigenmodes, progressively partitioning the FC into a larger number of modules and submodules, up to the level where each module coin-cides with a single region, indicative of completely segregated activity. The first eigenmode has the same sign throughout the entire cortex, reflecting global integration. At the next level, two partitions can be detected based on their different signs in the second eigenmode, and each in turn is subdivided at the following level of the hierarchy (i.e., from the third eigenmode) on the basis of regional signs. Thus, segregated modules at one level of the hierarchy can become integrated by being part of the same superordinate module (note that this hierarchical modularity based on eigenmodes is not equivalent to the clustering or modularity maximisation methods [ 56 , 251 ]. During this nested partitioning process, we obtain the module number M i , ( i = 1… N ) and the modular size m j , ( i = 1.. M i ) at each level. Each level i of the hierarchy is characterised by two quantities: the number of modules M i into which the cortex is divided, and the covariance explained by the corresponding eigenmode (given by its squared eigenvalue ). However, the number of modules alone may not properly describe the picture of nested segregation and integration because the size of modules may be heterogeneous. The correction factor was calculated as p i = Σ j | m j − N/M i | /N which reflects the deviation from the optimized modular size in the ith level. Thus, the correction effect is stronger for a larger deviation of modular size from homogeneity [ 56 ]. Since the first eigenmode encompasses the entire cortex into one global module, the corresponding eigenvalue quantifies the overall contribution of global integration, [ 56 ]. Functional processing hierarchy A third way to conceptualise ‘hierarchical organisation’ in the brain is in terms of the distance between opposite ends of the information processing stream. Recently, this hierarchy has been quantified in terms of gradients of functional connectivity [ 55 , 95 , 96 , 98 , 99 , 252, 253 ]. Here, we delineate gradients using the common nonlinear dimensionality reduction technique known as diffusion map embedding implemented in the BrainSpace toolbox https://github.com/MICA-MNI/BrainSpace [ 252 ], with default parameters for kernel, similarity metric, and sparsity (see below). Following previous work, each functional connectivity matrix was thresholded row-wise to achieve 90% sparsity, retaining only the strongest connections in each row [ 95 , 98 ]. The cosine similarity matrix was calculated on the thresholded z-matrix to generate a similarity matrix reflecting the similarity in whole-brain connectivity patterns between vertices. While the FC matrix reflects how similar each pair of regions are in terms of their temporal cofluctuations, this similarity matrix reflects how similar two regions are in terms of their patterns of FC. The relative influence of density of sampling points on the manifold is controlled by an additional parameter in the range of 0 to 1, which for diffusion map embedding is set to 0.5 to provide a balance between local and global contributions to the embedding space estimation [ 254 ]. The high-dimensional similarity matrix is treated as a graph, with ‘connections’ (entries of the similarity matrix) reflecting the similarity between the regional patterns of FC. The technique estimates a low-dimensional set of embedding components (gradients); in this low-dimensional space, proximity reflects similarity of the patterns of FC: regions with similar FC patterns (which are strongly connected in the network) are placed close to each other, and regions with low similarity are placed far apart. In this way, each gradient represents one dimension of covariance in the inter-regional similarity between FC patterns, with a small number of gradients capturing most of the dimensions of inter-regional similarity [ 55 , 98 , 252 ]. In the embedding space, each gradient can be understood to be “anchored” at regions that have the strongest values for that gradient, suggesting that this particular embedding dimension captures their similarity profiles of FC well. In contrast, regions that are close to the origin (i.e. have a low absolute value for a particular gradient) mean that they are only minimally similar to the ‘anchor points’ of that gradient, which overall does not strongly capture their FC similarity profile well overall [ 55 , 98 , 252 , 253 ]. Therefore, the more different the extremes of a gradient differ along the axis of the gradient, the more the differentiation between regions is being captured by that gradient. To quantify this formally, we calculated the difference between the maximum and minimum values of each scan along the first gradient [ 95 , 96 , 98 ] (which mathematically captures most of the variation in FC profiles within each scan) and compared these differences across conditions. Dynamical features To extract the dynamical phenotype of each brain region, we performed time-series feature extraction using the catch22 toolbox Lubba et al. [ 124 ]. This set of 22 univariate dynamical features was identified as capturing a diverse range of interpretable time-series properties (such as autocorrelation, statistical properties of the distribution) that well summarise the broader literature on dynamical systems, exhibiting strong classification performance across a broad collection of time-series problems Lubba et al. [ 124 ]. Note that one of these 22 features, CO_HistogramAMI_even_2_5 , was excluded by pre-filtering in empirical data and therefore is not included among the features that we extract, leaving 21 (2). Each dynamical feature was extracted for each region, and we then obtained a single whole-brain value by averaging across all regions. Massive temporal feature extraction using hctsa We also performed massive time-series feature extraction using the highly comparative time-series analysis tool-box, hctsa [ 60 , 61 ], of which catch22 is a representative subset. For each region, the hctsa toolbox extracted >7 300 univariate dynamical features, derived from diverse fields including neuroscience, physics, ecology and economics [ 60 , 61 ]. Features range from basic statistics of the distribution of time-points, linear correlations among time-points, and stationarity, to measures of entropy, time-delay embeddings, and signal complexity, among others. Each individual feature is the implementation of a computation (termed ‘master operation’) on the input time-series, using specific parameters. For example, sample entropy (SampEn) computes the probability that similar sequences of observations in a time-series will remain similar as their size increases. Its computation therefore requires a threshold r for deciding when two sequences will be considered similar; and an embedding dimension m that determines the size of the sequences. Multiple individual features are obtained from this master operation as different combinations of r and m . We performed an initial pre-filtering, and did not compute any features that had returned NaN across all regions, or that had displayed no variance, in an independent dataset of human functional MRI (Human Connectome Project; [ 179 ]). The values of different features can vary across several orders of magnitude. Unless otherwise specified, here we do not normalise features across regions, since this could obscure differences across conditions. Instead, we use effect sizes computed on the original features (see below). Despite our initial pre-filtering, not all of the remaining time-series features could be extracted successfully. We therefore performed an additional post-filtering. Features that failed to be extracted were excluded. Dynamical profile similarity To quantify the similarity between the temporal profiles of each pair of brain regions, each dynamical feature is z-scored across regions. The vectors of z-scored regional features are then correlated for each pair of brain regions, producing a matrix of ‘dynamical profile similarity’ (also termed ‘temporal profile similarity’ [ 22 ]) that represents the strength of the similarity of the local dynamical fingerprints of brain areas. The coupling between DPS and functional connectivity is in turn obtained by correlating the vectorised DPS and FC matrices. FC is computed as the zero-lag correlation between pairs of regional time-series. NeuroSynth meta-analytic maps Continuous measures of the association between voxels and cognitive categories were obtained from NeuroSynth, an automated term-based meta-analytic tool that synthesizes results from more than 14 000 published fMRI studies by searching for high-frequency key words (such as “pain” and “attention” terms) that are systematically mentioned in the papers alongside fMRI voxel co-ordinates ( https://github.com/neurosynth/neurosynth ), using the volumetric association test maps [ 62 ]. This measure of association strength is the tendency that a given term is reported in the functional neuroimaging study if there is activation observed at a given voxel. The probabilistic measure reported by NeuroSynth can be interpreted as a quantitative representation of how regional activity is related to psychological processes, as indicated by their co-occurrence in the published literature. Specifically, we focus on seven brain maps reflecting fundamental cognitive operations: attention, cognitive control, emotion, vision (‘fixation’), language, memory, and movement. For each simulated individual, their regional BOLD signals at each point in time were spatially correlated against each of the seven NeuroSynth-derived cognitive patterns, and the magnitudes of these spatial correlations were averaged over time to obtain a single value per cognitive pattern, per individual. For each meta-analytic pattern, the resulting value quantifies its prevalence in the spontaneous brain dynamics. Statistical analyses The effect sizes were estimated using Hedge’s measure of the standardized mean difference, g , which is interpreted in the same way as Cohen’s d , but more appropriate for small sample sizes [ 255 ]. The Measures of Effect Size Toolbox for MATLAB https://github.com/ hhentschke/measures-of-effect-size-toolbox was used [ 256 ]. Spatial null models The statistical significance of spatial correlation between brain maps was assessed non-parametrically via comparison against a null distribution of null maps with preserved spatial autocorrelation [ 114 , 257 ]. For each map, parcel coordinates were projected onto the spherical surface and then randomly rotated and original parcels were reassigned the value of the closest rotated parcel (10 000 repetitions) Meta-analysis with NeuroSynth To contextualise the PC1 of local susceptibility, we performed a meta-analysis using 123 term-based meta-analytic brain maps from the NeuroSynth database (see above) [ 62 ]. Although more than a thousand terms are catalogued in the NeuroSynth engine, we refine our analysis by focusing on cognitive function and therefore we limit the terms of interest to cognitive and behavioural terms. To avoid introducing a selection bias, we opted for selecting terms in a data-driven fashion instead of selecting terms manually. Therefore, terms were selected from the Cognitive Atlas, a public ontology of cognitive science [ 258 ], which includes a comprehensive list of neurocognitive terms. This approach totaled to t = 123 terms, ranging from umbrella terms (“attention”, “emotion”) to specific cognitive processes (“visual attention”, “episodic memory”), behaviours (“eating”, “sleep”), and emotional states (“fear”, “anxiety”) (note that the 123 term-based meta-analytic maps from NeuroSynth do not explicitly exclude patient studies). The Cognitive Atlas subdivision has previously been used in conjunction with NeuroSynth [ 257 , 259 , 260 ], so we opted for the same approach to make our results comparable to previous reports. The full list of terms included in the present analysis is shown in Table ?? . To perform this analysis, the PC1 map was spatially correlated against each NeuroSynth map, and statistical significance was assessed against our autocorrelation-preserving null model. The false positive rate against multiple comparisons was further controlled using the false discovery rate (FDR) correction [ 261 ]. Connectomic predictors of local susceptibility PC1 We characterised the PC1 of local susceptibility in terms of its relationship with several well-known graph-theoretic properties of the structural connectome. From the consensus connectome we computed the weighted degree (sum of a node’s connection weights); local efficiency (a measure of how well interconnected a node’s neighbours are); participation coefficient (diversity of modules that a node connects to, here defined based on the modular assignment of each region to the well-known intrinsic connectivity networks [ 262 ]); and average and modal controllability, which account for connectivity across paths of varying length to estimate a node’s ability to steer network dynamics towards easy-to-reach (average controllability) or hard-to-reach (modal controllability) [ 120 , 263 ]. Average controllability of a network equals the average input energy needed at a set of control nodes, averaged over all possible target states. Average input energy is proportional to where W is the controllability Gramian. However, since the trace of the inverse Gramian is often uncomputable due to ill-conditioning, we follow previous work [ 120 ] in using instead, which encodes the energy of the network impulse response, since the traces of the Gramian and its inverse are inversely proportional. Modal controllability describes how easily the system can be induced to transition to a state that is distant on the energy landscape of its possible states. Technically, it corresponds to the ability of a node to control each of the dynamic modes of the network, and it can be computed from the matrix V of the eigenvectors of the adjacency matrix of the structural connectivity A . Following previous work, we define a scaled measure of the controllability from brain region i of all the N modes of the system as: From this definition, a region will have high modal controllability if it is able to control all the dynamic modes of the system, which implies that it is well-suited to drive the system towards difficult-to-reach configurations in the energy landscape [ 120 , 263 ]. Anatomical predictors of susceptibility PC1 We used neuromaps ( https://netneurolab.github.io/neuromaps/ ) [ 264 ] to fetch the map of intracortical myelination obtained from T1w/T2w MRI ratio [ 10 ], the principal component of variation in gene expression from the Allen Human Brain Atlas transcriptomic database (‘AHBA PC1’) [ 10 ], the principal component of variation in task activation from the NeuroSynth database (‘NeuroSynth PC1’) [ 123 ], the principal component of variation in receptor density (‘receptor PC1’) [ 2 ], and the principal gradient of FC [ 55 ]. Dominance analysis For both the anatomical and connectomic predictors, we used dominance analysis to consider all predictors together and evaluate their respective contributions. Dominance analysis seeks to determine the relative contribution (‘dominance’) of each independent variable to the overall fit of the multiple linear regression model when all predictors are considered (https://github.com/ dominance-analysis/dominance-analysis) [ 121 ]. This is done by fitting the same regression model on every combination of predictors (2 p ™1 submodels for a model with p predictors). Total dominance is defined as the average of the relative increase in explained variance ( R 2 ) when adding a single predictor of interest to a sub-model, across all 2 p ™ 1 submodels. The sum of the dominance of all input variables is equal to the total adjusted R 2 of the complete model, making the percentage of relative importance an intuitive method that partitions the total effect size across predictors. Therefore, unlike other methods of assessing predictor importance, such as methods based on regression coefficients or univariate correlations, dominance analysis accounts for predictor–predictor interactions and is interpretable. We establish the statistical significance of the dominance analysis model using a non-parametric permutation test (one-sided), by comparing the empirical variance explained against a null distribution of R 2 obtained from repeating the multiple regression with spatial autocorrelation-preserving null maps [ 114 , 257 ]. Data availability We have made the results of all simulations openly available through an interactive website ( https://systematic-causal-mapping.up.railway.app/ ). Human Connectome Project Young Adult resting-state, task-based, and diffusion MRI data are available from https://www.humanconnectome.org/study/hcp-young-adult . Diffusion MRI data for the Human Connectome Project in DSI Studio-compatible format are available at http://brain.labsolver.org/diffusion-mri-templates/hcp-842-hcp-1021 . The ENIGMA cortical thickness data are provided as part of the ENIGMA Toolbox (v1.1.3), available at https://github.com/MICA-MNI/ENIGMA . PET receptor maps are available at https://github.com/netneurolab/hansen_receptors . NeuroSynth meta-analytic maps are freely available from the NeuroSynth database at https://github.com/neurosynth/neurosynth . Code Availability Python and Octave/Matlab code for the dynamic mean-field model used in the present study is publicly available as FastDMF and maintained at http://www.gitlab.com/concog/fastdmf [ 64 ]. The HighlyComparative Time-Series Analysis (hctsa) toolbox is freely available at https://github.com/benfulcher/hctsa . The BrainSpace toolbox for gradient decomposition is available at https://brainspace.readthedocs.io/en/latest/ . The Brain Connectivity Toolbox used for graph-theoretical properties and to generate rewired networks is freely available at https://sites.google.com/site/bctnet/ . MATLAB code used to generate geometry-preserving null networks is freely available at https://www.brainnetworkslab.com/coderesources . The code for spin-based permutation testing of cortical correlations is freely available at https://github.com/frantisekvasa/rotate_parcellation . Third-party Python software (version 3.8 was used) for dominance analysis is freely available at https://github.com/dominance-analysis/dominance-analysis . The Enigma toolbox (v1.1.3) for fetching disorder-related maps is freely available at https://github.com/MICA-MNI/ ENIGMA. The Neuromaps toolbox for fetching brain maps (version 0.0.1) is freely available at https://netneurolab.github.io/neuromaps/.MATLAB/Octave and Python code to compute measures of Integrated Information Decomposition of timeseries with the Gaussian MMI solver is freely available at https://github.com/Imperial-MIND-lab/integrated-info-decomp . Author contributions AIL, BM, MLK conceived the work. AIL performed the analysis. FM, LES, GS contributed to the analysis. JV, YSP, GD, MLK, FR, PAMM contributed to interpretation. HA developed the online website. AIL made figures. AIL wrote the first draft with feedback from all coauthors. Conflicts of interest The authors have no conflicts of interest to declare. Alexandros Goulas, Jean-Pierre Changeux, Konrad Wagstyl, Katrin Amunts, Nicola Palomero-Gallagher, and Claus C Hilgetag. The natural axis of transmitter receptor distribution in the human cerebral cortex. Proceedings of the National Academy of Sciences , 118(3): e2020574118, 2021. View this table: View inline View popup Download powerpoint TABLE 1. Fixed parameters of the dynamic mean field model and their values, as per [ 18 ]. View this table: View inline View popup Download powerpoint TABLE 2. Representative subset of dynamical features from catch22 , along with broad category assignment. Note that ami2 (full feature ID: CO _ HistogramAMI _ even _2_5) was not included in the present work, as it failed to pass the pre-filtering stage. Acknowledgments A.I.L. acknowledges support from St John’s College, Cambridge; and a Wellcome Early Career Award (grant number 226924/Z/23/Z). G.S. was supported by a post-doctoral fellowship from the Canadian Institutes of Health Research (CIHR). The work of F.R. has been supported by the ARIA Safeguarded AI program and by PIBBSS affiliateship program. J.V. is supported by EU H2020 FET Proactive project Neurotwin (101017716). Y.S.P. is supported by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant 896354, and ‘ERDF A way of making Europe’, ERDF, EU, Project NEurological MEchanismS of Injury, and Sleep-like cellular dynamics (NEME-SIS; ref. 101071900) funded by the EU ERC Synergy Horizon Europe. F.M. was funded by a UNIQUE Neuro-AI Excellence Scholarship. M.L.K. is supported by the Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117), and Centre for Eudaimonia and Human Flourishing at Linacre College funded by the Pettit and Carlsberg Foundations. G.D. is supported by grant no. PID2022-136216NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ‘ERDF A way of making Europe’, ERDF, EU, Project NEurological MEchanismS of Injury, and Sleep-like cellular dynamics (NEMESIS; ref. 101071900) funded by the EU ERC Synergy Horizon Europe, and AGAUR research support grant (ref. 2021 SGR 00917) funded by the Department of Research and Universities of the Gener-alitat of Catalunya. B.M. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Canadian Institutes of Health Research (CIHR), Brain Canada Foundation Future Leaders Fund, the Canada Research Chairs Program, the Michael J. Fox Foundation, and the Healthy Brains for Healthy Lives initiative. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. 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