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Concepts shape the interpretation of facts. One of the most popular concepts in systems neuroscience is that of ‘hierarchy’. However, this concept has been interpreted in many different ways, which are not well aligned. This observation suggests that the concept is ill defined. Using the example of the organization of the primate visual cortical system, we explore several contexts in which ‘hierarchy’ is currently used in the description of brain networks. We distinguish at least four different uses, specifically, ‘hierarchy’ as a topological sequence of projections, as a gradient of features, as a progression of scales, or as a sorting of laminar projection patterns. We discuss the interpretation and functional implications of the different notions of ‘hierarchy’ in these contexts and suggest that more specific terms than ‘hierarchy’ should be used for a deeper understanding of the different dimensions of the organization of brain networks. This article is part of the theme issue ‘Unifying the essential concepts of biological networks: biological insights and philosophical foundations’.

The primate cerebral cortex displays a hierarchy that extends from primary sensorimotor to association areas, supporting increasingly integrated function underpinned by a gradient of heterogeneity in the brain’s microcircuits. The extent to which these hierarchical gradients are unique to primate or may reflect a conserved mammalian principle of brain organization remains unknown. Here we report the topographic similarity of large-scale gradients in cytoarchitecture, gene expression, interneuron cell densities, and long-range axonal connectivity, which vary from primary sensory to prefrontal areas of mouse cortex, highlighting an underappreciated spatial dimension of mouse cortical specialization. Using the T1-weighted:T2-weighted (T1w:T2w) magnetic resonance imaging map as a common spatial reference for comparison across species, we report interspecies agreement in a range of large-scale cortical gradients, including a significant correspondence between gene transcriptional maps in mouse cortex with their human orthologs in human cortex, as well as notable interspecies differences. Our results support the view of systematic structural variation across cortical areas as a core organizational principle that may underlie hierarchical specialization in mammalian brains.

Schizophrenia has been primarily conceptualized as a disorder of high-order cognitive functions with deficits in executive brain regions. Yet due to the increasing reports of early sensory processing deficit, recent models focus more on the developmental effects of impaired sensory process on high-order functions. The present study examined whether this pathological interaction relates to an overarching system-level imbalance, specifically a disruption in macroscale hierarchy affecting integration and segregation of unimodal and transmodal networks. We applied a novel combination of connectome gradient and stepwise connectivity analysis to resting-state fMRI to characterize the sensorimotor-to-transmodal cortical hierarchy organization (96 patients 122 controls). We demonstrated compression of the cortical hierarchy organization in schizophrenia, with a prominent compression from the sensorimotor region and a less prominent compression from the frontal-parietal region, resulting in a diminished separation between sensory and fronto-parietal cognitive systems. Further analyses suggested reduced differentiation related to atypical functional connectome transition from unimodal to transmodal brain areas. Specifically, we found hypo-connectivity within unimodal regions and hyper-connectivity between unimodal regions and fronto-parietal and ventral attention regions along the classical sensation-to-cognition continuum (voxel-level corrected, < 0.05). The compression of cortical hierarchy organization represents a novel and integrative system-level substrate underlying the pathological interaction of early sensory and cognitive function in schizophrenia. This abnormal cortical hierarchy organization suggests cascading impairments from the disruption of the somatosensory-motor system and inefficient integration of bottom-up sensory information with attentional demands and executive control processes partially account for high-level cognitive deficits characteristic of schizophrenia.

Many studies have identified the role of localized and distributed cognitive functionality by mapping either local task-related activity or distributed functional connectivity (FC). However, few studies have directly explored the relationship between a brain region’s localized task activity and its distributed task FC. Here we systematically evaluated the differential contributions of task-related activity and FC changes to identify a relationship between localized and distributed processes across the cortical hierarchy. We found that across multiple tasks, the magnitude of regional task-evoked activity was high in unimodal areas, but low in transmodal areas. In contrast, we found that task-state FC was significantly reduced in unimodal areas relative to transmodal areas. This revealed a strong negative relationship between localized task activity and distributed FC across cortical regions that was associated with the previously reported principal gradient of macroscale organization. Moreover, this dissociation corresponded to hierarchical cortical differences in the intrinsic timescale estimated from resting-state fMRI and region myelin content estimated from structural MRI. Together, our results contribute to a growing literature illustrating the differential contributions of a hierarchical cortical gradient representing localized and distributed cognitive processes. •Task activations and functional connectivity changes are negatively correlated across cortex.•Task activation and connectivity dissociations reflect differences in localized and distributed processes in cortex.•Differences in localized and distributed processes are associated with differences in intrinsic timescale organization.•Differences in localized and distributed processes are associated with differences in cortical myelin content.•Cortical heterogeneity in localized and distributed processes revealed by activity flow mapping prediction error.

When listening to spoken narratives, we must integrate information over multiple, concurrent timescales, building up from words to sentences to paragraphs to a coherent narrative. Recent evidence suggests that the brain relies on a chain of hierarchically organized areas with increasing temporal receptive windows to process naturalistic narratives. We hypothesized that the structure of this cortical processing hierarchy should result in an observable sequence of response lags between networks comprising the hierarchy during narrative comprehension. This study uses functional MRI to estimate the response lags between functional networks during narrative comprehension. We use intersubject cross-correlation analysis to capture network connectivity driven by the shared stimulus. We found a fixed temporal sequence of response lags—on the scale of several seconds—starting in early auditory areas, followed by language areas, the attention network, and lastly the default mode network. This gradient is consistent across eight distinct stories but absent in data acquired during rest or using a scrambled story stimulus, supporting our hypothesis that narrative construction gives rise to internetwork lags. Finally, we build a simple computational model for the neural dynamics underlying the construction of nested narrative features. Our simulations illustrate how the gradual accumulation of information within the boundaries of nested linguistic events, accompanied by increased activity at each level of the processing hierarchy, can give rise to the observed lag gradient.

The human cortex is characterized by local morphological features such as cortical thickness, myelin content, and gene expression that change along the posterior-anterior axis. We investigated if some of these structural gradients are associated with a similar gradient in a prominent feature of brain activity - namely the frequency of oscillations. In resting-state MEG recordings from healthy participants (N = 187) using mixed effect models, we found that the dominant peak frequency in a brain area decreases significantly along the posterior-anterior axis following the global hierarchy from early sensory to higher order areas. This spatial gradient of peak frequency was significantly anticorrelated with that of cortical thickness, representing a proxy of the cortical hierarchical level. This result indicates that the dominant frequency changes systematically and globally along the spatial and hierarchical gradients and establishes a new structure-function relationship pertaining to brain oscillations as a core organization that may underlie hierarchical specialization in the brain.

Neural activity underlying working memory is not a local phenomenon but distributed across multiple brain regions. To elucidate the circuit mechanism of such distributed activity, we developed an anatomically constrained computational model of large-scale macaque cortex. We found that mnemonic internal states may emerge from inter-areal reverberation, even in a regime where none of the isolated areas is capable of generating self-sustained activity. The mnemonic activity pattern along the cortical hierarchy indicates a transition in space, separating areas engaged in working memory and those which do not. A host of spatially distinct attractor states is found, potentially subserving various internal processes. The model yields testable predictions, including the idea of counterstream inhibitory bias, the role of prefrontal areas in controlling distributed attractors, and the resilience of distributed activity to lesions or inactivation. This work provides a theoretical framework for identifying large-scale brain mechanisms and computational principles of distributed cognitive processes.

•We comprehensively study structure-function coupling between dMRI-derived structural connectivity and MEG/fMRI-derived functional connectivity.•We show consistently spatially heterogeneous structure-function coupling across modalities.•We find stronger coupling in slower and intermediate frequency bands.•Network communication models capture different coupling patterns in different bands.•Structure-function coupling reflects the sensorimotor-association axis and laminar differentiation. The relationship between structural and functional connectivity in the brain is a key question in connectomics. Here we quantify patterns of structure-function coupling across the neocortex, by comparing structural connectivity estimated using diffusion MRI with functional connectivity estimated using both neurophysiological (MEG-based) and haemodynamic (fMRI-based) recordings. We find that structure-function coupling is heterogeneous across brain regions and frequency bands. The link between structural and functional connectivity is generally stronger in multiple MEG frequency bands compared to resting state fMRI. Structure-function coupling is greater in slower and intermediate frequency bands compared to faster frequency bands. We also find that structure-function coupling systematically follows the archetypal sensorimotor-association hierarchy, as well as patterns of laminar differentiation, peaking in granular layer IV. Finally, structure-function coupling is better explained using structure-informed inter-regional communication metrics than using structural connectivity alone. Collectively, these results place neurophysiological and haemodynamic structure-function relationships in a common frame of reference and provide a starting point for a multi-modal understanding of structure-function coupling in the brain.

The classical theory of cortical systematic variation has been independently described in reptiles, monotremes, marsupials and placental mammals, including primates, suggesting a common bauplan in the evolution of the cortex. The Structural Model is based on the systematic variation of the cortex and is a platform for advancing testable hypotheses about cortical organization and function across species, including humans. The Structural Model captures the overall laminar structure of areas by dividing the cortical architectonic continuum into discrete categories (cortical types), which can be used to test hypotheses about cortical organization. By type, the phylogenetically ancient limbic cortices—which form a ring at the base of the cerebral hemisphere—are agranular if they lack layer IV, or dysgranular if they have an incipient granular layer IV. Beyond the dysgranular areas, eulaminate type cortices have six layers. The number and laminar elaboration of eulaminate areas differ depending on species or cortical system within a species. The construct of cortical type retains the topology of the systematic variation of the cortex and forms the basis for a predictive Structural Model, which has successfully linked cortical variation to the laminar pattern and strength of cortical connections, the continuum of plasticity and stability of areas, the regularities in the distribution of classical and novel markers, and the preferential vulnerability of limbic areas to neurodegenerative and psychiatric diseases. The origin of cortical types has been recently traced to cortical development, and helps explain the variability of diseases with an onset in ontogeny.

Mapping individual differences in brain function has been hampered by poor reliability as well as limited interpretability. Leveraging patterns of brain‐wide functional connectivity (FC) offers some promise in this endeavor. In particular, a macroscale principal FC gradient that recapitulates a hierarchical organization spanning molecular, cellular, and circuit level features along a sensory‐to‐association cortical axis has emerged as both a parsimonious and interpretable measure of individual differences in behavior. However, the measurement reliabilities of this FC gradient have not been fully evaluated. Here, we assess the reliabilities of both global and regional principal FC gradient measures using test–retest data from the young adult Human Connectome Project (HCP‐YA) and the Dunedin Study. Analyses revealed that the reliabilities of principal FC gradient measures were (1) consistently higher than those for traditional edge‐wise FC measures, (2) higher for FC measures derived from general FC (GFC) in comparison with resting‐state FC, and (3) higher for longer scan lengths. We additionally examined the relative utility of these principal FC gradient measures in predicting cognition and aging in both datasets as well as the HCP‐aging dataset. These analyses revealed that regional FC gradient measures and global gradient range were significantly associated with aging in all three datasets, and moderately associated with cognition in the HCP‐YA and Dunedin Study datasets, reflecting contractions and expansions of the cortical hierarchy, respectively. Collectively, these results demonstrate that measures of the principal FC gradient, especially derived using GFC, effectively capture a reliable feature of the human brain subject to interpretable and biologically meaningful individual variation, offering some advantages over traditional edge‐wise FC measures in the search for brain–behavior associations. We demonstrate that a macroscale hierarchical functional connectivity gradient that recapitulates fundamental biological features of the human cortex has higher test–retest reliability than traditional edge‐wise measures, especially when derived from combined resting‐state and task‐based data. Further, gradient measures capture individual differences in aging and cognition.