The Connectomics of Brain Disorders

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The connectomics of brain disorders

Alex Fornito1, Andrew Zalesky2 and Michael Breakspear3,4 Abstract | Pathological perturbations of the brain are rarely confined to a single locus; instead, they often spread via axonal pathways to influence other regions. Patterns of such disease propagation are constrained by the extraordinarily complex, yet highly organized, topology of the underlying neural architecture; the so‑called connectome. Thus, network organization fundamentally influences brain disease, and a connectomic approach grounded in network science is integral to understanding neuropathology. Here, we consider how brain-network topology shapes neural responses to damage, highlighting key maladaptive processes (such as diaschisis, transneuronal degeneration and dedifferentiation), and the resources (including degeneracy and reserve) and processes (such as compensation) that enable adaptation. We then show how knowledge of network topology allows us not only to describe pathological processes but also to generate predictive models of the spread and functional consequences of brain disease.

The ancient Roman physician Galen was one of the first to From this perspective, the behavioural impairments propose that pathology in one part of the nervous system that arise from neural insult were thought to emerge could affect other regions when he posited that animal from damage to discrete and specialized brain regions, spirits could flow through interconnecting neural path- as exemplified by famous clinical case studies such as ways1,2. This hypothesis was revisited nearly two millen- Broca’s Leborgne12, Harlow’s Phineas Gage13, and Scoville nia later by Brown-Séquard, who suggested that the effects and Milner’s H.M.14. However, this view provides only a of focal brain damage on remote regions resulted from partial account of brain function. The brain is a highly actions at a distance3. von Monakow extended the concept, complex, interconnected network that balances regional and coined the term diaschisis (derived from Greek and segregation and specialization of function with strong meaning ‘shocked throughout’) to describe the depression integration15,16, a balance that gives rise to complex and

1Monash Clinical and Imaging of function that can arise in undamaged brain regions that precisely coordinated dynamics across multiple spatio 2,4 17 Neuroscience, School of are connected to a lesioned site (reviewed in REF. 5). At a temporal scales . A generic property of any network is Psychological Sciences and similar time, Wernicke proposed an associative theory of that dysfunction can spread easily between linked ele- Monash Biomedical Imaging, brain function, in which higher-order cognitive processes ments, leading to pathological cascades that can encom- Monash University, Clayton, 18 Victoria, Australia 3168. arose from the integration of multiple, spatially distrib- pass large swathes of the system . In the brain, axonal 2Melbourne Neuropsychiatry uted neural systems and in which disorders as diverse as and synaptic contacts can act as conduits for the propaga- Centre and Melbourne School aphasia and schizophrenia resulted from the disruption of tion of disease processes. This is exemplified by the rapid of Engineering, The University specific associative pathways6 (see also REF. 7). Wernicke’s spread of focal epileptogenic activity into generalized of Melbourne, Parkville, contemporaries, including Hughlings Jackson, Meynert, seizures19, the spatially distributed activation changes Victoria, Australia 3053. 20 3Systems Neuroscience Flechsig, Dejerine and Lichtheim, also viewed connectiv- resulting from regionally localized ischaemic insults Group, QIMR Berghofer ity to be central to any understanding of CNS pathology. and the gradual progression of pathology in degenera- Medical Research Institute, Their work paved the way for Geschwind’s introduction of tive diseases that are thought to have focal onset, such as Herston, Queensland, the ‘disconnexion syndrome’ and the concomitant expan- Huntington disease, Parkinson disease and other forms Australia 4029. 21,22 4Metro North Mental Health sion of the range of clinical symptoms that may now be of neurodegeneration . 8,9 Service, The Royal Brisbane attributed to disordered brain connectivity . These An important first step in understanding how neural and Women’s Hospital, developments complemented the emergence of neural- network organization influences the onset, expression Herston, Queensland, systems-based accounts of perception, cognition and and course of disease is the generation of a compre- Australia 4029. emotion10,11 (for a detailed review, see REF. 7). hensive map — a connectome23 — of the connectivity Correspondence to A.F. (BOX 1) e‑mail: Despite these early insights, a major focus of twenti- architecture of the brain . This goal has driven [email protected] eth-century clinical neuroscience was the localization of several recent, large-scale collaborative endeavours that doi:10.1038/nrn3901 psychological processes to specific areas of the brain. are unprecedented in neuroscience24–26, and has led to

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Box 1 | Mapping the human connectome MRI is the tool most widely used to map structural and functional properties of the human connectome. MRI connectomics involves three main steps. First, network nodes are defined, commonly using one of many heuristic approaches (see REF. 148 for a discussion of these methods; see the brain below figure parts a, b on which the green spheres depict an example of a priori-defined regions of interest). Second measures of structural, functional or effective connectivity between nodes are quantified. Both functional connectivity and effective connectivity can be measured during active task performance119,151–153 or task-free (‘resting’) states142,154–156 using functional MRI (see the figure, part a). Structural connectivity can be measured using diffusion tractography (see REFS 148,150 for limitations; see the figure, part b149). The final step involves analysis of either network connectivity or topology77. Connectivity analyses examine variations in the type and strength of connectivity between brain regions, and can be carried out at the level of candidate neural systems (candidate systems analysis) or across the entire brain (connectome-wide analysis)157. In the latter case, whole-brain connectivity can be succinctly represented as a matrix in which each row and column represents a different region, and each matrix element [i, j] encodes the type and strength of connectivity between region pairs (see the figure, parts c, d). The network can also be represented as a graph that comprises nodes (which represent regions) connected by edges (which represent connections; see the figure, parts e, f, in which line thickness represents strength of connectivity). In MRI analyses, connectivity matrices and graphs are often undirected (that is, they represent the presence but not direction of a connection) and weighted to reflect variations of inter-regional connectivity strength (see the figure, parts c, e). Models of effective connectivity can resolve directionality (see the figure, parts d, f). Topological analyses are grounded in graph theory15 and have uncovered several non-trivial characteristic properties of the brain. These properties include a short average path-length between nodes, which enables efficient communication (that is, a parallel and integrated topology), coupled with low wiring cost158,159; a heavy-tailed distribution of regional connectivity, which implies the existence of highly connected hub regions27,111; strong interconnectivity of hub regions, defining a topologically central core, or rich club113,126; and high clustering and hierarchical modularity across multiple resolution scales, which supports functional specialization160. Part g of the figure illustrates some of these key topological properties of brain networks; namely, the shortest path length between two nodes at opposite ends of the network (left; path length shown in orange), clustered connectivity (middle; orange lines represent edges linking a cluster of nodes), modular organization (right; modules outlined by grey shading) and rich-club organization (right; rich-club edges in orange). Image in part b is adapted, with permission, from REF. 149, PLoS http://creativecommons.org/licenses/by/3.0/.

a Functional connectivity b Structural connectivity c Undirected matrix d Directed matrix 1 1 2 2 3 3 . . i i . . . . N N 1 2 3 . . . N 1 2 3 . . . N j j

e Undirected graph f Directed graph

Diffusion tractography An MRI technique for reconstructing large-scale Topological analysis white-matter fibres based on g the preferential diffusion of water along the axes of these fibres.

Hierarchical modularity The nested organization of highly interconnected subsets, or modules, of nodes within a network, such that modules are contained within modules and so on, across multiple scales of organization. Nature Reviews | Neuroscience

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a b c d e 4 2 1

f Effective connectivity g Quantitative difference Qualitative difference Group A Group B Group A Group B

Normal Abnormal At risk

Figure 1 | Connectomics can track and predict patterns of disease spread. a | Typically,Nature a brain-imaging Reviews | Neuroscience experiment may compare a patient with a control population using a measure of neural structural or functional integrity across many locations in the brain. In this example, an analysis identifies two brain regions, 1 and 2, that exhibit significant group-dependent differences. These differences can be presented as a ‘map’ that localizes the abnormalities but offers no information regarding the interplay between these putative pathophysiological markers. b | Mapping the connectivity of these regions reveals that the abnormalities occur within a broader network context. In this example, there is no direct connection between regions 1 and 2, suggesting that pathology may affect these two areas independently; parts c–e depict scenarios in which regions 1 and 2 are directly connected. c | Regions 1 and 2 are abnormal, but the connection between them is intact. In this case, pathology may have originated in one area and affected the other via aberrant signalling along the intact pathway. Identification of the primary abnormality here would require either longitudinal data or an investigation of effective connectivity (f) (see also BOX 1). The connection linking regions 1 and 2 is considered to be at risk of deterioration because it is interposed between two dysfunctional regions. d | Regions 1 and 2, and the connection linking them, are abnormal, suggesting that there may be a direct association between the two regional abnormalities. In this case, a primary pathology in either region may have resulted in secondary deterioration of their connecting pathway and, subsequently, the other area. Alternatively, the pathology may have originated in the axonal tracts that link regions 1 and 2, and subsequently caused dysfunction in both regions. Again, longitudinal analysis would be required to distinguish between these possibilities. e | Dysfunction in regions 1 and/or 2 may alter their connectivity with other regions (red connections linking to regions 3 and 4). In this case, regions 3 and 4 are considered to be at risk of impairment given prolonged exposure to the aberrant signals emanating from regions 1 and 2. f | Study of effective connectivity can provide further clues regarding the primary source of pathology. For example, if region 2 influences 1 but not vice versa (left), then pathology is more likely to have originated in region 2. g | Case-control differences in connectivity can be quantitative (left) or qualitative (right). A quantitative difference occurs when patients and controls share the same underlying connectivity architecture, but show a difference in the strength of connectivity (represented by line thickness) between specific pairs of brain regions. A qualitative difference refers to a distinct pattern of connectivity in the patient group; for instance, a fibre bundle may be present in patients but not controls. Such differences can result from abnormal wiring of the connectome (BOX 2).

the construction of increasingly detailed maps of brain Network science and graph theory offer powerful connectivity at various resolutions in diverse species27–30. tools for overcoming these challenges to map, track and Graph theory However, the sheer scale of the data sets involved poses predict patterns of disease spread (BOX 1; FIG. 1). The A branch of mathematics difficulties for analysis and interpretation. The human application of these techniques has enabled detailed concerned with studying brain comprises an estimated 8.6 × 1011 neurons and descriptions of how disease affects the brain, and has networks of connected 14 31,32 elements. With graph theory, a approximately 10 synapses , a digital atlas of which uncovered new insights into the shared characteristics brain network can be modelled would require more memory than is required to store of diverse disease processes based on fundamental prop- as a graph of nodes (depicting all the written information present in the world today33. erties of brain network organization34,35. More recent single neurons, neuronal Representing, analysing and interpreting these data is conceptual and technical advances mean that the field populations or macroscopic challenging even at the macro-scale resolutions that is now ready to move beyond mere descriptions of dis- brain regions) linked by edges (depicting inter-regional are accessible with current in vivo MRI; on the order of ease processes to generate hypotheses about underlying 2 4 structural or functional ~10 to ~10 nodes (that is, brain regions) and ~5,000 to pathophysiological mechanisms and clinically useful interactions). ~5 × 106 connections. predictions concerning key prognostic indicators.

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In this Review, we consider how these goals can be Studies of patients who have suffered stroke suggest achieved by understanding the various responses of that the severity of behavioural impairment that follows the brain to pathological perturbation, and how neural focal neural damage often correlates with the extent of network topology constrains these responses (BOX 1). We activation and connectivity changes in regions remote examine well-known examples of adaptive and maladap- from the injured site41,42. These associations between tive neural responses to insult, and illustrate how brain behaviour and altered network functional connectivity connectivity shapes their expression at the level of large- occur even if anatomical connectivity between damaged scale neural systems. We then show how knowledge of and undamaged regions is intact43. This finding suggests network topology can be used to characterize and model that a ‘functional deafferentation’ of remote sites may vulnerability and resilience to disease and dysfunction. be sufficient to impair behaviour. Nonetheless, damage to anatomical pathways linking the lesioned area to Maladaptive responses and pathological spread unaffected regions seems to compound the severity of Connectomics offers a powerful analytic framework for behavioural impairment42,44. localizing pathology, tracking patterns of disease spread Diaschisis may manifest only during the performance and predicting which areas will be affected next (FIG. 1). of certain tasks (that is, it may be context-dependent)45 However, simply tracking the spread of a disease will not and may vary as a function of the type of lesion sustained46. necessarily elucidate the mechanisms through which this In some cases, the correlation between the severity of spread occurs. Such mechanisms may be construed as behavioural impairment and the extent of insult-related maladaptive, as they compound the degree of functional functional connectivity changes in remote regions can- compromise that results from the insult. Here, we con- not be explained by the characteristics of the lesion to the sider three major types of maladaptive response that can damaged area alone47 and performance improvements on mediate the spread of pathology throughout the con- key behavioural tasks correlate with the return of normal nectome: diaschisis, transneuronal degeneration and function in the affected network42–44. Together, these find- dedifferentiation (FIG. 2). ings indicate that the behavioural impairments that arise from damage to the CNS may often be the result of how Diaschisis. von Monakow defined diaschisis as a tempo- the insult affects distributed neural dynamics, rather than rary interruption of function in regions that are remote of its impact on the lesioned site alone. from an injured site4 (FIG. 2a). He attributed this interruption to a deafferentation of excitatory input to the remote Transneuronal degeneration. In contrast to diaschi- area. Although his definition identifies the changes as sis, which is an interruption of function in a region transient, von Monakow subsequently acknowledged that is remote from a lesion, transneuronal degenera- that more persistent forms of diaschisis are also possi- tion is a structural deterioration of areas remote from ble2,5. Diaschisis is now a well-established phenomenon, the initial insult. It is a process that evolves over time, particularly following stroke. It has been observed in the and therefore can only be characterized longitudinally forebrain after damage to the brainstem or cerebellum, (BOX 2; FIG. 2b). Transneuronal degeneration can be in cortical regions following subcortical infarction and either anterograde (whereby damage or dysfunction of in contralesional cortex following focal cortical insult20 one neuron causes the degeneration of its postsynaptic (reviewed in REF. 5; see also REF. 20). These distributed target) or retrograde (whereby a presynaptic neuron changes seem to be circuit-selective. For example, one deteriorates as a result of reduced trophic support from study found that lesions to either the fronto-parietal or an injured or necrotic postsynaptic target)48. The form the cingulo-opercular network — two dissociable neural of degeneration can vary, and encompasses changes systems involved in cognitive control — affected con- such as: neuronal shrinkage; reductions in dendrite and nected areas within the same system but not the func- synapse number; alterations of axonal myelin content tions of the other network36. Animal models of crossed and fibre number; and neuronal death48. cerebellar diaschisis, in which cerebellar function is Both anterograde and retrograde degeneration have depressed after a focal lesion in the contralateral cor- been identified in numerous neural circuits48–50. For tex, have shown that cerebellar neurons do indeed show example, studies of the visual system in humans and ani- reduced spiking output after the insult but maintain mals have shown anterograde changes in the optic tract, normal levels of excitability37. This result suggests that lateral geniculate nucleus and striate cortex following the functional depression of the cerebellum is caused surgical damage of the retina or optic nerve, or following by reduced excitatory drive from the damaged cortex, surgical closure of the eyes51–53. By contrast, retrograde Network topology a finding that is consistent with von Monakow’s original degeneration in the lateral geniculate and retina has been The way in which the deafferentation hypothesis. Whole-brain computational reported in monkeys following lesions of the visual cor- connections of a network are 54,55 organized with respect to each modelling has also suggested that focal lesions can have tex . Animal models also indicate that transneuronal other. a diffuse effect on inter-regional synchronization dynam- degeneration is generally more severe when damage is ics that extend well beyond the affected site, and in a way sustained at an early age51,54, highlighting how the stage Functional connectivity that critically depends on the connection topology of the of development may influence neural responses to insult A statistical dependence (such damaged region38,39 (FIG. 3). Accordingly, the concept of (BOX 2). as a correlation) between neurophysiological recordings diaschisis has recently been extended to include altera- Several mechanisms can mediate transneuronal acquired from distinct brain tions of functional connectivity between areas that may not degeneration. As a general rule, pathology in any single regions. even be directly linked to the lesioned area40. area can disrupt interactions with other regions, causing

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Maladaptation a Diaschisis b Transneuronal degeneration c Dediﬀerentiation Dysfunction in remote regions Degeneration of remote regions Desegregated, non-specialized activity

• Deaﬀerentation • Excitotoxicity • Altered neurodevelopment • Aberrant synchronization • Axonal transort • Impaired neuromodulation • Prion-like spread • Deﬁcient plasticity

Adaptation d Compensation e Neural reserve f Degeneracy Increased function in unaﬀected areas Intact tissue suﬃcient to Other systems assume function support function

• Plasticity • Limited pathology • Neurodevelopment • Cognitive ﬂexibility • High reserve • Experience-dependent plasticity

Normal Lesioned Reduced activity Increased activity

Figure 2 | Differentiating major classes of adaptive and maladaptive neural responsesNature to pathological Reviews | Neuroscience perturbation. The expected pattern of systems-level changes associated with maladaptive (parts a–c) and adaptive (parts d–f) responses, shown in a simple network of four nodes that is specialized for a particular behavioural output. Each panel illustrates what happens when one node is damaged as the result of some generic insult (black). The text below each illustration lists some candidate mechanisms that may cause, facilitate or exacerbate each response. We focus here on pathology of nodes and ignore changes in connectivity, for simplicity. Note that the spatial location of nodes is arbitrary and the effect of inter-node anatomical distances on these responses remains unclear. In a maladaptive response (parts a–c), the output of the network (for instance, behaviour) is compromised. a | Diaschisis occurs when a focal lesion depresses the function of remote, connected sites (red nodes). b | Transneuronal degeneration occurs when, over time (arrow) there is a structural deterioration of areas connected to the affected site (additional black nodes). This deterioration can only be identified via longitudinal analysis. Depicted here is a case in which initial diaschisis evolves into degeneration of the previously dysfunctional nodes. c | Dedifferentiation must be understood by considering how one specialized system that is damaged interacts with other areas. The characteristic pattern will involve reduced function of the neural system that supports the impaired behaviour (red nodes), and a diffuse increase of activity in other neural systems that are not typically associated with that behaviour (blue nodes), thus reflecting a break-down of normal functional specialization. In an adaptive response (parts d–f), behaviour or task performance is compensated for or preserved. d | Compensation occurs when either undamaged nodes within the impaired system, or nodes of other systems, increase their activity or connectivity to preserve behaviour (the former scenario is depicted here). e | Neural reserve is evident when the activity in remaining elements of the affected system is unchanged and behavioural performance is intact. f | Degeneracy is evident when a second system can support the behaviour that is normally mediated by the dysfunctional network, without any substantial change in the activity of this second system (see also REF. 104 for a discussion of other manifestations of degeneracy). Note that complex variations of these responses are possible. For example: compensation may be incomplete, only partially restoring function85; more than one of these responses may occur simultaneously; and one response may evolve into another over time, underscoring the importance of a longitudinal perspective (BOX 2).

irregular firing and metabolic stress in the connected It is also possible for focal pathology to disinhibit site56. Degeneration of remote regions may also result activity and cause cell death or damage in remote sites from diminished excitatory input or a loss of trophic sup- owing to excess neuronal stimulation. Such excitotoxic- port from damaged presynaptic neurons57. For example, ity plays a central part in the damage sustained to remote in Alzheimer disease, the accumulation of amyloid‑β in areas following focal cerebral ischaemia61 and may specific brain regions reduces their functional connectiv- underlie the distributed degenerative changes seen in ity with other areas58 and may cause hypometabolism in focal epilepsy19 and amyotrophic lateral sclerosis (ALS). the distal sites59, rendering them likely targets for disease In the specific case of ALS, hyperexcitability of cortical propagation60. Thus, diaschisis may precede transneu- motor neurons early in disease progression is thought ronal degeneration in some disorders. to damage monosynaptically connected neurons in the

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Posterior cingulate and precuneus b

Temporal pole

Figure 3 | Network topology constrains the distributed effects of focal lesions on brainNature dynamics. Reviews | NeuroscienceA model of the widespread effects that focal lesions can have on brain functional connectivity. An average connectome comprising 988 regions of interest was generated from diffusion tractography in five healthy individuals173. Lesions were simulated by deleting all of the structural connections that linked 50 contiguous regions that were centred on an area with high topological centrality (green nodes, part a) or 50 contiguous regions that were centred on an area with low topological centrality (green nodes, part b). A neural mass model and haemodynamic response function174 were used to simulate regional fluctuations in BOLD (blood-oxygenation-level-dependent) signal arising from the structural network before and after each lesion. Edges between nodes depict signficicant reductions (shown in red) and increases (shown in blue) of inter-regional functional connectivity resulting from each lesion. The lesion affecting the topologically central posterior cingulate precuneus region in part a caused widespread changes of functional connectivity that were characterized by a complex pattern of increases and decreases, unlike the lesion to the less central temporal pole depicted in part b. To determine whether the functional connectivity increases reflect diaschisis or dedifferentiation of neural activity requires an understanding of how the brain changes relate to behavioural impairment (see FIG. 2). Left hemisphere is depicted on left. Figures were generated using methods and structural connectivity data from REF. 39.

anterior horn of the spinal column62. This hypothesis is aid the suggested prion-like spread of tau and other supported by longitudinal studies of patients with ALS pathologies in certain neurodegenerative diseases67. that show that the brain regions at the highest risk of Such a mechanism may explain the spatial colocaliza- degeneration are connected to areas already showing tion of regional atrophy in neurodegenerative disease degenerative changes63. with the topography of structural and functional brain Fast axonal transport is another contributor to networks68,69 (FIG. 4). transneuronal degeneration, and has been implicated in the pathogenesis of several neurodevelopmental and neu- Dedifferentiation. Dedifferentiation is the diffuse, non- rodegenerative disorders, including ALS, Alzheimer dis- specific recruitment of brain regions to perform a task ease, Huntington disease, hereditary motor neuropathy (FIG. 2c), and is thought to result from a break-down and hereditary spastic paraplegia, multiple sclerosis and of usually specialized and segregated neural activ- Charcot–Marie–Tooth disease57,64,65. Molecular motors ity70,71. Dedifferentiation may be caused by aberrant continually shuttle organelles, lipids, mitochondria, neural plasticity or by a focal cortical pathology that neurotrophins and other molecules via microtubules and disrupts the balance between excitation and inhibition neurofilaments that link the soma and distal segments within discrete neural systems. For instance, analysis of the axon. This axonal transport is necessary to sus- of effective connectivity inferred from functional MRI tain neuronal activity and integrity, to meet metabolic (fMRI) data suggests that the increased activation of demands and to enable the clearance of misfolded and/ the contralesional primary motor cortex (M1) that is or aggregated proteins57,65. Thus, neuronal cell bodies and often observed in patients with subcortical stroke20 arises Effective connectivity axons depend on each other for survival. Pathology at the from complex alterations of excitatory and inhibitory The causal influence that one soma can disrupt anterograde transport of cargo that is interactions between the left and right cortical motor neuronal system exerts on necessary for the maintenance and repair of the axonal systems72. Persistence of this dedifferentiated state is another. Its measurement often cytoskeleton and surrounding myelin sheath. Conversely, associated with poorer recovery of motor function fol- requires a model of the 72 neuronal dynamics causing primary pathology of white matter can inhibit the retro lowing stroke , and recovery can be improved through variations in measured neural grade transport of trophic factors that are essential for the use of inhibitory repetitive transcranial magnetic signals. neuronal survival64,66. Transport mechanisms may also stimulation (TMS) of the contralesional M1 (REF. 73).

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Box 2 | Timing is everything with a dedifferentiation hypothesis (FIG. 2c). In support of this view, abnormal neuromodulation and an altered The age at which an insult to the brain occurs critically influences the outcome of the signal-to‑noise ratio of cortical function are well- injury. In some cases, the enhanced plasticity of the developing brain affords greater described characteristics of schizophrenia76 and may capacity for recovery from injuries sustained earlier in life than from those sustained 161 arise from neurodevelopmental abnormalities of the later in life . For example, children with congenital damage to the left hemisphere may 77,78 show age-appropriate language development and a relatively lower incidence of the wiring of the connectome in that disorder . aphasic symptoms that are seen in adults who have sustained damage to similar brain areas later in life162. In other cases, certain types of insult that occur prenatally or in the Adaptive responses to neural insult first few years of life can result in more severe functional impairment than do later The brain can also respond to pathological perturba- injuries (reviewed in REF. 163). tion in an adaptive manner to maintain homeostasis This variability may be partly explained by the timing of the insult relative to and performance where possible79. Here, we review developmentally critical periods164,165; highly regulated, circuit-specific maturational three concepts that are crucial for the ability of the brain periods that are characterized by exquisite sensitivity to environmental inputs167,168. to respond adaptively to pathology: compensation, These periods coincide with the activity-dependent elimination of excess synapses and degeneracy and reserve (FIG. 2). the consolidation of long-range axonal projections. These processes may underlie the dynamic changes in the topological organization of the connectome that occur throughout childhood and adolescence. Such changes include a reduction in Compensation. Increases in activity or functional con- modularity, an increase in topological integration (that is, a reduction in the average nectivity following a pathological insult that preserve minimum path-length; BOX 1), an increase in the number of connector hubs (FIG. 5b), behavioural output are commonly attributed to neu- and a shift from functional modules that comprise spatially adjacent regions to ral compensation (FIG. 2d). For example, in patients interconnected systems that extend over long distances166–168. The developmental with stroke a focal ischaemic insult often results in trajectories of these topological modifications are system-specific: sensorimotor and the extensive recruitment of unaffected, remote brain limbic systems develop adult-like topological properties by late childhood, whereas the areas80–83. Similar effects can be observed in healthy connection topology of associative areas continues to mature throughout volunteers after inhibitory stimulation of focal cortical 167 adolescence . The increased capacity for topological integration during critical areas with TMS84. In general, the extent of focal neural periods may promote enhanced degeneracy in the face of insult, as such integration damage and the severity of behavioural impairment facilitates the formation and recruitment of alternative networks to sustain a given 81,85 function169. However, this degeneracy can be realized only if appropriate environmental correlate with greater compensatory recruitment , 86 inputs are available; if these inputs are not available — owing to deprivation or disease functional reorganization and altered functional 82 — degeneracy will be limited, resulting in marked and persistent impairments51,165,170. connectivity of remote areas. Accordingly, func- Early damage to the brain may also interfere with subsequent maturational processes, tional recovery is compromised if there is damage to derailing the development of a normal brain-network topology. For example, in rodent the axonal tracts that link damaged regions to unaf- neurodevelopmental models of schizophrenia, early focal damage of the hippocampus fected areas with the capacity for compensation42. causes changes in the structure and function of the prefrontal cortex that only emerge Compensatory adaptations can persist for long peri- in adolescence171, which in humans is when the disease usually first presents. Thus, the ods of time and can preserve behaviour to varying distributed impact of an early focal insult may manifest only as connected regions degrees80,84. The causal role of compensatory activation mature or come ‘online’, making the timing of clinical symptoms difficult to predict. in preserving behaviour was shown by one study that Early insults may also provide a disordered foundation for subsequent neurodevelopment, resulting in a mis-wiring of the connectome. For example, found that inhibitory TMS of the right dorsal premo- abnormal development of the corpus callosum in humans often results in the tor cortex could disrupt right-handed motor function emergence of longitudinal fibres (such as Probust bundles) that run parallel to the in patients with ischaemic damage to the left motor inter-hemispheric fissure and that are not seen in healthy controls172. Such mis-wiring system85. In healthy controls, right dorsal premotor will result in a higher frequency of qualitative differences in brain connectivity (that is, cortex stimulation did not affect motor performance, the presence of a set of connections in patients that is not apparent in healthy suggesting that this region activates to support motor individuals; see FIG. 1). The functional significance of such qualitative changes remains function only if the left premotor cortex is damaged. an important topic for further investigation. This effect has been mimicked in healthy individuals after repetitive TMS was used to inhibit activity in the left dorsal premotor cortex. Following this ‘virtual’ Another possible cause of dedifferentiation is the lesion, a second stimulation pulse applied to the right disruption of ascending neuromodulatory systems that premotor cortex as these participants undertook a tune the signal-to‑noise ratio of neural information pro- motor task was found to disrupt performance84. cessing70. Such a mechanism may explain the diffuse Progressive normalization towards pre-injury activity patterns of task-related activation that are often seen in patterns in affected networks also predicts behavioural ageing populations compared with those observed in recovery72,80,87, suggesting that optimal recovery may younger volunteers71, and may also underlie the distrib- depend on a gradual return to baseline network dynamics. uted changes in neural activation and connectivity that Indeed, persistent hyperactivation in some regions may have been reported in neurodevelopmental disorders place neurons under undue metabolic stress, reducing such as schizophrenia74. For example, one meta-analysis their viability and rendering them susceptible to degen- of fMRI activation changes in the brains of people with eration56,88. This mechanism may explain the consistent schizophrenia who were performing executive function reports of increased task-evoked activation or functional tasks found reduced activity in cortico-subcortical net- connectivity in the brains of patients with early-stage neu- Neuromodulation The regulation of neuronal works that are typically associated with executive abili- rodegenerative disease — whether it is Alzheimer disease, activity by ascending ties, and increased activation of regions outside these Huntington disease or multiple sclerosis — followed by neurotransmitter systems. canonical neural systems75. This pattern is consistent declines in these measures at later disease stages89–92.

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a Syndrome-speciﬁc grey-matter atrophy Degeneracy and reserve. Degeneracy is the capacity of AD bvFTD SD PNFA CBS RPMC structurally distinct elements of a system to carry out the LIFG same function102; in other words, it describes the ability of distinct neuronal systems to make overlapping contribu- tions to the same output, offering both functional adapt- ability and robustness to damage102 (see also REF. 103). Degeneracy is a necessary condition for compensation: RANG RFI LTPL compensatory activity is simply not possible if other neural systems cannot assume the functions of a compro- b Spontaneous functional connectivity in controls mised network (that is, if degeneracy is low). Degeneracy may manifest in different ways. For instance, for any given task, multiple neural systems may become activated in a parallel and redundant way to support performance; only one of several degenerate systems may become activated at any one time (reflecting the use of different strategies); or only one system may be consistently activated while c Structural covariance in controls other systems remain latent until they are ‘unmasked’ by dysfunction of the canonical network104. Degeneracy is apparent at multiple levels of the neural hierarchy, from the scale of individual neurons and microcircuits (reviewed in REF. 79) to large-scale macroscopic systems. An example that is evident at the level of macroscopic systems is given by two function- Figure 4 | Transneuronal degeneration in brain networks.Nature Neurodegeneration Reviews | Neuroscience ally segregated systems that are known to support read- spreads throughout functionally connected neural systems in Alzheimer disease (AD), ing ability. One network involves left inferior frontal behavioural-variant frontotemporal dementia (bvFTD), semantic dementia (SD), and anterior occipito-temporal regions and the other progressive non-fluent aphasia (PNFA) and corticobasal syndrome (CBS)69. a | Spatial comprises right inferior parietal and left posterior patterns of disease-specific grey-matter atrophy (shown in blue) in each disease. 105 b | Resting-state networks (shown in yellow), mapped in healthy individuals, that are occipito-temporal areas . Reading performance is functionally connected to the seed regions located in areas of maximal atrophy for each impaired following damage to elements of both net- disease (represented by the red circles in part a). c | Regional grey-matter volume works, but not after damage to either network alone106. covariance (shown in green) with these same seed regions. The spatial correspondence Therefore, each system is sufficient, but neither is nec- between these networks suggests that degeneration occurs within functionally and essary, for reading. This implies that the two systems structurally connected networks. Lighter colour shades indicate higher statistical are degenerate, with each being capable of achieving significance of the depicted association. LIFG, left inferior frontal gyrus; LTPL, left comparable behavioural output. It remains unclear temporal pole; RANG, right angular gyrus; RFI, right frontoinsular cortex; RPMC, right whether, in such circumstances, reliance on just one premotor cortex. Reprinted from Neuron, , Seeley, W. W., Crawford, R. K., Zhou, J., 62 of the degenerate systems has secondary consequences Miller, B. L. & Greicius, M. D. Neurodegenerative diseases target large-scale human brain networks. 42–52, Copyright (2009), with permission from Elsevier. for other functions. Degeneracy provides a neural network basis for cognitive reserve — the ability to flexibly engage alterna- This pattern of increased activity followed by subsequent tive cognitive or compensatory strategies to deal with degeneration has been mimicked in computational mod- a behavioural impairment caused by neural insult107,108. els88 and may reflect evidence of an early, adaptive and The ability to engage such alternative strategies is an plastic response that is gradually overwhelmed as patho- important component of compensation, and the extent logical burden increases91. In this regard, compensation to which such strategies are possible depends on degen- could precede subsequent decline and transneuronal eracy104. In general, we can expect a higher level of neural degeneration in some cases. degeneracy to result in a greater cognitive reserve and Structural plasticity is an important neural substrate thus a greater capacity for compensation107. It is there- for compensation93. Animal models94 and human studies95 fore expected that patients with higher degeneracy and have shown that focal ischaemic damage can cause wide- reserve will be better positioned to adapt to the functional spread depolarization of connected regions — particularly impairments arising from a cerebral insult107. homotopic contralateral areas — resulting in persistent Cognitive reserve also depends on neural reserve, hyperexcitability or disinhibition of functionally related, which refers to the amount of remaining intact brain but spatially distributed, networks94,96. Hyperexcitability in tissue that can still carry out a given task. Generally, a these connected areas can be accompanied by increased brain with high neural reserve will be able to withstand synaptogenesis, and axonal and dendritic sprouting of greater damage before cognitive or behavioural deficits undamaged axons97–100. This remodelling can take place manifest107 (FIG. 2e). Although degeneracy, compensa- over long distances, is activity-dependent99,100 and can tion and reserve are closely related, degeneracy does not cause volumetric changes detectable with MRI101. These necessarily imply that compensatory (increased) activ- plastic changes may afford greater flexibility in adopt- ity of unaffected regions will occur following an insult ing alternative strategies to preserve behaviour as much (FIG. 2f). As the example of the reading system shows, as possible. each of two distinct neural systems may be sufficient to

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carry out a task, and failure of one need not necessarily to highly central regions and/or to connections between increase activation of the other. Increased or atypical rich-club members has a more diffuse effect on brain activation will occur only when degeneracy is partial network structure and function than does damage to or incomplete. topologically peripheral nodes or to the connections between them38,39,113. From description to prediction via topology Distinct hub types can be defined according to the We have so far illustrated how an understanding of the modular organization of a network (BOX 1). Network brain’s varied responses to insult can augment the descrip- analyses of structural connectivity and functional con- tion of critical pathophysiological processes and facilitate nectivity commonly identify four to ten large-scale the generation of hypotheses concerning underlying canonical modules in the brain, each of which can be mechanistic causes (FIGS 1,2). However, to translate these linked to a broad behavioural domain113,116,117. Hubs are descriptions into tools that can improve prognostic evalu- typically distinguished from non-hubs as they are more ations and treatment planning, it is imperative to develop highly connected to other nodes in the same module formal, computational models that allow testable predic- (known as strong inter-modular connectivity). Further, tions to be made about the specific profile of neural or the presumed functional role of these hubs can be behavioural changes that are expected to occur following determined by their pattern of connectivity with other an insult. In this section, we consider how an understand- modules (known as inter-module connectivity)118–120. ing of connectome topology can guide the development ‘Provincial’ hubs link primarily to other nodes in the of such models. Specifically, we consider progress in same module and have an important role in functional modelling the maladaptive responses that spread pathol- specialization, whereas putative ‘connector’ hubs have ogy throughout the brain, and models of how network links that are distributed across multiple different organization might constrain the adaptive processes that modules, and thereby have a central role in functional promote recovery. integration (FIG. 5a,b). Consistent with this organization, computational studies suggest that damage to connector Centrality and maladaptation. Mapping inter-regional hubs has a more widespread effect on network dynam- connectivity allows simple predictions to be made about ics, whereas lesions to provincial hubs exert a more how pathology in one region might affect the structure profound effect on local subsystems38. Thus, we would and function of other brain areas (FIG. 1). More nuanced predict that damage to provincial hubs should yield spe- predictions of disease spread are possible if we consider cific clinical deficits, whereas damage to connector hubs higher-order aspects of connectome topology. To this will result in more complex and pervasive dysfunction. end, graph theory (BOX 1) can be used to identify spe- This hypothesis is supported by recent evidence that cific regions that represent critical vulnerability points patients who have sustained damage to regions such as — putative Achilles’ heels — in the brain. Such research the dorsomedial prefrontal cortex and anterior insular suggests that not all brain regions are equal; rather, the cortex — regions that are functionally connected to functional impact of damage to any single network ele- many diverse modules — display a pervasive profile ment strongly depends on the connection topology of of neuropsychological impairment that extends across that region38,39 (FIG. 3). several cognitive domains121. These findings do not The best-studied topological dimension in this discount the disability caused by specific deficits (for context is centrality: the influence that a node has on instance, a lesion to primary visual cortex can lead to other network elements. Most simply, centrality can be the specific yet disabling impairment of blindness); quantified using node degree (the number of connec- rather, they suggest that impairments will manifest tions attached to a given node), although other meas- across a broader range of functional domains following ures of centrality have been proposed109. Structural and damage to topologically central areas. functional brain networks, like many other complex Collectively, these considerations indicate that mal systems110, are characterized by a heavy-tailed degree adaptive responses to insult — such as diaschisis and 27,111 Degree distribution distribution ; that is, they have many low-degree nodes dedifferentiation — should occur more frequently and The distribution of degree and a small number of putative hub nodes, which have should be more widespread following damage to topo- values obtained across network a very high degree. Such networks are robust to random logically central regions than after damage to regions nodes. node failures because the probability of affecting a hub with a more peripheral role in the network. Moreover, Network fragmentation node is low. However, they are highly vulnerable to a tar- topologically central hubs can act as conduits for the The splitting of a network into geted hub attack, as damage to high-degree nodes affects rapid spread and progression of transneuronal degen- disconnected subsets of nodes. a disproportionate number of connections and can result eration122. This assertion is supported by evidence that The lack of connectivity in rapid network fragmentation112. the brain regions that are most vulnerable to deteriora- between these subsets precludes any communication In the brain, high-degree and topologically central tion are those that are linked or topologically proximal 58–60,63 between them, meaning the hub regions are highly interconnected, forming a ‘rich to sites that are already affected by the disease . In nodes no longer function as an club’ — a central core of hubs that facilitates efficient this context, greater functional compromise is expected integrated system. communication between disparate network elements113 once the disease process has encroached on hub nodes. (BOX 1). These central hub nodes are concentrated in Indeed, the differential involvement of topologically Structural connectivity The physical connections (that heteromodal association cortices. By contrast, primary central versus peripheral regions at varying stages of is, axonal fibres) between brain sensory cortices tend to have low topological central- illness may explain the punctuated and nonlinear pat- regions. ity113–115. Computational studies have shown that damage tern of functional decline that is often associated with

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a b Non-bridges Bridges Node role Inter-module Module identity edge

Provincial Connector Bridge hub hub hub Hubs

Intra-module connectivity Intra-module Non-hub Non-hub Peripheral connector bridge Non-hubs

Intra-module edge Inter-module connectivity

c d Poorer prognosis Expected impairment

Better Degeneracy prognosis Local module density Centrality 0% 80%

Nature Reviews | Neuroscience Figure 5 | Modules, hubs and the topological characteristics of vulnerability and resilience. a | Schematic of the modular organization of the brain, depicting overlapping module structure. In networks with overlapping modules, nodes can belong to more than one module. This structure has not been studied extensively in brain networks, as most graph theory-based methods for module decomposition that have been used so far separate nodes into unique, non-overlapping modules. However, a model of neural architecture that allows for overlapping modules offers a more realistic model of brain-network organization (for instance, cortical association areas are known to have a role in multiple networks). Internal node colours denote the module to which each node belongs. Intra-module edges are coloured accordingly; inter-module edges are grey. Colours of node outlines denote node roles, as defined in part b. The central module represents a core of interconnected, high-degree nodes, many of which are also involved in other modules114,136. For simplicity, we ignore hierarchy in modular organization (that is, modules within modules)160. b | The roles of nodes are often assessed using the within-module degree z‑score (a measure of intra-module connectivity) and the participation coefficient (a measure of inter-module connectivity)118. Hubs typically have high intra-modular connectivity. Connector hubs also have many links to different modules, whereas bridge nodes represent the more extreme case of nodes, with a relatively equal distribution of connectivity to different modules. It is thus difficult to assign these nodes to any single module; rather, they belong to multiple modules. Bridgeness is best quantified using methods that allow analysis of overlapping module structure134. The colours representing each role are the same as those used to distinguish different types of nodes in part a. c | A map of regions that are thought to contribute to the functions of diverse modules, representing candidate bridge hubs. These regions (indicated by red and ‘warmer’ colours) provide a topological substrate for degeneracy, and their dysfunction is likely to have a major impact on brain-network integrity and on behaviour. The colour scale indexes the local module density; regions with high module density are likely to participate in multiple systems120. The medial wall is depicted in grey. d | The hypothetical relationship between the centrality of a node subjected to a pathological perturbation, the degeneracy of that node, the expected level of functional impairment following node damage and prospects for recovery following the insult. The extent of network dysfunction, and the behavioural impairment associated with it, is expected to increase with greater centrality of the affected region. This relationship is moderated by the degeneracy of the damaged system; higher degeneracy of the affected node affords a better prognosis. Parts b and c reprinted from Neuron, 79, Power, J. D., Schlaggar, B. L., Lessov-Schlaggar, C. N. & Petersen, S. E. Evidence for hubs in human functional brain networks. 798–813, Copyright (2013), with permission from Elsevier120.

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the progression of neurodegenerative disorders123, such that reflects a breakdown of modularity — can facilitate that the largest declines in function may occur when dis- the spread of network failures131, reduce functional spe- ease impinges on a hub region. Encouragingly, one study cialization and result in dedifferentiated neural activity70 showed that these topological constraints on degeneration (FIG. 2c). In more extreme cases, such a break-down may can be exploited to predict disease spread. Specifically, the engender a propensity for hypersynchronized, seizure-like spatial distribution of grey-matter atrophy seen in patients activity132,133. with Alzheimer disease and behavioural variant fronto- Another topological substrate for degeneracy is pro- temporal dementia could be reproduced by a simple com- vided by bridge nodes — regions that are involved in putational model of disease diffusion that was simulated multiple modules134. These areas act as ‘convergence on empirically derived connectomic maps124. This finding zones’ (REFS 120,135) that allow the integration of special- demonstrates how knowledge of network topology can be ized processes between distinct neural systems (FIG. 5a–c). used to generate prognostically useful models of disease Preliminary evidence suggests that high-degree nodes in progression. association cortices tend to show high ‘bridgeness’ (that Several converging lines of evidence also indicate that is, they are involved in multiple modules)136, consistent central hub regions have an increased susceptibility to the with their role in supporting the integration of other- effects of brain disease. First, empirical findings suggest wise segregated processes. They are thus well-positioned that many brain disorders disproportionately affect hub to support the engagement of alternative systems that regions35,125. Second, a high proportion of the shortest top- can promote functional compensation and recovery ological paths (BOX 1) between brain regions pass through after insult. As a corollary, damage to bridge nodes is hub regions126, suggesting that these nodes can be easily expected to have a marked effect on network integrity, reached by trans-synaptic pathological processes that orig- as these nodes are both topologically central and integral inate elsewhere in the brain60. Third, many of the connec- to degeneracy. Consistent with this hypothesis, recent tions to and from hubs extend across long distances115,126 work in patients with diverse brain lesions showed that and are thus more susceptible to white-matter injury (for damage to putative bridge hubs often results in pervasive instance, axonal shearing in traumatic brain injury) or dis- cognitive impairment121. ease (for example, demyelinating lesions in multiple scle- In summary, empirical and computational studies rosis)34. Finally, the high baseline activity and metabolic suggest that damage to topologically central brain regions requirements of hub regions127,128 may render their con- is associated with widespread effects on network func- stituent neurons particularly vulnerable to metabolic stress tion. The expression of these effects will vary depend- or activity-dependent degeneration, especially if activity ing on the topological role of the affected region, such levels increase beyond this high baseline (for instance, if that pathology of provincial hubs is expected to produce these regions are recruited for compensation)34,56,88. specific deficits, whereas dysfunction of connector hubs is proposed to impair multiple behavioural domains. Degeneracy and adaptation. The capacity of the brain Furthermore, these effects will be modified by the for resilience, compensation and functional restitution degeneracy of the affected neural network. Specifically, following insult is closely tied to its degeneracy. The recovery of function may be more probable following degeneracy of a brain network can be quantified directly, damage to regions with a high clustering coefficient or using metrics from information theory102, or indirectly a high degree of topological overlap with other nodes, ,using measures of topological overlap between nodal- and/or to regions that are deeply embedded within mod- connectivity profiles114 and relatively simple indices ules. Conversely, recovery is less likely following damage such as the clustering coefficient (the probability that to topologically central areas, or to regions that support two nodes connected to a third node are also connected degeneracy, such as bridge nodes. Following this logic, to each other) (BOX 1). Indeed, a defining characteristic we can use the topological dimensions of centrality and of some hub regions is low clustering113,129, and many degeneracy to define a broad parameter space that ena- rich-club nodes tend to occupy the apex within open bles us to make testable predictions regarding the extent three-node motifs; that is, they often act as bridges that of functional compromise, and prognosis for recovery, connect otherwise unconnected pairs of nodes115. This following insult (FIG. 5d). property compounds the deleterious effects of rich-club damage, as removal of the apex node will prevent com- Conclusions and future directions munication between the remaining regions. By contrast, We have considered here how connectomics can areas that are embedded within a specific module are improve the description and prediction of the clini- likely to display higher topological degeneracy, as they cal expression, course and functional impact of brain form part of a tightly interconnected ‘clique’ of nodes120. disease. The description of disease processes can be In addition to supporting degeneracy within specific enhanced by understanding how adaptive and maladap- subsystems, the interconnectivity of nodes within a topo- tive neural responses to insult are expressed at the level logical module (BOX 1) affords the brain added resilience to of large-scale networks. In particular, this knowledge disease because this interconnectivity can ‘entrap’ a patho- can be used to move beyond traditional characteriza- Motifs logical process, preventing it from spreading to other parts tions of case-control differences in neurobiological Simple, recurring patterns or 130 subgraphs that represent of the network . Accordingly, computational studies measures as abnormal ‘increases’ or ‘decreases’ to infer building blocks of a larger suggest that too much integration between systems that underlying pathophysiological mechanisms (see, for network. should normally be segregated — a shift in organization example, FIGS 1,2).

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Non-stationarity However, the responses considered here are not example, computational models of neural or disease The tendency of some time exhaustive; cataloguing other possible responses and dynamics can be simulated on empirically mapped series to show fluctuations in their underlying mechanisms will provide a more com- network structures38,88,124, and the effects of various their mean, covariance and plete picture of how disease affects the brain. Large-scale structural lesions on network activity may be simulated other descriptive measures 39 over time. Non-stationary longitudinal studies that track the progression of brain in silico . This integrated approach enables rigorous activity in the brain means that network changes over time will also be crucial to elu- and testable predictions about the effects of disease on long-term temporal averages of cidate how pathology dynamically evolves in the brain. the brain. In this context, open-source platforms (for neural activity may not Improvements in imaging technologies and network- example, The Virtual Brain; see Further information) accurately summarize mapping techniques will enhance the precision with for integrating computational modelling with empirical dynamics over shorter 146,147 timescales. which we are able to track these processes in patients. data offer considerable promise for researchers and For structural connectivity, this will involve developing clinicians alike. more accurate fibre-reconstruction algorithms, measures Our understanding of functional specialization in the of connectivity that have a clear physiological interpreta- brain is sufficiently advanced to allow general predictions tion137,138, and the capacity to resolve the source and target to be made about the pattern of behavioural deficits of a projection (see BOX 1). For analysis of brain network expected to result from focal pathology. For example, we function, the scaling of effective connectivity models to expect memory problems following hippocampal dam- deal with large-scale brain networks139 and diverse exper- age, executive deficits following prefrontal insults, and imental paradigms and empirical phenomena140,141 will be visuospatial impairments following parietal dysfunc- particularly important. Indeed, such models will enable tion. However, our understanding of how changes in us to track the mechanisms and direction of pathological large-scale integrated network structure and dynamics spread throughout the brain with much greater certainty relate to behaviour is relatively immature, and few stud- than is afforded by undirected measures of connectivity ies have attempted to link variations in network proper- (BOX 1; FIG. 1). Moreover, accounting for the known non- ties to measures of behavioural performance. Such work stationarity of brain dynamics142 will be crucial for more will inform the mapping of specific network changes precisely mapping fluctuations in psychological states to distinct behavioural outputs. One possible approach to variations in neural states. Multi-modal validation of would involve the development of computational mod- imaging measures143, combined with detailed biophysical els of putative disease mechanisms that are informed by, models144, may help to mitigate the limitations of existing and validated against, experimental connectomic data. approaches145. In turn, model predictions and experimental measures We have also illustrated how knowledge of network should be tested for their ability to predict changes in topology can be used to generate simple, testable pre- behaviour following an insult. Such an integrated frame- dictions about the spread, clinical manifestations and work will be necessary to formulate a coherent and com- prognosis of brain disease. Indeed, a key advantage prehensive understanding of how neural connectivity of graph theory is that it readily enables the integra- mediates and constrains the phenotypic expression of tion of experimental and theoretical neuroscience. For brain disease.

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