Andrew Zalesky

Network-based statistic: identifying differences in brain networks.

Large-scale functional or structural brain connectivity can be modeled as a network, or graph. This paper presents a statistical approach to identify connections in such a graph that may be associated with a diagnostic status in case-control studies, changing psychological contexts in task-based studies, or correlations with various cognitive and behavioral measures. The new approach, called the network-based statistic (NBS), is a method to control the family-wise error rate (in the weak sense) when mass-univariate testing is performed at every connection comprising the graph. To potentially offer a substantial gain in power, the NBS exploits the extent to which the connections comprising the contrast or effect of interest are interconnected. The NBS is based on the principles underpinning traditional cluster-based thresholding of statistical parametric maps. The purpose of this paper is to: (i) introduce the NBS for the first time; (ii) evaluate its power with the use of receiver operating characteristic (ROC) curves; and, (iii) demonstrate its utility with application to a real case-control study involving a group of people with schizophrenia for which resting-state functional MRI data were acquired. The NBS identified a expansive dysconnected subnetwork in the group with schizophrenia, primarily comprising fronto-temporal and occipito-temporal dysconnections, whereas a mass-univariate analysis controlled with the false discovery rate failed to identify a subnetwork.

Whole-brain anatomical networks: Does the choice of nodes matter?

Whole-brain anatomical connectivity in living humans can be modeled as a network with diffusion-MRI and tractography. Network nodes are associated with distinct grey-matter regions, while white-matter fiber bundles serve as interconnecting network links. However, the lack of a gold standard for regional parcellation in brain MRI makes the definition of nodes arbitrary, meaning that network nodes are defined using templates employing either random or anatomical parcellation criteria. Consequently, the number of nodes included in networks studied by different authors has varied considerably, from less than 100 up to more than 10(4). Here, we systematically and quantitatively assess the behavior, structure and topological attributes of whole-brain anatomical networks over a wide range of nodal scales, a variety of grey-matter parcellations as well as different diffusion-MRI acquisition protocols. We show that simple binary decisions about network organization, such as whether small-worldness or scale-freeness is evident, are unaffected by spatial scale, and that the estimates of various organizational parameters (e.g. small-worldness, clustering, path length, and efficiency) are consistent across different parcellation scales at the same resolution (i.e. the same number of nodes). However, these parameters vary considerably as a function of spatial scale; for example small-worldness exhibited a difference of 95% between the widely-used automated anatomical labeling (AAL) template (approximately 100 nodes) and a 4000-node random parcellation (sigma(AAL)=1.9 vs. sigma(4000)=53.6+/-2.2). These findings indicate that any comparison of network parameters across studies must be made with reference to the spatial scale of the nodal parcellation.

Schizophrenia, neuroimaging and connectomics

Schizophrenia is frequently characterized as a disorder of brain connectivity. Neuroimaging has played a central role in supporting this view, with nearly two decades of research providing abundant evidence of structural and functional connectivity abnormalities in the disorder. In recent years, our understanding of how schizophrenia affects brain networks has been greatly advanced by attempts to map the complete set of inter-regional interactions comprising the brains intricate web of connectivity; i.e., the human connectome. Imaging connectomics refers to the use of neuroimaging techniques to generate these maps which, combined with the application of graph theoretic methods, has enabled relatively comprehensive mapping of brain network connectivity and topology in unprecedented detail. Here, we review the application of these techniques to the study of schizophrenia, focusing principally on magnetic resonance imaging (MRI) research, while drawing attention to key methodological issues in the field. The published findings suggest that schizophrenia is associated with a widespread and possibly context-independent functional connectivity deficit, upon which are superimposed more circumscribed, context-dependent alterations associated with transient states of hyper- and/or hypo-connectivity. In some cases, these changes in inter-regional functional coupling dynamics can be related to measures of intra-regional dysfunction. Topological disturbances of functional brain networks in schizophrenia point to reduced local network connectivity and modular structure, as well as increased global integration and network robustness. Some, but not all, of these functional abnormalities appear to have an anatomical basis, though the relationship between the two is complex. By comprehensively mapping connectomic disturbances in patients with schizophrenia across the entire brain, this work has provided important insights into the highly distributed character of neural abnormalities in the disorder, and the potential functional consequences that these disturbances entail.

The connectomics of brain disorders

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.

Graph analysis of the human connectome: Promise, progress, and pitfalls

The human brain is a complex, interconnected network par excellence. Accurate and informative mapping of this human connectome has become a central goal of neuroscience. At the heart of this endeavor is the notion that brain connectivity can be abstracted to a graph of nodes, representing neural elements (e.g., neurons, brain regions), linked by edges, representing some measure of structural, functional or causal interaction between nodes. Such a representation brings connectomic data into the realm of graph theory, affording a rich repertoire of mathematical tools and concepts that can be used to characterize diverse anatomical and dynamical properties of brain networks. Although this approach has tremendous potential - and has seen rapid uptake in the neuroimaging community - it also has a number of pitfalls and unresolved challenges which can, if not approached with due caution, undermine the explanatory potential of the endeavor. We review these pitfalls, the prevailing solutions to overcome them, and the challenges at the forefront of the field.

Disrupted Axonal Fiber Connectivity in Schizophrenia

BACKGROUND Schizophrenia is believed to result from abnormal functional integration of neural processes thought to arise from aberrant brain connectivity. However, evidence for anatomical dysconnectivity has been equivocal, and few studies have examined axonal fiber connectivity in schizophrenia at the level of whole-brain networks. METHODS Cortico-cortical anatomical connectivity at the scale of axonal fiber bundles was modeled as a network. Eighty-two network nodes demarcated functionally specific cortical regions. Sixty-four direction diffusion tensor-imaging coupled with whole-brain tractography was performed to map the architecture via which network nodes were interconnected in each of 74 patients with schizophrenia and 32 age- and gender-matched control subjects. Testing was performed to identify pairs of nodes between which connectivity was impaired in the patient group. The connectional architecture of patients was tested for changes in five network attributes: nodal degree, small-worldness, efficiency, path length, and clustering. RESULTS Impaired connectivity in the patient group was found to involve a distributed network of nodes comprising medial frontal, parietal/occipital, and the left temporal lobe. Although small-world attributes were conserved in schizophrenia, the cortex was interconnected more sparsely and up to 20% less efficiently in patients. Intellectual performance was found to be associated with brain efficiency in control subjects but not in patients. CONCLUSIONS This study presents evidence of widespread dysconnectivity in white-matter connectional architecture in a large sample of patients with schizophrenia. When considered from the perspective of recent evidence for impaired synaptic plasticity, this study points to a multifaceted pathophysiology in schizophrenia encompassing axonal as well as putative synaptic mechanisms.

Time-resolved resting-state brain networks

Significance Large-scale organizational properties of brain networks mapped with functional magnetic resonance imaging have been studied in a time-averaged sense. This is an oversimplification. We demonstrate that brain activity between multiple pairs of spatially distributed regions spontaneously fluctuates in and out of correlation over time in a globally coordinated manner, giving rise to sporadic intervals during which information can be efficiently exchanged between neuronal populations. We argue that dynamic fluctuations in the brain’s organizational properties may minimize metabolic requirements while maintaining the brain in a responsive state. Neuronal dynamics display a complex spatiotemporal structure involving the precise, context-dependent coordination of activation patterns across a large number of spatially distributed regions. Functional magnetic resonance imaging (fMRI) has played a central role in demonstrating the nontrivial spatial and topological structure of these interactions, but thus far has been limited in its capacity to study their temporal evolution. Here, using high-resolution resting-state fMRI data obtained from the Human Connectome Project, we mapped time-resolved functional connectivity across the entire brain at a subsecond resolution with the aim of understanding how nonstationary fluctuations in pairwise interactions between regions relate to large-scale topological properties of the human brain. We report evidence for a consistent set of functional connections that show pronounced fluctuations in their strength over time. The most dynamic connections are intermodular, linking elements from topologically separable subsystems, and localize to known hubs of default mode and fronto-parietal systems. We found that spatially distributed regions spontaneously increased, for brief intervals, the efficiency with which they can transfer information, producing temporary, globally efficient network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time, possibly achieving a balance between efficient information-processing and metabolic expenditure.

Network Scaling Effects in Graph Analytic Studies of Human Resting-State fMRI Data

Graph analysis has become an increasingly popular tool for characterizing topological properties of brain connectivity networks. Within this approach, the brain is modeled as a graph comprising N nodes connected by M edges. In functional magnetic resonance imaging (fMRI) studies, the nodes typically represent brain regions and the edges some measure of interaction between them. These nodes are commonly defined using a variety of regional parcellation templates, which can vary both in the volume sampled by each region, and the number of regions parcellated. Here, we sought to investigate how such variations in parcellation templates affect key graph analytic measures of functional brain organization using resting-state fMRI in 30 healthy volunteers. Seven different parcellation resolutions (84, 91, 230, 438, 890, 1314, and 4320 regions) were investigated. We found that gross inferences regarding network topology, such as whether the brain is small-world or scale-free, were robust to the template used, but that both absolute values of, and individual differences in, specific parameters such as path length, clustering, small-worldness, and degree distribution descriptors varied considerably across the resolutions studied. These findings underscore the need to consider the effect that a specific parcellation approach has on graph analytic findings in human fMRI studies, and indicate that results obtained using different templates may not be directly comparable.

Competitive and cooperative dynamics of large-scale brain functional networks supporting recollection

Analyses of functional interactions between large-scale brain networks have identified two broad systems that operate in apparent competition or antagonism with each other. One system, termed the default mode network (DMN), is thought to support internally oriented processing. The other system acts as a generic external attention system (EAS) and mediates attention to exogenous stimuli. Reports that the DMN and EAS show anticorrelated activity across a range of experimental paradigms suggest that competition between these systems supports adaptive behavior. Here, we used functional MRI to characterize functional interactions between the DMN and different EAS components during performance of a recollection task known to coactivate regions of both networks. Using methods to isolate task-related, context-dependent changes in functional connectivity between these systems, we show that increased cooperation between the DMN and a specific right-lateralized frontoparietal component of the EAS is associated with more rapid memory recollection. We also show that these cooperative dynamics are facilitated by a dynamic reconfiguration of the functional architecture of the DMN into core and transitional modules, with the latter serving to enhance integration with frontoparietal regions. In particular, the right posterior cingulate cortex may act as a critical information-processing hub that provokes these context-dependent reconfigurations from an intrinsic or default state of antagonism. Our findings highlight the dynamic, context-dependent nature of large-scale brain dynamics and shed light on their contribution to individual differences in behavior.

On the use of correlation as a measure of network connectivity

Numerous studies have demonstrated that brain networks derived from neuroimaging data have nontrivial topological features, such as small-world organization, modular structure and highly connected hubs. In these studies, the extent of connectivity between pairs of brain regions has often been measured using some form of statistical correlation. This article demonstrates that correlation as a measure of connectivity in and of itself gives rise to networks with non-random topological features. In particular, networks in which connectivity is measured using correlation are inherently more clustered than random networks, and as such are more likely to be small-world networks. Partial correlation as a measure of connectivity also gives rise to networks with non-random topological features. Partial correlation networks are inherently less clustered than random networks. Network measures in correlation networks should be benchmarked against null networks that respect the topological structure induced by correlation measurements. Prevalently used random rewiring algorithms do not yield appropriate null networks for some network measures. Null networks are proposed to explicitly normalize for the inherent topological structure found in correlation networks, resulting in more conservative estimates of small-world organization. A number of steps may be needed to normalize each network measure individually and control for distinct features (e.g. degree distribution). The main conclusion of this article is that correlation can and should be used to measure connectivity, however appropriate null networks should be used to benchmark network measures in correlation networks.