Brain structure varies between people in a markedly organized fashion. Communities of brain regions co-vary in their morphological properties. For example, cortical thickness in one region influences the thickness of structurally and functionally connected regions. Such networks of structural co-variance partially recapitulate the functional networks of healthy individuals and the foci of grey matter loss in neurodegenerative disease. This architecture is genetically heritable, is associated with behavioural and cognitive abilities and is changed systematically across the lifespan. The biological meaning of this structural co-variance remains controversial, but it appears to reflect developmental coordination or synchronized maturation between areas of the brain. This Review discusses the state of current research into brain structural co-variance, its underlying mechanisms and its potential value in the understanding of various neurological and psychiatric conditions.

A critical issue in many neuroimaging studies is the comparison between brain maps. Nonetheless, it remains unclear how one should test hypotheses focused on the overlap or spatial correspondence between two or more brain maps. This "correspondence problem" affects, for example, the interpretation of comparisons between task-based patterns of functional activation, resting-state networks or modules, and neuroanatomical landmarks. To date, this problem has been addressed with remarkable variability in terms of methodological approaches and statistical rigor. In this paper, we address the correspondence problem using a spatial permutation framework to generate null models of overlap by applying random rotations to spherical representations of the cortical surface, an approach for which we also provide a theoretical statistical foundation. We use this method to derive clusters of cognitive functions that are correlated in terms of their functional neuroatomical substrates. In addition, using publicly available data, we formally demonstrate the correspondence between maps of task-based functional activity, resting-state fMRI networks and gyral-based anatomical landmarks. We provide open-access code to implement the methods presented for two commonly-used tools for surface based cortical analysis (https://www.github.com/spin-test). This spatial permutation approach constitutes a useful advance over widely-used methods for the comparison of cortical maps, thereby opening new possibilities for the integration of diverse neuroimaging data.

Human brain functional networks are embedded in anatomical space and have topological properties-small-worldness, modularity, fat-tailed degree distributions-that are comparable to many other complex networks. Although a sophisticated set of measures is available to describe the topology of brain networks, the selection pressures that drive their formation remain largely unknown. Here we consider generative models for the probability of a functional connection (an edge) between two cortical regions (nodes) separated by some Euclidean distance in anatomical space. In particular, we propose a model in which the embedded topology of brain networks emerges from two competing factors: a distance penalty based on the cost of maintaining long-range connections; and a topological term that favors links between regions sharing similar input. We show that, together, these two biologically plausible factors are sufficient to capture an impressive range of topological properties of functional brain networks. Model parameters estimated in one set of functional MRI (fMRI) data on normal volunteers provided a good fit to networks estimated in a second independent sample of fMRI data. Furthermore, slightly detuned model parameters also generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia. We therefore anticipate that many aspects of brain network organization, in health and disease, may be parsimoniously explained by an economical clustering rule for the probability of functional connectivity between different brain areas.neuroimaging | graph theory | systems | trade-off T he human brain is a large and complex network, operating over several decades of scale in space and time (1, 2). Its organization defies complete description at a cellular scale (3); but neuroimaging techniques for whole-brain scanning have been used to describe network organization, or connectomics, at anatomical scales on the order of millimeters and centimeters (2). In the language of graph theory, these large-scale human brain networks have already been shown consistently to demonstrate a number of key topological properties in common with other complex networks. For example, human brain networks have the smallworld property of high clustering and high efficiency (or short path length) (4); they are also modular (5) and comprise a number of highly connected hub nodes in a fat-tailed degree distribution (6).It is well known that the brain overall is expensive, in the sense of having high metabolic cost relative to its mass (7), and that cost control or cost minimization is likely to have been an important selection criterion for the evolution of the nervous system (8-11). One measure of cost in a spatially embedded network like the brain is the physical distance of connections between nodes: generally, connection costs will increase with distance (8, 12). In the nervous system of the nematode worm Caenorhabditis elegans, which has been mapped completely at the cellular level of synaptic conn...