Smallworld networks by watts and strogatz are a class of networks that are highly. But seldom researches explore the effects of mental fatigue on the small world brain functional network organization. Smallworld brain networks in schizophrenia ncbi nih. The brainstem reticular for mation is a small world, not scale free, network. The smallworld trust network, applied intelligence 10. Disrupted smallworld brain networks in moderate alzheimer. He describes new links between network anatomy and function and investigates how networks shape complex brain dynamics and enable adaptive neural computation. Disrupted small world brain functional network topology in osa patients properties of the functional brain networks of untreated male patients with severe osa. Many complex networks have a small world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any distant pair of nodes due to the existence of relatively few longrange connections.
Efficient smallworld and scalefree functional brain networks at rest. Jan 19, 2009 brain functional networks were constructed by thresholding the correlation matrix between 90 cortical and subcortical regions and further analyzed by applying graph theoretical approaches. Altered smallworld properties of gray matter networks in. Abstract smallworld networks, according to watts and strogatz, are a. The following is the supplementary data related to this article. Apr 18, 2015 brain connectivity is traditionally established by invasive histochemical tracing of connections in the brains of animal models.
Healthy participants were free of any dsmiv tr axis i disorder or. This is an attractive model for the organization of brain anatomical and functional networks because a small world topology. Relationships between these small world properties and clinical and neuropsychological assessments were investigated in osa patients. Evaluating the smallworldness of a sampled network.
Dec 19, 2006 the authors analysis reveals that the small world topology of brain functional networks is largely preserved across multiple frequency bands and behavioral tasks. Mapping the smallworld properties of brain networks in. Open access full text article disrupted smallworld brain. After describing the basic concepts of network theory and the fundamentals of brain connectivity, sporns discusses how network approaches can reveal principles of brain architecture. Smallworld networks can change from scalefree class to broad scale class whose. In this study, we investigated the topological properties of human. Watts and strogatz formalized the concept of a small world network by describing a simple theoretical model on binary networks. Small world networks in computational neuroscience springerlink. In 1998, in order to describe the transition from a regular lattice to a random graph, watts and strogatz ws introduced the concept of small world network 5. Pdf many complex networks have a smallworld topology characterized by dense local clustering or cliquishness of connections between neighboring. Disrupted smallworld brain networks in moderate alzheimers. It contains networks of neurons that constitute centres for the control of vital functions such as breathing and blood.
Abrainnetworkconstructedonanl1normregressionmodelis more. Small world networks are apparently ubiquitous in nature and possess some special properties which make them highly suitable to model the brain. Brain is then a book about the encounter between two worlds. Some previous smallworld brain network studies liu et al. The small world structure reflects the balance of brain network at both global and local. Many studies of neuroscience have reported that the complex brain networks are characterized by small world or scale free properties. Previous multimodal imaging studies have consistently demonstrated that the topological architecture of the brain network is disrupted in alzheimers disease ad. Brain imaging data was collected from 11 healthy older adults as.
Pdf many complex networks have a small world topology characterized by dense local clustering or cliquishness of connections between neighboring. The structure of networks has been analyzed extensively in the social sciences 2 and in physics and information technology 3. Introductionthe small world network model of watts and strogatz is quite possibly the pinnacle of network science. The small world organization in the human brain extends previous observations in the neural network of the nematode caenorhabditis elegans watts and strogatz, 1998 and brain networks of the mouse oh et al. The ubiquity of smallworld networks brain connectivity. The following is the supplementary data related to this a. Previous multimodal imaging studies have consistently demonstrated that the topological architecture of the brain network is. Altered smallworld brain networks in temporal lobe in. Networks, as efficient representations of complex systems, have appealed to scientists for. A resilient, lowfrequency, small world human brain functional network with highly connected association cortical hubs. Moreover, small world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity.
Complex network measures of brain connectivity umd school of. Next, we evaluated the relationships between the topological properties and clinical and neuropsychological data. The kevin bacon game is a curious thing to be sure. The networks of both osa patients and gss exhibited efficient small world topology. The smallworld network is an important model for describing complex. This research contributes to our knowledge related to brain activity underlying movement. However, direct, detailed comparisons are needed to elucidate the influences of different frequency bands on the topological analysis of functional brain networks. Jun 04, 1998 networks of coupled dynamical systems have been used to model biological oscillators1,2,3,4, josephson junction arrays5,6, excitable media7, neural networks8,9,10, spatial games11, genetic control. In the present study, 20 healthy individuals were included to do a consecutive mental arithmetic task to. Nov 14, 2014 networks with spatial constraints typically have shortrange edges and it is thus relevant that both the original wattsstrogatz small world model 2 and many real networks with the small world. The values of small world vary along with the change of brain functions 20, 21. For those who dont know him, kevin bacon is an actor best known fornotbeing the star of many films. Here, we study the characteristics of functional brain networks at the. Smallworld brain networks danielle smith bassett, ed.
These characteristics result in networks with unique properties of regional specialization with efficient information transfer. This paper contributes to verify that the trust network is the small world network, and its small world topology is independent of its dynamics. May 28, 2012 since small world characteristics were described quantitatively for brain structural networks, there have been multiple graphtheoretical studies seeking to assess the structural correlation networks constructed from regional gray matter volume, cortical thickness and surface area 12, 20, 22, 23. A smallworld network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other and most nodes can be reached from every other node by a small number of hops or steps. Altered smallworld brain networks in schizophrenia patients. Brain functional network has been widely applied to investigate brain function changes among different conditions and proved to be a small world like network. Agerelated differences in the modulation of smallworld. Recently, topological measures based on graph theory have provided a new approach to quantify largescale cortical networks. Keywords small world network, graph theory, human brain functional networks, functional magnetic resonance imaging achard s, salvador r, whitcher b, suckling j, bullmore e.
There is presently a trend of revealing neural mechanisms using measures of brain networks. Here, we investigated the topological properties of the human brain networks of 22 healthy subjects under sufficient sleep and sleep. Smallworld propensity and weighted brain networks scientific. Smallworld networks, according to watts and strogatz, are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. A brain network with such features, when characterized using graph analysis, would present smallworld and scalefree properties. Wells s world brain for your kindle, tablet, ipad, pc or mobile.
Small world properties are found in many real world phenomena, including websites with navigation menus, food webs, electric power grids, metabolite processing networks, networks of brain neurons, voter networks, telephone call graphs, airport networks, and social influence networks. To explore the small world properties of brain functional networks in patients with. The complex network of the brain can be described as a small. Classification of pure conduct disorder from healthy. As a physical system with graphlike properties, a largescale brain network has both nodes and edges and cannot be identified simply by the coactivation of brain areas. Longterm changes in the smallworld organization of brain. However, since the users can join trust network ubiquitously, the structure of the highly dynamic trust network is still unknown. In their seminal work 1, the authors showed that there exists an intermediate state between regular and random graphs, where high clustering of network connections and low distance between any two nodes coexist, and that this intermediate small world state is reached by random.
They conclude that smallworld models provide a powerful and versatile approach to understanding the structure and function of human brain systems. In addition to the small world features, eguiluz et al. To explore the smallworld properties of brain functional networks in patients with. Conduct disorder cd is an important mental health problem in childhood and adolescence. Effects of different correlation metrics and preprocessing. Smallworld properties of the wholebrain functional networks. It is nearly 20 years since the concept of a small world network was first quantitatively defined, by a combination of high clustering and short path length. Hierarchical organization of human cortical networks in. The brain stem is divided into hind brain, mid brain and a between brain called the diencephalon.
Disrupted smallworld networks in schizophrenia brain. Functional disorganization of smallworld brain networks in mild alzheimers disease and amnestic mild cognitive impairment. Introduction the human brain network has been proven to possess small world properties that confer several advantages 1, 2 includ. Experimental results showed that, although brain networks of both groups exhibited economical small.
The neural network of the worm caenorhabditis elegans, the power grid of the western united states, and the collaboration graph of. While there has long been strong evidence that brain anatomy can be thought of as a complex network at micro as well as macro scales, the use of functional imaging techniques has recently shown that brain dynamics also has a network like structure. The 2d cvm can potentially function as a secondary free energy minimization. The smallworld structure reflects the balance of brain network at both global and local. Smallworld properties of the wholebrain functional networks in. By analogy to social networks, these algorithmically gener ated graphs were called small world networks. These methods have been applied to anatomical connectivity data on nonhuman species, and cortical networks have been shown to have small world topology, associated with high local and. Extensive collations of such data for the macaque monkey cortex felleman and van essen 1991. The small world organization has been hypothesized to reflect a balance between local processing and global integration in the human brain. In recent decades, the analysis of brain networks was made feasible by advances in imaging techniques as well as new tools from graph theory and dynamical systems.
We hypothesized that the functional network of taskrelated brain regions would change according to wm load in all subjects, and that sz will show less. An emerging paradigm in neuroscience is that cognitive tasks are performed not by individual brain regions working in isolation but by networks consisting of several discrete brain regions. Our aim was not only to show that functional brain connectivity networks behave like complex scale free small worlds, but also to derive new information about aspects not reflected in the classical methods for investigating brain activity. In this survey the theory of small world networks and their applications in computational neuroscience is. It is notable that the small world phenomenon is indeed very common. Apr 27, 2010 the topology of the trust network is important to optimize its usage in the trustaware applications.
Moreover, functional brain networks derived from rfmri data exhibit differential small world attributes across different frequency bands 6,7,39. We found that in both age groups, brain networks in theta, alpha or beta band for either response execution go or response inhibition nogo condition showed prominent small world property. The small world network is one of the three basic types of networks. The small world network model of watts and strogatz is quite possibly the. Jun 01, 2017 the small world organization in the human brain extends previous observations in the neural network of the nematode caenorhabditis elegans watts and strogatz, 1998 and brain networks of the mouse oh et al. Effects of mental fatigue on smallworld brain functional. The concept was formalized by watts and strogatz 1998, who derived small world networks from regular networks by including a small. Models of dynamical systems with small world coupling display enhanced signalpropagation speed, computational power, and synchronizability. Spatially embedded growing smallworld networks scientific. A smallworld network is a type of mathematical graph in which most nodes are not neighbors. Smallworldness of brain networks after brachial plexus injury. Functional connectivity can be well quantified based on statistical dependencies, such as transfer entropy, coherence and correlations.
Modulation of smallworld brain networks during a gonogo task. Both the mi and motor networks were efficient, exhibiting small world properties. The complex organization of connectivity in the human brain is incompletely understood. Brain networks are small world networks is only the. Jul 26, 20 network models were recognized as a crucial tool in analyzing dynamics of complex systems. The human brain is a large, dynamic functional network with an economical, small world architecture and is characterized by high local clustering of connections between neighbouring nodes but with short path lengths between any pair of nodes sporns and honey, 2006.
Characterizing the brain s anatomical and dynamical organization and how this enables it to carry out complex tasks is highly. Review smallworld brain networks rutgers university. Pdf functional disorganization of smallworld brain. The brain consists of the brain stemand the cerebral hemispheres. The small world feature is also obtained in brain structural anatomical networks revealed by cortical thickness 19. Specifically, a smallworld network is defined to be a network where the typical distance l between two randomly chosen. The identification of nodes is the key factor in studying the properties of networks on the macro, micro or mesoscale in both structural and functional networks. However, little is known about the small world properties of brain networks in the context of a task. It is nearly 20 years since the concept of a small world network was first. A network is a mathematical representation of a real world.
Furthermore, small world property of brain networks showed signi. The second aim was to show the usefulness of graph theory measures in the study of neurocognitive mechanisms. But a few years ago, brett tjadena computer scientist at the university of virginiacatapulted bacon to true international recognition with the claim that he was somehow at the centre of the movie universe. In this work, we revisit the quantification of small worldness in neural. Oct 01, 2019 the human brain functional networks constructed by different brain atlases all satisfied the small world conditions, but each of its parameter properties had significant differences between groups, including the network, the shortest path length l p, cluster coefficient c p, e global and e local, which is consistent with the results in this. Brain networks can be analysed at the level of connectivity or topology. Small world functional brain networks achard and others 2006. A major step forward to further understanding small world networks was made by watts and strogatz. These methods have been applied to anatomical connectivity data on nonhuman species, and cortical networks have been shown to have small world topology, associated with high. Humphries md, gurney k, prescott tj 2006 the brainstem re. Smallworld anatomical networks in the human brain revealed. Altered topological properties of functional network.
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