There are billions of neurons in our brains, but what are neurons? Just cells. The brain has no knowledge untill connections are made between neurons. All that we know, all that we are, comes from the way our neurons are connected.
Our brain: a complex network
Our brains are not just the most complex structures that we know off, they are above all complex networks. The idea that complex systems like the brain that consist of large numbers of weakly interacting parts can be studied effectively within a mathematical framework derived from mathematical graph theory has been revolutionized by two papers published in 1998 and 1999. In a Nature letter in 1998 Watts and Strogatz proposed a new model for so-called “small-world” networks, that combine properties of ordered and random systems. The central nervous system of the worm C. elegans was shown to be a typical “small-world” network, combing high local clustering of connections with small pathlengths and global integration. One year later Barabasi and Albert introduced in a Science paper an elegant model for growing networks, where new nodes preferentially attach to existing nodes that already have many nodes. The resulting networks displayed scale-free properties of the distribution of links explaining similar patterns in many real networks ranging from the Internet to the brain. Together, these two papers changed the face of complexity and gave rise to the modern science of networks.
Application of network theory to the brain
This website is about the application of modern network science to the brain. We explain the basic principles of modern network theory at a level relevant for neuroscientists, and point the way to advanced papers and books on the topic. Network theory is especially important for neuroscience if we want to understand structural and functional connectivity, that is: how neurons and neuronal structures connect and communicate. The study of structural and functional brain connectivity has changed enormously under the influence of graph theory since it provides a mathematical framework to describe, quantify and model the properties of large systems of interconnected elements. At the department of Clinical Neurophysiology of the VU University Medical Center graph theory has been applied to various neuroimaging techniques such as electroencephalography (EEG), magnetoencephalography (MEG) and MRI since 2004. We give an overview of past and ongoing research relating to healthy subjects as well as different categories of patients with neuropsychiatric disorders such as Alzheimer’s disease, Parkinson’s disease, multiple sclerosis, brain tumours, epilepsy and schizophrenia and refer to other relevant websites, papers and books.
Healthy brains: how connections make you smart
One of the key findings of modern network theory of the brain is that our brains combine high levels of local clustering with strong global integration. This pattern of connectivity is characteristic of “small-world” networks and has now been demonstrated in brains of animals, ranging from C. elegans to cats and monkeys, as well as humans. Brain networks show a characteristic pattern of development from a more random towards a more organized state. This pattern is under strong genetic control, and strongly determines our cognitive abilities. A major discovery by Martijn van den Heuvel is that in healthy subjects a higher IQ is correlated with a small pathlength, that is a small number of links between any two brain areas.
Disrupted networks and brain disease
The optimal small-world pattern of healthy brain networks becomes disrupted in brain disorders. Usually brain disease manifests itself as a kind of regression from a “small-world” network towards a more random network. This pattern has been demonstrated in disorders like Alzheimer’s disease, brain tumours and schizophrenia. In addition disease-specific scenario’s are emerging. In Alzheimer’s disease the key nodes of the network the so-called “hubs”, are affected more severely than other parts. Of interest, these hub regions are also most active during a no-task resting-state, are associated with deposition of the abnormal protein amyloid, and play a key role in cognition. Perhaps Alzheimer’s disease is a hub disorder? Another pattern is becoming clear in epilepsy. Here networks have an abnormally tendency to synchronize their activity. The architecture of the brain network, that can be changed by genetic deficits or acquired brain lesions such as tumours or hemorrhages, is probably responsible for this tendency towards hypersynchronization. In fact, abnormally strong pathological hub-like brain areas could well underlie the common neurological problem of epilepsy. If this idea turns out to be true, new avenues for treatment may come within reach.
Brain network research: connecting brains
Research into complex brain networks is a fascinating, but also a collaborative effort. It is not only about how the brain is connected, it is also about how you connect brains. In the spirit of Tim Berners-Lee, the creator of the web, we strongly believe that sharing knowledge and facilities is the way forward. Open access and shareware are the future. In addition to describing our own research in this field we aim to point to relevant work by other groups. The agenda shows freely accessible weekly seminars on brain network research at the VU University Department, and points our other relevant meetings. Students who want to spend time at the department are welcome. We use Java-based software developed at our department for connectivity and network studies of EEG and MEG; this software is free and can be downloaded and used by other investigators. We also point out other websites that provide free software. You can apply to obtain a 1500 euro grant to start a small pilot study with EEG or MEG. Finally, we welcome any comments and suggestions, especially if they help to promote further studies in complex brain networks.
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