Large Scale Brain Networks of Neural Fields
Neural fields describe neural activations continuous in space and time. Neurons at a particular location in the brain receive input from its local neighbors and from far distant neuronal populations. Both types of connectivity, local and global, contribut
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Large Scale Brain Networks of Neural Fields Viktor Jirsa
Abstract Neural fields describe neural activations continuous in space and time. Neurons at a particular location in the brain receive input from its local neighbors and from far distant neuronal populations. Both types of connectivity, local and global, contribute approximately equally to the complete connectivity, but differ qualitatively in their connection topology. The local connectivity is characterized by a connection density that monotonously decreases with the distance, typically independent of the location in the brain, whereas the global connectivity is characterized by sparse long-range connections (Connectome) between brain areas. In this chapter I discuss some developments of local-global descriptions of neural fields culminating in the international neuroscience project The Virtual Brain.
16.1 Introduction The binome Structure-Function has intrigued human mankind across all disciplines of science for many centuries. Paradoxically, it is nowhere as exciting and as little understood as in system neuroscience. The human brain – on the system level – is effectively a network. A network is composed of network nodes and network links. Traditionally researchers choose a level of observation for the network nodes, such as neurons, neuronal populations or complexes composed of neurons, astrocytes and glial cells. Less commonly discussed, and more difficult to justify, is the selection of network links. About half of all synaptic connections in a given area stem from intracortical fibers and are hence of short length and local, typically smaller than 1 cm [7]. The other half of incoming fibers is corticocortical (global) and originates in distant regions with length distributions of 1–20 cm and a mean value of about
V. Jirsa () Institute de Neurosciences des Systèmes, UMR Inserm 1106, Aix-Marseille University, Marseille, France e-mail: [email protected] S. Coombes et al. (eds.), Neural Fields, DOI 10.1007/978-3-642-54593-1__16, © Springer-Verlag Berlin Heidelberg 2014
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8 cm [45]. The two fiber systems are differentiated also regarding time delays via signal transmission and topology. The local fibers are typically not myelinated (with the exception of fibers from interneurons that tend to be longer) and the signal transmission is slow with speeds of 0.1–1 m/s. The associated time delays are on the order of 1–10 ms. The connectivity of the short fiber system is translationally invariant and the connection density falls off exponentially with increasing distance. The global fiber system is differently organized. Its axons are all myelinated and make up the white matter with characteristic transmission speeds of 6–9 m/s and transmission delays on the order of 10–100 ms. The key difference to the local fiber system is its sparse connectivity, which is not translationally invariant and has become to be known under the expression connectome, the finite and countable set of connections of corticocortical white matter fibers [12].
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