Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 484812, 17 pages
Research Article

Structural Models of Cortical Networks with Long-Range Connectivity

1Faculty of Biology, University of Freiburg, 79104 Freiburg, Germany
2Eye Clinic, University Medical Center Freiburg, 79106 Freiburg, Germany
3Bernstein Center Freiburg, University of Freiburg, Hansastrβe9a, 79104 Freiburg, Germany

Received 4 July 2011; Accepted 17 August 2011

Academic Editor: Zidong Wang

Copyright © 2012 Nicole Voges et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Most current studies of neuronal activity dynamics in cortex are based on network models with completely random wiring. Such models are chosen for mathematical convenience, rather than biological grounds, and additionally reflect the notorious lack of knowledge about the neuroanatomical microstructure. Here, we describe some families of new, more realistic network models and explore some of their properties. Specifically, we consider spatially embedded networks and impose specific distance-dependent connectivity profiles. Each of these network models can cover the range from purely local to completely random connectivity, controlled by a single parameter. Stochastic graph theory is then used to describe and analyze the structure and the topology of these networks.