Table of Contents
ISRN Biomathematics
Volume 2013, Article ID 871472, 37 pages
http://dx.doi.org/10.1155/2013/871472
Review Article

Modeling Neural Activity

Departments of Pediatrics and Neurology, Committee on Computational Neuroscience, Computation Institute, KCBD Room 4124, 900 E 57th Street, Chicago, IL 60637, USA

Received 13 September 2012; Accepted 4 November 2012

Academic Editors: T. Liu, D. Mogul, and M. R. Roussel

Copyright © 2013 Wim van Drongelen. 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.

Abstract

This paper provides an overview of different types of models for studying activity of nerve cells and their networks with a special emphasis on neural oscillations. One part describes the neuronal models based on the Hodgkin and Huxley formalism first described in the 1950s. It is discussed how further simplifications of this formalism enable mathematical analysis of the process of neural excitability. The focus of the paper’s second component is on network activity. Understanding network function is one of the important frontiers remaining in neuroscience. At present, experimental techniques can only provide global recordings or samples of the activity of the huge networks that form the nervous system. Models in neuroscience can therefore play a critical role by providing a framework for integration of necessarily incomplete datasets, thereby providing insight into the mechanisms of neural function. Network models can either explicitly contain individual network nodes that model the neurons, or they can be based on representations of compound population activity. The latter approach was pioneered by Wilson and Cowan in the 1970s. Finally I provide an overview and discuss how network models are employed in the study of neuronal network pathology such as epilepsy.