Encyclopedia of Computational Neuroscience

2015 Edition
| Editors: Dieter Jaeger, Ranu Jung

Equivalent Cylinder Model (Rall)

  • William R. Holmes
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6675-8_33

Definition

The equivalent cylinder model is a means to reduce the complex branching structure of a dendritic tree to a simple cylinder by making a set of assumptions about the morphological and electrotonic properties of the dendrites, allowing tractable mathematical analyses that can provide useful insights into dendritic function.

Detailed Description

It is difficult to gain mathematical insight into the function of complex branched dendritic trees. Analysis requires that the cable equation be solved for each dendritic segment, given boundary conditions at the ends of the segments, plus an initial condition. Mathematical solutions become unwieldy, even with small numbers of dendritic segments (see “ Cable Equation” entry). In 1962, Rall showed that with a few assumptions complex dendritic morphology could be reduced to a simple cylinder. This simplification is known as Rall’s equivalent cylinder model, and its application has provided much insight into neuron function.

Motivation

The...
This is a preview of subscription content, log in to check access.

References

  1. Rall W (1962a) Theory of physiological properties of dendrites. Ann NY Acad Sci 96:1071–1092PubMedGoogle Scholar
  2. Rall W (1962b) Electrophysiology of a dendritic neuron model. Biophys J 2:145–167PubMedCentralPubMedGoogle Scholar
  3. Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Reiss RF (ed) Neural theory and modeling. Stanford University Press, Stanford, pp 73–97Google Scholar
  4. Rall W, Rinzel J (1973) Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. Biophys J 13:648–688PubMedCentralPubMedGoogle Scholar
  5. Rinzel J, Rall W (1974) Transient response in a dendritic neuron model for current injected at one branch. Biophys J 14:759–790PubMedCentralPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Biological SciencesOhio UniversityAthensUSA