Equivalent Cylinder Model (Rall)
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.
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.
- 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