Skip to main content

Numerical analysis of an active dendrite (HH) using a compact difference scheme

Dendrites are extensions to the neuronal cell body in the brain which are posited in several functions ranging from electrical and chemical compartmentalization to coincident detection. Dendrites vary across cell types but one common feature they share is a branched structure. Passive dendrites do not contain voltage sensitive ion channels thus voltage varies linearly with time. Active dendrites on the other hand have voltage sensitive ion channels which bring about a nonlinearity in the change of voltage with respect to time in these dendrites [1]. The Hodgkin Huxley equations describe the change in voltage with respect to time in an active dendrite. A solution to these equations is normally found using the finite difference scheme [2, 3]. Spectral methods have also been used to solve these equations with better accuracy [4]. Here we report the solutions to these equations using the compact difference scheme which gives spectral like resolution but can be more easily used with modifications to the HH equations like nonlinearity, branching and other morphological transforms[5].Widely used in the study of turbulent flow and wave propagation, this is the first time it is being used to study conduction in the brain. Here we discuss its usage in a soma dendrite construct with cylindrical geometry. Different dendritic distributions of voltage gated ion channels are considered. The superior resolving power of the scheme compared to the central difference scheme becomes apparent with increasing complexity of the model.


  1. Koch C: Biophysics of Information Processing in Single Neurons. 1999, New York: Oxford University Press

    Google Scholar 

  2. Lindsay KA, Ogden JM, Halliday DM, Rosenberg JR: Modern Techniques in Neuroscience Research. 1999, New York: Springer – Verlag

    Google Scholar 

  3. Lindsay KA, Ogden JM, Rosenberg JR: Biophysical Neural Networks. 2001, Mary Ann Liebert Inc

    Google Scholar 

  4. Toth TI, Crunelli V: Solution of the nerve equations using Chebyshev approximations. J.Neurosci Methds. 1999, 87: 119-136. 10.1016/S0165-0270(98)00153-8.

    Article  CAS  Google Scholar 

  5. Lele SK: Compact finite difference schemes with spectral like resolution. J.Comp Phy. 1992, 103: 16-42. 10.1016/0021-9991(92)90324-R.

    Article  Google Scholar 

Download references


AG would like to thank Joseph Mathew, Associate Professor, Department of Aerospace Engineering, IISc, Bangalore for suggesting the use of the compact difference scheme as an alternate to spectral methods and for teaching her the usage of this method and fielding innumerable questions during this process.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Asha Gopinathan.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Gopinathan, A. Numerical analysis of an active dendrite (HH) using a compact difference scheme. BMC Neurosci 11 (Suppl 1), P119 (2010).

Download citation

  • Published:

  • DOI:


  • Difference Scheme
  • Spectral Method
  • Central Difference
  • Finite Difference Scheme
  • Neuronal Cell Body