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  • Poster presentation
  • Open Access

An analytical solution of the cable equation predicts the frequency preference of a passive non-uniform cylindrical cable in response to extracellular oscillating electrical fields

  • 1Email author,
  • 2, 4,
  • 2, 4,
  • 3,
  • 3 and
  • 1, 4
BMC Neuroscience200910 (Suppl 1) :P38

  • Published:


  • Pyramidal Neuron
  • Fourier Expansion
  • Local Field Potential
  • Apical Dendrite
  • Recent Experimental Study
Under physiological and artificial conditions, the dendrites of neurons can be exposed to electrical fields [13]. Recent experimental studies suggested that the membrane resistivity of the distal apical dendrites of cortical and hippocampal pyramidal neurons may be significantly lower than those of the proximal dendrites and the soma [46]. To understand the behavior of dendrites in time varying extracellular electrical fields, we obtained analytical solutions of the cable equation for finite cylindrical cables with and without a leak conductance at one end by employing the Green's function method. The solution of a cable with leak at one end for DC electrical fields shows a reversal of polarization at the leaky end (Figure 1), as has been shown previously by employing the method of variable separation and Fourier expansion [7]. The solution of a cable with leak at one end for AC electrical fields shows that the leaky end has a frequency preference in the response amplitude (Figure 2).
Figure 1
Figure 1

Response to extracellular DC fields. The black line is a numerical solution of the cable equation by using the implicit method, and the red line is a theoretical solution by using the Green's function method. The theoretical solution shows slower hyperpolarization after rapid depolarization, i.e., a biphasic change.

Figure 2
Figure 2

Response to extracellular AC fields. By applying an AC field with a linearly changing frequency (below), the numerically obtained amplitude of the AC responses (black line) was maximized at a certain frequency, i.e., frequency preference (Arrow). The red line denotes the amplitude of the theoretical solution.

Our results suggest that a passive dendrite with low resistivity at the distal end would show a frequency preference in response to sinusoidal extracellular local field potentials. The Green's function obtained in our study can be used to calculate response for any form of extracellular electrical field.

Authors’ Affiliations

Dep. of Computational Intelligence and System Science, Tokyo Tech, Yokohama 2268502, Japan
Dep. of Complexity Science and Engineering, Univ. of Tokyo, Kashiwa 2778561, Japan
Dep. of Life Science, Tokyo Univ. of Pharmacy and Life Science, Hachioji 1920392, Japan
Brain Science Institute, RIKEN, Wako 3510198, Japan


  1. Bikson M, et al: Effects of uniform extracellular DC electrical fields on excitability in rat hippocampal slices in vitro. J Physiol. 2004, 557: 175-195. 10.1113/jphysiol.2003.055772.PubMed CentralPubMedView ArticleGoogle Scholar
  2. Faber DS, Korn H: Electrical Field Effects: Their relevance in central neural networks. Physiol Review. 1989, 69: 821-863.Google Scholar
  3. Jefferys JGR: Nonsynaptic modulation of neuronal activity in the brain: Electric currents and extracellular ions. Physiol Review. 1995, 75: 689-723.Google Scholar
  4. Inoue M, et al: Dendritic attenuation of synaptic potentials in the CA1 region of rat hippocampal slices detected with an optical method. Eur J Neurosci. 2001, 13: 1711-1721. 10.1046/j.0953-816x.2001.01550.x.PubMedView ArticleGoogle Scholar
  5. Omori T, et al: Estimated Distribution of Specific Membrane Resistance in Hippocampal CA1 Pyramidal Neuron. Brain Research. 2006, 1125: 199-208. 10.1016/j.brainres.2006.09.095.PubMedView ArticleGoogle Scholar
  6. Stuart G, Spruston N: Determinants of voltage attenuation in neocortical pyramidal neuron dendrites. J Neurosci. 1998, 18: 3501-3510.PubMedGoogle Scholar
  7. Svirskis G, et al: Detection of a Membrane Shunt by DC Field Polarization during Intracellular and Whole Cell Recording. J Neurophysiol. 1997, 77: 579-586.PubMedGoogle Scholar


© Monai et al; licensee BioMed Central Ltd. 2009

This article is published under license to BioMed Central Ltd.