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Dendritic processing is now considered to be important in pre-processing ofsignals coming into a cell. Dendrites are involved in both propagation andbackpropagation of signals. In a cylindrical dendrite, signals moving in eitherdirection will be similar. However, if the dendrites taper, then this is notthe case any more. The picture gets more complex if the ion channeldistribution along the dendrite is also non-uniform. These equations have beensolved using the Chebyshev pseudo-spectral method. Here we look at non-uniformdendritic voltage gated channels in both cylindrical and tapering dendrites.For back-propagating signals, the signal is accentuated in the case of taperingdendrites. We assume a Hodgkin-Huxley formulation of ion channels and solvethese equations with the compact finite-difference scheme. The scheme givesspectral-like spatial resolution while being easier to solve than spectralmethods. We show that the scheme is able to reproduce the results obtained fromspectral methods. The compact difference scheme is widely used to studyturbulence in airflow, however it is being used for the first time in ourlaboratory to solve the equations involving transmission of signals in thebrain.

Solving Hodgkin-Huxley equations using the compact difference scheme -tapering dendrite