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Dendrites are extensions to the neuronal cell body in the brain which areposited in several functions ranging from electrical and chemicalcompartmentalization to coincident detection. Dendrites vary across cell typesbut one common feature they share is a branched structure. The cable equationis a partial differential equation that describes the evolution of voltage inthe dendrite. A solution to this equation is normally found using finitedifference schemes. Spectral methods have also been used to solve this equationwith better accuracy. Here we report the solution to the cable equation using acompact finite difference scheme which gives spectral like resolution and canbe more easily used with modifications to the cable equation like nonlinearity,branching and other morphological transforms. Widely used in the study ofturbulent flow and wave propagation, this is the first time it is being used tostudy conduction in the brain. Here we discuss its usage in a passive, somadendrite construct. The superior resolving power of this scheme compared to thecentral difference scheme becomes apparent with increasing complexity of themodel.

Solving the Cable Equation Using a Compact Difference Scheme -- Passive Soma Dendrite