Simulating neurons or how to solve delay differential equations in R

November 13, 2012
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(This article was originally published at mages' blog, and syndicated at StatsBlogs.)

I discussed earlier how the action potential of a neuron can be modelled via the Hodgkin-Huxely equations. Here I will present a simple model that describes how action potentials can be generated and propagated across neurons. The tricky bit here is that I use delay differential equations (DDE) to take into account the propagation time of the signal across the network.

My model is based on the paper: Epileptiform activity in a neocortical network: a mathematical model by F. Giannakopoulos, U. Bihler, C. Hauptmann and H. J. Luhmann. The article presents a flexible and efficient modelling framework for:
  • large populations with arbitrary geometry
  • different synaptic connections with individual dynamic characteristics
  • cell specific axonal dynamics
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