Neuroscience Equations

The membrane potential () in a single branch of a neuron is described by the one dimensional cable equation:

If we consider the axial resistance and dendritic diameter constant, this is simplified to a cylindrical cable equation:

In the the Hodgkin-Huxley formalism, the current is defined as:

, and are voltage and time dependent variables between 0 and 1, each satisfying a simple exponential curve, described by: