A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons
Fig 2
Electrodiffusion in a simple 1-D system containing no current sources.
The system had an initial step concentration of NaX being 140 mM for x < 0 and 150 mM for x > 0. (A) Dynamics of the potential difference between the left and right sides of the system on a short timescale. Δϕ is defined as Δϕ = ϕ(xright) − ϕ(xleft), where xright = 0.1 μm and xleft = −0.1 μm. In PNP simulations, the system spent about 10 ns building up the potential difference across the system. In KNP simulations, the steady-state potential was assumed to occur immediately. After 10 ns, the schemes were virtually indistinguishable. (B) Dynamics of the potential between xright = 50 μm and xleft = −50 μm on a long timescale. The PNP- and KNP-schemes gave identical predictions. (C) The concentration profiles in the system at t = 1.0 s as obtained with KNP, DO and according to the theoretical approximation when NaX develops as a single concentration moving by diffusion with a modified diffusion coefficient.