www.neuron.yale.edu

Has anyone ever heard of a neuron simulator using adaptive mesh refinement (AMR) for the cables?

I'm looking for a little research project to do and this came to mind. A cursory look through available software and research papers had no results for AMR applied to the Cable equation. Does anyone know if there's a good reason for this, such as the speedup, if any, doesn't justify the extra complexity? The adaptive mesh never has the opportunity to adapt because the voltages never level out enough? etc. Wanted to check with the experts before reinventing the wheel. Otherwise, I'm going to give it a shot.

Cheers,
Mitchal

Not exactly what you're looking for, but check out Rempe and Chopp 2006, A Predictor‐Corrector Algorithm for Reaction‐Diffusion Equations Associated with Neural Activity on Branched Structures.

In particular, section 8 is entitled "spatial adaptivity."

They demonstrate this on a morphologically detailed cell with Hodgkin-Huxley style dynamics.

(Don't be confused by the term "reaction-diffusion" in the title. They mean that in the mathematical sense, of which the cable equation is an example... And in particular, they only apply their algorithm to the cable equation.)

Thanks for the reference!

So basically they didn't update branches of the neuron that were at steady state, but updating an entire branch if it was not at steady state. I found their followup paper where they did some simulations.

Rempe MJ, Spruston N, Kath WL, Chopp DL. Compartmental Neural Simulations with Spatial Adaptivity.

The abstract says up to 80% decrease in computation time, but other other experiments in the paper say 40% to 50%. Still quite an improvement.

The adaptive mesh might not offer much improvement over this approach since AMR has a lot more bookkeeping, but worth investigating. Now I have confidence I won't be reinventing the wheel. Thanks!