The math behind extracellular mechanisms
Posted: Tue May 26, 2009 9:36 am
Hello, we're trying to port a NEURON model over to another simulator system in order to take advantage of some non-standard hardware and accelerate our simulations. The model we're working with makes use of the extracellular mechanism, and I'm running into a problem getting the results to line up between NEURON and the other simulator (the simulators line up when the extracellular mechanisms are not included). I think that the problem comes down to understanding what the underlying math used by the extracellular mechanism is, but I'm having a great deal of trouble understanding that from the extcell.c source.
The model is using the extracellular mechanism to model the effects of a myelin sheath on an axon, so there is only one extracellular layer for which xraxial, xc, xg, and vext are defined. From the mechanism documentation at http://www.neuron.yale.edu/neuron/stati ... racellular, my understanding is that there should a differential equation associated with vext, something along the lines of d_vext/dt = -(1/xc)(I_membrane + I_myelin + I_periaxonal) where I_membrane is the current flowing through the cell membrane, I_myelin is the current flowing through the myelin sheath, which should be equal to xg*vext and I_periaxonal is the current flowing along the periaxonal space, which should be equal to xraxial*(vext - vext_neighbor) where vext_neighbor is the neighboring section.
My questions are:
1. Are the equations I've outlined above correct, or is there something else going on in the extracellular mechanism that I'm missing.
2. For converting the "densities" of xraxial, xc, and xg to absolute values (i.e. Mhos/cm^2 to Mhos) does the extracellular mechanism use the standard length and diameter defined for the section? Because we're modeling a myelin sheath the diameter of the sheath is different from the diameter of the section, but I don't see anywhere that this would be defined in the extracellular mechanism.
The model is using the extracellular mechanism to model the effects of a myelin sheath on an axon, so there is only one extracellular layer for which xraxial, xc, xg, and vext are defined. From the mechanism documentation at http://www.neuron.yale.edu/neuron/stati ... racellular, my understanding is that there should a differential equation associated with vext, something along the lines of d_vext/dt = -(1/xc)(I_membrane + I_myelin + I_periaxonal) where I_membrane is the current flowing through the cell membrane, I_myelin is the current flowing through the myelin sheath, which should be equal to xg*vext and I_periaxonal is the current flowing along the periaxonal space, which should be equal to xraxial*(vext - vext_neighbor) where vext_neighbor is the neighboring section.
My questions are:
1. Are the equations I've outlined above correct, or is there something else going on in the extracellular mechanism that I'm missing.
2. For converting the "densities" of xraxial, xc, and xg to absolute values (i.e. Mhos/cm^2 to Mhos) does the extracellular mechanism use the standard length and diameter defined for the section? Because we're modeling a myelin sheath the diameter of the sheath is different from the diameter of the section, but I don't see anywhere that this would be defined in the extracellular mechanism.