Where ωD is the variable that has a probability density function f(ωD), and mD, hD and nD are functions of ωD too. They have HH-type dynamics. The other terms that have integration interval between 1 and ∞ can be solved. But terms like this cannot be simplified further. Does the Equation object of Brian support such integral expressions? I didn’t find any statement in the guide.
Minimal code to reproduce problem
None
What you have aready tried
I try to replace the integral term with the sum of discrete ωD values, and functions related to it, just like the method of rectangular numerical integration. But state variables like mD have dynamics like:
Hi @czx. I’m not familiar with this kind of model – do you have any reference to point me to? Brian’s equations do not support integrals, but there might be workarounds of the type you describe. But I’d like to understand the model better first.
Hi @mstimberg . Thanks for your reply. The model shown above is not exactly what it is. It is actually a modified version based on HH, assuming that for a macroscopic injured nerve bundle, the total membrane potential is given by the sum of ion currents of each microscopic axon. And each microscopic axon has an injury factor ωD, which follows a specific probability distribution, with the density distribution function f(ωD). The reversal potentials and gate functions are related to ωD as well. Thus for a microscopic axon with an injury factor ωD, its ion currents are given by:
And the total membrane potential is given by:
Expand the equation and simplified it we can get integral terms as shown in the above post. And I wonder how to solve it if Brian’s equations don’t support integrals.
