Integrate and Fire Neuron Model

Integrate and fire neuron models are commonly used by computational neuroscientists because they can describe key characteristics of neuronal behavior while requiring relatively little computational power. The basic idea is that membrane voltage steadily increases as the neuron is injected with current until it reaches a threshold value, after which there is a "spike", or action potential. Then the neuron becomes refractory at a specified refractory potential for a specified amount of time. The voltage then continues to rise from the refractory potential with injected current, and so on. The voltage rise is described by the equation

V_{m(k+1)}=V^\infty_k+(V_k-V^\infty_k)e^{-\Delta{}t/\tau},

where   V^\infty{}\equiv{}V_{rest}+IR   and   \tau=RC,

In these equations, [math]V_m[/math] is the membrane voltage, [math]V_{rest}[/math] is the resting membrane potential (found using the Goldman-Hodgkin-Katz equation), [math]I[/math] is the input current, [math]R[/math] is the resistance, and [math]C[/math] is the capacitance. I implemented this model using MATLAB, and I post the code, as well as an example voltage trace, below. This model can be improved upon, and I will hopefully include the option of a relative refractory period soon. Hopefully it will be of help to those who may be looking for a start for their own models. Have any code of your own you'd like to share? Please feel free to post excerpts or links in the comments section!

Integrate and Fire Neuron MATLAB Code

Here's a PDF of the voltage trace (after some beautifying) elicited by the command "plot(-10:0.01:100,expIF_neuron(-10:0.01:100,[-60 -50 -70 40 -60],[1 1 10],2,[0 11]))" : IF Neuron Voltage Trace. Enjoy!

Posted January 29th, 2011 in Neuroscience, Science.