Modeling an external input voltage to the circuit?

Support
2

Hi @itq. Injecting an external current into a neuron with an electrode is actually something that is done quite commonly in experiments (the technical term is “current clamp”). To inject such a current, you include it in the equations. This is what is done in the HH model you linked to:

# The model
eqs = Equations('''
dv/dt = (gl*(El-v) - g_na*(m*m*m)*h*(v-ENa) - g_kd*(n*n*n*n)*(v-EK) + I)/Cm : volt
# ...
I : amp
''')
group = NeuronGroup(...)
group.v = El
group.I = '0.7*nA * i / num_neurons'

The I is an injected current that is set to a value between 0 and 0.7nA, linearly spaced based on the index i of each neuron.

Now, your model is formulated slightly differently for simplicity, basically things are divided by gl from the HH equations. In your case, you’d therefore indeed “add a constant voltage” to the neuron, which physics-wise is a bit odd to say, but it’ll do :slight_smile:

You can either do:

    v_ext = 1*mV  # external input
    eqs = '''
    dv/dt = (v_0 - v + g + v_ext) / t_mbr : volt (unless refractory)
    dg/dt = -g / tau               : volt (unless refractory) 
    rfc                            : second
    '''

for the same input to all neurons, or:

    eqs = '''
    dv/dt = (v_0 - v + g + v_ext) / t_mbr : volt (unless refractory)
    dg/dt = -g / tau               : volt (unless refractory) 
    rfc                            : second
    v_ext                          : volt (constant)
    '''
    ...
    neu.v_ext = ... # one value for each neuron

to have a different input into each neuron.

Hope that helps!