Custom Neuron Model

Neuron model is the most important part in neural dynamics simulation. Different models and parameters will produce different phenomena. SPAIC includes many common neuron models in order to meet the needs of different applications. However, SPAIC is sometimes out of reach and users need to add their own personalized neurons that are more appropriate for their experiments. The neuron definition step can follow the the format in spaic.Neuron .

Define Variables

At first, we need to introduce some typical variable type in SPAIC :

  • _variables – normal variable

  • _tau_variables – exponential decay time constant

  • _membrane_variables – decay time constant

  • _parameter_variables – parameters

  • _constant_variables – constant

To _tau_variables , we will transmit it as tau_var = np.exp(-dt/tau_var) . To _membrane_variables , we will transmit it as membrane_tau_var = dt/membrane_tau_var ,

When defining variables, initial value also should be given, since all the neuron parameters will be reset to the initial value after each model run. Some parameters can be change based on the parameters received. We use lif neuron model as the example:

"""
LIF model:
# V(t) = tuaM * V^n[t-1] + Isyn[t]   # tauM: constant membrane time (tauM=RmCm)
O^n[t] = spike_func(V^n[t-1])
"""

In the formula of lif model, the original formula should be transmitted to the differential equation by users themselves. Then, tauM and the threshold v_th are changeable, so we get parameters from kwargs:

# The complete add code
self._variables['V'] = 0.0
self._variables['O'] = 0.0
self._variables['Isyn'] = 0.0

self._parameter_variables['Vth'] = kwargs.get('v_th', 1)
self._constant_variables['Vreset'] = kwargs.get('v_reset', 0.0)

self._tau_variables['tauM'] = kwargs.get('tau_m', 20.0)

Define Calculation

Compute operation is the most important part of Neuron Model. These operations decide the change of elements during simulation. When add compute operations, there are some rules to follow. At first, every operation can only do one compute process, so users need to decomposition formula to independent operations. The whole build-in calculate operator can be found in spaic.backend.backend , and here is the example about LIF model:

# Recently, [updated] represent that here it needs the updated value instead of the old value from last round of
# calculation. Temporary variable don't need [updated].
# Vtemp = V * tauM + I, to be mentioned, tauM is a '_tau_variables' variable, which means it was not the initial value.
self._operations.append(('Vtemp', 'var_linear', 'tauM', 'V', 'Isyn[updated]'))

# O = 1 if Vtemp >= Vth else 0， 'threshold' used to check whether 'Vtemp' reaches the threshold 'Vth'
self._operations.append(('O', 'threshold', 'Vtemp', 'Vth'))

# Used to reset voltage after spike is sent
self._operations.append(('V', 'reset', 'Vtemp',  'O[updated]'))

Also, we need to add NeuronModel.register("lif", LIFModel) to combine the name with the model for front-end use.