2021-12-02 • LIF vs Izhikevich subthreshold
Contents
2021-12-02 • LIF vs Izhikevich subthreshold¶
Comparing neuron models: subthreshold behaviour of leaky integrate and fire vs Izhikevich neuron.
Not included: HH, AdEx.
[Prelude]¶
from voltage_to_wiring_sim.notebook_init import *
Preloading: numpy, numba, matplotlib.pyplot, seaborn.
Importing from submodules … ✔
Imported `np`, `mpl`, `plt`, `sns`, `pd`
Imported codebase (`voltage_to_wiring_sim`) as `v`
Imported `*` from `v.support.units`
Setup autoreload
v.print_reproducibility_info()
This cell was last run by lpxtf3 on DUIP74576 on Thu 09 Dec 2021, at 09:52 (UTC+0000).
Last git commit (Thu 09 Dec 2021, 05:32).
Uncommited changes to 3 files.
Input¶
from voltage_to_wiring_sim.support.test_current import *
dt = 0.1 * ms
duration = 1700 * ms
timesteps = v.to_indices(duration, dt)
I = np.zeros(timesteps)
Q = 0.15 * nA * 10 * ms
T = 200*ms
τ = 10*ms
add_δ(Q, (t_δ_up := 100*ms), I, dt)
add_δ(-Q, (t_δ_down := 200*ms), I, dt)
add_pulse_with_decay(Q, 300*ms, T, I, dt, τ)
add_pulse_with_decay(-Q, 450*ms, T, I, dt, τ)
add_pulse_with_decay(2*Q, 600*ms, T, I, dt, τ)
add_pulse_with_decay(-2*Q, 750*ms, T, I, dt, τ)
add_plateau(7.5*Q, 900*ms, T, I, dt)
add_ramp(5*Q, 1200*ms, T, I, dt)
add_pulse_with_decay(1.3*Q, 1500 * ms, T-100*ms, I, dt)
add_pulse_with_decay(1.3*Q, 1530 * ms, T-100*ms, I, dt)
add_pulse_with_decay(1.3*Q, 1560 * ms, T-100*ms, I, dt)
ylims = (-0.38, 0.38);
# fig, ax = plt.subplots(**v.figsize(aspect=5, width=1000))
# t = np.linspace(0, duration/ms, timesteps, False)
# plot_test_current(ax, t, I/nA, ylims)
Leaky integrate and fire¶
C = 100 * pF; # from Izh cortical RS.
def sim_LIF(I):
V_L = -60 * mV
V_th = -40 * mV
V_peak = 35 * mV # just for plotting
V_reset = V_L
V0 = V_reset
R = 80 * Mohm # from Izhikevich book: Cortical RS section.
# τ = 15 * ms # = CR
N = I.size
V = np.ones(N) * V0
for i in range(N-1):
V[i+1] = V[i] + dt * ((V_L - V[i])/R + I[i]) / C
if V[i+1] > V_th:
V[i] = V_peak
V[i+1] = V_reset
return v.Signal(V, dt)
V_LIF = sim_LIF(I);
Izhikevich¶
k = 0.7 * (nS/mV)
b = -2 * nS
V_r = -60 * mV
V_t = -40 * mV
V_peak = 35 * mV
c = -50 * mV
a = 0.03 / ms
d = 100 * pA
def sim_Izh(I):
N = I.size
V = np.ones(N) * V_r
u = np.zeros(N)
for i in range(N-1):
V[i+1] = V[i] + dt * (k * (V[i] - V_r)*(V[i] - V_t) - u[i] + I[i]) / C
u[i+1] = u[i] + dt * a * (b * (V[i] - V_r) - u[i])
if V[i+1] > V_peak:
V[i] = V_peak
V[i+1] = c
u[i+1] += d
return v.Signal(V, dt), v.Signal(u, dt)
V_Izh, u = sim_Izh(I);
Parameters from Izhikevich book: cortical regular spiking neuron.
Plot¶
fig, axs = plt.subplots(nrows=4, sharex=True,
**v.figsize(aspect=1.3, width=1000),
gridspec_kw=dict(height_ratios=[1, 0.6, 0.6, 0.6]))
ax_Izh = axs[0]
ax_I_Izh = axs[1]
ax_LIF = axs[2]
ax_I = axs[3]
t = np.linspace(0, duration/ms, timesteps, False)
ax_LIF.plot(t, V_LIF / mV, c="C1")
ax_Izh.plot(t, V_LIF / mV, c="C1", alpha=0.4, label="Leaky–integrate")
ax_Izh.plot(t, V_Izh / mV, c="C0", label="Izhikevich")
v.add_reordered_legend(ax_Izh, [1,0])
ax_I_Izh.plot(t, k * (V_Izh.data - V_r)*(V_Izh.data - V_t) / nA, label="$k(V-V_r)(V-V_t)$", c="C2")
ax_I_Izh.plot(t, -u.data / nA, label="$u$", c="C0");
v.add_reordered_legend(ax_I_Izh, [1, 0])
plot_test_current(ax_I, t, I/nA, ylims, yδ=0.82)
ax_I.set_xlabel("Time (ms)")
v.ylabel_inside(ax_LIF, "Leaky–integrate membrane voltage (mV)")
v.ylabel_inside(ax_Izh, "Membrane voltage $V$ (mV)")
v.ylabel_inside(ax_I_Izh, "Izhikevich membrane currents (nA)")
v.ylabel_inside(ax_I, "Input current $I$ (nA)", ylim_shift=16)
ax_LIF.set_xlim(left=0, right=duration/ms);
[Reproducibility]¶
v.print_reproducibility_info(verbose=True)
This cell was last run by lpxtf3 on DUIP74576
on Thu 09 Dec 2021, at 04:11 (UTC+0000).
Last git commit (Tue 07 Dec 2021, 03:59).
Uncommited changes to:
M codebase/voltage_to_wiring_sim/__init__.py
M codebase/voltage_to_wiring_sim/support/plot_util.py
AM codebase/voltage_to_wiring_sim/support/test_current.py
M codebase/voltage_to_wiring_sim/support/units.py
M notebooks/2021-12-02__LIF_vs_Izh_subthreshold.ipynb
M notebooks/2021-12-06__local_HH_dV_shape.ipynb
?? notebooks/2021-11-18__constant_input_spikes.ipynb
?? notebooks/2021-11-18__prototype_new_sim.ipynb
?? notebooks/2021-12-08__Izh_subthreshold_nonlinear.ipynb
?? notebooks/2021-12-08__cortical_HH_vs_Izh_dV_shape.ipynb
Platform:
Windows-10
CPython 3.9.6 (C:\miniforge3\python.exe)
Intel(R) Xeon(R) W-2123 CPU @ 3.60GHz
Dependencies of voltage_to_wiring_sim and their installed versions:
numpy 1.21.1
matplotlib 3.4.2
numba 0.53.1
joblib 1.0.1
seaborn 0.11.1
scipy 1.7.0
preload 2.2
nptyping 1.4.2
Full conda list:
# packages in environment at C:\miniforge3:
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