Activation function

In this script, the activation function for a point source electrode is ploted to anodic and cathodic stimulation. Then two simulation are performed. The first is an example of stimulation over the threshold and a spike is initiated at the midle of the fiber and propagates. The second show a sub-threshold stimulation with no AP produced.

import nrv
import matplotlib.pyplot as plt
import matplotlib as mpl
from scipy import signal
import numpy as np

window_length_filter = 501
polyorder_filter = 3
def get_first_derivative(ftp):
    ftp = signal.savgol_filter(ftp, window_length=window_length_filter, polyorder=polyorder_filter, mode="nearest")
    ftp = np.gradient(ftp)
    ftp = signal.savgol_filter(ftp, window_length=window_length_filter, polyorder=polyorder_filter, mode="nearest")
    return(ftp)

def get_second_derivative(ftp):
    ftp=get_first_derivative(ftp)
    ftp = np.gradient(ftp)
    ftp = signal.savgol_filter(ftp, window_length=window_length_filter, polyorder=polyorder_filter, mode="nearest")
    return(ftp)

nseg = 1500
tsim = 4
# axon def
y = 0                                               # axon y position, in [um]
z = 0                                               # axon z position, in [um]
d = 1                                               # axon diameter, in [um]
L = 5000                                    # axon length, along x axis, in [um]
axon1 = nrv.unmyelinated(y,z,d,L,Nsec = nseg,model ='Sundt')

# electrode def
x_elec = L/2                                # electrode x position, in [um]
y_elec = 100                                # electrode y position, in [um]
z_elec = 0                                  # electrode y position, in [um]
E1 = nrv.point_source_electrode(x_elec,y_elec,z_elec)

# load material properties
epineurium = nrv.load_material('endoneurium_bhadra')

# stimulus def
start = 0.2
I_cathod = 70
T_cathod = 100e-3

stim1 = nrv.stimulus()
stim1.biphasic_pulse(start, I_cathod, T_cathod, 0, 0)

# extracellular stimulation setup
extra_stim = nrv.stimulation(epineurium)
extra_stim.add_electrode(E1, stim1)
axon1.attach_extracellular_stimulation(extra_stim)

axon1.get_electrodes_footprints_on_axon()

ftp = axon1.footprints[0]
acti_function = get_second_derivative(-ftp)
acti_function = acti_function/np.max(acti_function)

acti_function_ano = get_second_derivative(ftp)
acti_function_ano = -acti_function_ano/np.min(acti_function_ano)


x_vect= np.linspace(0,5000,nseg)
color = 'teal'

plt.figure()
plt.plot(x_vect,acti_function_ano,color = color)
plt.ylabel(r'Activation Function ($\Delta^2V_e$)')
plt.xlabel('x-axis (µm)')
plt.xlim(np.min(x_vect),np.max(x_vect))
plt.title('Activation function for anodic stimulation')
plt.grid()

plt.figure()
plt.plot(x_vect,acti_function,color = color)
plt.ylabel(r'Activation Function ($\Delta^2V_e$)')
plt.xlabel('x-axis (µm)')
plt.xlim(np.min(x_vect),np.max(x_vect))
plt.title('Activation function for cathodic stimulation')
plt.grid()

# simulate the axon
results = axon1.simulate(t_sim=tsim)
del axon1

fig, ax = plt.subplots(1)
norm = mpl.colors.Normalize(vmin=-80, vmax=30)
cbar = results.colormap_plot(ax, "V_mem",norm=norm)
ax.set_xlabel('Time (ms)')
ax.set_ylabel('x-position (µm)')
ax.set_title('Example of supra threshold stimulation (AP)')
cbar.set_label(r'Membrane Voltage $V_m$ (mV)')


axon1 = nrv.unmyelinated(y,z,d,L,Nsec = nseg,model ='Sundt')

E1 = nrv.point_source_electrode(x_elec,y_elec,z_elec)
I_cathod =-70
stim1 = nrv.stimulus()
stim1.biphasic_pulse(start, I_cathod, T_cathod, 0, 0)
# extracellular stimulation setup
extra_stim = nrv.stimulation(epineurium)
extra_stim.add_electrode(E1, stim1)
axon1.attach_extracellular_stimulation(extra_stim)

# simulate the axon
results = axon1.simulate(t_sim=tsim)
del axon1

fig, ax = plt.subplots(1)
#norm = mpl.colors.Normalize(vmin=-80, vmax=30)
cbar = results.colormap_plot(ax, "V_mem",norm=norm)
ax.set_xlabel('Time (ms)')
ax.set_ylabel('x-position (µm)')
ax.set_title('Example of sub threshold stimulation (no AP)')
cbar.set_label(r'Membrane Voltage $V_m$ (mV)')

#plt.show()

Text(0.5, 1.0, 'Example of sub threshold stimulation (no AP)')