Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 16
sizeStates = 6
sizeConstants = 11
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "t in component environment (ms)"
legend_states[0] = "V_m in component membrane (mV)"
legend_algebraic[0] = "i_Stim in component membrane (mA_per_cm2)"
legend_constants[0] = "stim_amplitude in component membrane (mA_per_cm2)"
legend_constants[1] = "stim_duration in component membrane (ms)"
legend_algebraic[6] = "i_Naf in component fast_sodium_channel (mA_per_cm2)"
legend_algebraic[12] = "i_Nap in component persistent_sodium_channel (mA_per_cm2)"
legend_algebraic[13] = "i_Ks in component slow_potassium_channel (mA_per_cm2)"
legend_algebraic[14] = "i_Kf in component juxtaparanodal_fast_potassium_channel (mA_per_cm2)"
legend_algebraic[15] = "i_Lk in component leakage_channel (mA_per_cm2)"
legend_constants[2] = "C_n in component membrane (mF_per_cm2)"
legend_constants[3] = "E_Na in component membrane (mV)"
legend_constants[4] = "E_K in component membrane (mV)"
legend_constants[5] = "E_Lk in component membrane (mV)"
legend_constants[6] = "g_Naf in component fast_sodium_channel (S_per_cm2)"
legend_states[1] = "m in component fast_sodium_channel_m_gate (dimensionless)"
legend_states[2] = "h in component fast_sodium_channel_h_gate (dimensionless)"
legend_algebraic[1] = "alpha_m in component fast_sodium_channel_m_gate (per_ms)"
legend_algebraic[7] = "beta_m in component fast_sodium_channel_m_gate (per_ms)"
legend_algebraic[2] = "alpha_h in component fast_sodium_channel_h_gate (per_ms)"
legend_algebraic[8] = "beta_h in component fast_sodium_channel_h_gate (per_ms)"
legend_constants[7] = "g_Nap in component persistent_sodium_channel (S_per_cm2)"
legend_states[3] = "p in component persistent_sodium_channel_p_gate (dimensionless)"
legend_algebraic[3] = "alpha_p in component persistent_sodium_channel_p_gate (per_ms)"
legend_algebraic[9] = "beta_p in component persistent_sodium_channel_p_gate (per_ms)"
legend_constants[8] = "g_Ks in component slow_potassium_channel (S_per_cm2)"
legend_states[4] = "s in component slow_potassium_channel_s_gate (dimensionless)"
legend_algebraic[4] = "alpha_s in component slow_potassium_channel_s_gate (per_ms)"
legend_algebraic[10] = "beta_s in component slow_potassium_channel_s_gate (per_ms)"
legend_constants[9] = "g_Kf in component juxtaparanodal_fast_potassium_channel (S_per_cm2)"
legend_states[5] = "n in component juxtaparanodal_fast_potassium_channel_n_gate (dimensionless)"
legend_algebraic[5] = "alpha_n in component juxtaparanodal_fast_potassium_channel_n_gate (per_ms)"
legend_algebraic[11] = "beta_n in component juxtaparanodal_fast_potassium_channel_n_gate (per_ms)"
legend_constants[10] = "g_Lk in component leakage_channel (S_per_cm2)"
legend_rates[0] = "d/dt V_m in component membrane (mV)"
legend_rates[1] = "d/dt m in component fast_sodium_channel_m_gate (dimensionless)"
legend_rates[2] = "d/dt h in component fast_sodium_channel_h_gate (dimensionless)"
legend_rates[3] = "d/dt p in component persistent_sodium_channel_p_gate (dimensionless)"
legend_rates[4] = "d/dt s in component slow_potassium_channel_s_gate (dimensionless)"
legend_rates[5] = "d/dt n in component juxtaparanodal_fast_potassium_channel_n_gate (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -88.5901439103062
constants[0] = 0.05
constants[1] = 0.5
constants[2] = 0.002
constants[3] = 50
constants[4] = -90
constants[5] = -90
constants[6] = 3
states[1] = 0.0302964457761589
states[2] = 0.841520865130776
constants[7] = 0.01
states[3] = 0.0969864645712442
constants[8] = 0.08
states[4] = 0.00997371545602793
constants[9] = 0
states[5] = 0.000886041197111556
constants[10] = 0.007
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = (6.57000*(states[0]+20.4000))/(1.00000-exp(-(states[0]+20.4000)/10.3000))
algebraic[7] = (-0.304000*(states[0]+25.7000))/(1.00000-exp((states[0]+25.7000)/9.16000))
rates[1] = algebraic[1]*(1.00000-states[1])-algebraic[7]*states[1]
algebraic[2] = (-0.340000*(states[0]+114.000))/(1.00000-exp((states[0]+114.000)/11.0000))
algebraic[8] = 12.6000/(1.00000+exp(-(states[0]+31.8000)/13.4000))
rates[2] = algebraic[2]*(1.00000-states[2])-algebraic[8]*states[2]
algebraic[3] = (0.0353000*(states[0]+27.0000))/(1.00000-exp(-(states[0]+27.0000)/10.2000))
algebraic[9] = (-0.000883000*(states[0]+34.0000))/(1.00000-exp((states[0]+34.0000)/10.0000))
rates[3] = algebraic[3]*(1.00000-states[3])-algebraic[9]*states[3]
algebraic[4] = 0.300000/(1.00000+exp(-(states[0]+53.0000)/5.00000))
algebraic[10] = 0.0300000/(1.00000+exp(-(states[0]+90.0000)/1.00000))
rates[4] = algebraic[4]*(1.00000-states[4])-algebraic[10]*states[4]
algebraic[5] = (0.0462000*(states[0]+83.2000))/(1.00000-exp(-(states[0]+83.2000)/1.10000))
algebraic[11] = (-0.0824000*(states[0]+66.0000))/(1.00000-exp((states[0]+66.0000)/10.5000))
rates[5] = algebraic[5]*(1.00000-states[5])-algebraic[11]*states[5]
algebraic[0] = custom_piecewise([greater_equal(voi , 10.0000) & less_equal(voi , 10.0000+constants[1]), constants[0] , True, 0.00000])
algebraic[6] = constants[6]*(power(states[1], 3.00000))*states[2]*(states[0]-constants[3])
algebraic[12] = constants[7]*(power(states[3], 3.00000))*(states[0]-constants[3])
algebraic[13] = constants[8]*states[4]*(states[0]-constants[4])
algebraic[14] = constants[9]*(power(states[5], 4.00000))*(states[0]-constants[4])
algebraic[15] = constants[10]*(states[0]-constants[5])
rates[0] = -(-algebraic[0]+algebraic[6]+algebraic[12]+algebraic[13]+algebraic[14]+algebraic[15])/constants[2]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = (6.57000*(states[0]+20.4000))/(1.00000-exp(-(states[0]+20.4000)/10.3000))
algebraic[7] = (-0.304000*(states[0]+25.7000))/(1.00000-exp((states[0]+25.7000)/9.16000))
algebraic[2] = (-0.340000*(states[0]+114.000))/(1.00000-exp((states[0]+114.000)/11.0000))
algebraic[8] = 12.6000/(1.00000+exp(-(states[0]+31.8000)/13.4000))
algebraic[3] = (0.0353000*(states[0]+27.0000))/(1.00000-exp(-(states[0]+27.0000)/10.2000))
algebraic[9] = (-0.000883000*(states[0]+34.0000))/(1.00000-exp((states[0]+34.0000)/10.0000))
algebraic[4] = 0.300000/(1.00000+exp(-(states[0]+53.0000)/5.00000))
algebraic[10] = 0.0300000/(1.00000+exp(-(states[0]+90.0000)/1.00000))
algebraic[5] = (0.0462000*(states[0]+83.2000))/(1.00000-exp(-(states[0]+83.2000)/1.10000))
algebraic[11] = (-0.0824000*(states[0]+66.0000))/(1.00000-exp((states[0]+66.0000)/10.5000))
algebraic[0] = custom_piecewise([greater_equal(voi , 10.0000) & less_equal(voi , 10.0000+constants[1]), constants[0] , True, 0.00000])
algebraic[6] = constants[6]*(power(states[1], 3.00000))*states[2]*(states[0]-constants[3])
algebraic[12] = constants[7]*(power(states[3], 3.00000))*(states[0]-constants[3])
algebraic[13] = constants[8]*states[4]*(states[0]-constants[4])
algebraic[14] = constants[9]*(power(states[5], 4.00000))*(states[0]-constants[4])
algebraic[15] = constants[10]*(states[0]-constants[5])
return algebraic
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)